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From FiwikienMediaWiki 1.14.0Mon, 22 Jul 2019 01:36:33 GMTFreudenthal Institute
http://www.fisme.science.uu.nl/en/wiki/index.php/Freudenthal_Institute
<p>Vincent: </p>
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==General==<br />
The Freudenthal Institute for Science and Mathematics Education (FIsme) is part of Utrecht University in the Netherlands.<br />
<br />
==References==<br />
* http://en.wikipedia.org/wiki/Freudenthal_institute_for_science_and_mathematics_education<br />
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[[category:general]]</div>Fri, 07 Sep 2012 10:48:35 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Freudenthal_InstituteFreudenthal Institute
http://www.fisme.science.uu.nl/en/wiki/index.php/Freudenthal_Institute
<p>Vincent: Created page with '{{navigation algemeen}} ==General== The Freudenthal Institute for Science and Mathematics Education (FIsme) is part of Utrecht University in the Netherlands. ==References== * h...'</p>
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<br />
==General==<br />
The Freudenthal Institute for Science and Mathematics Education (FIsme) is part of Utrecht University in the Netherlands.<br />
<br />
==References==<br />
* http://en.wikipedia.org/wiki/Freudenthal_institute_for_science_and_mathematics_education<br />
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[[category:general]]</div>Fri, 07 Sep 2012 10:48:08 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Freudenthal_InstituteRealistic Mathematics Education
http://www.fisme.science.uu.nl/en/wiki/index.php/Realistic_Mathematics_Education
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{{nl|Realistisch_reken-wiskundeonderwijs}}<br />
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==General==<br />
Realistic Mathematics Education (RME) is a teaching and learning theory in mathematics education that was first introduced and developed by the [[Freudenthal Institute]] in the Netherlands. This theory has been adopted by a large number of countries all over the world such as England, Germany, Denmark, Spain, Portugal, South Africa, Brazil, USA, Japan, and Malaysia (de Lange, 1996).<br />
<br />
The present form of RME is mostly determined by Freudenthal's view on mathematics (Freudenthal, 1991). Two of his important points of views are mathematics must be connected to reality and mathematics as human activity. First, mathematics must be close to children and be relevant to every day life situations. However, the word ‘realistic’, refers not just to the connection with the real-world, but also refers to problem situations which are real in students' minds. For the problems to be presented to the students this means that the context can be a real-world context but this is not always necessary. De Lange (1996) stated that problem situations can also be seen as applications or modeling.<br />
<br />
Second, the idea of mathematics as a human activity is stressed. Mathematics education organized as a process of [[Guided Reinvention]], where students can experience a similar process compared to the process by which mathematics was invented. The meaning of invention is steps in learning processes while the meaning of guided is the instructional environment of the learning process. For example, the history of mathematics can be used as a source of inspiration for course design. Moreover, the reinvention principle can also be inspired by informal solution procedures. Informal strategies of students can often be interpreted as anticipating more formal procedures. In this case, the reinvention process uses concepts of mathematization as a guide.<br />
<br />
Two types of mathematization which were formulated explicitly in an educational context by Treffers (1987) are horizontal and vertical mathematization. In horizontal mathematization, the students come up with mathematical tools which can help to organize and solve a problem located in a real-life situation. The following activities are examples of horizontal mathematization: identifying or describing the specific mathematics in a general context, schematizing, formulating and visualizing a problem in different ways, discovering relations, discovering regularities, recognizing isomorphic aspect in different problems, transferring a real world problem to a mathematical problem, and transferring a real world problem to a known mathematical problem. On the other hand, vertical mathematization is the process of reorganization within the mathematical system itself. The following activities are examples of vertical mathematization: representing a relation in a formula, proving regularities, refining and adjusting models, using different models, combining and integrating models, formulating a mathematical model, and generalizing.<br />
<br />
==Characteristics==<br />
Treffers (1987) describes five characteristics of RME:<br />
* The use of [[context]]s<br />
* The use of [[model]]s<br />
* The use of students’ [[own production]]s and constructions<br />
* The interactive character of the teaching process<br />
* The intertwinement of various learning strands<br />
<br />
==The realistic approach versus the mechanistic approach==<br />
The use of context problems is very significant in RME. This is in contrast with the traditional, mechanistic approach to mathematics education, which contains mostly bare, "with no closes" problems. If context problems are used in the mechanistic approach, they are mostly used to conclude the learning process. The context problems function only as a field of application. By solving context problems the students can apply what was learned earlier in the bare situation.<br />
In RME this is different; Context problems function also as a source for the learning process. In other words, in RME, contexts problems and real-life situations are used both to constitute and to apply mathematical concepts.<br />
While working on context problems the students can develop mathematical tools and understanding. First, they develop strategies closely connected to the context. Later on, certain aspects of the context situation can become more general which means that the context can get more or less the character of a model and as such can give support for solving other but related problems. Eventually, the models give the students access to more formal mathematical knowledge.<br />
In order to fulfil the bridging function between the informal and the formal level, models have to shift from a [[model of]] to a [[model for]]. Talking about this shift is not possible without thinking about our colleague Leen Streefland, who died in April 1998. It was he who in 1985 (Streefland, 1985) detected this crucial mechanism in the growth of understanding. His death means a great loss for the world of mathematics education.<br />
Another notable difference between RME and the traditional approach to mathematics education is the rejection of the mechanistic, procedure-focused way of teaching in which the learning content is split up in meaningless small parts and where the students are offered fixed solving procedures to be trained by exercises, often to be done individually. RME, on the contrary, has a more complex and meaningful conceptualization of learning. The students, instead of being the receivers of ready-made mathematics, are considered as active participants in the teaching-learning process, in which they develop mathematical tools and insights. In this respect RME has a lot in common with [[Socio-constructivism|socio-constructivist]] based mathematics education. Another similarity between the two approaches to mathematics education is that it is crucial for the RME teaching methods that opportunities are offered to students to share their experiences with others.<br />
<br />
==References==<br />
* Cobb, P., Yackel, E., & Wood, T. (1992). {{refworks|A Constructivist Alternative to the Representational View of Mind in Mathematics Education|3016}}. Journal for Research in Mathematics Education, 23(1), 2-33.<br />
* Ernest, P. (1991). {{refworks|The Philosophy of Mathematics Education|3059}}. Hampshire: The Falmer Press.<br />
* Freudenthal, H. (1991). {{refworks|Revisiting Mathematics Education|3006}}. China Lectures. Dordrecht: Kluwer Academic Publishers.<br />
* Gravemeijer, K. P. E. (1994). {{refworks|Developing realistic mathematics education|2348}}. CDbeta press, Utrecht.<br />
* [[Guided Reinvention]]<br />
* [[Freudenthal Institute]]<br />
* [[IP-PMRI]]<br />
* Lange, J. de (1995). {{refworks|Assessment: No Change without Problems|2406}}. In: Romberg, T.A. (eds). (1995). Reform in School Mathematics and Authentic Assessment. New York, Sunny Press, 87-172.<br />
* Lange, J. de (1996). {{refworks|Using and Applying Mathematics in Education|2407}}. in: A.J. Bishop, et al. (eds). 1996. International handbook of mathematics education, Part one. 49-97. Kluwer academic publisher.<br />
* [http://www.geocities.com/ratuilma/rme.html Ratuilma] (PMRI, Indonesia)<br />
* Streefland, L. (1991). {{refworks|Fractions in Realistic Mathematics Education. A Paradigm of Developmental Research|3076}}. Dordrecht: Kluwer Academic Publishers.<br />
* Streefland (ed.) (1991). {{refworks|Realistic Mathematics Education in Primary School|3077}}. Utrecht: CD-b Press / Freudenthal Institute, Utrecht University.<br />
* Treffers, A. (1975). {{refworks|De Kiekkas van Wiskobas. Beschouwingen over Uitgangspunten en Doelstellingen van het Aanvangs- en Vervolgonderwijs in de Wiskunde. Leerplan publicatie nummer 1.|3306}}. Utrecht, the Netherlands: IOWO.<br />
* Treffers, A. (1987). {{refworks|Three dimensions: a model of goal and theory description in mathematics instruction - The Wiskobas project|3012}}. Dordrecht: Kluwer Academic Publishers.<br />
* Treffers, A. (1991). Realistic mathematics education in The Netherlands 1980-1990. In L. Streefland (ed.), Realistic Mathematics Education in Primary School. Utrecht: CD-b Press / Freudenthal Institute, Utrecht University.<br />
* Van den Heuvel-Panhuizen, M. (1996). {{refworks|Assessment and realistic mathematics education|2890}}. Utrecht: CD-b Press / Freudenthal Institute, Utrecht University. New Theory: Realistic Mathematics Education<br />
* Von Glasersfeld, E. (ed.). (1991). {{refworks|Radical Constructivism in Mathematics Education|3060}}. Kluwer, Academic Publisher, Dordrecht.<br />
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==Versions of this document==<br />
* 20080112, [[fiteam]]<br />
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[[category:research]]<br />
[[category:rme]]</div>Fri, 07 Sep 2012 10:46:52 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Realistic_Mathematics_EducationRealistic mathematics education
http://www.fisme.science.uu.nl/en/wiki/index.php/Realistic_mathematics_education
<p>Vincent: Redirected page to Realistic Mathematics Education</p>
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<div>#redirect [[Realistic Mathematics Education]]</div>Fri, 07 Sep 2012 10:45:19 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Realistic_mathematics_educationMathematical literacy
http://www.fisme.science.uu.nl/en/wiki/index.php/Mathematical_literacy
<p>Vincent: Redirected page to Mathematical Literacy</p>
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<div>#redirect [[Mathematical Literacy]]</div>Fri, 07 Sep 2012 10:44:25 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Mathematical_literacyMathematics and Agricultural Education
http://www.fisme.science.uu.nl/en/wiki/index.php/Mathematics_and_Agricultural_Education
<p>Vincent: </p>
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{{nl|RekenGroen}}<br />
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==General==<br />
* Project in the Netherlands to support students and teachers in Agricultural Education (age group 15-16) by emphasizing the role of mathematical skills in practical (agricultural) situations. <br />
* Duration: 2011-2012<br />
* Product: teaching materials for age group 15-16 (including a teacher guide)<br />
* Language: Dutch<br />
<br />
==Background==<br />
In the Netherlands extra attention is given to mathematical skills in secondary education in the years 2011-2014. This is caused by an extra investment (Ministry of Education), following criticism that students have insufficient skill levels in the areas mathematics and (mother tongue) language (Dutch). The Dutch students score well in international tests ([[PISA]], [[TIMSS]]), but improvements are possible, and in 2010 a law was introduced that describes skill levels (at age 12, 16 and 18) for all students. In 2014 National Tests/Exams will be part of the curriculum.<br />
<br />
From this background an initiative was started that pays attention to the combination of 'general skills' (in this case mathematical skills) and 'skills for the job' (agricultural education). The reason to make this combination is to prevent the situation that 'extra attention for mathematics' will lead to an isolated theoretical block of knowledge in the agricultural curriculum, that will give extra motivational problems for the students and didactical problems for the teachers.<br />
<br />
'RekenGroen' (Green Mathematics) is an effort to combine both the mathematics content that comes from outside the curriculum and the mathematics that is already part of the curriculum. Teachers and student do not always recognize that they already work with mathematical knowledge and skills embedded in a practical agricultural context/problem.<br />
<br />
===Design principles===<br />
Staff members of the [[Freudenthal Institute]] created the materials, using [[realistic mathematics education]] as a starting point. Teachers from three agricultural schools involved used the materials in pilot settings, and the feedback was used to make the final version of the materials.<br />
<br />
<br />
==References==<br />
* http://www.rekengroen.nl (Dutch)<br />
* [[Mathematical literacy]]<br />
<br />
==Versions of this document==<br />
* 20120907, [[wikiteam]]<br />
<br />
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[[category:project]]</div>Fri, 07 Sep 2012 10:43:25 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Mathematics_and_Agricultural_EducationMathematics and Agricultural Education
http://www.fisme.science.uu.nl/en/wiki/index.php/Mathematics_and_Agricultural_Education
<p>Vincent: Created page with '{{navigation algemeen}} {{nl|RekenGroen}} ==General== * Project in the Netherlands to support students and teachers in Agricultural Education (age group 15-16) by emphasizing th...'</p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|RekenGroen}}<br />
<br />
==General==<br />
* Project in the Netherlands to support students and teachers in Agricultural Education (age group 15-16) by emphasizing the role of mathematical skills in practical (agricultural) situations. <br />
* Duration: 2011-2012<br />
* Product: teaching materials for age group 15-16 (including a teacher guide)<br />
* Language: Dutch<br />
<br />
==Background==<br />
In the Netherlands extra attention is given to mathematical skills in secondary education in the years 2011-2014. This is caused by an extra investment (Ministry of Education), following criticism that students have insufficient skill levels in the areas mathematics and (mother tongue) language (Dutch). The Dutch students score well in international tests ([[PISA]], [[TIMMS]]), but improvements are possible, and in 2010 a law was introduced that describes skill levels (at age 12, 16 and 18) for all students. In 2014 National Tests/Exams will be part of the curriculum.<br />
<br />
From this background an initiative was started that pays attention to the combination of 'general skills' (in this case mathematical skills) and 'skills for the job' (agricultural education). The reason to make this combination is to prevent the situation that 'extra attention for mathematics' will lead to an isolated theoretical block of knowledge in the agricultural curriculum, that will give extra motivational problems for the students and didactical problems for the teachers.<br />
<br />
'RekenGroen' (Green Mathematics) is an effort to combine both the mathematics content that comes from outside the curriculum and the mathematics that is already part of the curriculum. Teachers and student do not always recognize that they already work with mathematical knowledge and skills embedded in a practical agricultural context/problem.<br />
<br />
<br />
==References==<br />
* http://www.rekengroen.nl (Dutch)<br />
* [[Mathematical literacy]]<br />
<br />
==Versions of this document==<br />
* 20120907, [[wikiteam]]<br />
<br />
<br />
[[category:project]]</div>Fri, 07 Sep 2012 10:28:22 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Mathematics_and_Agricultural_EducationSummerschool in Science and Mathematics Education
http://www.fisme.science.uu.nl/en/wiki/index.php/Summerschool_in_Science_and_Mathematics_Education
<p>Vincent: </p>
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{{nl|Summerschool_in_Science_and_Mathematics_Education}}<br />
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==General==<br />
Activity of the University Utrecht ([[FIsme]]).<br />
<br />
http://www.utrechtsummerschool.nl/index.php?type=courses&code=H7<br />
<br />
During the last decades the Netherlands has been very active in the innovation of science and mathematics education. Currently Dutch curriculum development projects are in progress for the subjects mathematics, physics, biology, chemistry and advanced integrated science and mathematics.<br />
This Summer School aims at providing secondary science and mathematics teachers with a blend of lectures, seminars and other activities on curriculum development and related research. Due to the presence of concurrent summer schools there will also be opportunities to attend lectures on new developments in science and mathematics research.<br />
<br />
{|<br />
|-<br />
|http://www.utrechtsummerschool.nl/img/sidebar/21.jpg<br />
|http://www.utrechtsummerschool.nl/img/sidebar/34.jpg<br />
|http://www.utrechtsummerschool.nl/img/sidebar/2.jpg<br />
|}<br />
<br />
==Program in brief==<br />
Theme: Making mathematics meaningful to students.<br />
* Monday: <br />
** Lecture: Introduction to the Dutch school system<br />
** Lectures and workshops: innovations in the educational practices of the secondary school in mathematics, physics, chemistry and biology.<br />
* Tuesday:<br />
** Mathematics: RME and Geometry. <br />
** Workshops about the history of mathematics and geometry<br />
** Digital Mathematics Environment<br />
* Wednesday<br />
** Mathematics: RME and the Algebra <br />
** Workshops about the use of graphic tools<br />
** Workshop in productive exercises<br />
** Workshop: supporting functional thinking<br />
* Thursday<br />
** The challenges of the Mathematics A-lympiad, an experience in mathematics competition<br />
* Friday<br />
** Exchanges between the participants <br />
** Presentations of the work done in the school <br />
** Evaluation<br />
** Closing off the Summer School<br />
<br />
==Course director==<br />
Prof.dr. Harrie M.C. Eijkelhof / Mr. Jaap den Hertog MSc<br />
<br />
==Lecturers==<br />
Staff members of [[FIsme]].<br />
<br />
==Target group==<br />
Secondary science and mathematics teachers, curriculum developers and researchers with proficiency in English. (Maximum number of participants: 60). <br />
<br />
==Contact==<br />
Jaap den Hertog, [[FIsme]]<br />
<br />
==When==<br />
* 2011: 15 - 26 August<br />
* 2010: 16 - 27 August<br />
* 2009: 17 - 21 August<br />
* 2008: 18 - 22 August<br />
<br />
==References==<br />
* http://www.utrechtsummerschool.nl <br />
* http://www.utrechtsummerschool.nl/index.php?type=courses&code=H7<br />
<br />
==Versions of this document==<br />
* 20100423<br />
* 20080826, [[wikiteam]]<br />
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[[category:general]]</div>Wed, 02 Feb 2011 04:48:14 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Summerschool_in_Science_and_Mathematics_EducationSecondary Algebra Education
http://www.fisme.science.uu.nl/en/wiki/index.php/Secondary_Algebra_Education
<p>Vincent: Created page with '{{navigation algemeen}} ==General== * Publication Freudenthal Institute, october 2010 http://www.fi.uu.nl/nl/wiki/algemeen/images/algebra_drijvers_2010.jpg Nowadays, algebra e...'</p>
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==General==<br />
* Publication Freudenthal Institute, october 2010<br />
<br />
http://www.fi.uu.nl/nl/wiki/algemeen/images/algebra_drijvers_2010.jpg<br />
<br />
Nowadays, algebra education is subject to worldwide scrutiny. Different opinions on its goals, approaches and achievements are at the heart of debates among teachers, educators, researchers and decision makers. What should the teaching of algebra in secondary school mathematics look like? Should it focus on procedural skills or on algebraic insight? Should it stress practice or integrate technology? Do we require formal proofs and notations, or do informal representations suffice? Is algebra in school an abstract subject, or does it take its relevance from application in (daily life) contexts? What should secondary school algebra education that prepares for higher education and professional practice in the twenty-first century look like?<br />
<br />
This book addresses these questions, and aims to inform in-service and future teachers, mathematics educators and researchers on recent insights in the domain, and on specific topics and themes such as the historical development of algebra, the role of productive practice, and algebra in science and engineering in particular. The authors, all affiliated with the Freudenthal Institute for Science and Mathematics Education in the Netherlands, share a common philosophy, which acts as a – sometimes nearly invisible – backbone for the overall view on algebra education: the theory of realistic mathematics education. From this point of departure, different perspectives are chosen to describe the opportunities and pitfalls of today’s and tomorrow’s algebra education. Inspiring examples and reflections illustrate current practice and explore the unknown future of algebra education to appropriately meet students’ needs.<br />
<br />
<br />
* ISBN 978-94-6091-333-4 <br />
* October 2010, 236 pages<br />
<br />
==References==<br />
* [[Algebra (General)]]<br />
<br />
==Versions of this document==<br />
* 20101128, [[wikiteam]]<br />
<br />
[[category:algebra]]</div>Sun, 28 Nov 2010 09:02:53 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Secondary_Algebra_EducationAlgebra (General)
http://www.fisme.science.uu.nl/en/wiki/index.php/Algebra_(General)
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==General==
==References==
* Secondary Algebra Education
==Versions of this document==
* 20101128, wikiteam
category:algebra'</p>
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<br />
==General==<br />
<br />
<br />
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==References==<br />
* [[Secondary Algebra Education]]<br />
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==Versions of this document==<br />
* 20101128, [[wikiteam]]<br />
<br />
[[category:algebra]]</div>Sun, 28 Nov 2010 09:01:24 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Algebra_(General)Algebra (General)
http://www.fisme.science.uu.nl/en/wiki/index.php/Algebra_(General)
<p>Vincent: Created page with '{{navigation algemeen}} ==General== Nowadays, algebra education is subject to worldwide scrutiny. Different opinions on its goals, approaches and achievements are at the heart...'</p>
<hr />
<div>{{navigation algemeen}}<br />
<br />
<br />
==General==<br />
<br />
Nowadays, algebra education is subject to worldwide scrutiny. Different opinions on its goals, approaches and achievements are at the heart of debates among teachers, educators, researchers and decision makers. What should the teaching of algebra in secondary school mathematics look like? Should it focus on procedural skills or on algebraic insight? Should it stress practice or integrate technology? Do we require formal proofs and notations, or do informal representations suffice? Is algebra in school an abstract subject, or does it take its relevance from application in (daily life) contexts? What should secondary school algebra education that prepares for higher education and professional practice in the twenty-first century look like?<br />
<br />
This book addresses these questions, and aims to inform in-service and future teachers, mathematics educators and researchers on recent insights in the domain, and on specific topics and themes such as the historical development of algebra, the role of productive practice, and algebra in science and engineering in particular. The authors, all affiliated with the Freudenthal Institute for Science and Mathematics Education in the Netherlands, share a common philosophy, which acts as a – sometimes nearly invisible – backbone for the overall view on algebra education: the theory of realistic mathematics education. From this point of departure, different perspectives are chosen to describe the opportunities and pitfalls of today’s and tomorrow’s algebra education. Inspiring examples and reflections illustrate current practice and explore the unknown future of algebra education to appropriately meet students’ needs.<br />
<br />
<br />
ISBN 978-94-6091-333-4 <br />
October 2010, 236 pages<br />
<br />
http://www.fi.uu.nl/nl/wiki/algemeen/images/algebra_drijvers_2010.jpg<br />
<br />
==References==<br />
<br />
==Versions of this document==<br />
* 20101128, [[wikiteam]]<br />
<br />
[[category:algebra]]</div>Sun, 28 Nov 2010 08:58:12 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Algebra_(General)PRIMAS
http://www.fisme.science.uu.nl/en/wiki/index.php/PRIMAS
<p>Vincent: </p>
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{{nl|PRIMAS}}<br />
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==General==<br />
* PRomoting Inquiry in Mathematics And Science education across Europe<br />
* European project (previously named Masiba)<br />
* Project duration 01-2010 to 12-2013<br />
<br />
==Background==<br />
This project aims to effect a change across Europe in the teaching and learning of mathematics and science with teachers supported to develop [[Inquiry Learning|inquiry-based learning]] (IBL) pedagogies so that students gain experience of IBL approaches. Ultimately, our objective is a greater number of students with more positive dispositions towards further study of these subjects and the desire to be employed in related fields.<br />
<br />
The proposal brings together 13 teams of experts in IBL in mathematics and science education from 12 nations and will be led and managed by a researcher who has recent successful experience of European work of this type. The nine working packages will be led by appropriate experts from the wider team, who will ensure the successful completion of each stage of the project. <br />
Overall, our design of the project throughout has been focused so as to provide a multi-level dissemination plan addressed to teachers and important stakeholders to ensure maximum impact. This plan includes the provision of high quality support for, and training of, teachers and teacher trainers; selection of high quality materials and methods with which to work with teachers, supporting actions addressed to teachers to advertise IBL, methods of working with out-of-school parties such as local authorities and parents and summaries of analyses that will inform a wide range of policy makers about how they can support the required changes. <br />
Throughout the project’s timeline national consultancy panels and two international panels will provide on-going advice and orientation at key stages. To maximise the project’s “reach” to teachers either established networks for professional development of teachers will be expanded, or new networks will be built using models which have proven efficacy. <br />
Rigorous evaluation both by an internal team and an outside agency will provide formative and summative feedback about the validity of the project and its effectiveness.<br />
<br />
==Partners==<br />
* University of Education, Freiburg Germany <br />
* Université Geneve Switzerland<br />
* Freudenthal Institute, University of Utrecht Netherlands<br />
* MARS - Shell Centre, University of Nottingham UK<br />
* University of Jaen Spain <br />
* Constantine the Philosopher University in Nitra Slovakia<br />
* University of Szeged Hungary <br />
* Cyprus University of Technology Cyprus <br />
* The University of Malta Malta <br />
* Roskilde University, Department of Science, Systems and Modells Denmark <br />
* The University of Manchester UK <br />
* Babeş-Bolyai University, Cluj Napoca Romania <br />
* Sør-Trøndelag University College Norway <br />
<br />
==References==<br />
* http://www.primas-project.eu<br />
* [[Inquiry Learning]]<br />
* [[LEMA]]<br />
* [[Science in Society]]<br />
<br />
==Versions of this document==<br />
* 20090819, [[wikiteam]]<br />
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[[category:europe]]<br />
[[category:science]]</div>Sun, 21 Nov 2010 11:18:41 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:PRIMASPierre van Hiele
http://www.fisme.science.uu.nl/en/wiki/index.php/Pierre_van_Hiele
<p>Vincent: </p>
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{{nl|Pierre_van_Hiele}}<br />
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==General==<br />
* Van Hiele's levels of learning mathematics.<br />
<br />
According to Van Hiele (cited in de Lange, 1996) the process of learning proceeds through three levels: (1) a pupil reaches the first level of thinking as soon as he can manipulate the known characteristics of a pattern that is familiar to him/her; (2) as soon as he/she learns to manipulate the interrelatedness of the characteristics he/she will have reached the second level; (3) he/she will reach the third level of thinking when he/she starts manipulating the intrinsic characteristics of relations.<br />
<br />
Pierre van Hiele died on November 1, in The Hague. He was 101 years old.<br />
<br />
==References==<br />
* [http://en.wikipedia.org/wiki/Van_Hiele_model Wikipedia]<br />
<br />
<br />
[[category:research]]</div>Sat, 06 Nov 2010 06:31:11 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Pierre_van_HielePierre van Hiele
http://www.fisme.science.uu.nl/en/wiki/index.php/Pierre_van_Hiele
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Pierre_van_Hiele}}<br />
<br />
==General==<br />
* Van Hiele's levels of learning mathematics.<br />
<br />
According to Van Hiele (cited in de Lange, 1996) the process of learning proceeds through three levels: (1) a pupil reaches the first level of thinking as soon as he can manipulate the known characteristics of a pattern that is familiar to him/her; (2) as soon as he/she learns to manipulate the interrelatedness of the characteristics he/she will have reached the second level; (3) he/she will reach the third level of thinking when he/she starts manipulating the intrinsic characteristics of relations.<br />
<br />
Pierre van Hiele died on November 1, in The Hague. He was 101 years old.<br />
<br />
<br />
[[category:research]]</div>Sat, 06 Nov 2010 06:30:14 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Pierre_van_HielePierre van Hiele
http://www.fisme.science.uu.nl/en/wiki/index.php/Pierre_van_Hiele
<p>Vincent: Created page with '{{navigation algemeen}} {{nl|Pierre_van_Hiele}} ==General== * Van Hiele's levels of learning mathematics. According to Van Hiele (cited in de Lange, 1996) the process of learni...'</p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Pierre_van_Hiele}}<br />
<br />
==General==<br />
* Van Hiele's levels of learning mathematics.<br />
<br />
According to Van Hiele (cited in de Lange, 1996) the process of learning proceeds through three levels: (1) a pupil reaches the first level of thinking as soon as he can manipulate the known characteristics of a pattern that is familiar to him/her; (2) as soon as he/she learns to manipulate the interrelatedness of the characteristics he/she will have reached the second level; (3) he/she will reach the third level of thinking when he/she starts manipulating the intrinsic characteristics of relations.<br />
<br />
Pierre van Hiele died on November 1, in The Hague. He was 101 years old.<br />
<br />
<br />
[[category:didactics]]</div>Sat, 06 Nov 2010 06:29:44 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Pierre_van_HieleWorkplace Learning
http://www.fisme.science.uu.nl/en/wiki/index.php/Workplace_Learning
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Werkplekleren_(Algemeen)}}<br />
<br />
==General==<br />
Workplace learning is an area of interest about learning in, from and for the workplace. It brings with it questions about the nature of interventions that might assist the learning process and of the roles of those responsible directly or indirectly for such interventions. <br />
<br />
==Background==<br />
* Definition UK National Institute of Adult Continuing Education 2008:<br />
"Workplace Learning is that learning which derives its purpose from the context of employment. It should address the needs and interests of a variety of stakeholders including employees, potential employees, employers and government. It is a process of learning which will :<br />
* enable individuals, employers and organisations to respond to the changing nature of economic activity;<br />
* contribute to improved efficiency and productivity in employment;<br />
* meet the personal and career development needs of individuals<br />
<br />
==References==<br />
* Adams, T. L. and Harrell, G. (2003). {{refworks|Estimation at Work|3562}} (In D. H. Clements (Ed.), Learning and Teaching Measurement (pp. 229-244). Reston, VA: National Council of Teachers of Mathematics.<br />
* Aikenhead, G. (2004). {{refworks|Science-Based Occupations and the Science Curriculum: Concepts of evidence|3566}}. Wiley InterScience, 89(2005), 12.<br />
* Coben, D. and Hodgen, J. (2008). {{refworks|Assessing numeracy for nursing|3559}}. British Society for Research into Learning Mathematics, 28(3), 18-23.<br />
* Wijers, M., Bakker, A. and Jonker, V. (2010). {{refworks|A framework for mathematical literacy in competence-based secondary vocational education|3432}}. In A. Araujo, A. Fernandes, A. Azevedo and J. Francisco Rodrigues (Eds.), Educational Interfaces Between Mathematics and Industry (EIMI) (pp. 583-596). Porto, Portugal: EIMI (ICMI/ICIAM).<br />
<br />
<br />
<br />
==Versions of this document==<br />
* 20080818, [[wikiteam]]<br />
<br />
[[category:mathematics in the workplace]]</div>Sun, 24 Oct 2010 06:45:12 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Workplace_LearningWorkplace Learning
http://www.fisme.science.uu.nl/en/wiki/index.php/Workplace_Learning
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Werkplekleren_(Algemeen)}}<br />
<br />
==General==<br />
Workplace learning is an area of interest about learning in, from and for the workplace. It brings with it questions about the nature of interventions that might assist the learning process and of the roles of those responsible directly or indirectly for such interventions. <br />
<br />
==Background==<br />
* Definition UK National Institute of Adult Continuing Education 2008:<br />
"Workplace Learning is that learning which derives its purpose from the context of employment. It should address the needs and interests of a variety of stakeholders including employees, potential employees, employers and government. It is a process of learning which will :<br />
* enable individuals, employers and organisations to respond to the changing nature of economic activity;<br />
* contribute to improved efficiency and productivity in employment;<br />
* meet the personal and career development needs of individuals<br />
<br />
==References==<br />
* Adams, T. L. and Harrell, G. (2003). {{refworks|Estimation at Work|3562}} (In D. H. Clements (Ed.), Learning and Teaching Measurement (pp. 229-244). Reston, VA: National Council of Teachers of Mathematics.<br />
* Aikenhead, G. (2004). {{refworks|Science-Based Occupations and the Science Curriculum: Concepts of evidence|3566}}. Wiley InterScience, 89(2005), 12.<br />
* Coben, D. and Hodgen, J. (2008). {{refworks|Assessing numeracy for nursing|3559}}. British Society for Research into Learning Mathematics, 28(3), 18-23.<br />
<br />
<br />
<br />
==Versions of this document==<br />
* 20080818, [[wikiteam]]<br />
<br />
[[category:mathematics in the workplace]]</div>Sun, 24 Oct 2010 06:42:27 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Workplace_LearningTowards the Development of a Common European Framework of Reference for Mathematics in the Workplace and Society
http://www.fisme.science.uu.nl/en/wiki/index.php/Towards_the_Development_of_a_Common_European_Framework_of_Reference_for_Mathematics_in_the_Workplace_and_Society
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Ontwikkeling_CEF_wiskunde_voor_beroep_en_burgerschap}}<br />
<br />
==General==<br />
This proposal (2009) aims to address the problem of describing the mathematical competencies involved in activity in the workplace, vocational and educational training and society by developing and exploring the use of a common reference framework across six partner nations. The proposed framework will improve the transparency of mathematical competencies for a wide range of stakeholders. It will facilitate educational and occupational mobility, whilst assisting recognition of prior learning and national developments in relation to the [[European Qualifications Framework]]. <br />
As a starting point the partnership will compare the recently developed frameworks in each partner nation and build on the strengths of each. Following a period of consultation with a wide range of stakeholders, including teachers and trainers, workers and students, and policy makers, in each nation, the partnership, through an iterative design process will reach consensus about a framework.<br />
Partners will draw on their extensive networks in the field to disseminate information about the project and to consult widely about future developments and implementation of the framework with the intention of taking this forward to become a common European Framework of reference for mathematics in the workplace and society. <br />
<br />
==Partners==<br />
* [[FIsme]], Utrecht, the Netherlands (Project co-coordinator)<br />
* [[ITT]], Dublin, Ireland<br />
* [[University of Manchester]], UK<br />
* [[VOX]], Norwegian Institute of Adult Education<br />
<br />
==References==<br />
* [[Common European Framework of Reference for Languages]]<br />
* [[EQF]]<br />
* [[Numeracy Canada]]<br />
* [[Numeracy England]]<br />
* [[Numeracy Ireland]]<br />
* [[Numeracy Netherlands]]<br />
* [[Numeracy Norway]]<br />
* [[Numeracy Scotland]]<br />
* Wijers, M., Bakker, A. and Jonker, V. (2010). {{refworks|A framework for mathematical literacy in competence-based secondary vocational education|3432}}. In A. Araujo, A. Fernandes, A. Azevedo and J. Francisco Rodrigues (Eds.), Educational Interfaces Between Mathematics and Industry (EIMI) (pp. 583-596). Porto, Portugal: EIMI (ICMI/ICIAM).<br />
<br />
==Versions of this document==<br />
* 20081220, meeting England, Ireland, Norway, Netherlands<br />
* 20080113, [[wikiteam]]<br />
<br />
[[category:research]]<br />
[[category:mathematics in the workplace]]</div>Mon, 11 Oct 2010 05:06:46 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Towards_the_Development_of_a_Common_European_Framework_of_Reference_for_Mathematics_in_the_Workplace_and_SocietyFramework Mathematics and Numeracy Netherlands
http://www.fisme.science.uu.nl/en/wiki/index.php/Framework_Mathematics_and_Numeracy_Netherlands
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Raamwerk_wiskunde_mbo_(Algemeen)}}<br />
<br />
==General==<br />
The [http://www.fi.uu.nl/mbo/raamwerkrekenenwiskunde/welcome.xml?language=en Reference framework mathematics and numeracy document] (developed in the Netherlands) is a framework for mathematics that is modeled after the Common European Framework for the Modern Languages ([[CEF]]). Its goals are similar to that of the CEF in the sense that the framework should assist in formulating attainment levels for education, and therefore allow easier comparison of different qualifications. Although the framework for mathematics is especially developed within and for senior secondary vocational education in the Netherlands, it is formulated in such a way that it should be useful in vocational education and training more widely.<br />
<br />
==Principles==<br />
Two principles have guided the design of the framework:<br />
# The framework should allow to define the levels of mathematical literacy required for different types of work.<br />
# It should allow to define a minimum mathematical literacy for citizens.<br />
<br />
The framework works with 6 levels of competency<br />
* Z<br />
** Z2 - The situation is complex and may require active influencing by adjusting and developing new mathematical models, defining new formulas and adjusting or constructing procedures. More complex computations are required to solve a problem.<br />
** Z1 - The situation is complex and may require active influencing by re-modeling mathematical models, redefining formulas and revisiting procedures. More complex computations are required to solve a problem.<br />
* Y<br />
** Y2 - The situation can be more or less familiar, more complex and requires certain actions based on familiar and set procedures, using known mathematical models, formulas and calculations. More actions are required to solve the problem.<br />
** Y1 - The situation can be more or less familiar, more complex and requires certain actions based on familiar and set procedures. More actions are required to solve the problem.<br />
* X<br />
** X2 - The situation is more or less familiar and familiarm unambiguous and clear. Actions are simple and concrete<br />
** X1 - The situation is familiar, unambiguous and clear. Actions are simple and concrete<br />
<br />
There are four strands to place the mathematical content:<br />
* Number, quantity, measure<br />
* Space and shape<br />
* Data handling and uncertainty<br />
* Relationships and change<br />
<br />
<br />
==References==<br />
* [http://www.fi.uu.nl/mbo/raamwerkrekenenwiskunde/welcome.xml?language=en Reference framework mathematics and numeracy] (the Netherlands)<br />
* [[Towards the Development of a Common European Framework of Reference for Mathematics in the Workplace and Society]]<br />
* Wijers, M., Bakker, A. and Jonker, V. (2010). {{refworks|A framework for mathematical literacy in competence-based secondary vocational education|3432}}. In A. Araujo, A. Fernandes, A. Azevedo and J. Francisco Rodrigues (Eds.), Educational Interfaces Between Mathematics and Industry (EIMI) (pp. 583-596). Porto, Portugal: EIMI (ICMI/ICIAM).<br />
<br />
==Versions of this document==<br />
* 20081220, [[wikiteam]]<br />
<br />
[[category:mathematics in the workplace]]</div>Mon, 11 Oct 2010 04:57:37 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Framework_Mathematics_and_Numeracy_NetherlandsMathematical Literacy
http://www.fisme.science.uu.nl/en/wiki/index.php/Mathematical_Literacy
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Mathematical_Literacy}}<br />
<br />
==General==<br />
Mathematical literacy entails the use of mathematical competencies at several levels, ranging from performance of standard mathematical operations to mathematical thinking and insight. It also requires the knowledge and application of a range of mathematical content.<br />
<br />
PISA assesses mathematical literacy in three dimensions:<br />
<br />
* First, the content of mathematics, as defined mainly in terms of broad mathematical concepts underlying mathematical thinking (such as chance, change and growth, space and shape, reasoning, uncertainty and dependency relationships), and only secondarily in relation to "curricular strands" (such as numbers, algebra and geometry). The PISA 2000 assessment, in which mathematics is a minor domain, focuses on two concepts: change and growth, and space and shape. These two areas allow a wide representation of aspects of the curriculum without giving undue weight to number skills.<br />
* Second, the process of mathematics as defined by general mathematical competencies. These include the use of mathematical language, modelling and problem-solving skills. The idea is not, however, to separate out such skills in different test items, since it is assumed that a range of competencies will be needed to perform any given mathematical task. Rather, questions are organized in terms of three "competency classes" defining the type of thinking skill needed.<br />
** The first class of mathematical competency consists of simple computations or definitions of the type most familiar in conventional mathematics assessments.<br />
** The second class requires connections to be made to solve straightforward problems.<br />
** The third competency class consists of mathematical thinking, generalization and insight, and requires students to engage in analysis, to identify the mathematical elements in a situation and to pose their own problems.<br />
* Third, the situations in which mathematics is used, ranging from private contexts to those relating to wider scientific and public issues.<br />
<br />
==References==<br />
* [http://www.pisa.gc.ca/math_e.shtml PISA]<br />
* De Lange, J. (2005). {{refworks|Measuring Mathematical Literacy|2559}} (In Encyclopedia of Social Measurement: Elsevier-Reed, Amsterdam.<br />
* Jablonka, E. (2003). {{refworks|Mathematical literacy|2524}} (In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick and F. K. S. Leung (Eds.), Second International Handbook of Mathematics Education (pp. 75-102). Dordrecht: Kluwer Academic Publishers.<br />
* [[Techno-Mathematical Literacy]]<br />
* [[Key competence]] (European Framework)<br />
* Wijers, M., Bakker, A. and Jonker, V. (2010). {{refworks|A framework for mathematical literacy in competence-based secondary vocational education|3432}}. In A. Araujo, A. Fernandes, A. Azevedo and J. Francisco Rodrigues (Eds.), Educational Interfaces Between Mathematics and Industry (EIMI) (pp. 583-596). Porto, Portugal: EIMI (ICMI/ICIAM).<br />
<br />
==Versions of this document==<br />
* 20080113, [[fiteam]]<br />
<br />
[[category:research]]<br />
[[category:mathematics in the workplace]]<br />
[[category:numeracy]]</div>Mon, 11 Oct 2010 04:57:04 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Mathematical_LiteracyFramework Mathematics and Numeracy Netherlands
http://www.fisme.science.uu.nl/en/wiki/index.php/Framework_Mathematics_and_Numeracy_Netherlands
<p>Vincent: /* References */</p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Raamwerk_wiskunde_mbo_(Algemeen)}}<br />
<br />
==General==<br />
The [http://www.fi.uu.nl/mbo/raamwerkrekenenwiskunde/welcome.xml?language=en Reference framework mathematics and numeracy document] (developed in the Netherlands) is a framework for mathematics that is modeled after the Common European Framework for the Modern Languages ([[CEF]]). Its goals are similar to that of the CEF in the sense that the framework should assist in formulating attainment levels for education, and therefore allow easier comparison of different qualifications. Although the framework for mathematics is especially developed within and for senior secondary vocational education in the Netherlands, it is formulated in such a way that it should be useful in vocational education and training more widely.<br />
<br />
==Principles==<br />
Two principles have guided the design of the framework:<br />
# The framework should allow to define the levels of mathematical literacy required for different types of work.<br />
# It should allow to define a minimum mathematical literacy for citizens.<br />
<br />
The framework works with 6 levels of competency<br />
* Z<br />
** Z2 - The situation is complex and may require active influencing by adjusting and developing new mathematical models, defining new formulas and adjusting or constructing procedures. More complex computations are required to solve a problem.<br />
** Z1 - The situation is complex and may require active influencing by re-modeling mathematical models, redefining formulas and revisiting procedures. More complex computations are required to solve a problem.<br />
* Y<br />
** Y2 - The situation can be more or less familiar, more complex and requires certain actions based on familiar and set procedures, using known mathematical models, formulas and calculations. More actions are required to solve the problem.<br />
** Y1 - The situation can be more or less familiar, more complex and requires certain actions based on familiar and set procedures. More actions are required to solve the problem.<br />
* X<br />
** X2 - The situation is more or less familiar and familiarm unambiguous and clear. Actions are simple and concrete<br />
** X1 - The situation is familiar, unambiguous and clear. Actions are simple and concrete<br />
<br />
There are four strands to place the mathematical content:<br />
* Number, quantity, measure<br />
* Space and shape<br />
* Data handling and uncertainty<br />
* Relationships and change<br />
<br />
<br />
==References==<br />
* [http://www.fi.uu.nl/mbo/raamwerkrekenenwiskunde/welcome.xml?language=en Reference framework mathematics and numeracy] (the Netherlands)<br />
* [[Towards the Development of a Common European Framework of Reference for Mathematics in the Workplace and Society]]<br />
* Wijers, M., Bakker, A. and Jonker, V. (2010). {{refworks|A framework for mathematical literacy in competence-based secondary vocational education|refID}}. In A. Araujo, A. Fernandes, A. Azevedo and J. Francisco Rodrigues (Eds.), EIMI 2010 (pp. 583-596). Barcelona: EIMI (ICMI/ICIAM).<br />
<br />
==Versions of this document==<br />
* 20081220, [[wikiteam]]<br />
<br />
[[category:mathematics in the workplace]]</div>Mon, 11 Oct 2010 04:51:06 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Framework_Mathematics_and_Numeracy_NetherlandsFramework Mathematics and Numeracy Netherlands
http://www.fisme.science.uu.nl/en/wiki/index.php/Framework_Mathematics_and_Numeracy_Netherlands
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Raamwerk_wiskunde_mbo_(Algemeen)}}<br />
<br />
==General==<br />
The [http://www.fi.uu.nl/mbo/raamwerkrekenenwiskunde/welcome.xml?language=en Reference framework mathematics and numeracy document] (developed in the Netherlands) is a framework for mathematics that is modeled after the Common European Framework for the Modern Languages ([[CEF]]). Its goals are similar to that of the CEF in the sense that the framework should assist in formulating attainment levels for education, and therefore allow easier comparison of different qualifications. Although the framework for mathematics is especially developed within and for senior secondary vocational education in the Netherlands, it is formulated in such a way that it should be useful in vocational education and training more widely.<br />
<br />
==Principles==<br />
Two principles have guided the design of the framework:<br />
# The framework should allow to define the levels of mathematical literacy required for different types of work.<br />
# It should allow to define a minimum mathematical literacy for citizens.<br />
<br />
The framework works with 6 levels of competency<br />
* Z<br />
** Z2 - The situation is complex and may require active influencing by adjusting and developing new mathematical models, defining new formulas and adjusting or constructing procedures. More complex computations are required to solve a problem.<br />
** Z1 - The situation is complex and may require active influencing by re-modeling mathematical models, redefining formulas and revisiting procedures. More complex computations are required to solve a problem.<br />
* Y<br />
** Y2 - The situation can be more or less familiar, more complex and requires certain actions based on familiar and set procedures, using known mathematical models, formulas and calculations. More actions are required to solve the problem.<br />
** Y1 - The situation can be more or less familiar, more complex and requires certain actions based on familiar and set procedures. More actions are required to solve the problem.<br />
* X<br />
** X2 - The situation is more or less familiar and familiarm unambiguous and clear. Actions are simple and concrete<br />
** X1 - The situation is familiar, unambiguous and clear. Actions are simple and concrete<br />
<br />
There are four strands to place the mathematical content:<br />
* Number, quantity, measure<br />
* Space and shape<br />
* Data handling and uncertainty<br />
* Relationships and change<br />
<br />
<br />
==References==<br />
* [http://www.fi.uu.nl/mbo/raamwerkrekenenwiskunde/welcome.xml?language=en Reference framework mathematics and numeracy] (the Netherlands)<br />
* [[Towards the Development of a Common European Framework of Reference for Mathematics in the Workplace and Society]]<br />
* Wijers, M., Bakker, A. and Jonker, V. (2010). {{refworks|A framework for mathematical literacy in competence-based secondary vocational education|refID}}. In A. Araujo, A. Fernandes, A. Azevedo and J. Francisco Rodrigues (Eds.), EIMI 2010. Barcelona: EIMI (ICMI/ICIAM).<br />
<br />
==Versions of this document==<br />
* 20081220, [[wikiteam]]<br />
<br />
[[category:mathematics in the workplace]]</div>Mon, 11 Oct 2010 04:45:00 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Framework_Mathematics_and_Numeracy_NetherlandsMathematical Literacy
http://www.fisme.science.uu.nl/en/wiki/index.php/Mathematical_Literacy
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Mathematical_Literacy}}<br />
<br />
==General==<br />
Mathematical literacy entails the use of mathematical competencies at several levels, ranging from performance of standard mathematical operations to mathematical thinking and insight. It also requires the knowledge and application of a range of mathematical content.<br />
<br />
PISA assesses mathematical literacy in three dimensions:<br />
<br />
* First, the content of mathematics, as defined mainly in terms of broad mathematical concepts underlying mathematical thinking (such as chance, change and growth, space and shape, reasoning, uncertainty and dependency relationships), and only secondarily in relation to "curricular strands" (such as numbers, algebra and geometry). The PISA 2000 assessment, in which mathematics is a minor domain, focuses on two concepts: change and growth, and space and shape. These two areas allow a wide representation of aspects of the curriculum without giving undue weight to number skills.<br />
* Second, the process of mathematics as defined by general mathematical competencies. These include the use of mathematical language, modelling and problem-solving skills. The idea is not, however, to separate out such skills in different test items, since it is assumed that a range of competencies will be needed to perform any given mathematical task. Rather, questions are organized in terms of three "competency classes" defining the type of thinking skill needed.<br />
** The first class of mathematical competency consists of simple computations or definitions of the type most familiar in conventional mathematics assessments.<br />
** The second class requires connections to be made to solve straightforward problems.<br />
** The third competency class consists of mathematical thinking, generalization and insight, and requires students to engage in analysis, to identify the mathematical elements in a situation and to pose their own problems.<br />
* Third, the situations in which mathematics is used, ranging from private contexts to those relating to wider scientific and public issues.<br />
<br />
==References==<br />
* [http://www.pisa.gc.ca/math_e.shtml PISA]<br />
* De Lange, J. (2005). {{refworks|Measuring Mathematical Literacy|2559}} (In Encyclopedia of Social Measurement: Elsevier-Reed, Amsterdam.<br />
* Jablonka, E. (2003). {{refworks|Mathematical literacy|2524}} (In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick and F. K. S. Leung (Eds.), Second International Handbook of Mathematics Education (pp. 75-102). Dordrecht: Kluwer Academic Publishers.<br />
* [[Techno-Mathematical Literacy]]<br />
* [[Key competence]] (European Framework)<br />
<br />
==Versions of this document==<br />
* 20080113, [[fiteam]]<br />
<br />
[[category:research]]<br />
[[category:mathematics in the workplace]]<br />
[[category:numeracy]]</div>Mon, 02 Aug 2010 06:20:24 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Mathematical_LiteracyMeasurement in occupations
http://www.fisme.science.uu.nl/en/wiki/index.php/Measurement_in_occupations
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Meten_in_het_beroep}}<br />
<br />
==General==<br />
This paper analyzes the nature and purposes of measurement in intermediate-level work, i.e. occupations for which Dutch senior secondary vocational education (MBO) prepares its students (aged 16+). A quantitative analysis was based on the 237 qualification files describing the competencies<br />
required in each of the MBO occupations, and a qualitative analysis was carried out on interview data in different educational programs with a focus on optician and lab technician. Half of the qualification files explicitly mention measurement in their competence indicators. More reference to measurement<br />
is made in the technical and business sectors than in the health care and agricultural sectors. In terms of the nature of measurement, we observed that occupational measurement has connections to arithmetic, geometry, data analysis, or science. Most notable, however, is the trend for mediation of<br />
measurement by digital technologies, which raises the question of how to prepare vocational students.<br />
<br />
Many MBO teachers prefer to start with old technologies in order to give students the opportunities to learn about what happens in the black boxes behind digital displays. The purposes of measurement in intermediate-level occupations can be categorized as meeting quality standards, stock and time management, monitoring production processes as well as their efficiency and effectiveness, making something fit (furniture, automotive assembly), and ensuring safety. Last, some implications for mathematics education are discussed.<br />
<br />
==References==<br />
* Bakker, A., Kent, P., Noss, R. and Hoyles, C. (2009). {{refworks|Alternative representations of statistical measures in computer tools to promote communication between employees in automotive manufacturing|3598}}. Technology Innovations in Statistics Education, 3(2).<br />
* Bakker, A., Kent, P., Derry, J., Noss, R. and Hoyles, C. (2008). {{refworks|Statistical inference at work: The case of statistical process control|3599}}. Statistics Education Research Journal, 7(2), 130-145.<br />
* Hoyles, C., Bakker, A., Kent, P. and Noss, R. (2007). {{refworks|Attributing meanings to representations of data: The case of statistical process control |3597}}. Mathematical Thinking and Learning, 9, 331-360.<br />
* Hoyles, C., Noss, R., Kent, P. and Bakker, A. (2010). {{refworks|Improving mathematics at work: The need for techno-mathematical literacies|3601}}. London: Routledge.<br />
* Konold, C. and Lehrer, R. (2008). {{refworks|Technology and mathematics education: An essay in honor of Jim Kaput|3591}} (In L. D. English (Ed.), Handbook of international research in mathematics education (2nd ed.). New York: Routledge.<br />
* [[Measurement (General)]]<br />
<br />
==Versions of this document==<br />
* 20100801, [[wikiteam]]<br />
<br />
[[category:numeracy]]<br />
[[category:research]]<br />
[[category:mathematics in the workplace]]<br />
[[category:measurement]]</div>Mon, 02 Aug 2010 06:17:28 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Measurement_in_occupationsMeasurement in occupations
http://www.fisme.science.uu.nl/en/wiki/index.php/Measurement_in_occupations
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Meten_in_het_beroep}}<br />
<br />
==General==<br />
This paper analyzes the nature and purposes of measurement in intermediate-level work, i.e. occupations for which Dutch senior secondary vocational education (MBO) prepares its students (aged 16+). A quantitative analysis was based on the 237 qualification files describing the competencies<br />
required in each of the MBO occupations, and a qualitative analysis was carried out on interview data in different educational programs with a focus on optician and lab technician. Half of the qualification files explicitly mention measurement in their competence indicators. More reference to measurement<br />
is made in the technical and business sectors than in the health care and agricultural sectors. In terms of the nature of measurement, we observed that occupational measurement has connections to arithmetic, geometry, data analysis, or science. Most notable, however, is the trend for mediation of<br />
measurement by digital technologies, which raises the question of how to prepare vocational students.<br />
<br />
Many MBO teachers prefer to start with old technologies in order to give students the opportunities to learn about what happens in the black boxes behind digital displays. The purposes of measurement in intermediate-level occupations can be categorized as meeting quality standards, stock and time management, monitoring production processes as well as their efficiency and effectiveness, making something fit (furniture, automotive assembly), and ensuring safety. Last, some implications for mathematics education are discussed.<br />
<br />
==References==<br />
* Bakker, A., Kent, P., Noss, R. and Hoyles, C. (2009). {{refworks|Alternative representations of statistical measures in computer tools to promote communication between employees in automotive manufacturing|3598}}. Technology Innovations in Statistics Education, 3(2).<br />
* Bakker, A., Kent, P., Derry, J., Noss, R. and Hoyles, C. (2008). {{refworks|Statistical inference at work: The case of statistical process control|3599}}. Statistics Education Research Journal, 7(2), 130-145.<br />
* Hoyles, C., Bakker, A., Kent, P. and Noss, R. (2007). {{refworks|Attributing meanings to representations of data: The case of statistical process control |3597}}. Mathematical Thinking and Learning, 9, 331-360.<br />
* Hoyles, C., Noss, R., Kent, P. and Bakker, A. (2010). {{refworks|Improving mathematics at work: The need for techno-mathematical literacies|3601}}. London: Routledge.<br />
* Konold, C. and Lehrer, R. (2008). {{refworks|Technology and mathematics education: An essay in honor of Jim Kaput|3591}} (In L. D. English (Ed.), Handbook of international research in mathematics education (2nd ed.). New York: Routledge.<br />
* [[Measurement (General)]]<br />
<br />
==Versions of this document==<br />
* 20100801, [[wikiteam]]<br />
<br />
[[category:numeracy]]<br />
[[category:research]]<br />
[[category:workplace learning]]<br />
[[category:measurement]]</div>Mon, 02 Aug 2010 06:17:02 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Measurement_in_occupationsMeasurement in occupations
http://www.fisme.science.uu.nl/en/wiki/index.php/Measurement_in_occupations
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Meten_in_het_beroep}}<br />
<br />
==General==<br />
This paper analyzes the nature and purposes of measurement in intermediate-level work, i.e. occupations for which Dutch senior secondary vocational education (MBO) prepares its students (aged 16+). A quantitative analysis was based on the 237 qualification files describing the competencies<br />
required in each of the MBO occupations, and a qualitative analysis was carried out on interview data in different educational programs with a focus on optician and lab technician. Half of the qualification files explicitly mention measurement in their competence indicators. More reference to measurement<br />
is made in the technical and business sectors than in the health care and agricultural sectors. In terms of the nature of measurement, we observed that occupational measurement has connections to arithmetic, geometry, data analysis, or science. Most notable, however, is the trend for mediation of<br />
measurement by digital technologies, which raises the question of how to prepare vocational students.<br />
<br />
Many MBO teachers prefer to start with old technologies in order to give students the opportunities to learn about what happens in the black boxes behind digital displays. The purposes of measurement in intermediate-level occupations can be categorized as meeting quality standards, stock and time management, monitoring production processes as well as their efficiency and effectiveness, making something fit (furniture, automotive assembly), and ensuring safety. Last, some implications for mathematics education are discussed.<br />
<br />
==References==<br />
* Bakker, A., Kent, P., Noss, R. and Hoyles, C. (2009). {{refworks|Alternative representations of statistical measures in computer tools to promote communication between employees in automotive manufacturing|3598}}. Technology Innovations in Statistics Education, 3(2).<br />
* Bakker, A., Kent, P., Derry, J., Noss, R. and Hoyles, C. (2008). {{refworks|Statistical inference at work: The case of statistical process control|3599}}. Statistics Education Research Journal, 7(2), 130-145.<br />
* Hoyles, C., Bakker, A., Kent, P. and Noss, R. (2007). {{refworks|Attributing meanings to representations of data: The case of statistical process control |3597}}. Mathematical Thinking and Learning, 9, 331-360.<br />
* Hoyles, C., Noss, R., Kent, P. and Bakker, A. (2010). {{refworks|Improving mathematics at work: The need for techno-mathematical literacies|3601}}. London: Routledge.<br />
* Konold, C. and Lehrer, R. (2008). {{refworks|Technology and mathematics education: An essay in honor of Jim Kaput|3591}} (In L. D. English (Ed.), Handbook of international research in mathematics education (2nd ed.). New York: Routledge.<br />
* [[Measurement (General)]]<br />
<br />
==Versions of this document==<br />
* 20100801, [[wikiteam]]<br />
<br />
[[category:vocational and educational training]]<br />
[[category:measurement]]</div>Mon, 02 Aug 2010 06:16:22 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Measurement_in_occupationsMeasurement (General)
http://www.fisme.science.uu.nl/en/wiki/index.php/Measurement_(General)
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Meten_(Algemeen)}}<br />
<br />
==General==<br />
In science, measurement is the process of estimating or determining the magnitude of a quantity, such as length or mass, relative to a unit of measurement, such as a metre or a kilogram. The term measurement can also be used to refer to a specific result obtained from the measurement process.<br />
<br />
<br />
<br />
==References==<br />
* ______. (2007). {{refworks|TAL - Meten en meetkunde bovenbouw|2805}}. Groningen: Wolters Noordhoff.<br />
* Adams, T. L. and Harrell, G. (2003). {{refworks|Estimation at Work|3562}} (In D. H. Clements (Ed.), Learning and Teaching Measurement (pp. 229-244). Reston, VA: National Council of Teachers of Mathematics.<br />
* Bright, G. W., Jordan, P. L., Malloy, C. and Watanabe, T. (2005). {{refworks|Navigating through measurement in grades 6-8|3603}}. Reston, VA: National Council of Teachers of Mathematics (NCTM).<br />
* Buys, K. (2003). {{refworks|Ontwikkeling van een leerlijn: meten|2861}}. Panama-Post. Tijdschrift voor nascholing en onderzoek van het reken-wiskundeonderwijs, 22(2), 3-10.<br />
* Coben, D. and Hodgen, J. (2008). {{refworks|Assessing numeracy for nursing|3559}}. British Society for Research into Learning Mathematics, 28(3), 18-23.<br />
* Cockcroft, W. (1982). {{refworks|Mathematics counts. Report of the Committee of Inquiry into the Teaching of Mathematics in Schools|3563}}. London: Her Majesty's Stationery Office.<br />
* Crosby, A. W. (1997). {{refworks|The Measure of Reality. Quantification and Western Society, 1250-1600|3602}}. Cambridge: Cambridge University Press.<br />
* De Schutter, J. (2009). {{refworks|Succesvol docentenstages realiseren: Ervaringen, praktijkvoorbeelden en aanbevelingen voor het mbo |3593}}. Hoorn: Van Beekveld & Terpstra.<br />
* Dilke, O. A. W. (1987). {{refworks|Mathematics and measurement|3594}}. London: British Museum.<br />
* Forman, S. L. and Steen, L. A. (1995). {{refworks|Mathematics for work and life|3595}} (In I. M. Carl (Ed.), Seventy-five years of progress: Prospects for school mathematics (pp. 219-241). Reston, VA: National Council of Teachers of Mathematics.<br />
* Glaudé, M., Verbeek, F. and Felix, C. (2010). {{refworks|Onderzoek naar de stand van zaken en effecten van de ontwikkeling van ‘les- en examenmateriaal en docentstages’|3592}}. Amsterdam: Kohnstamm Instituut.<br />
* Latour, B. (1999). {{refworks|Pandora’s Hope: Essays on the Reality of Science Studies|3596}}. Cambridge, Mass., London: Harvard University Press.<br />
* Lehrer, R., Jaslow, L. and Curtis, C. L. (2003). {{refworks|Developing an understanding of measurement in the elementary grades|3560}} (In D. H. Clements and G. Bright (Eds.), Learning and teaching measurement (pp. 1001-121). Reston, VA: National Council of Teachers of Mathematics.<br />
* [[Measurement in occupations]]<br />
* Prins, G. T., Bulte, A. M. W., Van Driel, J. H. and Pilot, A. (2009). {{refworks|Students’ involvement in authentic modelling practices as contexts in chemistry education|3590}}. Research in Science Education, 39, 681-700.<br />
* Steinback, M., Schmitt, M. J., Merson, M. and Leonelli, E. (2003). {{refworks|Measurement in Adult Education: Starting with Students' Understandings|3561}} (In D. H. Clements (Ed.), Yearbook of the National Council of Teachers of Mathematics (pp. 318-331). Reston, VA: National Council of Teachers of Mathematics.<br />
* Stephan, M. L., Bowers, J. and Cobb, P. (Eds.). (2003). {{refworks|Supporting students’ development of measuring conceptions: Analyzing students’ learning in social context|3535}}. Reston, VA: National Council of Teachers of Mathematics.<br />
* Van den Heuvel-Panhuizen, M. and Buijs, K. (Eds.). (2004). {{refworks|Young children learn measurement and geometry|2895}}. Utrecht: Freudenthal instituut.<br />
* [http://en.wikipedia.org/wiki/Measurement Wikipedia]<br />
<br />
<br />
==Versions of this document==<br />
* 20100717, [[wikiteam]]<br />
<br />
[[category:measurement]]</div>Mon, 02 Aug 2010 06:15:58 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Measurement_(General)Measurement (General)
http://www.fisme.science.uu.nl/en/wiki/index.php/Measurement_(General)
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Meten_(Algemeen)}}<br />
<br />
==General==<br />
In science, measurement is the process of estimating or determining the magnitude of a quantity, such as length or mass, relative to a unit of measurement, such as a metre or a kilogram. The term measurement can also be used to refer to a specific result obtained from the measurement process.<br />
<br />
<br />
<br />
==References==<br />
* ______. (2007). {{refworks|TAL - Meten en meetkunde bovenbouw|2805}}. Groningen: Wolters Noordhoff.<br />
* Adams, T. L. and Harrell, G. (2003). {{refworks|Estimation at Work|3562}} (In D. H. Clements (Ed.), Learning and Teaching Measurement (pp. 229-244). Reston, VA: National Council of Teachers of Mathematics.<br />
* Bright, G. W., Jordan, P. L., Malloy, C. and Watanabe, T. (2005). {{refworks|Navigating through measurement in grades 6-8|3603}}. Reston, VA: National Council of Teachers of Mathematics (NCTM).<br />
* Buys, K. (2003). {{refworks|Ontwikkeling van een leerlijn: meten|2861}}. Panama-Post. Tijdschrift voor nascholing en onderzoek van het reken-wiskundeonderwijs, 22(2), 3-10.<br />
* Coben, D. and Hodgen, J. (2008). {{refworks|Assessing numeracy for nursing|3559}}. British Society for Research into Learning Mathematics, 28(3), 18-23.<br />
* Cockcroft, W. (1982). {{refworks|Mathematics counts. Report of the Committee of Inquiry into the Teaching of Mathematics in Schools|3563}}. London: Her Majesty's Stationery Office.<br />
* Crosby, A. W. (1997). {{refworks|The Measure of Reality. Quantification and Western Society, 1250-1600|3602}}. Cambridge: Cambridge University Press.<br />
* De Schutter, J. (2009). {{refworks|Succesvol docentenstages realiseren: Ervaringen, praktijkvoorbeelden en aanbevelingen voor het mbo |3593}}. Hoorn: Van Beekveld & Terpstra.<br />
* Dilke, O. A. W. (1987). {{refworks|Mathematics and measurement|3594}}. London: British Museum.<br />
* Forman, S. L. and Steen, L. A. (1995). {{refworks|Mathematics for work and life|3595}} (In I. M. Carl (Ed.), Seventy-five years of progress: Prospects for school mathematics (pp. 219-241). Reston, VA: National Council of Teachers of Mathematics.<br />
* Glaudé, M., Verbeek, F. and Felix, C. (2010). {{refworks|Onderzoek naar de stand van zaken en effecten van de ontwikkeling van ‘les- en examenmateriaal en docentstages’|3592}}. Amsterdam: Kohnstamm Instituut.<br />
* Latour, B. (1999). {{refworks|Pandora’s Hope: Essays on the Reality of Science Studies|3596}}. Cambridge, Mass., London: Harvard University Press.<br />
* Lehrer, R., Jaslow, L. and Curtis, C. L. (2003). {{refworks|Developing an understanding of measurement in the elementary grades|3560}} (In D. H. Clements and G. Bright (Eds.), Learning and teaching measurement (pp. 1001-121). Reston, VA: National Council of Teachers of Mathematics.<br />
* Prins, G. T., Bulte, A. M. W., Van Driel, J. H. and Pilot, A. (2009). {{refworks|Students’ involvement in authentic modelling practices as contexts in chemistry education|3590}}. Research in Science Education, 39, 681-700.<br />
* Steinback, M., Schmitt, M. J., Merson, M. and Leonelli, E. (2003). {{refworks|Measurement in Adult Education: Starting with Students' Understandings|3561}} (In D. H. Clements (Ed.), Yearbook of the National Council of Teachers of Mathematics (pp. 318-331). Reston, VA: National Council of Teachers of Mathematics.<br />
* Stephan, M. L., Bowers, J. and Cobb, P. (Eds.). (2003). {{refworks|Supporting students’ development of measuring conceptions: Analyzing students’ learning in social context|3535}}. Reston, VA: National Council of Teachers of Mathematics.<br />
* Van den Heuvel-Panhuizen, M. and Buijs, K. (Eds.). (2004). {{refworks|Young children learn measurement and geometry|2895}}. Utrecht: Freudenthal instituut.<br />
* [http://en.wikipedia.org/wiki/Measurement Wikipedia]<br />
<br />
<br />
==Versions of this document==<br />
* 20100717, [[wikiteam]]<br />
<br />
[[category:measurement]]</div>Mon, 02 Aug 2010 06:15:38 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Measurement_(General)Measurement
http://www.fisme.science.uu.nl/en/wiki/index.php/Measurement
<p>Vincent: Created page with 'REDIRECT Measurement (General)'</p>
<hr />
<div>REDIRECT [[Measurement (General)]]</div>Mon, 02 Aug 2010 06:15:25 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:MeasurementMeasurement in occupations
http://www.fisme.science.uu.nl/en/wiki/index.php/Measurement_in_occupations
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Meten_in_het_beroep}}<br />
<br />
==General==<br />
This paper analyzes the nature and purposes of measurement in intermediate-level work, i.e. occupations for which Dutch senior secondary vocational education (MBO) prepares its students (aged 16+). A quantitative analysis was based on the 237 qualification files describing the competencies<br />
required in each of the MBO occupations, and a qualitative analysis was carried out on interview data in different educational programs with a focus on optician and lab technician. Half of the qualification files explicitly mention measurement in their competence indicators. More reference to measurement<br />
is made in the technical and business sectors than in the health care and agricultural sectors. In terms of the nature of measurement, we observed that occupational measurement has connections to arithmetic, geometry, data analysis, or science. Most notable, however, is the trend for mediation of<br />
measurement by digital technologies, which raises the question of how to prepare vocational students.<br />
<br />
Many MBO teachers prefer to start with old technologies in order to give students the opportunities to learn about what happens in the black boxes behind digital displays. The purposes of measurement in intermediate-level occupations can be categorized as meeting quality standards, stock and time management, monitoring production processes as well as their efficiency and effectiveness, making something fit (furniture, automotive assembly), and ensuring safety. Last, some implications for mathematics education are discussed.<br />
<br />
==References==<br />
* [[Measurement (General)]]<br />
<br />
==Versions of this document==<br />
* 20100801, [[wikiteam]]<br />
<br />
[[category:vocational and educational training]]<br />
[[category:measurement]]</div>Mon, 02 Aug 2010 06:15:07 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Measurement_in_occupationsMeasurement in occupations
http://www.fisme.science.uu.nl/en/wiki/index.php/Measurement_in_occupations
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Meten_in_het_beroep}}<br />
<br />
==General==<br />
This paper analyzes the nature and purposes of measurement in intermediate-level work, i.e. occupations for which Dutch senior secondary vocational education (MBO) prepares its students (aged 16+). A quantitative analysis was based on the 237 qualification files describing the competencies<br />
required in each of the MBO occupations, and a qualitative analysis was carried out on interview data in different educational programs with a focus on optician and lab technician. Half of the qualification files explicitly mention measurement in their competence indicators. More reference to measurement<br />
is made in the technical and business sectors than in the health care and agricultural sectors. In terms of the nature of measurement, we observed that occupational measurement has connections to arithmetic, geometry, data analysis, or science. Most notable, however, is the trend for mediation of<br />
measurement by digital technologies, which raises the question of how to prepare vocational students.<br />
<br />
Many MBO teachers prefer to start with old technologies in order to give students the opportunities to learn about what happens in the black boxes behind digital displays. The purposes of measurement in intermediate-level occupations can be categorized as meeting quality standards, stock and time management, monitoring production processes as well as their efficiency and effectiveness, making something fit (furniture, automotive assembly), and ensuring safety. Last, some implications for mathematics education are discussed.<br />
<br />
==References==<br />
* [[Measurement]]<br />
<br />
==Versions of this document==<br />
* 20100801, [[wikiteam]]<br />
<br />
[[category:vocational and educational training]]<br />
[[category:measurement]]</div>Mon, 02 Aug 2010 06:14:44 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Measurement_in_occupationsMeasurement in occupations
http://www.fisme.science.uu.nl/en/wiki/index.php/Measurement_in_occupations
<p>Vincent: Created page with '{{navigation algemeen}} {{nl|Meten in het beroep}} ==General== This paper analyzes the nature and purposes of measurement in intermediate-level work, i.e. occupations for which...'</p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Meten in het beroep}}<br />
<br />
==General==<br />
This paper analyzes the nature and purposes of measurement in intermediate-level work, i.e. occupations for which Dutch senior secondary vocational education (MBO) prepares its students (aged 16+). A quantitative analysis was based on the 237 qualification files describing the competencies<br />
required in each of the MBO occupations, and a qualitative analysis was carried out on interview data in different educational programs with a focus on optician and lab technician. Half of the qualification files explicitly mention measurement in their competence indicators. More reference to measurement<br />
is made in the technical and business sectors than in the health care and agricultural sectors. In terms of the nature of measurement, we observed that occupational measurement has connections to arithmetic, geometry, data analysis, or science. Most notable, however, is the trend for mediation of<br />
measurement by digital technologies, which raises the question of how to prepare vocational students.<br />
<br />
Many MBO teachers prefer to start with old technologies in order to give students the opportunities to learn about what happens in the black boxes behind digital displays. The purposes of measurement in intermediate-level occupations can be categorized as meeting quality standards, stock and time management, monitoring production processes as well as their efficiency and effectiveness, making something fit (furniture, automotive assembly), and ensuring safety. Last, some implications for mathematics education are discussed.<br />
<br />
==Versions of this document==<br />
* 20100801, [[wikiteam]]<br />
<br />
[[category:vocational and educational training]]</div>Mon, 02 Aug 2010 06:13:58 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Measurement_in_occupationsMeasurement (General)
http://www.fisme.science.uu.nl/en/wiki/index.php/Measurement_(General)
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Meten_(Algemeen)}}<br />
<br />
==General==<br />
In science, measurement is the process of estimating or determining the magnitude of a quantity, such as length or mass, relative to a unit of measurement, such as a metre or a kilogram. The term measurement can also be used to refer to a specific result obtained from the measurement process.<br />
<br />
==Measurement and the workplace==<br />
* Bakker, A., Kent, P., Noss, R. and Hoyles, C. (2009). {{refworks|Alternative representations of statistical measures in computer tools to promote communication between employees in automotive manufacturing|3598}}. Technology Innovations in Statistics Education, 3(2).<br />
* Bakker, A., Kent, P., Derry, J., Noss, R. and Hoyles, C. (2008). {{refworks|Statistical inference at work: The case of statistical process control|3599}}. Statistics Education Research Journal, 7(2), 130-145.<br />
* Hoyles, C., Bakker, A., Kent, P. and Noss, R. (2007). {{refworks|Attributing meanings to representations of data: The case of statistical process control |3597}}. Mathematical Thinking and Learning, 9, 331-360.<br />
* Hoyles, C., Noss, R., Kent, P. and Bakker, A. (2010). {{refworks|Improving mathematics at work: The need for techno-mathematical literacies|3601}}. London: Routledge.<br />
* Konold, C. and Lehrer, R. (2008). {{refworks|Technology and mathematics education: An essay in honor of Jim Kaput|3591}} (In L. D. English (Ed.), Handbook of international research in mathematics education (2nd ed.). New York: Routledge.<br />
<br />
==References==<br />
* ______. (2007). {{refworks|TAL - Meten en meetkunde bovenbouw|2805}}. Groningen: Wolters Noordhoff.<br />
* Adams, T. L. and Harrell, G. (2003). {{refworks|Estimation at Work|3562}} (In D. H. Clements (Ed.), Learning and Teaching Measurement (pp. 229-244). Reston, VA: National Council of Teachers of Mathematics.<br />
* Bright, G. W., Jordan, P. L., Malloy, C. and Watanabe, T. (2005). {{refworks|Navigating through measurement in grades 6-8|3603}}. Reston, VA: National Council of Teachers of Mathematics (NCTM).<br />
* Buys, K. (2003). {{refworks|Ontwikkeling van een leerlijn: meten|2861}}. Panama-Post. Tijdschrift voor nascholing en onderzoek van het reken-wiskundeonderwijs, 22(2), 3-10.<br />
* Coben, D. and Hodgen, J. (2008). {{refworks|Assessing numeracy for nursing|3559}}. British Society for Research into Learning Mathematics, 28(3), 18-23.<br />
* Cockcroft, W. (1982). {{refworks|Mathematics counts. Report of the Committee of Inquiry into the Teaching of Mathematics in Schools|3563}}. London: Her Majesty's Stationery Office.<br />
* Crosby, A. W. (1997). {{refworks|The Measure of Reality. Quantification and Western Society, 1250-1600|3602}}. Cambridge: Cambridge University Press.<br />
* De Schutter, J. (2009). {{refworks|Succesvol docentenstages realiseren: Ervaringen, praktijkvoorbeelden en aanbevelingen voor het mbo |3593}}. Hoorn: Van Beekveld & Terpstra.<br />
* Dilke, O. A. W. (1987). {{refworks|Mathematics and measurement|3594}}. London: British Museum.<br />
* Forman, S. L. and Steen, L. A. (1995). {{refworks|Mathematics for work and life|3595}} (In I. M. Carl (Ed.), Seventy-five years of progress: Prospects for school mathematics (pp. 219-241). Reston, VA: National Council of Teachers of Mathematics.<br />
* Glaudé, M., Verbeek, F. and Felix, C. (2010). {{refworks|Onderzoek naar de stand van zaken en effecten van de ontwikkeling van ‘les- en examenmateriaal en docentstages’|3592}}. Amsterdam: Kohnstamm Instituut.<br />
* Latour, B. (1999). {{refworks|Pandora’s Hope: Essays on the Reality of Science Studies|3596}}. Cambridge, Mass., London: Harvard University Press.<br />
* Lehrer, R., Jaslow, L. and Curtis, C. L. (2003). {{refworks|Developing an understanding of measurement in the elementary grades|3560}} (In D. H. Clements and G. Bright (Eds.), Learning and teaching measurement (pp. 1001-121). Reston, VA: National Council of Teachers of Mathematics.<br />
* Prins, G. T., Bulte, A. M. W., Van Driel, J. H. and Pilot, A. (2009). {{refworks|Students’ involvement in authentic modelling practices as contexts in chemistry education|3590}}. Research in Science Education, 39, 681-700.<br />
* Steinback, M., Schmitt, M. J., Merson, M. and Leonelli, E. (2003). {{refworks|Measurement in Adult Education: Starting with Students' Understandings|3561}} (In D. H. Clements (Ed.), Yearbook of the National Council of Teachers of Mathematics (pp. 318-331). Reston, VA: National Council of Teachers of Mathematics.<br />
* Stephan, M. L., Bowers, J. and Cobb, P. (Eds.). (2003). {{refworks|Supporting students’ development of measuring conceptions: Analyzing students’ learning in social context|3535}}. Reston, VA: National Council of Teachers of Mathematics.<br />
* Van den Heuvel-Panhuizen, M. and Buijs, K. (Eds.). (2004). {{refworks|Young children learn measurement and geometry|2895}}. Utrecht: Freudenthal instituut.<br />
* [http://en.wikipedia.org/wiki/Measurement Wikipedia]<br />
<br />
<br />
==Versions of this document==<br />
* 20100717, [[wikiteam]]<br />
<br />
[[category:measurement]]</div>Sun, 01 Aug 2010 09:48:38 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Measurement_(General)Measurement (General)
http://www.fisme.science.uu.nl/en/wiki/index.php/Measurement_(General)
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Meten_(Algemeen)}}<br />
<br />
==General==<br />
In science, measurement is the process of estimating or determining the magnitude of a quantity, such as length or mass, relative to a unit of measurement, such as a metre or a kilogram. The term measurement can also be used to refer to a specific result obtained from the measurement process.<br />
<br />
==References==<br />
* ______. (2007). {{refworks|TAL - Meten en meetkunde bovenbouw|2805}}. Groningen: Wolters Noordhoff.<br />
* Adams, T. L. and Harrell, G. (2003). {{refworks|Estimation at Work|3562}} (In D. H. Clements (Ed.), Learning and Teaching Measurement (pp. 229-244). Reston, VA: National Council of Teachers of Mathematics.<br />
* Bakker, A., Kent, P., Noss, R. and Hoyles, C. (2009). {{refworks|Alternative representations of statistical measures in computer tools to promote communication between employees in automotive manufacturing|3598}}. Technology Innovations in Statistics Education, 3(2).<br />
* Bakker, A., Kent, P., Derry, J., Noss, R. and Hoyles, C. (2008). {{refworks|Statistical inference at work: The case of statistical process control|3599}}. Statistics Education Research Journal, 7(2), 130-145.<br />
* Bright, G. W., Jordan, P. L., Malloy, C. and Watanabe, T. (2005). {{refworks|Navigating through measurement in grades 6-8|3603}}. Reston, VA: National Council of Teachers of Mathematics (NCTM).<br />
* Buys, K. (2003). {{refworks|Ontwikkeling van een leerlijn: meten|2861}}. Panama-Post. Tijdschrift voor nascholing en onderzoek van het reken-wiskundeonderwijs, 22(2), 3-10.<br />
* Coben, D. and Hodgen, J. (2008). {{refworks|Assessing numeracy for nursing|3559}}. British Society for Research into Learning Mathematics, 28(3), 18-23.<br />
* Cockcroft, W. (1982). {{refworks|Mathematics counts. Report of the Committee of Inquiry into the Teaching of Mathematics in Schools|3563}}. London: Her Majesty's Stationery Office.<br />
* Crosby, A. W. (1997). {{refworks|The Measure of Reality. Quantification and Western Society, 1250-1600|3602}}. Cambridge: Cambridge University Press.<br />
* De Schutter, J. (2009). {{refworks|Succesvol docentenstages realiseren: Ervaringen, praktijkvoorbeelden en aanbevelingen voor het mbo |3593}}. Hoorn: Van Beekveld & Terpstra.<br />
* Dilke, O. A. W. (1987). {{refworks|Mathematics and measurement|3594}}. London: British Museum.<br />
* Forman, S. L. and Steen, L. A. (1995). {{refworks|Mathematics for work and life|3595}} (In I. M. Carl (Ed.), Seventy-five years of progress: Prospects for school mathematics (pp. 219-241). Reston, VA: National Council of Teachers of Mathematics.<br />
* Glaudé, M., Verbeek, F. and Felix, C. (2010). {{refworks|Onderzoek naar de stand van zaken en effecten van de ontwikkeling van ‘les- en examenmateriaal en docentstages’|3592}}. Amsterdam: Kohnstamm Instituut.<br />
* Hoyles, C., Bakker, A., Kent, P. and Noss, R. (2007). {{refworks|Attributing meanings to representations of data: The case of statistical process control |3597}}. Mathematical Thinking and Learning, 9, 331-360.<br />
* Hoyles, C., Noss, R., Kent, P. and Bakker, A. (2010). {{refworks|Improving mathematics at work: The need for techno-mathematical literacies|3601}}. London: Routledge.<br />
* Konold, C. and Lehrer, R. (2008). {{refworks|Technology and mathematics education: An essay in honor of Jim Kaput|3591}} (In L. D. English (Ed.), Handbook of international research in mathematics education (2nd ed.). New York: Routledge.<br />
* Latour, B. (1999). {{refworks|Pandora’s Hope: Essays on the Reality of Science Studies|3596}}. Cambridge, Mass., London: Harvard University Press.<br />
* Lehrer, R., Jaslow, L. and Curtis, C. L. (2003). {{refworks|Developing an understanding of measurement in the elementary grades|3560}} (In D. H. Clements and G. Bright (Eds.), Learning and teaching measurement (pp. 1001-121). Reston, VA: National Council of Teachers of Mathematics.<br />
* Prins, G. T., Bulte, A. M. W., Van Driel, J. H. and Pilot, A. (2009). {{refworks|Students’ involvement in authentic modelling practices as contexts in chemistry education|3590}}. Research in Science Education, 39, 681-700.<br />
* Steinback, M., Schmitt, M. J., Merson, M. and Leonelli, E. (2003). {{refworks|Measurement in Adult Education: Starting with Students' Understandings|3561}} (In D. H. Clements (Ed.), Yearbook of the National Council of Teachers of Mathematics (pp. 318-331). Reston, VA: National Council of Teachers of Mathematics.<br />
* Stephan, M. L., Bowers, J. and Cobb, P. (Eds.). (2003). {{refworks|Supporting students’ development of measuring conceptions: Analyzing students’ learning in social context|3535}}. Reston, VA: National Council of Teachers of Mathematics.<br />
* Van den Heuvel-Panhuizen, M. and Buijs, K. (Eds.). (2004). {{refworks|Young children learn measurement and geometry|2895}}. Utrecht: Freudenthal instituut.<br />
* [http://en.wikipedia.org/wiki/Measurement Wikipedia]<br />
<br />
<br />
==Versions of this document==<br />
* 20100717, [[wikiteam]]<br />
<br />
[[category:measurement]]</div>Sun, 01 Aug 2010 09:47:22 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Measurement_(General)Boundary crossing between school and work for developing techno-mathematical competencies in vocational education
http://www.fisme.science.uu.nl/en/wiki/index.php/Boundary_crossing_between_school_and_work_for_developing_techno-mathematical_competencies_in_vocational_education
<p>Vincent: /* References */</p>
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<div>{{navigation algemeen}}<br />
{{nl|Boundary_crossing_between_school_and_work_for_developing_techno-mathematical_competencies_in_vocational_education}}<br />
<br />
<br />
==General==<br />
In a high-tech knowledge-based economy many employees need Techno-mathematical Competencies<br />
(TmC): these are combinations of technological and mathematical competencies that are mediated by<br />
technology and situated in specific work contexts. At the boundaries between vocational colleges (mbo)<br />
and learning-work sites, the proposed project focuses on the question: How can new learning<br />
arrangements support the development of the TmC required for technical work? Among the results will<br />
be a task-specific instruction theory and computer tools for developing such TmC. The theoretical focus is<br />
on boundary crossing between school and work as a tool to promote progressive recontextualisation of<br />
techno-mathematical knowledge.<br />
<br />
<br />
==Problem definition==<br />
<br />
===Boundary crossing between school and work===<br />
A major challenge for students in vocational education and training (VET) is to make connections between school and work settings. For example, as Van der Sanden and Teurlings (2003) observe, even though the vocational school system aims at connecting students’ codified knowledge acquired at school to episodic knowledge developed from workplace practice periods, this often does not lead to the required integration of different knowledge forms. The boundary between school and work is therefore an interesting location to study what is metaphorically called transfer. Traditionally, general subjects such as mathematics were (and often still are) taught in a general way assuming that the knowledge acquired during education can later be applied in specific contexts, but there are two problems with this view on transfer. <br />
<br />
Firstly, this view has been criticised by many proponents of situated cognition, constructivism and socio-cultural theories of learning for its lack of attention for context, participation in communities, history and available tools (e.g., Beach, 1999; Lave, 1988; Van Oers, 1998). Secondly, the implied abstract approach makes general subjects such as mathematics and science difficult for many students and this is an important cause for school failure (Onstenk, 2002). These are among the reasons that Dutch VET has moved to a competency-based approach in which general subjects are increasingly integrated into practical tasks, for example by using a problem-centred approach. Although positive examples are reported (Van der Sanden, 2004), communication between school and work is characterised as mostly uni-directional from school to work sites, and concerns are expressed that too much emphasis on practical learning leads to decreasing quality of education and disappearance of general subjects (e.g., SCP, 2006). <br />
<br />
From an educational-theoretical point of view there is a pressing need for a theoretical basis of how to characterise the required competencies and how to integrate relevant knowledge forms. Because transfer always involves a learning process in the new situation, Van der Sanden and Teurlings (2003) propose to focus on “continuous progressive recontextualisation” (cf., Guile & Young, 2003; Van Oers, 1998). When entering new situations, students always have to recontextualise their knowledge and when supported in reflecting on their experiences and progressively organising their knowledge, they improve relevant competencies. An important question is then how to promote this process of recontextualisation.<br />
<br />
Tuomi-Gröhn and Engeström (2003) argue that one way is by “boundary crossing” between different activity systems, for example at school and at work. An activity system can be seen as the smallest unit of analysis that takes into account the purpose of work, available tools, division of labour and the rules of discourse in workplace communities. In transitions from one system to another, students as well as their teachers and practical supervisors take part in different communities, which have different goals, tools and sometimes even opposite interests (SCP, 2006). More concretely, Onstenk (2003) and Van der Sanden (2004) offer suggestions on how the required boundary crossing can be achieved. For example, teachers should visit workplaces more often and school tasks should more often be related to the core tasks (in the sense of Onstenk; 2003) of the profession. Designing a powerful learning environment thus involves the boundary crossing by many participants such as college teachers, practical work supervisors and technical expertise centres.<br />
<br />
===Techno-mathematical Competencies===<br />
Though recent developments in educational research such as the activity-theoretical approach have brought an interesting perspective on the issue of transfer in VET, Guile and Young (2003, p.79) observe that “the role of scientific concepts seems to have got lost in recent developments in activity theory with their stress on activities, context and horizontal development”. This proposal will therefore address the role of technical and mathematical knowledge in workplaces, which involves vertical development and some level of generalisation, while taking into account recent insights from educational-theoretical approaches. <br />
<br />
As such the proposed project builds upon ESRC-funded research that has been carried out in the UK, in particular the Techno-mathematical Literacies in the Workplace project (www.ioe.ac.uk/tlrp/<br />
technomaths) in which the candidate for this proposal has been a research officer for two years. Techno-mathematical Literacies (TmL) can be characterised as combination of technical and mathematical competencies, mediated by technology available in work situations (Bakker et al., 2006). In the context of Dutch competency-based VET we use the term TmC (Techno-mathematical Competencies) instead of TmL (Literacies). In line with Van der Sanden (2004) and others, competencies are characterised as conglomerates of knowledge, skills and attitudes required to carry out particular professions.<br />
<br />
The need for TmC is apparent in labour-market survey studies (e.g., Felstead et al., 2002) and in case studies of workplaces (Bakker et al., 2006; Bessot & Ridgway, 2000). This is mainly due to the increasing use of IT at work: instead of using a spanner, an operator might have to use data and graphs in a control panel to fix a production problem. A detailed study of skills levels and needs of operational and supervisory staff in life sciences shows that among the most problematic and yet important skills are those “concerned with understanding and use of Statistical Process Control (SPC), monitoring use of SPC techniques during routine production, monitoring data.” (MerseyBio, 2006, p. 46). To substantiate this finding we give one example from the TmL project (Hoyles et al., in press).<br />
<br />
===An example of TmC===<br />
Many industrial companies use statistical control charts, which display key measures of manufactured items produced in relation to a target value, statistical control limits and specification limits. The control limits are defined such that 99.7% of the common cause variation stays within those limits (mean +/-3 standard deviations) whereas special cause variation can be seen as trends, patterns or as data points outside the limits. Operators are expected to monitor the process and spot anything deviating from random, common cause variation. Particularly if software is used, these control charts are often experienced as black boxes that do things users are not aware of. For example, software packages may ignore outliers in their calculations of control limits. To make data-informed decisions, it is therefore crucial to know some of the statistics embedded in these tools as well as features of the technology itself. Despite the importance of SPC in most business improvement programmes as used by companies such as Philips, Douwe Egberts and ABN Amro, it is hardly addressed in Dutch vocational education. Qualification profiles include competencies such as “care for quality” but the appropriate statistical techniques are generally not specified or taught (e.g., competentie.kenteq.nl/cms/publish/content/<br />
showpage.asp?pageid=700).<br />
<br />
More generally there is a discrepancy between the competencies required at work and what is taught at school. The TmL project has shown that technical work (such as industrial production) is increasingly mediated by technology (e.g., via control panels). This implies that students should develop TmC rather than abstractly represented mathematical knowledge. Rather than calculating by hand or with a calculator, students should learn how to use the mathematics embedded in the tools and develop a situated model of the variables relevant in the work process (Bakker et al., 2006). The need for TmC is especially apparent in communication: within a work team, with managers or customers etc. We expect similar results for multimedia design and ICT system management, which are included in the present proposal. Note that the proposed project is not a replication of the TmL project because it takes place in Dutch vocational colleges and focuses on engineering, graphical design and ICT system management whereas the TmL project took place in English workplaces and focused on manufacturing (Bakker et al., 2006; Hoyles et al., in press) and financial services (Kent et al., in press).<br />
<br />
===Hypothesis and research questions===<br />
The proposed project intends to test the following hypothesis: <br />
* TmC that are tailored to the context and tools of professions will improve students’ ability to perform core tasks during at school and during work practice periods at learning-work sites (leerbedrijven).<br />
<br />
The theoretical framework mentioned above and the Dutch situation of VET lead to the following three questions, answered in three research phases. To identify the TmC that need to be developed the main question in the first, ethnographic phase is:<br />
# What Techno-mathematical Competencies are required in technical workplaces and can serve as instructional targets within the existing qualification profiles?<br />
:The first research phase will yield authentic core tasks that are relevant for the professions at stake and have a clear techno-mathematical aspect.<br />
:The second, design-based research phase will focus on the following main question, where core tasks can be performed at school or at learning-work sites:<br />
# How can new learning arrangements support the development of the techno-mathematical competencies required for performing core tasks at school and learning-work sites? <br />
:The second research phase will involve the design of learning arrangements for developing TmC in VET, collaboratively with teachers and practical work supervisors, and the analysis of participants’ learning processes. At college, students will work through new learning materials focusing on techno-mathematical knowledge relevant to practical core tasks, and they will reflect on their experiences during practice periods in relation to relevant knowledge. Computer tools are designed to represent the techno-mathematical aspects of those core tasks in such a way that they facilitate recontextualisation. The teaching experiments aim for discussion amongst students about school and work contexts in relation to the tools to support integration of different knowledge forms across the boundaries. Because mathematics education in VET does not have abstraction and generality as its central tenets, typical instructional design models known from mathematics education research that suggest a progression from situational to formal mathematical knowledge are not applicable. Hence students’ progression in recontextualising their techno-mathematical knowledge is to be judged not by an increasing level of mathematical generality but by the integration of appropriate contextual and techno-mathematical knowledge and skills in new problem situations and the success of dealing with these situations in performing core tasks as judged by practical supervisors. In the third, comparative phase the question is:<br />
# In what ways does the development of TmC improve students’ performance of core tasks whether at college or learning-work sites?<br />
:The research will be carried out in the mainly college-based BOL stream of senior secondary vocational education (mbo) rather than in the mainly work-based BBL stream because students in BOL spend 20-40% of their time at work rather than 60+% in BBL. It is therefore expected that the design of the learning environments is more feasible in BOL than in BBL.<br />
<br />
==14.2 setup and methods==<br />
<br />
The method involves a transition from ethnographic studies (to answer question 1) to design-based research (question 2) with a comparative last phase (question 3). The schools and workplaces fall under the technical sector (Techniek) of the PGO Consortium and Fontys, multimedia design of the Grafisch Lyceum Utrecht, and ICT system management of ROC Utrecht. In most colleges, mathematics is taught as a separate subject, but it is increasingly addressed in relation to projects. Collaboration with the TOP3C project (www.fontys.nl/top3c) ensures close contact with several companies (mechanical, electrical and process engineering) via Goris, who is a member of the advisory board. The Freudenthal Institute is one of the accredited learning-work sites for the other sectors.<br />
<br />
===Phase 1: ethnographic studies and study of existing VET===<br />
Surveys generally do not yield the type of data required to identify areas in which TmC might be an issue because they yield data on a more aggregate level. Ethnographic studies will therefore be carried out in learning-work sites linked to mbo schools to answer question 1. We take a “theory-driven” approach (Pawson & Tilley, 1997) to study specific phenomena such as TmC, which are already known from previous research. Semi-structured interviews will be carried out with practical work supervisors and college teachers in the technical sector (electrical and mechanical engineering) and students will be interviewed during apprenticeships or practice periods about the techno-mathematical knowledge they feel they have not sufficiently developed. The data gathered (audio, pictures, calculations and copies of artefacts such as graphs) will be used to identify key elements of the activity systems in which they work: the tools they use (in particular the techno-mathematical ones), the community in which they work as well as techno-mathematical aspects of core tasks. The post-doctoral and junior researcher will analyse the data resources according to methods described in Hammersley and Atkinson (1995). It is expected that the TmC involve interpreting graphs of work process (in engineering sector), mathematical transformations and working with coordinates (in the multimedia design sector). At least twelve activity systems in four different companies will be analysed in total to define authentic core tasks. In collaboration with teachers and supervisors, a selection will be made of core tasks to address their techno-mathematical aspects more explicitly in relation to projects and practice periods.<br />
<br />
===Phase 2: design-based research to enhance TmC ===<br />
To answer question 2, the methodology of design research (e.g., Edelson, 2002) is appropriate because the project aims more at “understanding how” than at “knowing whether” learning arrangements can support the development of TmC in an ecologically valid way. These learning arrangements can be developed on the theoretical and practical knowledge basis of the TmL project and the design experience of the TWIN curriculum authors Goris and Van der Kooij, who are part of the advisory board. Design-based research as deployed here aims at shaping innovative instructional sequences, developing a local (domain-specific) instruction theory and general theoretical knowledge (progressive recontextualisation, boundary crossing). The design is based on design heuristics from VET research (as summarised by Fürstenau, 2003) and Realistic Mathematics Education theory (Gravemeijer, 1994) to ensure a sound theoretical design basis. The focus will be on the techno-mathematical side of core tasks (e.g., quality control, defining mathematical functions in ICT systems). <br />
<br />
The research set-up is characterised by an iterative, cyclic design. Both phase 2 and 3 consist of a preliminary stage in which instructional activities are designed that embody task-specific conjectures, a teaching experiment stage in which the conjectures that form the basis of the student activities are tested, and a retrospective stage which generates revised conjectures (Gravemeijer & Cobb, 2006). The first preliminary stage is based on the findings of the ethnographic phase 1. The designed instructional sequence aims at developing TmC, in particular graphs of workplace data to make decisions based on the core tasks identified in research phase 1. <br />
<br />
The three teaching experiments in each of the phases 2 and 3 involve at least 20 students and will take place at college (engineering) or during a practice period (graphical design and ICT system management). In phases 2 and 3, data resources are audio and video recordings of the students during the teaching experiment and log-files of their work (Camtasia) with the computer tools (Flash). The post-doctoral and junior researcher act as participating observers; observations and interventions are based on the pre-formulated conjectures of the local instruction theory (e.g., about students’ responses to an instructional activity and what they learn from it). With the help of software for data analysis (MEPA), the data resources will be used to test these conjectures. <br />
<br />
The researcher will record decisions in a logbook to capture the empirical basis and theoretical considerations for choices made during the design process. He will also record examples of boundary crossing between college teachers and practical supervisors and other interested parties. For reach of the three contexts, three techno-mathematical core tasks will be designed collaboratively with teachers and supervisors to analyse students’ progressive recontextualisation (beginning, middle and end of the teaching experiment or practice period). Assessment takes place by the teacher or supervisor.<br />
<br />
In the retrospective stage, the theoretical orientation towards activity theory, competencies literature and in particular the TmL research forms the interpretative and explanatory framework. In particular, examples of boundary crossing situations will be analysed to understand better how recontextualisation can be supported. The results of the analysis of the students’ learning include indicative conclusions on the task-specific conjectures and new insights that are embedded into the design of the instructional sequence in the next phase. They also include the development of a local instruction theory and suggestions for analysing progressive recontextualisation of techno-mathematical knowledge in phase 3. <br />
<br />
To assist in the design of materials, interpretation of data and developing the theoretical frameworks, an advisory board of nine researchers and educators has been established: seven VET, mathematics and workplace researchers (3 Dutch, 4 UK: Jonker, Onstenk, Wijers, Brown, Guile, Hoyles and Noss) and two authors of the TWIN curriculum (Van der Kooij and Goris). The mbo teachers and practical work supervisors who are involved in the design process and teaching experiments will also be invited. During a two-day expert meeting theoretical themes that arise will be discussed and results from the international research teams on similar themes will be compared.<br />
<br />
===Phase 3: the comparative phase ===<br />
During the preliminary stage of this phase, the design team revises the instructional sequence on the basis of the results of phase 2 and the advisory board members individually reflect on the revised design. The style of working is similar to the one described for phase 2, but – to answer question 3 – this time a comparison will be made on the three core tasks identified for analysing progressive recontextualisation between the students of the experimental groups (at least 20 across three colleges) and at least 16 other students who will function as the control groups. These students do the same work projects or similar practice periods as the experimental students and their performance on the three core tasks is analysed but they are not involved in the teaching experiments that specifically aim at developing TmC. Practical work supervisors will assess their performance of core tasks. The teaching experiment in phase 3 includes a pre-test and a post-test on techno-mathematical knowledge. Students in both groups will be matched on their performance on the pre-test and on the first core task.<br />
<br />
The method of analysis in phase 3 is similar to that of phase 2, but focuses on finding confirmations and refutations of the task-specific conjectures stated in the previous phase. Students’ work with the tools and their discussions are coded by both the post-doctoral and junior researcher and tested for interreliability. After that, a second two-day expert meeting is held with the advisory board to evaluate the analysis and the conclusions, to make international comparisons and to discuss theoretical themes such as boundary crossing, progressive recontextualisation and TmC in relation to the competencies issues. Then a revised local instruction theory is formulated and the empirical findings will be used to contribute – where appropriate jointly with members of the advisory board – to the development of the theoretical themes.<br />
<br />
==References==<br />
* Bakker, A., Hoyles, C., Kent, P. and Noss, R. (2005). {{refworks|Designing Learning Opportunities for Techno-mathematical Literacies in Financial Workplaces: A status report.|2712}} (Translator, Trans.). London: Institute of Education, University of London.<br />
* [[Boundary object]]<br />
* Kent, P., Hoyles, C., Noss, R. and Guile, D. (2004). {{refworks|Techno-mathematical Literacies in workplace activity|2574}}.<br />
* [[Techno-Mathematical Literacy]]<br />
* Tuomi-Gröhn, T. and Engeström, Y. (2003). {{refworks|Conceptualizing transfer: From standard notions to developmental perspectives|2845}} (In T. Tuomi-Gröhn and Y. Engeström (Eds.), Between school and work: New perspectives on transfer and boundary-crossing (pp. 19-38). Amsterdam: Pergamon.<br />
<br />
==Versions of this document==<br />
* 20080716, [[wikiteam]]<br />
<br />
[[category:research]]<br />
[[category:mathematics in the workplace]]</div>Wed, 21 Jul 2010 06:59:30 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Boundary_crossing_between_school_and_work_for_developing_techno-mathematical_competencies_in_vocational_educationBoundary crossing between school and work for developing techno-mathematical competencies in vocational education
http://www.fisme.science.uu.nl/en/wiki/index.php/Boundary_crossing_between_school_and_work_for_developing_techno-mathematical_competencies_in_vocational_education
<p>Vincent: /* References */</p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Boundary_crossing_between_school_and_work_for_developing_techno-mathematical_competencies_in_vocational_education}}<br />
<br />
<br />
==General==<br />
In a high-tech knowledge-based economy many employees need Techno-mathematical Competencies<br />
(TmC): these are combinations of technological and mathematical competencies that are mediated by<br />
technology and situated in specific work contexts. At the boundaries between vocational colleges (mbo)<br />
and learning-work sites, the proposed project focuses on the question: How can new learning<br />
arrangements support the development of the TmC required for technical work? Among the results will<br />
be a task-specific instruction theory and computer tools for developing such TmC. The theoretical focus is<br />
on boundary crossing between school and work as a tool to promote progressive recontextualisation of<br />
techno-mathematical knowledge.<br />
<br />
<br />
==Problem definition==<br />
<br />
===Boundary crossing between school and work===<br />
A major challenge for students in vocational education and training (VET) is to make connections between school and work settings. For example, as Van der Sanden and Teurlings (2003) observe, even though the vocational school system aims at connecting students’ codified knowledge acquired at school to episodic knowledge developed from workplace practice periods, this often does not lead to the required integration of different knowledge forms. The boundary between school and work is therefore an interesting location to study what is metaphorically called transfer. Traditionally, general subjects such as mathematics were (and often still are) taught in a general way assuming that the knowledge acquired during education can later be applied in specific contexts, but there are two problems with this view on transfer. <br />
<br />
Firstly, this view has been criticised by many proponents of situated cognition, constructivism and socio-cultural theories of learning for its lack of attention for context, participation in communities, history and available tools (e.g., Beach, 1999; Lave, 1988; Van Oers, 1998). Secondly, the implied abstract approach makes general subjects such as mathematics and science difficult for many students and this is an important cause for school failure (Onstenk, 2002). These are among the reasons that Dutch VET has moved to a competency-based approach in which general subjects are increasingly integrated into practical tasks, for example by using a problem-centred approach. Although positive examples are reported (Van der Sanden, 2004), communication between school and work is characterised as mostly uni-directional from school to work sites, and concerns are expressed that too much emphasis on practical learning leads to decreasing quality of education and disappearance of general subjects (e.g., SCP, 2006). <br />
<br />
From an educational-theoretical point of view there is a pressing need for a theoretical basis of how to characterise the required competencies and how to integrate relevant knowledge forms. Because transfer always involves a learning process in the new situation, Van der Sanden and Teurlings (2003) propose to focus on “continuous progressive recontextualisation” (cf., Guile & Young, 2003; Van Oers, 1998). When entering new situations, students always have to recontextualise their knowledge and when supported in reflecting on their experiences and progressively organising their knowledge, they improve relevant competencies. An important question is then how to promote this process of recontextualisation.<br />
<br />
Tuomi-Gröhn and Engeström (2003) argue that one way is by “boundary crossing” between different activity systems, for example at school and at work. An activity system can be seen as the smallest unit of analysis that takes into account the purpose of work, available tools, division of labour and the rules of discourse in workplace communities. In transitions from one system to another, students as well as their teachers and practical supervisors take part in different communities, which have different goals, tools and sometimes even opposite interests (SCP, 2006). More concretely, Onstenk (2003) and Van der Sanden (2004) offer suggestions on how the required boundary crossing can be achieved. For example, teachers should visit workplaces more often and school tasks should more often be related to the core tasks (in the sense of Onstenk; 2003) of the profession. Designing a powerful learning environment thus involves the boundary crossing by many participants such as college teachers, practical work supervisors and technical expertise centres.<br />
<br />
===Techno-mathematical Competencies===<br />
Though recent developments in educational research such as the activity-theoretical approach have brought an interesting perspective on the issue of transfer in VET, Guile and Young (2003, p.79) observe that “the role of scientific concepts seems to have got lost in recent developments in activity theory with their stress on activities, context and horizontal development”. This proposal will therefore address the role of technical and mathematical knowledge in workplaces, which involves vertical development and some level of generalisation, while taking into account recent insights from educational-theoretical approaches. <br />
<br />
As such the proposed project builds upon ESRC-funded research that has been carried out in the UK, in particular the Techno-mathematical Literacies in the Workplace project (www.ioe.ac.uk/tlrp/<br />
technomaths) in which the candidate for this proposal has been a research officer for two years. Techno-mathematical Literacies (TmL) can be characterised as combination of technical and mathematical competencies, mediated by technology available in work situations (Bakker et al., 2006). In the context of Dutch competency-based VET we use the term TmC (Techno-mathematical Competencies) instead of TmL (Literacies). In line with Van der Sanden (2004) and others, competencies are characterised as conglomerates of knowledge, skills and attitudes required to carry out particular professions.<br />
<br />
The need for TmC is apparent in labour-market survey studies (e.g., Felstead et al., 2002) and in case studies of workplaces (Bakker et al., 2006; Bessot & Ridgway, 2000). This is mainly due to the increasing use of IT at work: instead of using a spanner, an operator might have to use data and graphs in a control panel to fix a production problem. A detailed study of skills levels and needs of operational and supervisory staff in life sciences shows that among the most problematic and yet important skills are those “concerned with understanding and use of Statistical Process Control (SPC), monitoring use of SPC techniques during routine production, monitoring data.” (MerseyBio, 2006, p. 46). To substantiate this finding we give one example from the TmL project (Hoyles et al., in press).<br />
<br />
===An example of TmC===<br />
Many industrial companies use statistical control charts, which display key measures of manufactured items produced in relation to a target value, statistical control limits and specification limits. The control limits are defined such that 99.7% of the common cause variation stays within those limits (mean +/-3 standard deviations) whereas special cause variation can be seen as trends, patterns or as data points outside the limits. Operators are expected to monitor the process and spot anything deviating from random, common cause variation. Particularly if software is used, these control charts are often experienced as black boxes that do things users are not aware of. For example, software packages may ignore outliers in their calculations of control limits. To make data-informed decisions, it is therefore crucial to know some of the statistics embedded in these tools as well as features of the technology itself. Despite the importance of SPC in most business improvement programmes as used by companies such as Philips, Douwe Egberts and ABN Amro, it is hardly addressed in Dutch vocational education. Qualification profiles include competencies such as “care for quality” but the appropriate statistical techniques are generally not specified or taught (e.g., competentie.kenteq.nl/cms/publish/content/<br />
showpage.asp?pageid=700).<br />
<br />
More generally there is a discrepancy between the competencies required at work and what is taught at school. The TmL project has shown that technical work (such as industrial production) is increasingly mediated by technology (e.g., via control panels). This implies that students should develop TmC rather than abstractly represented mathematical knowledge. Rather than calculating by hand or with a calculator, students should learn how to use the mathematics embedded in the tools and develop a situated model of the variables relevant in the work process (Bakker et al., 2006). The need for TmC is especially apparent in communication: within a work team, with managers or customers etc. We expect similar results for multimedia design and ICT system management, which are included in the present proposal. Note that the proposed project is not a replication of the TmL project because it takes place in Dutch vocational colleges and focuses on engineering, graphical design and ICT system management whereas the TmL project took place in English workplaces and focused on manufacturing (Bakker et al., 2006; Hoyles et al., in press) and financial services (Kent et al., in press).<br />
<br />
===Hypothesis and research questions===<br />
The proposed project intends to test the following hypothesis: <br />
* TmC that are tailored to the context and tools of professions will improve students’ ability to perform core tasks during at school and during work practice periods at learning-work sites (leerbedrijven).<br />
<br />
The theoretical framework mentioned above and the Dutch situation of VET lead to the following three questions, answered in three research phases. To identify the TmC that need to be developed the main question in the first, ethnographic phase is:<br />
# What Techno-mathematical Competencies are required in technical workplaces and can serve as instructional targets within the existing qualification profiles?<br />
:The first research phase will yield authentic core tasks that are relevant for the professions at stake and have a clear techno-mathematical aspect.<br />
:The second, design-based research phase will focus on the following main question, where core tasks can be performed at school or at learning-work sites:<br />
# How can new learning arrangements support the development of the techno-mathematical competencies required for performing core tasks at school and learning-work sites? <br />
:The second research phase will involve the design of learning arrangements for developing TmC in VET, collaboratively with teachers and practical work supervisors, and the analysis of participants’ learning processes. At college, students will work through new learning materials focusing on techno-mathematical knowledge relevant to practical core tasks, and they will reflect on their experiences during practice periods in relation to relevant knowledge. Computer tools are designed to represent the techno-mathematical aspects of those core tasks in such a way that they facilitate recontextualisation. The teaching experiments aim for discussion amongst students about school and work contexts in relation to the tools to support integration of different knowledge forms across the boundaries. Because mathematics education in VET does not have abstraction and generality as its central tenets, typical instructional design models known from mathematics education research that suggest a progression from situational to formal mathematical knowledge are not applicable. Hence students’ progression in recontextualising their techno-mathematical knowledge is to be judged not by an increasing level of mathematical generality but by the integration of appropriate contextual and techno-mathematical knowledge and skills in new problem situations and the success of dealing with these situations in performing core tasks as judged by practical supervisors. In the third, comparative phase the question is:<br />
# In what ways does the development of TmC improve students’ performance of core tasks whether at college or learning-work sites?<br />
:The research will be carried out in the mainly college-based BOL stream of senior secondary vocational education (mbo) rather than in the mainly work-based BBL stream because students in BOL spend 20-40% of their time at work rather than 60+% in BBL. It is therefore expected that the design of the learning environments is more feasible in BOL than in BBL.<br />
<br />
==14.2 setup and methods==<br />
<br />
The method involves a transition from ethnographic studies (to answer question 1) to design-based research (question 2) with a comparative last phase (question 3). The schools and workplaces fall under the technical sector (Techniek) of the PGO Consortium and Fontys, multimedia design of the Grafisch Lyceum Utrecht, and ICT system management of ROC Utrecht. In most colleges, mathematics is taught as a separate subject, but it is increasingly addressed in relation to projects. Collaboration with the TOP3C project (www.fontys.nl/top3c) ensures close contact with several companies (mechanical, electrical and process engineering) via Goris, who is a member of the advisory board. The Freudenthal Institute is one of the accredited learning-work sites for the other sectors.<br />
<br />
===Phase 1: ethnographic studies and study of existing VET===<br />
Surveys generally do not yield the type of data required to identify areas in which TmC might be an issue because they yield data on a more aggregate level. Ethnographic studies will therefore be carried out in learning-work sites linked to mbo schools to answer question 1. We take a “theory-driven” approach (Pawson & Tilley, 1997) to study specific phenomena such as TmC, which are already known from previous research. Semi-structured interviews will be carried out with practical work supervisors and college teachers in the technical sector (electrical and mechanical engineering) and students will be interviewed during apprenticeships or practice periods about the techno-mathematical knowledge they feel they have not sufficiently developed. The data gathered (audio, pictures, calculations and copies of artefacts such as graphs) will be used to identify key elements of the activity systems in which they work: the tools they use (in particular the techno-mathematical ones), the community in which they work as well as techno-mathematical aspects of core tasks. The post-doctoral and junior researcher will analyse the data resources according to methods described in Hammersley and Atkinson (1995). It is expected that the TmC involve interpreting graphs of work process (in engineering sector), mathematical transformations and working with coordinates (in the multimedia design sector). At least twelve activity systems in four different companies will be analysed in total to define authentic core tasks. In collaboration with teachers and supervisors, a selection will be made of core tasks to address their techno-mathematical aspects more explicitly in relation to projects and practice periods.<br />
<br />
===Phase 2: design-based research to enhance TmC ===<br />
To answer question 2, the methodology of design research (e.g., Edelson, 2002) is appropriate because the project aims more at “understanding how” than at “knowing whether” learning arrangements can support the development of TmC in an ecologically valid way. These learning arrangements can be developed on the theoretical and practical knowledge basis of the TmL project and the design experience of the TWIN curriculum authors Goris and Van der Kooij, who are part of the advisory board. Design-based research as deployed here aims at shaping innovative instructional sequences, developing a local (domain-specific) instruction theory and general theoretical knowledge (progressive recontextualisation, boundary crossing). The design is based on design heuristics from VET research (as summarised by Fürstenau, 2003) and Realistic Mathematics Education theory (Gravemeijer, 1994) to ensure a sound theoretical design basis. The focus will be on the techno-mathematical side of core tasks (e.g., quality control, defining mathematical functions in ICT systems). <br />
<br />
The research set-up is characterised by an iterative, cyclic design. Both phase 2 and 3 consist of a preliminary stage in which instructional activities are designed that embody task-specific conjectures, a teaching experiment stage in which the conjectures that form the basis of the student activities are tested, and a retrospective stage which generates revised conjectures (Gravemeijer & Cobb, 2006). The first preliminary stage is based on the findings of the ethnographic phase 1. The designed instructional sequence aims at developing TmC, in particular graphs of workplace data to make decisions based on the core tasks identified in research phase 1. <br />
<br />
The three teaching experiments in each of the phases 2 and 3 involve at least 20 students and will take place at college (engineering) or during a practice period (graphical design and ICT system management). In phases 2 and 3, data resources are audio and video recordings of the students during the teaching experiment and log-files of their work (Camtasia) with the computer tools (Flash). The post-doctoral and junior researcher act as participating observers; observations and interventions are based on the pre-formulated conjectures of the local instruction theory (e.g., about students’ responses to an instructional activity and what they learn from it). With the help of software for data analysis (MEPA), the data resources will be used to test these conjectures. <br />
<br />
The researcher will record decisions in a logbook to capture the empirical basis and theoretical considerations for choices made during the design process. He will also record examples of boundary crossing between college teachers and practical supervisors and other interested parties. For reach of the three contexts, three techno-mathematical core tasks will be designed collaboratively with teachers and supervisors to analyse students’ progressive recontextualisation (beginning, middle and end of the teaching experiment or practice period). Assessment takes place by the teacher or supervisor.<br />
<br />
In the retrospective stage, the theoretical orientation towards activity theory, competencies literature and in particular the TmL research forms the interpretative and explanatory framework. In particular, examples of boundary crossing situations will be analysed to understand better how recontextualisation can be supported. The results of the analysis of the students’ learning include indicative conclusions on the task-specific conjectures and new insights that are embedded into the design of the instructional sequence in the next phase. They also include the development of a local instruction theory and suggestions for analysing progressive recontextualisation of techno-mathematical knowledge in phase 3. <br />
<br />
To assist in the design of materials, interpretation of data and developing the theoretical frameworks, an advisory board of nine researchers and educators has been established: seven VET, mathematics and workplace researchers (3 Dutch, 4 UK: Jonker, Onstenk, Wijers, Brown, Guile, Hoyles and Noss) and two authors of the TWIN curriculum (Van der Kooij and Goris). The mbo teachers and practical work supervisors who are involved in the design process and teaching experiments will also be invited. During a two-day expert meeting theoretical themes that arise will be discussed and results from the international research teams on similar themes will be compared.<br />
<br />
===Phase 3: the comparative phase ===<br />
During the preliminary stage of this phase, the design team revises the instructional sequence on the basis of the results of phase 2 and the advisory board members individually reflect on the revised design. The style of working is similar to the one described for phase 2, but – to answer question 3 – this time a comparison will be made on the three core tasks identified for analysing progressive recontextualisation between the students of the experimental groups (at least 20 across three colleges) and at least 16 other students who will function as the control groups. These students do the same work projects or similar practice periods as the experimental students and their performance on the three core tasks is analysed but they are not involved in the teaching experiments that specifically aim at developing TmC. Practical work supervisors will assess their performance of core tasks. The teaching experiment in phase 3 includes a pre-test and a post-test on techno-mathematical knowledge. Students in both groups will be matched on their performance on the pre-test and on the first core task.<br />
<br />
The method of analysis in phase 3 is similar to that of phase 2, but focuses on finding confirmations and refutations of the task-specific conjectures stated in the previous phase. Students’ work with the tools and their discussions are coded by both the post-doctoral and junior researcher and tested for interreliability. After that, a second two-day expert meeting is held with the advisory board to evaluate the analysis and the conclusions, to make international comparisons and to discuss theoretical themes such as boundary crossing, progressive recontextualisation and TmC in relation to the competencies issues. Then a revised local instruction theory is formulated and the empirical findings will be used to contribute – where appropriate jointly with members of the advisory board – to the development of the theoretical themes.<br />
<br />
==References==<br />
* Bakker, A., Hoyles, C., Kent, P. and Noss, R. (2005). {{refworks|Designing Learning Opportunities for Techno-mathematical Literacies in Financial Workplaces: A status report.|2712}} (Translator, Trans.). London: Institute of Education, University of London.<br />
* [[Boundary object]]<br />
* Kent, P., Hoyles, C., Noss, R. and Guile, D. (2004). {{refworks|Techno-mathematical Literacies in workplace activity|2574}}.<br />
* [[Techno-Mathematical literacy]]<br />
* Tuomi-Gröhn, T. and Engeström, Y. (2003). {{refworks|Conceptualizing transfer: From standard notions to developmental perspectives|2845}} (In T. Tuomi-Gröhn and Y. Engeström (Eds.), Between school and work: New perspectives on transfer and boundary-crossing (pp. 19-38). Amsterdam: Pergamon.<br />
<br />
==Versions of this document==<br />
* 20080716, [[wikiteam]]<br />
<br />
[[category:research]]<br />
[[category:mathematics in the workplace]]</div>Wed, 21 Jul 2010 06:59:17 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Boundary_crossing_between_school_and_work_for_developing_techno-mathematical_competencies_in_vocational_educationBoundary crossing between school and work for developing techno-mathematical competencies in vocational education
http://www.fisme.science.uu.nl/en/wiki/index.php/Boundary_crossing_between_school_and_work_for_developing_techno-mathematical_competencies_in_vocational_education
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Boundary_crossing_between_school_and_work_for_developing_techno-mathematical_competencies_in_vocational_education}}<br />
<br />
<br />
==General==<br />
In a high-tech knowledge-based economy many employees need Techno-mathematical Competencies<br />
(TmC): these are combinations of technological and mathematical competencies that are mediated by<br />
technology and situated in specific work contexts. At the boundaries between vocational colleges (mbo)<br />
and learning-work sites, the proposed project focuses on the question: How can new learning<br />
arrangements support the development of the TmC required for technical work? Among the results will<br />
be a task-specific instruction theory and computer tools for developing such TmC. The theoretical focus is<br />
on boundary crossing between school and work as a tool to promote progressive recontextualisation of<br />
techno-mathematical knowledge.<br />
<br />
<br />
==Problem definition==<br />
<br />
===Boundary crossing between school and work===<br />
A major challenge for students in vocational education and training (VET) is to make connections between school and work settings. For example, as Van der Sanden and Teurlings (2003) observe, even though the vocational school system aims at connecting students’ codified knowledge acquired at school to episodic knowledge developed from workplace practice periods, this often does not lead to the required integration of different knowledge forms. The boundary between school and work is therefore an interesting location to study what is metaphorically called transfer. Traditionally, general subjects such as mathematics were (and often still are) taught in a general way assuming that the knowledge acquired during education can later be applied in specific contexts, but there are two problems with this view on transfer. <br />
<br />
Firstly, this view has been criticised by many proponents of situated cognition, constructivism and socio-cultural theories of learning for its lack of attention for context, participation in communities, history and available tools (e.g., Beach, 1999; Lave, 1988; Van Oers, 1998). Secondly, the implied abstract approach makes general subjects such as mathematics and science difficult for many students and this is an important cause for school failure (Onstenk, 2002). These are among the reasons that Dutch VET has moved to a competency-based approach in which general subjects are increasingly integrated into practical tasks, for example by using a problem-centred approach. Although positive examples are reported (Van der Sanden, 2004), communication between school and work is characterised as mostly uni-directional from school to work sites, and concerns are expressed that too much emphasis on practical learning leads to decreasing quality of education and disappearance of general subjects (e.g., SCP, 2006). <br />
<br />
From an educational-theoretical point of view there is a pressing need for a theoretical basis of how to characterise the required competencies and how to integrate relevant knowledge forms. Because transfer always involves a learning process in the new situation, Van der Sanden and Teurlings (2003) propose to focus on “continuous progressive recontextualisation” (cf., Guile & Young, 2003; Van Oers, 1998). When entering new situations, students always have to recontextualise their knowledge and when supported in reflecting on their experiences and progressively organising their knowledge, they improve relevant competencies. An important question is then how to promote this process of recontextualisation.<br />
<br />
Tuomi-Gröhn and Engeström (2003) argue that one way is by “boundary crossing” between different activity systems, for example at school and at work. An activity system can be seen as the smallest unit of analysis that takes into account the purpose of work, available tools, division of labour and the rules of discourse in workplace communities. In transitions from one system to another, students as well as their teachers and practical supervisors take part in different communities, which have different goals, tools and sometimes even opposite interests (SCP, 2006). More concretely, Onstenk (2003) and Van der Sanden (2004) offer suggestions on how the required boundary crossing can be achieved. For example, teachers should visit workplaces more often and school tasks should more often be related to the core tasks (in the sense of Onstenk; 2003) of the profession. Designing a powerful learning environment thus involves the boundary crossing by many participants such as college teachers, practical work supervisors and technical expertise centres.<br />
<br />
===Techno-mathematical Competencies===<br />
Though recent developments in educational research such as the activity-theoretical approach have brought an interesting perspective on the issue of transfer in VET, Guile and Young (2003, p.79) observe that “the role of scientific concepts seems to have got lost in recent developments in activity theory with their stress on activities, context and horizontal development”. This proposal will therefore address the role of technical and mathematical knowledge in workplaces, which involves vertical development and some level of generalisation, while taking into account recent insights from educational-theoretical approaches. <br />
<br />
As such the proposed project builds upon ESRC-funded research that has been carried out in the UK, in particular the Techno-mathematical Literacies in the Workplace project (www.ioe.ac.uk/tlrp/<br />
technomaths) in which the candidate for this proposal has been a research officer for two years. Techno-mathematical Literacies (TmL) can be characterised as combination of technical and mathematical competencies, mediated by technology available in work situations (Bakker et al., 2006). In the context of Dutch competency-based VET we use the term TmC (Techno-mathematical Competencies) instead of TmL (Literacies). In line with Van der Sanden (2004) and others, competencies are characterised as conglomerates of knowledge, skills and attitudes required to carry out particular professions.<br />
<br />
The need for TmC is apparent in labour-market survey studies (e.g., Felstead et al., 2002) and in case studies of workplaces (Bakker et al., 2006; Bessot & Ridgway, 2000). This is mainly due to the increasing use of IT at work: instead of using a spanner, an operator might have to use data and graphs in a control panel to fix a production problem. A detailed study of skills levels and needs of operational and supervisory staff in life sciences shows that among the most problematic and yet important skills are those “concerned with understanding and use of Statistical Process Control (SPC), monitoring use of SPC techniques during routine production, monitoring data.” (MerseyBio, 2006, p. 46). To substantiate this finding we give one example from the TmL project (Hoyles et al., in press).<br />
<br />
===An example of TmC===<br />
Many industrial companies use statistical control charts, which display key measures of manufactured items produced in relation to a target value, statistical control limits and specification limits. The control limits are defined such that 99.7% of the common cause variation stays within those limits (mean +/-3 standard deviations) whereas special cause variation can be seen as trends, patterns or as data points outside the limits. Operators are expected to monitor the process and spot anything deviating from random, common cause variation. Particularly if software is used, these control charts are often experienced as black boxes that do things users are not aware of. For example, software packages may ignore outliers in their calculations of control limits. To make data-informed decisions, it is therefore crucial to know some of the statistics embedded in these tools as well as features of the technology itself. Despite the importance of SPC in most business improvement programmes as used by companies such as Philips, Douwe Egberts and ABN Amro, it is hardly addressed in Dutch vocational education. Qualification profiles include competencies such as “care for quality” but the appropriate statistical techniques are generally not specified or taught (e.g., competentie.kenteq.nl/cms/publish/content/<br />
showpage.asp?pageid=700).<br />
<br />
More generally there is a discrepancy between the competencies required at work and what is taught at school. The TmL project has shown that technical work (such as industrial production) is increasingly mediated by technology (e.g., via control panels). This implies that students should develop TmC rather than abstractly represented mathematical knowledge. Rather than calculating by hand or with a calculator, students should learn how to use the mathematics embedded in the tools and develop a situated model of the variables relevant in the work process (Bakker et al., 2006). The need for TmC is especially apparent in communication: within a work team, with managers or customers etc. We expect similar results for multimedia design and ICT system management, which are included in the present proposal. Note that the proposed project is not a replication of the TmL project because it takes place in Dutch vocational colleges and focuses on engineering, graphical design and ICT system management whereas the TmL project took place in English workplaces and focused on manufacturing (Bakker et al., 2006; Hoyles et al., in press) and financial services (Kent et al., in press).<br />
<br />
===Hypothesis and research questions===<br />
The proposed project intends to test the following hypothesis: <br />
* TmC that are tailored to the context and tools of professions will improve students’ ability to perform core tasks during at school and during work practice periods at learning-work sites (leerbedrijven).<br />
<br />
The theoretical framework mentioned above and the Dutch situation of VET lead to the following three questions, answered in three research phases. To identify the TmC that need to be developed the main question in the first, ethnographic phase is:<br />
# What Techno-mathematical Competencies are required in technical workplaces and can serve as instructional targets within the existing qualification profiles?<br />
:The first research phase will yield authentic core tasks that are relevant for the professions at stake and have a clear techno-mathematical aspect.<br />
:The second, design-based research phase will focus on the following main question, where core tasks can be performed at school or at learning-work sites:<br />
# How can new learning arrangements support the development of the techno-mathematical competencies required for performing core tasks at school and learning-work sites? <br />
:The second research phase will involve the design of learning arrangements for developing TmC in VET, collaboratively with teachers and practical work supervisors, and the analysis of participants’ learning processes. At college, students will work through new learning materials focusing on techno-mathematical knowledge relevant to practical core tasks, and they will reflect on their experiences during practice periods in relation to relevant knowledge. Computer tools are designed to represent the techno-mathematical aspects of those core tasks in such a way that they facilitate recontextualisation. The teaching experiments aim for discussion amongst students about school and work contexts in relation to the tools to support integration of different knowledge forms across the boundaries. Because mathematics education in VET does not have abstraction and generality as its central tenets, typical instructional design models known from mathematics education research that suggest a progression from situational to formal mathematical knowledge are not applicable. Hence students’ progression in recontextualising their techno-mathematical knowledge is to be judged not by an increasing level of mathematical generality but by the integration of appropriate contextual and techno-mathematical knowledge and skills in new problem situations and the success of dealing with these situations in performing core tasks as judged by practical supervisors. In the third, comparative phase the question is:<br />
# In what ways does the development of TmC improve students’ performance of core tasks whether at college or learning-work sites?<br />
:The research will be carried out in the mainly college-based BOL stream of senior secondary vocational education (mbo) rather than in the mainly work-based BBL stream because students in BOL spend 20-40% of their time at work rather than 60+% in BBL. It is therefore expected that the design of the learning environments is more feasible in BOL than in BBL.<br />
<br />
==14.2 setup and methods==<br />
<br />
The method involves a transition from ethnographic studies (to answer question 1) to design-based research (question 2) with a comparative last phase (question 3). The schools and workplaces fall under the technical sector (Techniek) of the PGO Consortium and Fontys, multimedia design of the Grafisch Lyceum Utrecht, and ICT system management of ROC Utrecht. In most colleges, mathematics is taught as a separate subject, but it is increasingly addressed in relation to projects. Collaboration with the TOP3C project (www.fontys.nl/top3c) ensures close contact with several companies (mechanical, electrical and process engineering) via Goris, who is a member of the advisory board. The Freudenthal Institute is one of the accredited learning-work sites for the other sectors.<br />
<br />
===Phase 1: ethnographic studies and study of existing VET===<br />
Surveys generally do not yield the type of data required to identify areas in which TmC might be an issue because they yield data on a more aggregate level. Ethnographic studies will therefore be carried out in learning-work sites linked to mbo schools to answer question 1. We take a “theory-driven” approach (Pawson & Tilley, 1997) to study specific phenomena such as TmC, which are already known from previous research. Semi-structured interviews will be carried out with practical work supervisors and college teachers in the technical sector (electrical and mechanical engineering) and students will be interviewed during apprenticeships or practice periods about the techno-mathematical knowledge they feel they have not sufficiently developed. The data gathered (audio, pictures, calculations and copies of artefacts such as graphs) will be used to identify key elements of the activity systems in which they work: the tools they use (in particular the techno-mathematical ones), the community in which they work as well as techno-mathematical aspects of core tasks. The post-doctoral and junior researcher will analyse the data resources according to methods described in Hammersley and Atkinson (1995). It is expected that the TmC involve interpreting graphs of work process (in engineering sector), mathematical transformations and working with coordinates (in the multimedia design sector). At least twelve activity systems in four different companies will be analysed in total to define authentic core tasks. In collaboration with teachers and supervisors, a selection will be made of core tasks to address their techno-mathematical aspects more explicitly in relation to projects and practice periods.<br />
<br />
===Phase 2: design-based research to enhance TmC ===<br />
To answer question 2, the methodology of design research (e.g., Edelson, 2002) is appropriate because the project aims more at “understanding how” than at “knowing whether” learning arrangements can support the development of TmC in an ecologically valid way. These learning arrangements can be developed on the theoretical and practical knowledge basis of the TmL project and the design experience of the TWIN curriculum authors Goris and Van der Kooij, who are part of the advisory board. Design-based research as deployed here aims at shaping innovative instructional sequences, developing a local (domain-specific) instruction theory and general theoretical knowledge (progressive recontextualisation, boundary crossing). The design is based on design heuristics from VET research (as summarised by Fürstenau, 2003) and Realistic Mathematics Education theory (Gravemeijer, 1994) to ensure a sound theoretical design basis. The focus will be on the techno-mathematical side of core tasks (e.g., quality control, defining mathematical functions in ICT systems). <br />
<br />
The research set-up is characterised by an iterative, cyclic design. Both phase 2 and 3 consist of a preliminary stage in which instructional activities are designed that embody task-specific conjectures, a teaching experiment stage in which the conjectures that form the basis of the student activities are tested, and a retrospective stage which generates revised conjectures (Gravemeijer & Cobb, 2006). The first preliminary stage is based on the findings of the ethnographic phase 1. The designed instructional sequence aims at developing TmC, in particular graphs of workplace data to make decisions based on the core tasks identified in research phase 1. <br />
<br />
The three teaching experiments in each of the phases 2 and 3 involve at least 20 students and will take place at college (engineering) or during a practice period (graphical design and ICT system management). In phases 2 and 3, data resources are audio and video recordings of the students during the teaching experiment and log-files of their work (Camtasia) with the computer tools (Flash). The post-doctoral and junior researcher act as participating observers; observations and interventions are based on the pre-formulated conjectures of the local instruction theory (e.g., about students’ responses to an instructional activity and what they learn from it). With the help of software for data analysis (MEPA), the data resources will be used to test these conjectures. <br />
<br />
The researcher will record decisions in a logbook to capture the empirical basis and theoretical considerations for choices made during the design process. He will also record examples of boundary crossing between college teachers and practical supervisors and other interested parties. For reach of the three contexts, three techno-mathematical core tasks will be designed collaboratively with teachers and supervisors to analyse students’ progressive recontextualisation (beginning, middle and end of the teaching experiment or practice period). Assessment takes place by the teacher or supervisor.<br />
<br />
In the retrospective stage, the theoretical orientation towards activity theory, competencies literature and in particular the TmL research forms the interpretative and explanatory framework. In particular, examples of boundary crossing situations will be analysed to understand better how recontextualisation can be supported. The results of the analysis of the students’ learning include indicative conclusions on the task-specific conjectures and new insights that are embedded into the design of the instructional sequence in the next phase. They also include the development of a local instruction theory and suggestions for analysing progressive recontextualisation of techno-mathematical knowledge in phase 3. <br />
<br />
To assist in the design of materials, interpretation of data and developing the theoretical frameworks, an advisory board of nine researchers and educators has been established: seven VET, mathematics and workplace researchers (3 Dutch, 4 UK: Jonker, Onstenk, Wijers, Brown, Guile, Hoyles and Noss) and two authors of the TWIN curriculum (Van der Kooij and Goris). The mbo teachers and practical work supervisors who are involved in the design process and teaching experiments will also be invited. During a two-day expert meeting theoretical themes that arise will be discussed and results from the international research teams on similar themes will be compared.<br />
<br />
===Phase 3: the comparative phase ===<br />
During the preliminary stage of this phase, the design team revises the instructional sequence on the basis of the results of phase 2 and the advisory board members individually reflect on the revised design. The style of working is similar to the one described for phase 2, but – to answer question 3 – this time a comparison will be made on the three core tasks identified for analysing progressive recontextualisation between the students of the experimental groups (at least 20 across three colleges) and at least 16 other students who will function as the control groups. These students do the same work projects or similar practice periods as the experimental students and their performance on the three core tasks is analysed but they are not involved in the teaching experiments that specifically aim at developing TmC. Practical work supervisors will assess their performance of core tasks. The teaching experiment in phase 3 includes a pre-test and a post-test on techno-mathematical knowledge. Students in both groups will be matched on their performance on the pre-test and on the first core task.<br />
<br />
The method of analysis in phase 3 is similar to that of phase 2, but focuses on finding confirmations and refutations of the task-specific conjectures stated in the previous phase. Students’ work with the tools and their discussions are coded by both the post-doctoral and junior researcher and tested for interreliability. After that, a second two-day expert meeting is held with the advisory board to evaluate the analysis and the conclusions, to make international comparisons and to discuss theoretical themes such as boundary crossing, progressive recontextualisation and TmC in relation to the competencies issues. Then a revised local instruction theory is formulated and the empirical findings will be used to contribute – where appropriate jointly with members of the advisory board – to the development of the theoretical themes.<br />
<br />
==References==<br />
* Bakker, A., Hoyles, C., Kent, P. and Noss, R. (2005). {{refworks|Designing Learning Opportunities for Techno-mathematical Literacies in Financial Workplaces: A status report.|2712}} (Translator, Trans.). London: Institute of Education, University of London.<br />
* [[Boundary object]]<br />
* Kent, P., Hoyles, C., Noss, R. and Guile, D. (2004). {{refworks|Techno-mathematical Literacies in workplace activity|2574}}.<br />
* [[Technomathematical literacy]]<br />
* Tuomi-Gröhn, T. and Engeström, Y. (2003). {{refworks|Conceptualizing transfer: From standard notions to developmental perspectives|2845}} (In T. Tuomi-Gröhn and Y. Engeström (Eds.), Between school and work: New perspectives on transfer and boundary-crossing (pp. 19-38). Amsterdam: Pergamon.<br />
<br />
==Versions of this document==<br />
* 20080716, [[wikiteam]]<br />
<br />
[[category:research]]<br />
[[category:mathematics in the workplace]]</div>Wed, 21 Jul 2010 06:58:47 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Boundary_crossing_between_school_and_work_for_developing_techno-mathematical_competencies_in_vocational_educationMathematizing
http://www.fisme.science.uu.nl/en/wiki/index.php/Mathematizing
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Mathematiseren}}<br />
<br />
==General==<br />
Treffers (1975):<br />
"Mathematizing refers to more than achieving mathematical knowledge and becoming adept at mathematical operations.<br />
Rather, mathematizing involves gaining an understanding of underlying mathematical skills such as ordering, classifying, generalizing and formalizing"<br />
<br />
==References==<br />
* [[Chain of signification]]<br />
* Treffers, A. (1975). {{refworks|De Kiekkas van Wiskobas. Beschouwingen over Uitgangspunten en Doelstellingen van het Aanvangs- en Vervolgonderwijs in de Wiskunde. Leerplan publicatie nummer 1.|3306}}. Utrecht, the Netherlands: IOWO.<br />
* Treffers, A. (1987). {{refworks|Three dimensions. A model of goal and theory description in mathematics instruction - The Wiskobas project|3012}}. Dordrecht: Kluwer Academic Publishers.<br />
<br />
<br />
==Versions of this document==<br />
* 20080326, [[wikiteam]]<br />
<br />
<br />
[[category:rme]]</div>Wed, 21 Jul 2010 06:54:12 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:MathematizingMathematical Literacy
http://www.fisme.science.uu.nl/en/wiki/index.php/Mathematical_Literacy
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Mathematical_Literacy}}<br />
<br />
==General==<br />
Mathematical literacy entails the use of mathematical competencies at several levels, ranging from performance of standard mathematical operations to mathematical thinking and insight. It also requires the knowledge and application of a range of mathematical content.<br />
<br />
PISA assesses mathematical literacy in three dimensions:<br />
<br />
* First, the content of mathematics, as defined mainly in terms of broad mathematical concepts underlying mathematical thinking (such as chance, change and growth, space and shape, reasoning, uncertainty and dependency relationships), and only secondarily in relation to "curricular strands" (such as numbers, algebra and geometry). The PISA 2000 assessment, in which mathematics is a minor domain, focuses on two concepts: change and growth, and space and shape. These two areas allow a wide representation of aspects of the curriculum without giving undue weight to number skills.<br />
* Second, the process of mathematics as defined by general mathematical competencies. These include the use of mathematical language, modelling and problem-solving skills. The idea is not, however, to separate out such skills in different test items, since it is assumed that a range of competencies will be needed to perform any given mathematical task. Rather, questions are organized in terms of three "competency classes" defining the type of thinking skill needed.<br />
** The first class of mathematical competency consists of simple computations or definitions of the type most familiar in conventional mathematics assessments.<br />
** The second class requires connections to be made to solve straightforward problems.<br />
** The third competency class consists of mathematical thinking, generalization and insight, and requires students to engage in analysis, to identify the mathematical elements in a situation and to pose their own problems.<br />
* Third, the situations in which mathematics is used, ranging from private contexts to those relating to wider scientific and public issues.<br />
<br />
==References==<br />
* [http://www.pisa.gc.ca/math_e.shtml PISA]<br />
* De Lange, J. (2005). {{refworks|Measuring Mathematical Literacy|2559}} (In Encyclopedia of Social Measurement: Elsevier-Reed, Amsterdam.<br />
* [[Gecijferdheid (Algemeen)]]<br />
* Jablonka, E. (2003). {{refworks|Mathematical literacy|2524}} (In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick and F. K. S. Leung (Eds.), Second International Handbook of Mathematics Education (pp. 75-102). Dordrecht: Kluwer Academic Publishers.<br />
* [[Techno-Mathematical Literacy]]<br />
* [[Key competence]] (European Framework)<br />
<br />
==Versions of this document==<br />
* 20080113, [[fiteam]]<br />
<br />
[[category:research]]<br />
[[category:mathematics in the workplace]]</div>Sun, 18 Jul 2010 08:12:47 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Mathematical_LiteracyNumber sense
http://www.fisme.science.uu.nl/en/wiki/index.php/Number_sense
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Getalbegrip}}<br />
<br />
==General==<br />
In mathematics education, number sense can refer to "an intuitive understanding of numbers, their magnitude, relationships, and how they are affected by operations."<br />
<br />
==Background==<br />
Many other definitions exist, but are similar to the one given. Some definitions emphasize an ability to work outside of the traditionally taught algorithms, e.g., "a well organised conceptual framework of number information that enables a person to understand numbers and number relationships and to solve mathematical problems that are not bound by traditional algorithms".<br />
<br />
There are also some differences in how number sense is defined in the field of mathematical cognition. For example, Gersten and Chard say number sense "refers to a child's fluidity and flexibility with numbers, the sense of what numbers mean and an ability to perform mental mathematics and to look at the world and make comparisons."<br />
<br />
==References==<br />
* Arcavi, A. (1994). {{refworks|Symbol sense: Informal sense-making in formal mathematics. |2705}}. For the Learning of Mathematics, 14(3), 24-35.<br />
* Dolk, M., & Fosnot, C. (2005). Fostering Children's Mathematical Development, Grades 5-8. The Landscape of Learning. . New York: Heinemann.<br />
* Dehaene, S. (1997). {{refworks|Number Sense|2535}}: Oxford University Press.<br />
* Griffin, S. (2004). {{refworks|Teaching number sense|2539}}. Educational Leadership, February 2004, 39-24.<br />
* Griffin, S. {{refworks|Building number sense with Number Worlds: a mathematics program for young children|2364}}. Early childhood research quarterly.<br />
* [http://en.wikipedia.org/wiki/Number_sense Wikipedia]<br />
<br />
==Versions of this document==<br />
* 20091024, [[wikiteam]]<br />
<br />
[[category:research]]</div>Sat, 17 Jul 2010 21:32:26 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Number_senseMathematizing
http://www.fisme.science.uu.nl/en/wiki/index.php/Mathematizing
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Mathematiseren}}<br />
<br />
==General==<br />
Treffers (1975):<br />
"Mathematizing refers to more than achieving mathematical knowledge and becoming adept at mathematical operations.<br />
Rather, mathematizing involves gaining an understanding of underlying mathematical skills such as ordering, classifying, generalizing and formalizing"<br />
<br />
==References==<br />
* [[Chain of signification]]<br />
* Treffers, A. (1975). {{refworks|De Kiekkas van Wiskobas. Beschouwingen over Uitgangspunten en Doelstellingen van het Aanvangs- en Vervolgonderwijs in de Wiskunde. Leerplan publicatie nummer 1.|3306}}. Utrecht, the Netherlands: IOWO.<br />
* Treffers, A. (1987). Three dimensions: a model of goal and theory description in mathematics instruction - The Wiskobas project. Dordrecht: Kluwer Academic Publishers.<br />
<br />
<br />
==Versions of this document==<br />
* 20080326, [[wikiteam]]<br />
<br />
<br />
[[category:rme]]</div>Sat, 17 Jul 2010 21:31:14 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:MathematizingSituated learning
http://www.fisme.science.uu.nl/en/wiki/index.php/Situated_learning
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Situated_learning}}<br />
<br />
==Algemeen==<br />
Situated learning is a model of learning first proposed by Jean Lave and Etienne Wenger. It suggests that all learning is contextual, embedded in a social and physical environment.<br />
<br />
Lave and Wenger assert that situated learning "is not an educational form, much less a pedagogical strategy" (1991, p.40). <br />
<br />
==Literatuur==<br />
* Lave, J. and Wenger, E. (1991). {{refworks|Situated learning: Legitimate peripheral participation|2436}}. Cambridge, England: Cambridge University Press.<br />
<br />
==Verwijzingen==<br />
* [http://en.wikipedia.org/wiki/Situated_learning Wikipedia]<br />
* [[Situated Cognition]]<br />
<br />
==Versies van dit document==<br />
* 20080613, [[wikiteam]]<br />
<br />
[[category:research]]<br />
[[category:mathematics in the workplace]]</div>Sat, 17 Jul 2010 21:30:44 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Situated_learningLong division
http://www.fisme.science.uu.nl/en/wiki/index.php/Long_division
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Staartdeling}}<br />
<br />
==General==<br />
In arithmetic, long division is the standard procedure suitable for dividing simple or complex multidigit numbers. It breaks down a division problem into a series of easier steps. As in all division problems, one number, called the dividend, is divided by another, called the divisor, producing a result called the quotient<br />
<br />
==References==<br />
* Hoogland, K. (2008). {{refworks|Nostalgische terugblik op de staartdeling.|3292}} Nieuw Archief voor de Wiskunde, 5(9).<br />
* [http://en.wikipedia.org/wiki/Long_division Wikipedia]<br />
<br />
==Versions of this document==<br />
* 20081214, [[wikiteam]]<br />
<br />
[[category:research]]</div>Sat, 17 Jul 2010 21:30:16 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Long_divisionEpistemic Games
http://www.fisme.science.uu.nl/en/wiki/index.php/Epistemic_Games
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Epistemic_games}}<br />
<br />
==General==<br />
Epistemic games are computer games that can help players learn to think like engineers, urban planners, journalists, architects, and other innovative professionals, giving them the tools they need to survive in a changing world.<br />
<br />
==References==<br />
* http://epistemicgames.org/eg/<br />
* Shaffer, D.W., Hatfield, D., Navoa Svarovsky, G., Nash, P., Nulty, A., Bagley, E., Franke, K., Rupp, A.A. and Mislevy, R. (2008). {{refworks|Epistemic Network Analysis: A prototype for 21st Century assessment of learning.|3280}}, 46.<br />
<br />
==Versions of this document==<br />
* 20081203, [[wikiteam]]<br />
<br />
[[category:games]]<br />
[[category:research]]</div>Sat, 17 Jul 2010 21:29:36 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Epistemic_GamesTIMSS
http://www.fisme.science.uu.nl/en/wiki/index.php/TIMSS
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|TIMSS}}<br />
<br />
==General==<br />
Trends in International Mathematics and Science Study<br />
<br />
Since 1995 about 50 countries have been assessing trends in students' mathematics and science achievement on a regular four-year cycle. Countries participate at the fourth and eighth grades as well as the final year of schooling. With results of 2003 reported in december 2004, countries are now enrolling in TIMSS 2007.<br />
TIMSS 2007 will collect data in mathematics and science at fourth and eighth grades (leeftijden 9/10 en 13/14 jaar)<br />
In addition, following expressions of interest from a number of countries in assessing the final grade of schooling, TIMSS 2007 is offering an option to collect data at twelfth grade for students with advanced preparation in mathematics and two branches of science: biology and physics. <br />
<br />
<br />
==References==<br />
* http://www.timss.org/<br />
* Hiebert, J., Gallimore, R., Garnier, H., Givvin, K., Hollingsworth, H., Jacobs et al. (2003). {{refworks|Teaching Mathematics in Seven Countries. Results From the TIMSS 1999 Video Study |3254}}. Washington, DC: U.S. Department of Education, National Center for Education Statistics, 236.<br />
* [[NAEP]]<br />
* [[PISA]]<br />
<br />
==Versions of this document==<br />
* 20081125, [[wikiteam]]<br />
<br />
[[category:assessment]]</div>Sat, 17 Jul 2010 21:29:05 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:TIMSSNLVM
http://www.fisme.science.uu.nl/en/wiki/index.php/NLVM
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|NLVM}}<br />
<br />
==General==<br />
National Library for Virtual Manipulatives.<br />
<br />
A digital library containing Java applets and activities for K-12 mathematics (financed by the NSF, USA).<br />
<br />
==References==<br />
* [http://nlvm.usu.edu/ National Library of Virtual Manipulatives] (USA)<br />
* Moyer, P. S., Niezgoda, D., & Stanley , J. (2005). {{refworks|Young Children’s Use of Virtual Manipulatives and Other Forms of Mathematical Representations|3078}}. In W. J. Masalski & P. C. Elliott (Eds.), Technology-supported mathematics learning environments. Sixty-seventh yearbook (pp. 17-35). Reston, VA, USA: National Council of Teachers of Mathematics.<br />
* [[Virtual manipulatives]]<br />
<br />
==Versions of this document==<br />
* 20080420, [[wikiteam]]<br />
<br />
<br />
[[category:institutions]]<br />
[[category:ict]]</div>Sat, 17 Jul 2010 21:28:25 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:NLVMVirtual manipulatives
http://www.fisme.science.uu.nl/en/wiki/index.php/Virtual_manipulatives
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Virtual_manipulatives}}<br />
<br />
<br />
==General==<br />
<br />
==References==<br />
* Moyer, P. S., Niezgoda, D., & Stanley , J. (2005). {{refworks|Young Children’s Use of Virtual Manipulatives and Other Forms of Mathematical Representations|3078}}. In W. J. Masalski & P. C. Elliott (Eds.), Technology-supported mathematics learning environments. Sixty-seventh yearbook (pp. 17-35). Reston, VA, USA: National Council of Teachers of Mathematics.<br />
* [[NLVM]]<br />
<br />
<br />
==Versions of this document==<br />
* 20081027, [[wikiteam]]<br />
<br />
[[category:games]]<br />
[[category:ict]]</div>Sat, 17 Jul 2010 21:27:58 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Virtual_manipulativesCompetence
http://www.fisme.science.uu.nl/en/wiki/index.php/Competence
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Competentie}}<br />
<br />
==General==<br />
Competence is generally characterised as the conglomerate of knowledge, skills and attitudes required for particular professions (Van der Sanden, 2003; Van Merriënboer et al., 2002?)<br />
<br />
==References==<br />
* Van der Sanden, J.M.M. and Teurlings, C.C.J. (2003). {{refworks|Developing competence during practice periods: The learner's perspective.|2838}} School and work: New perspectives on transfer and boundary-crossing. Amsterdam: Pergamon, 119-138.<br />
<br />
<br />
==Versions of this document==<br />
* 20081019, [[wikiteam]]<br />
<br />
[[category:research]]<br />
[[category:mathematics in the workplace]]</div>Sat, 17 Jul 2010 21:27:25 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:CompetenceBig Mathematics Day
http://www.fisme.science.uu.nl/en/wiki/index.php/Big_Mathematics_Day
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Grote_Rekendag}}<br />
<br />
==General==<br />
A Dutch initiative to have an annual Arithmetic Experience for all students and teachers in primary schools<br />
<br />
Students in Dutch primary schools spend quite some time working on mathematics and arithmetic. Most teachers spend time on mathematics and arithmetic almost every school day. In the higher grades students are working between 3 and 7,5 hours per week on mathematics and arithmetic, with an average of 5 hours weekly (Janssen, Van der Schoot & Hemker, 2005).<br />
In these lessons teachers in general follow instructions from the textbook. All available textbooks are based on ideas from realistic mathematics education; however, these textbooks do not focus students and teachers on reasoning and negotiating on strategies. Textbooks provide all elements for teaching mathematics and arithmetic; every subject is covered and the educational material offers enough for the time spent on mathematics and arithmetic. We observed that this resulted in a situation where mathematics and arithmetic in many Dutch primary school classrooms is limited to relatively short introductions and for the rest of the time paper and pencil work. As a consequence we see that many students and their teachers do not experience arithmetic and mathematics as an inspiring activity.<br />
<br />
A very limited number of primary school teachers choose to professionalize themselves in mathematics and arithmetic teaching. We do not know why that is so, but observe that most schools do not experience mathematics and arithmetic as a problematic teaching area and as a consequence invest in other fields.<br />
<br />
Our consideration for developing the National Arithmetic Day was that the above mentioned situation asked for an easily accessible activity that focuses on mathematical reasoning and that inspires both students and teachers.<br />
<br />
{| width="100%"<br />
|-<br />
|'''Year'''<br />
|'''Data'''<br />
|'''Theme'''<br />
|'''Dutch schools''' <br />
<br />
|-<br />
|2009<br />
|Wednesday 9 April<br />
|Money<br />
|<br />
<br />
|-<br />
|2008<br />
|Wednesday 16 April<br />
|It’s about time<br />
|683<br />
<br />
|-<br />
|2007<br />
|Wednesday 17 April<br />
|Geometry, patterns and art<br />
|673 <br />
<br />
|-<br />
|2006<br />
|Wednesday 8 March<br />
|Playing with numbers<br />
|637 <br />
<br />
|-<br />
|2005<br />
|Friday 25 February<br />
|Counting, tally, drawing. Collect, order and visualize<br />
|398 <br />
<br />
|-<br />
|2004<br />
|Wednesday 18 February<br />
|Geometry and measurement<br />
|509 <br />
<br />
|-<br />
|2003<br />
|<br />
|Pilot<br />
|20<br />
<br />
|}<br />
<br />
<br />
==References==<br />
* Jansen, J., Van der Schoot, F. and Hemker, B. (2005). {{refworks|PPON (periodieke peiling van het onderwijsniveau). Balans (32) van het reken-wiskundeonderwijs aan het einde van de basisschool 4.|2719}}. Arnhem: Cito Instituut voor toetsontwikkeling.<br />
* [[Mathematics A-lympiad]] (for secondary education)<br />
<br />
<br />
==Versions of this document==<br />
* 2008, [[wikiteam]]<br />
<br />
[[category:contest]]<br />
[[category:po]]<br />
[[category:problem solving]]</div>Sat, 17 Jul 2010 21:26:38 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Big_Mathematics_DayEdutainment
http://www.fisme.science.uu.nl/en/wiki/index.php/Edutainment
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Edutainment}}<br />
<br />
==General==<br />
Edutainment (also educational entertainment or entertainment-education) is a form of entertainment designed to educate as well as to amuse. Edutainment typically seeks to instruct or socialize its audience by embedding lessons in some familiar form of entertainment: television programs, computer and video games, films, music, websites, multimedia software, etc. Examples might be guided nature tours that entertain while educating participants on animal life and habitats, or a video game that teaches children conflict resolution skills.<br />
<br />
==References==<br />
* Egenfeldt-Nielsen, S. (2005). {{refworks|Beyond Edutainment: Exploring the Educational Potential of Computer Games|2757}}. IT-university, Kopenhagen.<br />
* Holland, W., Jenkins, H., & Squire, K. (2002). {{refworks|Theory by design (Games to teach)|2336}}.<br />
* Kirriemuir, J., & McFarlane, A. (2003, 4-6 November 2003). {{refworks|Use of computer and video games in the classroom|2342}}. Paper presented at the Level Up: The digital games research conference, Utrecht University, The Netherlands.<br />
* Squire, K. (2002). {{refworks|Video games in education|2333}}. International Journal of Intelligent Games & Simulation, 2(1).<br />
* [http://en.wikipedia.org/wiki/Edutainment Wikipedia]<br />
<br />
* http://edutainment2008.eegame.cn/<br />
<br />
==Versions of this document==<br />
* 20080922, [[wikiteam]]<br />
<br />
[[category:games]]<br />
[[category:ict]]</div>Sat, 17 Jul 2010 21:26:02 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:EdutainmentFeedback
http://www.fisme.science.uu.nl/en/wiki/index.php/Feedback
<p>Vincent: </p>
<hr />
<div>{{navigation algemeen}}<br />
{{nl|Feedback_(Algemeen)}}<br />
<br />
==General==<br />
Feedback is a circular causal process whereby some proportion of a system's output is returned (fed back) to the input. This is often used to control the dynamic behavior of the system. Examples of feedback can be found in most complex systems, such as engineering, architecture, economics, thermodynamics, and biology.<br />
<br />
<br />
==References==<br />
* Bokhove, C., Boon, P., Heck, A. and Koolstra, G. (2006).{{refworks|Digitale wiskunde oefenomgeving|2747}}. In. Zaandam: Galois project.<br />
* Bokhove, C., Boon, P., Heck, A. and Koolstra, G. (2006).{{refworks|Een wiskunde -oefenomgeving in de eigen ELO|2749}}. In. Zaandam: Galois project.<br />
* Bokhove, C., Heck, A. and Koolstra, G. (2006).{{refworks|Intelligente feedback bij digitale toetsen en oefeningen|2748}}. In. Zaandam: Galois project.<br />
* Bouwens, E. (2007).{{refworks|Improving Automated Feedback Building a Generic Rule-Feedback Generator|2909}}. In (pp. 89). Utrecht: Computer Science, Utrecht University.<br />
* Bransford, J. D., Brown, A. and Cocking, R. (2000). {{refworks|How people learn. Brain, mind, experience and school|2346}}. Washington: National Academy Press.<br />
* Brown, J. S. and Burton, B. B. {{refworks|Buggy|2685}}. In: School of Psychology and Education of the University of Geneva, Ch.<br />
* Harlen, W. and Crick, R. D. (2003). {{refworks|A systematics review of the impact on students and teachers of the use of ICT for assessment of creative and critical thinking skills. Review conducted by the Assessment and Learning Research Synthesis Group|2721}}. London: Institute of Education, University of London.<br />
* Harskamp, E. G. and Suhre, C. J. M. (2001). {{refworks|Computerondersteund oplossen van toepassingsopgaven wiskunde|2503}}. GION: Groningen.<br />
* Mason, B. J. and Bruning, R. Providing Feedback in Computer-based Instruction: What the Research Tells Us.|2693}}. In: University of Nebraska-Lincoln, Us.<br />
* Musch, J. (2000).{{refworks|Die Gestaltung von Feedback in computergestützten Lernumgebungen: Modelle und Befunde|2694}}. In, Zeitschrift für Pädagogische Psychologie, 2000, Bd. 13, 148-160. .<br />
* Passier, H. and Jeuring, J. (2006).{{refworks|Feedback in an interactive equation solver|2779}}. In, WebALT 2006.<br />
* Ponomarenko, V. (2003). {{refworks|Depository of Repetitive Internet-based probLems and Lessons (Drill 3.1)|2510}}. Journal of online mathematics and its applications, 3.<br />
* Sangwin, C. (2004). {{refworks|Assessing mathematics automatically using computer algebra and the internet|2504}}. Teaching mathematics and its applications, 23(1), 1-14.<br />
* Sleeman, D. and Brown, J. S. (Eds.). (1982). {{refworks|Intelligent tutoring systems|2502}}. London: Academic Press.<br />
* Wijers, M. and Jonker, V. (2007). {{refworks|Digitaal authentiek toetsen van wiskunde|2846}}. Utrecht: Universiteit Utrecht.<br />
* [http://en.wikipedia.org/wiki/Feedback Wikipedia]<br />
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==Versions of this document==<br />
* 20080916, [[wikiteam]]<br />
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[[category:research]]</div>Sat, 17 Jul 2010 21:24:50 GMTVincenthttp://www.fisme.science.uu.nl/en/wiki/index.php/Talk:Feedback