Dealing with linguistic diversity is one of the major challenges in mathematics education. To fully participate in mathematical discourse, all pupils need to become active users of the subject-specific content language.
The CLIMATE project draws on previous research carried out at FIsme, which aimed at elaborating a “content-based approach” for Dutch mathematics classrooms. Such approach implies that mathematics teachers need to be prepared to develop pupils’ language ability while teaching mathematical content. More specifically, the main research question of this project is how primary teachers in multilingual mathematics classrooms can learn to scaffold pupils’ language development needed for learning and reasoning about line graphs.
The first phase of this research has led to a repertoire of scaffolding strategies that were enacted, as well as insight into how a teacher learned to scaffold as part of dual design research. This type of design research promotes and studies both students’ and their teacher’s learning.

Supervisor: prof. dr. M. van den Heuvel-Panhuizen l Category: research, primary education, l Status: in progress
no website

The committee for the future of mathematics education (cTWO) has the following assignments:

propose examination programmes for mathematics A, B, C and D for 2010
prepare developments for mathematics C in upper general secondary education and pre-university education in 2007
advise about the teaching-learning trajectories of mathematics
advise about educational development.

Supervisor: dr. T. van den Bogaart l Category: secundary education, l Status: in progress
http://www.fi.uu.nl/ctwo

This project will provide teachers with rich, meaningful materials to implement interdisciplinary approaches that bring together mathematics and science to allow young people to explore meaningful problems in a European context in ways that develop their scientific problem solving and inquiry skills.

The development of a set of materials that requires an interdisciplinary approach to the teaching and learning of mathematics and science, through the modeling perspective is innovative and important for teachers and students across the EU. Adopting such an approach and using ICT tools is also among the core goals of many calls in the US and Australia, providing evidence for the importance and innovative aspects of the project.

Supervisor: mw. prof. dr. K. Maass (Freiburg University) l Category: research, secundary education, l Status: in progress
http://www.compass-project.eu/

The Expertise Centre for Teacher Training in Science and Technology (ECENT) aims to disseminate findings from educational research and curriculum innovation projects among teacher educators in the fields of primary and secondary education.

Supervisor: dr. M. Pieters l Category: secundary education, l Status: in progress
http://www.ecent.nl

Since its founding in 1971, the Freudenthal Institute has developed a domain-specific instruction theory on the learning and teaching of mathematics, known as Realistic Mathematics Education (RME). RME incorporates views on what mathematics is, how students learn mathematics, and how mathematics should be taught. It is the result of many years of design research, and is a ‘living’ theory, which is being continually adapted as new insights are gained.
The principles that underlie the RME approach have been strongly influenced by Hans Freudenthal’s idea of mathematics as a human activity. Freudenthal felt that students should not be considered as passive recipients of ready-made mathematics, but rather that education should guide the students towards using opportunities to reinvent mathematics by putting it into practice themselves. RME requires a high intellectual autonomy of the students. To put it a different way, one of the key principles of the RME approach is that students should actively participate in the learning process. In a stimulating learning environment they should have the opportunity to build up their own knowledge and understanding.

Supervisor: l Category: primary education, secundary education, l Status: in progress
http://www.fi.uu.nl/en/fius/welcome.html

The 'Nieuwe Wiskrant', a journal for mathematics and computer science education, provides news of recent developments in these areas. Its focus is mainly on secondary education.
In recent years, the Nieuwe Wiskrant has published articles on the new curricula for 12 - 16 year olds, (spatial) geometry, algebra, statistics, calculus, methods of mathematics education, the (graphics) calculator, computers in mathematics education, computer algebra, history of mathematics, language and mathematics education, girls and mathematics, assessment and evaluation issues, the Mathematics A-lympiad, the new mathematics for upper secondary school, the National Mathematics Days. Mathematical puzzles also appear frequently.
Authors include teachers, teacher trainers, and staff members at various mathematical and educational institutions.
Occasionally, a special issue appears, dedicated to a specific theme. Special issues in the past have included topics such as computers and mathematics education, the Mathematics 12-16 project, and geometry.
The Nieuwe Wiskrant appears quarterly. The subscription rate for the Netherlands is € 21,50, for other countries in Europe € 30 , and for the rest of the world it is US $35.-. Subscriptions should be sent to the Freudenthal Institute and may be paid by a bank check or by international money order.
The articles in the magazine are written in Dutch language.

Supervisor: dr. P. Drijvers l Category: secundary education, l Status: in progress
http://www.fi.uu.nl/wiskrant/

For a number of years, the annual Mathematics Olympiad has been organized by the Dutch Mathematics Education Committee. In 1989, an experimental competition took place along the lines of `Mathematics A' (mathematics for non-specialists), a new approach to mathematics recently available to Dutch secondary students. This was called the `Mathematics A-lympiad'. Since then, the A-lympiad takes place nationally each year. Teams of three or four students compete in the qualifying round for a place in the final round. The participating schools receive a problem, for which little specific Mathematics A knowledge is necessary. This makes it possible for eleventh graders to participate as well.

On the day of the qualifying round, the teams may work on the problem from 9:00 am to 4:00 pm. The students are permitted to use textbooks and computers. The teams are distributed into twelve groups corresponding to region. One team from each group proceeds to the final round. During the final round, computers are available to the students. The results are evaluated by a jury.

The A-lympiad is sponsored by Texas Instruments, the Department of Mathematics and Computer Science [at Utrecht University] and the Freudenthal Institute. The Mathematics A-lympiad Committee hopes that the A-lympiad will give the subject Mathematics A and its evaluation a push in the right direction.

A selection of problems can be found on www: http://www.fi.uu.nl/Alympiade/en

Supervisor: T. Goris l Category: conference/course, secundary education, l Status: in progress
http://www.fi.uu.nl/alympiade/

In Dutch upper secondary education, students can choose between two math courses: mathematics A (preparing for social sciences at university level) and mathematics B (preparing for mathematics and natural sciences at university level). Mathematics A is less formal than mathematics B. At the end of the final year (grade 12) a national exam assesses knowledge and skills. Since 1999 assessment should also include process skills. A timed written exam is not appropriate for that. For that reason an 'alternative' assessment is developed. For the mathematics B program, this assessment is called the Mathematics B-day.

At school, teams of 3 or 4 students work for a whole day on an investigative, open ended task. At the end they hand in a report with their findings. The presented problem does not necessarily reflect the typical math B subject matter. Instead, students are challenged to show process skills in developing strategies, making conjectures and try to prove or reject them, logical reasoning, critically reviewing models and adjust them and also co-operate.

Officially, the Mathematics B-day is a contest for teams of students. Most participating schools use the task for the school exam of the process skills; the result is part of the final grade. About half of the schools is involved in the contest. The best papers are sent in and are ranked by teachers in four regional groups. The final ten best papers are ranked by a national jury.

An annually increasing number of schools participates, with over 5000 students.

Supervisor: ir. H. van der Kooij l Category: conference/course, secundary education, l Status: in progress
http://www.fi.uu.nl/wisbdag

In this project educational material is developed with which students construct and test their own computer models.

Supervisor: dr. E. Savelsbergh l Category: research, secundary education, l Status: in progress
http://www.fisme.uu.nl/modelleren/

The Freudenthal Institute is the drive of innovation in many aspects of mathematics education. Crucial for that role is the fact that all aspects should be dealt with in an integrated way. Therefore the Institute also takes responsibility in certain aspects of in-service teacher training. One of the more innovative ideas in this area is the National Mathematics Days. Teachers meet mathematicians to exchange their experiences and get an idea about the state of the art of their profession.
Several plenary speakers from the Netherlands and abroad and a variety of parallel sessions complete these days, let alone the happy hours.

The program consists of several themes like:

mathematics and technology

mathematics and statistics

mathematics and natural sciences

mathematics and sports

mathematics in a historical and cultural perspective

pure mathematics The National Mathematics Days are organized by the Freudenthal Institute, together with some other institutions.
Prof. Jan de Lange is the chairman of the program committee; Michiel Doorman and Martin van Reeuwijk chair the executive committee.

Supervisor: dr. M. Doorman l Category: conference/course, secundary education, l Status: in progress
http://www.fi.uu.nl/nwd/

In this research project it is examined whether the learning of mathematics of kindergartners can be supported by picture books.
Although picture books play a significant role in Dutch kindergarten classes, they are not generally used for the learning of mathematics. Still, more and more indications that picture books support the learning of mathematics by kindergartners come from abroad (see 'Vruchtbare verhalen' in NRC-Handelsblad dd. 14-9-2004).
The theoretical foundation for how picture books for example offer the informal experience basis to explore and develop mathematical concepts and skills is nevertheless limited. This research project wants to extend the initiatives that are taken in the Netherlands.

Supervisor: mw. prof. dr. M. van den Heuvel-Panhuizen l Category: research, primary education, l Status: in progress
no website

Panama's primary objective is the implementation and coordination of in-service teacher education activities for teacher trainers, school counselors, supervisors, mathematics specialists, primary school and special education teachers and other groups in the support structures for mathematics education.
An annual conference, especially organized for the groups mentioned above, focuses each year on one important theme. For the topics of the conference, many persons in the field of mathematics education in primary school are consulted and the conference is organized in collaboration with several other institutes.
In addition, Panama annually organizes seminars including, for instance, the Teacher Trainers Day, and participates in the 'Networkdays for School Counselors'. These days give mathematics and didactics teacher trainers and school counselors the opportunity to meet and to discuss new themes. In mid May Panama organizes a seminar on mathematics called 'Spring Day', for the benefit of mathematics specialists, primary school and special education teachers, teacher trainers and supervisors.
Four times a year Panama publishes a journal, the 'Reken-wiskundeonderwijs: onderzoek, ontwikkeling, praktijk' [Mathematics education: research, development, practice].

Supervisor: drs. M. van Zanten l Category: conference/course, primary education, l Status: in progress
http://www.fi.uu.nl/panama/

PRIMAS is a transnational project in which universities, school authorities, teacher training institutions, schools, teachers, students and parents are working together to change this situation by providing new approaches to mathematics and science education through problem solving and inquiry based learning.

Mathematics and science can be interesting and exciting, giving students opportunities to solve problems, follow their own ideas and explore situations that are important to all of us. Yet, students often do not realize the potential of these subjects!

Primas is supported by the European Commission's FP7 Capacities programme

Supervisor: mw. prof. dr. K. Maass (Freiburg University) l Category: research, secundary education, l Status: in progress
http://www.primas-project.eu/

WisWeb is the website at the Freudenthal Institute dedicated to students at secondary schools (and higher). That is for students from age 12 and up. On the WisWeb-site you will find a wide collection of applets, worksheets, applications for graphing calculators, other software packages, instructional materials not related to technology, publications, and reports and memos about testing and field testing. More than 100 applets with supporting and additional instructional materials are now available on the WisWeb-site.

The WisWeb-site is the result of experimental activities related to the development and research of web-based educational materials. These activities started in the early nineties as a spin-off of other research and development projects, and were officially tied together in the WisWeb-project (2000-2002) and the WELP project (a technology implementation project 2002-2004). The WELP-project focused on the use of applets in the domain of school algebra for students of 13-14 years old. In these projects four secondary schools and PAS-wiskunde (a school counseling organization) participated in the development, testing and implementation of the applets and related educational materials, and the Dutch Association of Math Teachers (NVvW) supported the project as well. In the WELP-project, educational publishers and Texas Instruments joined the team.

Besides the educational and instructional materials (including the applets), various networks have been established:

a network of webmasters of (educational) mathematics websites in The Netherlands.
a network of (commercial) educational publishers
a network of inservice trainers and institutions that provide professional development.

The WELP-project will end in August 2004, but the WisWeb-site will stay alive and will be frequently updated with new "products". Please visit www.wisweb.nl

Supervisor: P. Boon l Category: secundary education, l Status: in progress
http://www.fi.uu.nl/wisweb/

The goal of the Rekennet project (mathnet) is to support primary school teachers in their task to teach realistic mathematics. The Math net consists of two components: a social mathematics network and a website.
In the social network primary school teachers meet and talk about the mathematics of their daily professional practice. We call this horizontal professionalization: teachers learning from teachers. Didactical experts of the Freudenthal Institute join the meetings and hear what the problems are in order to reflect efficiently.
The website offers the ultimate opportunity to communicate with colleagues. The RekenWeb also contains an ever increasing number of computer games for children, printable activity sheets for teachers to use in the classroom, practical suggestions etc. The content of the Math net is based on suggestions of the teachers.
Thus the Math net creates many opportunities to reach the teachers and to provide them with useful ideas and materials for their daily lesson.

Supervisor: drs. F. van Galen & drs. V. Jonker l Category: conference/course, primary education, l Status: afwachting vervolg
http://www.fi.uu.nl/rekenweb/

Goal of this developmental research project was to find out how students can learn the basic principles of calculus and kinematics by modeling movement. The idea is that many of the problems of students concerning these topics have its origin in the traditional transfer method of education.

Alternatives to the traditional transfer method stress the importance of modeling activities. In these alternatives two approaches are recognized. One uses simulations for exploratory modeling and the other uses (computer) tools for expressive modeling. In the expressive approach students can express the evolving concepts. This approach has many similarities with the importance of emerging models in realistic mathematics education. The expressive approach does also fit the discussion about the dialectic relation between symbolizing and understanding.

In this project we try to find out how these ideas can be implemented, how information technology supports expressive modeling and how students can learn calculus and kinematics in an integrated course in upper secondary education.

This research project will result in a dissertation.

Supervisor: dr. L.M. Doorman l Category: research, secundary education, l Status: completed
no website

This research project was connected to the TWIN project.
The hypothesis is that the use of IT tools (in particular the Graphic Calculator) in a setting of cooperative, small group work will improve students' flexibility in solving mathematical problems in an engineering context.
Teachers of four schools are being supported in using the graphing calculator as a problem solving and learning tool and for applying mathematics as well as in guiding small group work.

Classroom observations and interviews with teachers and students were used to test the hypothesis.

Supervisor: prof. dr. K.P.E.Gravemeijer l Category: research, secundary education, l Status: completed
no website

This research project focused on the learning of algebra in an environment that makes use of a computer algebra system (CAS) . In such an environment the performance of algebraic operations can be left to a machine. This context is poor in the light of the 'real world', but mathematically rich. This richness might stimulate reinvention and, more specifically, vertical mathematization: two important aspects of RME.

The research concentrates on central topics of the algebra curriculum for 14 - 16 year old students, i.e. variables, formulas and functions. It is conjectured that the students' experiences with these topics in a computer algebra environment are so intensive, that they may lead to the organization of the phenomena. This can result in the deepening of the insight.

The first research question is on the improvement of insight. It splits up into two sub-questions:

How can the use of computer algebra improve the insight in variables, in the different roles variables play in algebraic expressions, and specifically in the 'higher' roles of variables such as changing quantity and parameter?
How can the use of computer algebra promote that students consider relations and functions and the corresponding formulas as entities, as objects to which processes such as composition and substitution can be applied?

As far as teacher independent and self -reliant learning is concerned, we conjecture that it is supported by the availability of a computer algebra device that serves as 'answering machine' , as example generator and as explorative environment. This may improve the self-reliance of a student, unless s/he lacks familiarity with the computer algebra environment. Therefore, much attention is paid to the process of getting familiar with the tool, so that it develops into a useful instrument in the hands of the student. The second research question is:

How can the use of computer algebra promote a more self-reliant, teacher independent learning? What kind of preliminary instrumentalisation process is required?

Educational experiments take place in grades 9 and 10 of secondary education with high achieving students. Computer algebra is available as software for PC's or as hand-held symbolic calculators, so that platform-independent results can be distinguished from platform-specific findings.

The research has resulted in a dissertation.

Supervisor: dr. P. Drijvers l Category: research, secundary education, l Status: completed
http://www.fi.uu.nl/~pauld/dissertation

In connection with the 'Professionalization of grade 3 teachers' project, a study was done to assess if teaching according to the principles of Realistic Mathematics Education leads to better results than traditional mathematics teaching. It is expected that students will be more flexible in their use of solution strategies, obtain higher scores, and have a more positive attitude towards mathematics.

Supervisor: mw. dr. H. Vermeer l Category: research, primary education, l Status: completed
no website

This project was concerned with statistics in grade 7 and 8 (11 to 13 years old). The aim of the developed instruction materials and computer tools is to give the students the opportunity to develop the notion of distribution. This notion has to become an object-like entity that can be described and reasoned with. In a process of guided reinvention, the students learn conventional graphs such as the histogram and the boxplot. These graphs are ways to describe distributions. Measures of central tendency can be seen as characteristics of distributions.
The so-called minitools are designed in such a way that the students can start with very informal symbolizations before they develop more conventional symbolizations. The central question of the research is how the process of developing these symbolizations and their meaning in several contexts can be described and understood.

Supervisor: dr. A. Bakker l Category: research, secundary education, l Status: completed
no website

Over the years 1987-1993 a new mathematics curriculum for lower secondary school was introduced in the Netherlands. This new curriculum has the following major characteristics:

Emphasis on the use of mathematics in daily life and professional situations;
Mathematics education is about situations that are recognizable for students;
Stimulation of an investigative attitude on the part of the student;
Formal techniques are not a goal in itself.

In the algebra strand of the curriculum, different representations of relationships (descriptions in words, graphs, tables and formulas) play a major role and interpretation oriented skills are considered more important than formula manipulation skills.
At this moment most teachers agree that this change works out positively for students ending their education through lower and middle vocational schools.
The original set up of the new curriculum showed some attention for the connection of this 'daily life connected algebra' with the more abstract needs that are required for students in upper secondary school preparing for higher vocational education and university. During the experiments this part of the curriculum was only sketched in general outlines and not worked out in detail. As a consequence, commercial text book writers often fall back in old formats of algebra education: isolated practising of skills, the use of formulas often not even remotely related to other parts of the curriculum and all this in a much shorter time than before. The bad results of this are easily observed everywhere in upper secondary school, an opinion shared by all teachers and informed people.
The Freudenthal Institute is currently setting up a research and developmental project to reconnect both sides of the algebra curriculum: the intuitive start in lower secondary school and the more abstract use of algebra in mathematics and science in upper secondary school.
Among other issues, the project includes observations of the situation in middle secondary school, the development of special units focussing on so called 'structural exercises', where skill acquirement remains connected to mathematical insight. Currently some JAVA applets, focusing on the didactical use of geometrical algebra, are under construction.

Supervisor: mw. drs. H.B. Verhage l Category: secundary education, l Status: completed
no website

The project 'Algebra investigations in a digital learning environment for mathematics' aimed at two goals:

To explore to what extent a digital learning environment for mathematics enables the development of an investigative attitude with distant support.
To investigate to what extent a digital learning environment for mathematics can help to bridge the gap that students experience between algebra at the lower secondary level and algebra at the upper secondary level.

High achieving students of grade 10 work on investigation tasks in a digital mathematical environment. These tasks concern topics from algebra. Students exchange their work electronically with colleagues, teachers and researchers.

The results of the project included reports of classroom experiences and conclusions with respect to the question on the development of an investigative attitude. Other conclusions addressed the learning of algebra in such digital environments.

Further concrete products consisted of digital student materials and reports of teacher experiences.

Supervisor: T. Erich l Category: secundary education, l Status: completed
http://www.fi.uu.nl/adlo/

A group of about 20 teachers annotated a list of about 2000 mathematics sites (starting with Dutch sites) in order to get an idea of the possible use of internet in the mathematics lesson.
The result of this project will be used within the search engine of the Dutch KennisNet, an initiative of the Dutch government, to develop an educational web for all Dutch schools.

Supervisor: drs. V. Jonker l Category: secundary education, l Status: completed
no website

The AMI-project (Applying Mathematics International) is a continuation of the Dutch National Option for population 1(third and fourth grade students) that was connected to TIMSS. The aim of the project is the improvement of international comparisons of mathematics achievements of primary school students.

The research focuses on applying mathematics as an important goal of mathematics education.
In the first part of the research project a tool for assessing applying mathematics is developed and field tested. Four European neighbour countries were involved in the research: Denmark, England, Germany and The Netherlands.
The Dutch part of the study and the coordination of the complete project is collectively carried out by the Freudenthal Institute and OCTO, University Twente.

Supervisor: mw. prof. dr. M. van den Heuvel-Panhuizen l Category: research, primary education, l Status: completed
no website

Over the years 1993-1999 the Freudenthal Institute was sub-contracted by COMAP (COnsortium for Mathematics and its APplications) to develop assessment materials and exams, and to observe on-site classes for the ARISE project (Applications based Reform In Secondary Education).
COMAP is a non profit, American organization that produces application oriented mathematics materials for college and pre college levels. The ARISE project has been awarded a six year grant by the National Science Foundation to design a complete mathematics textbook series for grades 9 - 12.

In the ARISE program the learning process is stronger emphasized than are the learning products: mathematics is developed as a result of questions regarding the world around us. Modeling activities, a critical attitude, interpreting results in a 'real life' context, qualitative reasoning, and other such aspects are emphasized more strongly than are mathematical techniques and (standard) algorithms.

The Freudenthal Institute's assessment materials therefore cover problems in which certain skills are evaluated, such as using a mathematical concept in a different context, answering questions that go beyond the specific level of the unit, and the ability of dealing with new concepts and open questionings.
The completed 9-12 program is published as MMOW: Mathematics Modeling Our World.

Supervisor: ir. H. van der Kooij l Category: secundary education, l Status: completed
no website

The Blue Print is the result of working out the performing standards for mathematics education that have been compiled by the SLO in 1989 and established officially by the Committee for Revision of Final Goals in 1990. The objectives for mathematics education in primary school are split up in general (theoretical) objectives and practical objectives. Both are illustrated with a great number of examples. The practical objectives encompass the fields of basic capabilities, arithmetics, proportions and percentages, fractions and decimal numbers, measuring and geometry. The publications focus on teacher training, in-service teacher training and support.

Supervisor: prof. dr. A. Treffers l Category: research, l Status: completed
no website

The main focus of the Classroom Assessment as a Basis for Teacher Change (CATCH) project (2001-2003) was to develop and test a program of professional development that seeks to bring about fundamental changes in teachers' instruction by helping them change their formative assessment practices.
The CATCH project was an effort to apply and scale up results from a previous project Research in Assessment Practices (RAP). Both projects were part of the work of the National Center for Improving Student Learning and Achievement in Mathematics and Science (NCISLA) and funded by the Office of Educational Research and Improvement (OERI).
Teachers and administrators from two US research sites (Philadelphia, PA and S. Milwaukee, WI) were involved in the project. They took part in an initial seminar, received ongoing on site support from the CATCH team, carried out assessment experiments and informed their colleagues during successive local summer institutes. In order to answer the research questions both quantitative and qualitative data were gathered: student achievement data from compulsory state and district tests, an initial survey, three rounds of teacher interviews and classroom observations, assessment portfolios, and an exit survey. We found changes in participating teachers' attitude toward formative assessment as well as changes in their classroom practices as a result of the professional development program offered to them.
Based on the research data we carefully conclude that the scores on standardized tests of students taught by teachers involved in the project went up considerably. Finally, we found evidence of CATCH related ideas travelling to other curriculum areas as well as to larger groups of teachers and other grade levels. Appropriate organizational structures have also enabled travel on a district level.
Products from this project are:

Insight stories: Assessing Middle School Mathematics
A framework for Classroom Assessment
Great Assessment Problems
Elements for Professional Development
Research publications
Newsletters
Website

Supervisor: mw. T. Dekker (MA), dr. D. Webb l Category: conference/course, secundary education, l Status: completed
http://www.fi.uu.nl/catch/

The project Coherent learning in secondary education develops teaching material in which the link between mathematics and natural sciences is reinforced. The reasoning pattern "relations between quantities" is developed in a continuing study path during several school years and subjects.

Supervisor: drs. A.H. Mooldijk l Category: secundary education, l Status: completed
http://www.salvoproject.nl

Goal of the project was the design of a model for "Quality Care per subject" for schools and teacher teams. The model is a cyclic one; in a sequence that is decided by the teacher team, a vision on the subject is developed, quality of the learning and teaching process is assessed, and decisions are made about necessary changes in the upcoming school year.
The model is designed by teachers and administrators in collaboration with support from external experts from the Freudenthal Institute and University of Utrecht.
Koeno Gravemeijer is supervisor and Truus Dekker is project manager.

Supervisor: mw. T. Dekker M.A. l Category: research, secundary education, l Status: completed
no website

COCA is a research project funded by SANPAD and carried out by the School of Education of the University of Cape Town (UCT) and it's Schools Development Unit (SDU), The Cape Technikon in Cape Town, and the Freudenthal Institute, Utrecht University.
To improve the teaching and learning of mathematics in the South African Foundation Phase, this project is aimed at the design and implementation of a new educational tool in South African mathematics education. This tool - called a Learning Pathway for Number (LPN) - can be considered as a mediator between the Revised National Curriculum Statement and mathematics textbooks, teaching and learning resource materials and educators' knowledge.

The learning pathway is intended to provide educators with a coherent conceptual educational map for didactical decision making when teaching number in the early grades of the Primary School.
The Learning Pathway gives educators an overview of the longitudinal learning process and the main stepping stones children have to pass in this process in order to develop an understanding of number in such a way that it gives children access to the mathematics in the higher grades by establishing a firm foundation for further growth.

The development of the pathway is based on the TAL trajectory for number and the related materials for professional development (TAL Information and NCRC modules) that were developed in the Netherlands.

The project is aimed at:

Answering research questions
- about the learning pathway the children go through when they develop understanding of number in the foundation phase of their schooling
- about how educators can be supported in their professional development.
Developing resource materials
- for teaching number in foundation phase
- for professional development of educators in foundation phase.

Project leader SA:	prof. dr. Paula Ensor, Dean of Humanities, UCT
Project leader NL:	dr. Marja van den Heuvel-Panhuizen, Freudenthal Institute, UU
Project team:	Corvell Cranfield, SDU (project manager)
	Cally Kuhne, SDU
	Shadeeda Jaffer, SDU
	AnaPaula Lombard, Cape Technikon

Contact SA:	Corvell Cranfield (ccranfie@humanities.uct.ac.za)
Contact NL:	Marja van den Heuvel-Panhuizen (m.vandenheuvel@fi.uu.nl)

Supervisor: mw. prof. dr. M. van den Heuvel-Panhuizen l Category: research, primary education, l Status: completed
http://www.fi.uu.nl/coca/welcome.html

The project Mejoramiento de la Ensenanza de Matematica e Informatica (MEMI) aimed at the improvement of mathematics and computing science education at the Universidad Mayor de San Simon in Cochabamba, Bolivia. In the area of mathematics there are activities on two levels.

For secondary education: Mathematics teachers at the secondary level of the whole region have been trained through a 2-year course on modern methods of teaching mathematics. Furthermore a program is designed for the formation of future secondary level mathematics teachers at the Universidad Mayor de San Simon. The university will also play the role of knowledge center for mathematics education. The project has supported the set up of a national council for mathematics teachers in Bolivia.

For the Tertiary level: Staff has been trained through a 'Maestria en Matematica' program in co-operation with the Universidad Catolica del Norte, Antofagasta, Chile. The curriculum for the Licenciatura in mathematics study has been modernized. In cooperation with this Chilean university all students can choose a program that results in a Master's degree in mathematics.
For Computing science: Staff is also being trained through a 'Maestria en Informatica' program in cooperation with the Universidad de Chile and the Universidad Catolica in Santiago, Chile, as wel as the University of Utrecht in the Netherlands. The curriculum for the Licenciatura in computing science study has been modernized while the capacity of the computing laboratories was greatly increased . With the assistence of the universities mentioned above a regular program will be implemented that leads to a Master's degree in computing science at the Universidad Mayor de San Simon.

Supervisor: drs. H. Nilwik l Category: secundary education, l Status: completed
no website

The ProFi research group worked from 1995-1998 on the development of experimental student and teacher materials for mathematics (the innovation in secondary school is meant for all disciplines). These experimental materials have been tested on two pilot schools. In this experiment the use of the graphic calculator was integrated. The research concentrated on three main objectives.

the development will point out the new content for mathematics textbook authors
the development will work as a convergence for mathematics textbooks
this development will function as a source for (in-service) teacher training.

Of course there will also be a strong influence on the type of assessment being used. The experimental test will be used to get a good interpretation of the new content. Besides, the National Innovation Project Profiles likes to have worked out the idea of working individually or working in groups (the idea of the `Learning House', where everybody takes his own part in the educational system). Another emphasis is on technology. Profi integrates the use of the graphic calculator in the curriculum and also stimulates the use of the computer.

Supervisor: M. Kindt l Category: secundary education, l Status: completed
no website

The project objective is to enhance the achievements of primary school students. The primary target group is the staff of the local teacher training institutes (LPTK’s). The Institut Pengembangan PMRI undertakes efforts to improve the quality of mathematics teachers in a participative way, providing them with teaching tools and methodologies on PMRI (the Indonesian adaptation of Realistic Mathematics Education - RME), that give pupils better chances to like, appreciate and understand mathematics.
This project will build up the capacity of the lecturers at the LPTKs, by training them in the theories and research of PMRI, and provide skills in practical implementation of PMRI, including management of the new to be established PMRI Resource Centres.
The main activity is training the people involved, next to that assistance will be given on keeping track of the project progress, on supporting research activities, on maintaining a database and on providing access through the internet to the PMRI team members as well as the broader public.

Supervisor: dr. M. Dolk l Category: primary education, secundary education, l Status: completed
http://www.fi.uu.nl/pmri

Many secondary school students have difficulty in learning how to construct and solve equations. In recent years, a lot of research has been done on the problems that students encounter when translating arithmetic word problems into algebraic equations. For example, in the transition from arithmetic to algebra it is claimed to be a discrepancy which hampers manipulations of algebraic expressions. This discrepancy is also known as 'cognitive gap' or 'didactic cut'.

In the current curriculum of Dutch mathematics education, algebra is introduced in the first year of secondary school. Initially the students study linear relations (patterns, graphs, word formulas) followed, in the second year, by formal letter manipulations and linear and quadratic equations.
However, classroom experiments in The Netherlands and the American Middle School Project have shown that pre-algebraic reasoning and symbolizing can be learned at an informal level in primary school, which can help to familiarize students with certain arithmetic and algebraic characteristics.

In our point of view, a return to the origins of algebra can provide the researcher with new insights on the learning of pre-algebra. Recent research on the advantages and possibilities of implementing history of mathematics in the classroom has led to a growing interest in the role of history of mathematics in math education.

Hence in 1995 a developmental research project called 'Reinvention of Algebra' was started at the Freudenthal Institute. This project investigates which didactical means will enable students to make a smooth transition from arithmetic to elementary algebra. Specifically, the 'invention' of algebra from a historical perspective will be compared with possibilities of 're-invention' by the students.

This research project will result in a dissertation.

Supervisor: mw. dr. B.A. van Amerom l Category: research, secundary education, l Status: completed
no website

Since 1995 Dutch vocational training is organized in so-called Regional Training Centers. All vocational training programs (basic education, profession-specific education, adults education) are brought together in one organizational structure.
New standards have been set for these educational programs, with a strong focus on professional mobility (life long learning) and more direct connections between educational programs and professional practice. In the TWIN project a new curriculum was developed for both mathematics and science in the upper level training programs for engineering courses.
The two main goals of the project are to design a program that

really supports vocational courses and practice
integrates the use of technology in both the learning process and assessment

In this project, the drive for the study and use of mathematics and science is found in problems in the context of engineering.
Tools from Information Technology (like the graphic calculator and internet) are used to support the learning of concepts and to broaden the scope of problem solving capabilities.

Supervisor: ir H. van der Kooij l Category: secundary education, l Status: completed
http://www.fi.uu.nl/twin/

In december of 1995 the Fi started a first pilot research on the differences between mathematical ability of girls and boys. The pilot research focused on matching the right schools in order to investigate the more complex problems in this research. This second part was a collaboration between the University of Leiden and Utrecht. Its focus was on finding teaching and teacher characteristics which are of influence on the differences in ability. In the first part the Fi will investigate data from the National Institute for Educational Measurement (Cito) and will distinguish between: schools where girls score higher than boys (on average) schools where boys score higher than girls (on average) schools where gender makes no difference

Supervisor: mw. prof. dr. M. van den Heuvel-Panhuizen l Category: research, primary education, l Status: completed
no website

BOLBEWONERS' - Dutch for: 'Earth inhabitants' or 'Globe trotters' - is the title of a reading book on spherical geometry, designed in dialog with pupils of grades 4 and 5 (primary school). Four children - Willemien, Kikkie, Noor and Frank - are characters in the story. They build a cottage and a mysterious professor X enables it to fly. Taking off, the straight horizon becomes a curved line! this one and a lot of other problems, conflicts and solutions appear during the world trip. For example, how to understand the earth is both spherical and flat at the same time? A sensational result was pupils identified with the characters of the story. Points of discussion in the story were continued anew by the pupils in school. Internet setted in as a helpdesk: pupils in the classroom could communicate with all BOOK CHARACTERS - acted by some mathematics teachers (internet site Pupils of different schools in the world (Amsterdam, Caribbean) asked questions - often too difficult for their teachers. The internet site provided them also with the equipment to take satellite pictures from their own and other person's position to investigate the earth from different viewpoints. Moreover the site contained animations to gain a deeper insight into geometrical concepts incorporated in the book and to have children experiment, like driving a dinky toy on a globe.

Supervisor: dr. F.J. van den Brink l Category: research, primary education, l Status: completed
no website

The project focused on the following issues: the use of the graphics calculator

as an aid to existing subject matter,
when the emphasis in mathematics education shifts from techniques to concepts within existing subject matter,
as a means of exploring terrains new to mathematics education that are within the realm of the graphics calculator.

The objective of the project is to provide recommendations on these three points, as well as recommendations for evaluation and in-service training. The project's first year was characterized by a number of short-term experiments, in which teachers of various schools were given a great deal of freedom to introduce their own ideas. During this first year, the use of the graphics calculator as an aid to existing subject matter (point 1) was dealt with extensively. The conclusions drawn from this work were mentioned in the first annual report. Further research will focus on points 2 and 3. For the second and third years, the design of the project has been altered so that the experiment will be conducted at only two schools. These are the Liemers College in Zevenaar and the Cals College in Nieuwegein. The emphasis here will be on mathematics B in all but the final year of high school. The emphasis on mathematics B is based on two considerations. In the first place, it is generally agreed that mathematics B is in need of revision; the graphics calculator could play a role in this revision. In the second place, use of the graphics calculator fits more naturally in mathematics A, whereby development research in this area is less penetrating. The school experiments are primarily concerned with points 2 and 3: the influence of the graphics calculator on the contents, didactics and assessment of mathematics education.

Supervisor: M. Kindt l Category: research, secundary education, l Status: completed
no website

In The Netherlands, a structural reform has been introduced in upper secondary schools. This reform consists of two parts: an institutional and a pedagogical reform.
The institutional reform involves program changes, among others the introduction of new subjects and of streams, and changes in the way the time tables are organized: from classes to 'study-time'. Through this institutional reform the conditions should be created to realize the second innovation, the pedagogical reform.
This reform aims at switching the focus from teaching to learning. The idea is to transform the upper secondary schools into places of study (studiehuis) as a preparation for life long learning. In the 'studiehuis' students should progress towards autonomy in learning, planning and reasoning.
The institutional reform implies that students choose one of four streams, so-called 'profiles', instead of a more or less random selection of subjects. Two of the four streams are science profiles. These profiles each have as its core subjects science (physics and chemistry) and mathematics and both profiles prepare students for studies in science, mathematics and technology in tertiary education.
An important feature of the profiles is that their subjects form a coherent program. This requires cooperation among the school departments involved, both at the level of subject matter as well as at the level of pedagogy to implement the objectives of the reform.

The BPS project started in 1998. The project was carried out by CD-beta, the center for didactical studies in mathematics and science of Utrecht University, in which the Freudenthal Institute participates. The project focused on the two science profiles and aimed at developing and implementing together with participating schools a shared pedagogy for mathematics and the sciences in the 'studiehuis'. Multidisciplinary teams of science and mathematics teachers were formed to work in the schools together with educational researchers on the following activities:

developing integrated tasks for science and mathematics
integrating IT in the classroom
having students do research and investigations
developing larger tasks that form part of the school exam
discussing the use of tools and language common for the core subjects (e.g. graphs, tables, formulas and concepts like ratio in all subjects, chance in math and biology, gas in chemistry and physics).
Using pedagogical tools like: motivating tasks, task orientation, reflection, cooperative learning, etc. to prepare students for independent learning.

Supervisor: dr. A.E. van der Valk l Category: secundary education, l Status: completed
http://www.fi.uu.nl/bps/

This research project was a developmental study of participation processes of students of minority groups in Dutch secondary education, in particular Moroccan students. The classroom discourse in mathematics lessons is analyzed as a process of interactive learning. Ways of participation and non-participation in the process of meaning construction are analyzed with a focus on minority students.
These analyses are related to the cultural background of the students and to the teaching strategies and the educational policy of the school.

In the interdisciplinary team, researchers in the field of mathematics and (second) language education work together with psychologists and antropologists.

Supervisor: mw. dr. D. van Eerde l Category: research, secundary education, l Status: completed
no website

The IMA-project was focussed on the development of a multi-media assessment tool that can be used by teachers from both primary and secondary school level. The project was funded by the National Science Foundation (USA) and was a collaboration between Learning in Motion inc. and the Fi. The objectives of the project were to improve the assessment currently used by teachers by using a wide range of assessment items with background information. The background information contains: objectives of the items, possible solutions and hints for the teacher. Finally the tool can be used by the teachers themselves. The projects starts with the development for grades 3-4 and 7-8. Apart from the American version there will also be a Dutch version of this Tool (in collaboration with the National Institute for Educational Measurement (Cito).

Supervisor: drs. M. van Reeuwijk l Category: research, l Status: completed
no website

Jumping ahead was a developmental research project on low achievers in arithmetic in grade 2 (6-8 year olds). Purpose of the research project was to develop a support program so that at the end of one year of practice all children can do their arithmetic up to 100 at least by structured calculations on the empty number line.

The research sofar has resulted in a program for interactive whole-class teaching which can be offered in combination with any realistic textbook.
The assumption is that so called fundamental skills lay the foundation for later to learn operations like addition, subtraction, multiplication and division in a structured and flexible way.
Important fundamental skills are: counting on from any number, locating of numbers and jumping towards numbers on the number line.

Repeatedly training fundamental skills would offer children the opportunity of well understanding the structure of the number line. To reach this goal several visual models can be used, like: the arithmetic rack, the empty number line, the chain of beads. These models all have in common that they allow for certain structures like: doubling, 5-, 10- and 25-structure.
For memorizing, automatizing and understanding of number relations many activities with visual aids are designed.

Besides didactical characteristics, pedagogical and methodological aspects are of great importance for effective practice. Pedagogical characteristics ask teachers to act in a consequent way. There are rules like: pupils may make mistakes, but absolutely no one may laugh because of it. Rules of a more methodical nature are find in duration and frequency of the practices: three times a week during 10 to 15 minutes.

This research will result in a Training Program and a dissertation in 2001.

Supervisor: mw. dr. J.J.M. Menne l Category: research, primary education, l Status: completed
no website

The group of MENS researchers has taken on the challenge of combining knowledge about mathematics in education with research in neuropsychology, in order to discover more about the process of learning mathematics. The neuropsychological component is contributed by the Helmholtz Institute which is part of the Faculty of Social Sciences at the University of Utrecht.
This group of researchers and two doctorate students will work together over the course of four years to determine what cognitive processes underlie the ability to learn mathematics.

Which processes are innate?
Which components contribute to the development of these processes?
How can these processes best be stimulated and formed?

One of the doctorate students will mostly be concerned with examining cognitive processes for the development of mathematical abilities. She will first make an inventory of tasks, tests and activities that have previously been developed and applied. Eventually, she will compile a set of activities that she can present to children ranging in age from three to six years. The aim is to observe the children as they learn, and to apply these observations to the development of new and improved activities.
The second doctorate student is in charge of the neuropsychological component of the project. As the children perform the activities, their cortical activation will be measured with the use of modern neuroimaging techniques such as EEG.
The combination of these two perspectives should tell us more about how children develop and about how development may be affected by specific activities.

This project is specifically concerned with how healthy children learn mathematics. However, we will also divert to what happens when children with dyscalculia perform the activities. Dyscalculia is a deficiency in mathematical insight. By presenting the activities to dyscalculia patients, we hope to gain a clearer definition of what is meant with a 'normal' development of mathematical thinking.

Supervisor: prof. dr. Jan de Lange (FIsme) & prof. dr. Edward de Haan (HH) l Category: research, primary education, l Status: completed
http://www.fi.uu.nl/mens

In the past decade the number of questions about adequate teaching materials from schools for children with Special Needs was increasing. Most of these schools use traditional textbook series, instead of the more realistic ones. This is partly because useful realistic materials have never been developed for this group of children. In the year 1998 - 1999 some experiments are done at five schools for children with special needs in order to get information and hints for the way the materials should be developed. The first results of the experiments doesn't show a real difference in didactical approach for those children compared to the approach for the children of regular schools. Learning strands could be the same. The contexts that are used could differ sometimes. For the very low achievers, the didactical concept may differ as well. In this project there is a network of teachers working at the special schools. In collaboration with developers of the Freudenthal Institute, the teachers look for solutions for the problems they have in dealing with the practice of realistic mathematics in their classroom.

Supervisor: mw. B. Terlouw l Category: research, conference/course, primary education, l Status: completed
http://www.fi.uu.nl/speciaalrekenen

A new project started on November 1st, 2002: Revision of the Mathematics in Context Materials (MIC-revision) The WCER (Wisconsin Center for Education Research in Madison, USA), together with the Freudenthal Institute will revise, update, and augment the existing middle school curriculum: "Mathematics in Context: A Connected Curriculum for Grades 5-8" published by Encyclopaedia Britannica and sold and distributed by Holt, Rinehard, and Winston.
Additional materials like courseware for teachers, information for parents and administrators will also be developed.

More information about the current MIC materials:
Math in Context on line: http://www.ebmic.com/mic/

Supervisor: prof. dr. J. de Lange l Category: primary education, secundary education, l Status: completed
http://www.hrw.com

The 'Mathematics in the city' project was a cooperation between the City College New York and the Freudenthal Institute. It involved over the course of five years (from 1995 till 2000), assessment of teachers (K-6) from five school districts in New York City in an in-service project in mathematics education. Twelve whole schools were targeted and developed as demonstration / resource sites for the districts as well as for the student teaching program at CCNY, providing the city with a systemic model. The project had five phases encompassing a two week summer institute, a year long course involving in-class collaboration (co-teaching, co-reflecting, and co-planning), teachers collaborating with teachers on-site, field research and writing, and developing teachers as leaders to co-teach the institutes.
Specific objectives were: Develop twelve demonstration sites K-6 where mathematics is taught: emphasizing problem solving in realistic situations, as the investigation of patterns and the putting forth and proving of conjectures; as the learner construction of algorithms, proofs and models encouraging the arguing of such learner-generated ideas in collaborative communities Develop a model in-service project connected to the Freudenthal Institute in The Netherlands, utilizing their video and videodisc materials.

As a follow-up and under a new NSF grant, both partners will develop professional development materials to accompany the NCTM Principles and Standards for School Mathematics (Standards 2000), specifically PreK-2, 3-5, and 6-8, Number and Operation. The materials will consist of print, videotape, and CD-Roms that will be interactive in nature and that will have the potential to be used on the Internet and/or in distance learning. The materials will allow participants in pre and in-service courses to develop an understanding of the important role of context for mathematizing, to use mental math mini-lessons to develop efficient computation strategies evidencing number sense, to construct learning lines for each operation comprised of important strategies, models, and big ideas, and to become competent in scaffolding and structuring math congresses around important mathematical ideas and strategies.

Supervisor: dr. M.L.A.M. Dolk l Category: conference/course, primary education, l Status: completed
http://www.mic3217.addr.com/intro/index.html

Ethnic minority groups in the Dutch education system still find themselves in a disadvantaged position. Particularly in mathematics the results of the students of these groups stay behind the results of the Dutch students. Nowadays more attention is paid to the educational problems of students with a non Dutch background, but this is limited to more general problems or to problems with language. In The Netherlands research on the ethnic minority groups in the science subjects is hardly carried out.

Within the Center for Science and Mathematics Education a research project is started. The goal of this project is to find ways to cope with the specific problems of students from an ethnic minority group in mathematics and natural science.
In the Freudenthal Institute the research is carried out about the problems with mathematics for students of 12 to 15 years. The research questions are:

Which aspects with regard to subject matter content and which pedagogical aspects are responsible for the continuance of the disadvantaged position of students from an ethnic minority group?
Which pedagogical interventions can contribute to a successful participation of these students in the education of (realistic) mathematics education?

This research project will result in a dissertation.

Supervisor: mw. dr. C.J.E.M. van den Boer l Category: research, secundary education, l Status: completed
no website

Within the larger framework of the School Mathematics and Science Achievement Center (SMSAC) which is funded by the American Office of Education, Research and Improvement (OERI), a five-year project was carried out at Vanderbilt University. This project, that was headed by Paul Cobb and in which the Freudenthal Institute participated, focused on the role models can play in teaching statistics at the middle school level. The central notion is that of modeling as an organizing activity. Usually, mathematical modeling of applied problems is thought of as finding out how certain ready-made mathematical models can be applied in the given situation.
In this project a reverse route is aimed for. Here, applied problems are taken as a point of departure, and the students are stimulated to develop tools with which they can organize the available information. The subject matter can be labeled as descriptive statistics, which is conceived as describing data in a conceit and efficient manner, in light of a specific question.

Supervisor: prof. dr. K.P.E. Gravemeijer l Category: research, secundary education, l Status: completed
no website

The aim of the project Modern Physics is the development of material for pre-university/VWO-students about subjects in the area of modern physics.

Supervisor: drs. D.J. Hoekzema l Category: secundary education, l Status: completed
http://www.fisme.uu.nl/mn/

MILE is a Multimedia Interactive Learning Environment for future primary school teachers with content for primary mathematics teachers' education programs. It consists of a video database, communication tools, and a search engine. At the heart of MILE is a video database, composed of a digital representation of mathematics lessons in primary education. This digital school contains more then 65 lessons in kindergarten to grade 6 (4-12 years old). The lessons' topics vary from early number sense and early addition to percentages. In grade 2 the video database contains no fewer then 23 successive mathematics lessons.

The learning environment contains also all the materials related to each lesson: the textbook series, the teacher's manual, the teacher's journal, a videotaped 'interview' with the teacher, the students' workbooks and other written materials.

Each lesson is divided into short fragments, each of which can be seen as narratives, telling a story about teaching and the practical knowledge of teachers. Together the fragments follow the events of an entire lesson. Each narrative is accompanied by an abstract. Furthermore, the dialogue of the lesson is also available. Both, the abstract and the dialogue, can be used by student teachers to search for particular video fragments. Interesting fragments in the digital school can serve as a starting point for investigating all facets of mathematics education in primary schools.

Such investigations enable student teachers to develop knowledge based on the practical knowledge of the MILE-teachers. The student teachers also develop mathematical and pedagogical content knowledge from analyses of the children's math work, the teachers' activities and the knowledge construction of the children. In this way, MILE serves as an environment in which student teachers can build an understanding of the nature of both the learning of mathematics and its teaching.

At the moment there are 34 teacher education colleges in the Netherlands using MILE. Initial experience shows that the students' discussions about the practical knowledge they acquire in MILE is essential. So far, this discourse have been limited to fellow student teachers in the same teacher education college, but MILE can put these discussions into a wider context.

Supervisor: dr. M. Dolk l Category: primary education, l Status: completed
http://www.fi.uu.nl/mile

MILE is a Multimedia Interactive Learning Environment for future primary school teachers with content for primary mathematics teachers' education programs. It consists of a video database, communication tools, and a search engine. At the heart of MILE is a video database, composed of a digital representation of mathematics lessons in primary education. This digital school contains more then 65 lessons in kindergarten to grade 6 (4-12 years old). The lessons' topics vary from early number sense and early addition to percentages. In grade 2 the video database contains no fewer then 23 successive mathematics lessons.

The learning environment contains also all the materials related to each lesson: the textbook series, the teacher's manual, the teacher's journal, a videotaped 'interview' with the teacher, the students' workbooks and other written materials.

Each lesson is divided into short fragments, each of which can be seen as narratives, telling a story about teaching and the practical knowledge of teachers. Together the fragments follow the events of an entire lesson. Each narrative is accompanied by an abstract. Furthermore, the dialogue of the lesson is also available. Both, the abstract and the dialogue, can be used by student teachers to search for particular video fragments. Interesting fragments in the digital school can serve as a starting point for investigating all facets of mathematics education in primary schools.

Such investigations enable student teachers to develop knowledge based on the practical knowledge of the MILE-teachers. The student teachers also develop mathematical and pedagogical content knowledge from analyses of the children's math work, the teachers' activities and the knowledge construction of the children. In this way, MILE serves as an environment in which student teachers can build an understanding of the nature of both the learning of mathematics and its teaching.

At the moment there are 34 teacher education colleges in the Netherlands using MILE. Initial experience shows that the students' discussions about the practical knowledge they acquire in MILE is essential. So far, this discourse have been limited to fellow student teachers in the same teacher education college, but MILE can put these discussions into a wider context.

Supervisor: dr. J. B. den Hertog l Category: research, conference/course, primary education, l Status: completed
no website

The NCRC project was aimed at the professionalization of primary school teachers in mathematics education. The purpose of this project was to develop a advanced course for primary school teachers who either are or want to become a mathematics coordinator at their school. Before starting with this advanced course it is recommended that the teachers first follow the basic course for mathematics coordinators. Within the NCRC project the Freudenthal Institute collaborates with several other institutes.
In the reform of classroom practice the mathematics coordinator can play a crucial role. In order to fulfill this function the course has two main goals: it offers opportunities to teachers to work on their own teaching practice and didactical knowledge and to develop counseling and change-agent abilities which are needed for their work as a mathematics coordinator.
The course has a module structure. Each module is meant for five meetings, spread out over one school year. In the period between the meetings the participants have to do a number of homework activities.
The underlying idea of the modular structure is that each research/development project in the field of mathematics education that has relevant findings for school practice will result in a module as part of its output. The modules are considered as powerful means to share new ideas about mathematics education.

The project team has developed modules involving the following topics:

Realistic practicing
Girls and Boys in primary school mathematics education
Early number activities in kindergarten and grade 1
Calculations up to 100 for weak students, based on the program 'Jumping ahead'
Mental arithmetic in the upper grades of primary school
High achievers in primary school (in progress).

Teachers can attend these modules at their local teacher education college or school advisory center. The pre-schooling of the mathematics educators and school counselors who will give the course is done by the team that developed and field tested the module.

Supervisor: prof.dr.M. van den Heuvel=Panhuizen l Category: conference/course, primary education, l Status: completed
http://www.fi.uu.nl/ncrc/

The question of how to employ IT in such a way that it can support students' learning mathematics in a more independent way, forms the main theme of five research projects that are subsidized as a group by the National Institute for Scientific Research NWO. Point of departure is that mathematics education that is based on Freudenthal's conception of guided reinvention, requires both the appropriate instructional sequences and an appropriate classroom culture. The research focused on the question how IT can support these two elements. This especially concerns (a) the possible role of IT in the development of mathematical symbolizations, and (b) the way IT may support independent learning. A consortium of research groups carries out the five projects:

Graduate School for Teacher Education, Amsterdam University
Department of Educational Sciences, Utrecht University
Department of Physics Education, Utrecht University
Center for the Study of Education and Instruction, Leiden University
Freudenthal Institute, Utrecht University in collaboration with the Department of Teaching and Learning of Peabody College, Vanderbilt University.

Individual projects:
Symbolizing in Statistics Education
Calculus and Kinematics
Information Technology in secondary vocational education
Learning algebra, using CAS

Supervisor: prof. dr. K.P.E. Gravemeijer l Category: research, secundary education, l Status: completed
no website

The aim of the PISA-project (Programme for International Student Assessment) is to collect data on students' knowledge, skills and competencies in reading, mathematics and science for OECD-countries. Target population were students aged 15.
For the implementation of the project a consortium was formed of ACER (Australia), CITO (The Netherlands), Westat inc (AMerica) and SPE (Belgium, Luik).

Supervisor: mw. T. Dekker l Category: research, secundary education, l Status: completed
http://www.fi.uu.nl/pisa-nl/

Although technology is integrated in education, little is known about the relationship between the use of technological tools and cognitive development, and the way in which the teacher ‘orchestrates’ tool use. This issue is addressed for the case of mathematics education. The theoretical framework consists of domain specific theories, activity theory and the instrumental approach. In a design research methodology, an innovative instructional sequence using applets is developed and tested in grade 8.
To investigate the interplay between learning, teaching and the use of technological artefacts within a suitable learning ecology, the following research questions specify the more general research topic:

How can applets be integrated in an instructional sequence for algebra, so that their use fosters the learning?
How can teachers orchestrate tool use in the classroom community?

The first question concerns the individual learning. As a paradigm, the study focuses on the use of applets to develop the concept of function, and in particular on working with chains of operations. The concept of function is essential in algebra and calculus, but students have difficulties to make a shift from functions as local calculation processes to functions as global mathematical objects that signify unidirectional dependence relationships and can be submitted to operations of a higher order. The design of a specific instructional sequence for this topic serves as paradigm for more general knowledge on the influence of the use of technological artefacts on learning.
The second research question focuses on classroom practice and on the role of the teacher, which is identified as an important factor in the integration of technology.
The results of the study include a theoretically and empirically based local instruction theory on learning the function concept with technological artefacts, a framework for orchestration of tool use in mathematics teaching, and a more general elaboration of the theoretical framework for using computerized artefacts in education, which this study is a case of.

Supervisor: dr. P. Drijvers l Category: research, secundary education, l Status: completed
http://www.fi.uu.nl/tooluse

In this project, research was done into solving mathematics problems by primary school students who excel in mathematics. The research is done in cooperation with the Assessment and Evaluation Unit of the School of Education of the University of Leeds.
The purpose of the research project was to examine how Dutch children perform on a mathematics test that has been developed in England. The test is intended for those 9-year olds who are within the best 15-20% performers in mathematics in their class. In total, data from around one hundred students were collected.

Supervisor: mw. prof. dr. M. van den Heuvel-Panhuizen l Category: research, primary education, l Status: completed
http://www.fi.uu.nl/wiki/index.php/Popo

The Profi project aimed to develop and test a new national math course for students with an interest in the physical sciences (physics, chemistry, math) in the last two years of pre-university education. The principle we have adopted for this new course is that the material should pay attention to modeling, abstraction and reasoning in a balanced way.

In its first phase the Profi project has produced eight booklets on calculus and four on geometry. Some of the striking features of these books include the integrated and didactic use of IT (from graphing calculator to Cabri,), the use of contexts from the physical sciences, the references to the history of math and the build up from discrete to continuous concepts. In the geometry series there is a surprising interweaving of modern applications (Voronoi diagrams) with classic subjects (theory of cyclic quadrangles, conics). In these classic subjects a lot of attention is payed to the process of obtaining a proof and the heuristics thereof.

In the second phase of the Profi project, the emphasis is on the development of more or less open research tasks for small groups of students. IT also plays an important role in this part of the program. It is the intention that students finish off their research tasks by writing a report or giving a (verbal) presentation.

Supervisor: M. Kindt l Category: secundary education, l Status: completed
no website

Remesa stands for REalistic Mathematics Education in South A frica. It is a joint project of the Faculty of Education of the University of the Western Cape in South Africa and the Freudenthal Institute of the University of Utrecht in the Netherlands. Remesa is funded by the CENESA programme, NUFFIC, The Netherlands.
The aim of the Remesa project is to develop and research the impact of innovatory mathematics learning and teaching materials based on the premise that 'reality is the basis and the domain of application of mathematics'.
It is intended that the materials developed by Remesa would form a useful resource from which teachers, textbook authors and others can develop school mathematics programs that are relevant to the South African situation.

Supervisor: mw. drs. H.B. Verhage l Category: secundary education, l Status: completed
http://www-dev.fi.uu.nl/intern/_sources/oude_sites/remesa/

SamenRekenen Onderzocht is a research project carried out by the Freudenthal Institute. The aim was to systematically investigate the effects of the SamenRekenen approach on the development and learning of young children. SamenRekenen is a special project developed by Eduniek (formerly: Schooladvies Centrum Utrecht) in partnership with Daaladvies (formerly: Stichting Samenspel Op Maat).

SamenRekenen was aimed at disadvantaged young children (aged 18 months to four years) and their parents. The program is carried out in so called Samenspel groups, childcare centers, preschools and primary schools (in the Netherlands starting at age 4). In these groups, once or twice a week parents (mothers) together with their children join in informal (play) activities involving mathematical concepts. The activities are closely connected to young children’s spontaneous interests and consequently are meaningful to the children. One of the characteristics of SamenRekenen was the active involvement of parents: they join in the activities, ask questions and stimulate their child. The group leaders or teachers give information about the activities, discuss experiences with parents and present ideas about how to repeat or vary on the activities at home. The Samenspel philosophy highly values experiential learning, both for the children and their parents.
Since the start of the project, activities for children aged 1.5 to 6 years old have been piloted in different locations in Den Haag, Rotterdam and Utrecht. These activities fit in the Realistic Mathematics Education approach as developed by the Freudenthal Institute and which is reflected in primary school textbooks.
SamenRekenen is supported financially by the Bernard van Leer Foundation, VSB fonds Utrecht and Fonds 1818 Den Haag.
Information: www.eduniek.nl and www.daaladvies.nl (or info@daaladvies.nl).

SamenRekenen Onderzocht (January 2004 – December 2008) is meant to examine the conditions under which the SamenRekenen program has a positive influence on the developmental opportunities of young children. Furthermore, the way this program works will be compared with some frequently used other programs through qualitative research focusing on processes, in combination with observation of children in controlled situations that will be analyzed both qualitatively and quantitatively. And, finally, the aim is to prepare policy-related information on successful programs that seek to prevent developmental setbacks in young children and to support the dissemination of the SamenRekenen program at a national level.
The expected outcomes of this research project are:

relevant information for the implementation of the SamenRekenen program and the inservice materials;
answers to important questions regarding sustained effects of young children and which children have benefited most, also compared with children participating in other programs;
concrete suggestions for parents (mothers) on how to best support their children in their development while building on their own educational practices;
improvement in the work of early childhood educators and instruments to better monitor children’s progress;
policy recommendations based on an explicit overview of what is needed to further implement and disseminate SamenRekenen.

SamenRekenen Onderzocht is supported financially by the Bernard van Leer Foundation, VSB fonds Utrecht and the Stichting Kinderpostzegels Nederland.

Supervisor: mw. dr. C. van den Boer l Category: research, primary education, l Status: completed
no website

The Show Me Center, a partnership with five National Science Foundation-sponsored middle grades curriculum development satellites and their publishers, provides information and resources to support selection and implementation of Standards based middle grades mathematics curricula.
The five NSF sponsored middle school mathematics curricula that participate in the Show Me Center are:

Connected Mathematics Project (CMP)
Mathematics in Context (MiC)
MathScape (STM)
Middle Grades Math Thematics (STEM)
Middle Mathematics Through Applications (MMAP)

The FI took part in the support of implementation of MiC and provides generic information on reform assessment in the five middle grades mathematics curricula.

Supervisor: mw. drs. E. Feijs l Category: secundary education, l Status: completed
http://showmecenter.missouri.edu

The TAL Project that started in 1997 is initiated and granted by the Dutch Ministry of Education. The goal of the project was to describe longitudinal teaching-learning trajectories for mathematics in primary school.
The trajectories offer a global overview of how children's mathematical understanding develops from grades K to 6 and how education can stimulate this process. The stepping stones that the children will pass on their way to achieving the goals at the end of primary school form crucial elements in this overview. They can be seen as intermediate goals. The teaching learning trajectories are meant as a guiding tool for the macro-didactic tracking and as a framework for making macro-didactic decisions. They can, for instance, help teachers to enrich their use of textbooks. As such, they can contribute to the improvement of classroom practice and can give support to the teachers' professional development. The general intention of the project is to develop learning-teaching trajectories for all domains within primary school mathematics.

The TAL Project is carried out by the Freudenthal Institute (FI) of Utrecht University and the National Institute for Curriculum Development (SLO) and has been supported in part by the school advisory center CED in Rotterdam.

Up to now, the TAL Project covers four learning-teaching trajectories:
TAL I: Calculation with whole numbers in the lower grades of primary school
TAL II: Calculation with whole numbers in the higher grades of primary school
TAL III: Measurement and geometry in the lower grades of primary school
TAL IV: Rational numbers in the higher grades of primary school.

TAL I, II and III have already resulted in the publication of their respective learning-teaching trajectories. TAL I was published in 1998 and TAL II in 2000. These two trajectories on whole number were integrated in an English version that appeared in 2001. TAL III on measurement and geometry was released in the beginning of 2004. For the latter domain, it is the first time that a longitudinal pathway for the lower primary-school grades in the Netherlands has been developed. An English version of the learning-teaching trajectory for measurement and geometry will appear later this year. See TAL publications.

In August 2003, TAL IV was launched. This project deals with rational numbers, a subject where difficulties appear complex and urgent. Important points of attention for the project are the connections between the various manifestations of rational numbers - decimals, fractions, proportions and percentages - as well as the question of how to accommodate for the differences in ability between students. The project aims at fostering a discussion with teachers on the problems and key issues in this area, among other things, by developing and disseminating prototypical lessons.

Supervisor: mw. prof. dr. M. van den Heuvel-Panhuizen l Category: conference/course, primary education, l Status: completed
http://www.fi.uu.nl/archief/tal/tal.html

Mathematics education for vocational purposes (especially engineering) is experienced as too theoretical in both lower secondary and upper secondary vocational education.
Is there a possibility to develop a mathematics program that is more or less integrated in the practice of the job?

In a project that is funded by both the government and industry, the Freudenthal Institute works together with other institutes, math-, science- and vocational teachers of several schools for vocational education in the area of engineering (students' age 14/16) trying to find answers to this question.
A central focus of this project is the development of interactive IT materials (like Java applets) that integrate the vocational subject and math and science .

Supervisor: mw. drs. M. Wijers en drs. P. van der Zwaart (SLO) l Category: secundary education, l Status: completed
http://www.fi.uu.nl/winst/

Mathematics education for vocational purposes (especially engineering) is experienced as too theoretical in both lower secondary and upper secondary vocational education.
Is there a possibility to develop a mathematics program that is more or less integrated in the practice of the job?

In a project that is funded by both the government and industry, the Freudenthal Institute works together with other institutes, math-, science- and vocational teachers of several schools for vocational education in the area of engineering (students' age 14/16) trying to find answers to this question.
A central focus of this project is the development of interactive IT materials (like Java applets) that integrate the vocational subject and math and science.

Supervisor: mw. drs. M. Wijers l Category: secundary education, l Status: completed
http://www.fi.uu.nl/winst/

The Krygowska Project aimed both to develop and to evaluate the effectiveness of a particular approach to the Professional Development of Teacher-Researchers (PDTR) as the principal fulcrum of systematic transformation of mathematics education. It tends towards a system that, while respecting the standards and contents of national curricula, would be more responsive to pupils intellectual needs, promoting independence and creativity of though and better utilizing capital and potential of all students and participating teachers. PDTR is organized as a large-scale teaching experiment with collaborative teaching-research teams of teachers of mathematics mentored by university educators.

The project addresses a crisis in mathematics education, which is both widely acknowledged and wide-spread. It does this through the development of evidence-based instructional strategies, which improve learning of the mathematics competencies evaluated by PISA 2000 and PISA 2003 international tests.
The project lays the foundations for the formation of an international program of doctorate studies with TR specialization. Its outputs will include a teaching-research handbook, and a handbook of eight mathematical competencies. The teaching-research handbook will serve as the textbook of the graduate course on the methodology of teaching-research, one of the core courses of the projected doctoral program.
There are collaborative TR teams from Hungary, Italy, Poland, Portugal and The Netherlands participating in the project, integrating multicultural teaching-research experience of united Europe.

Supervisor: drs. H. Broekman l Category: research, secundary education, l Status: completed
no website

WisWeb is the website of the Freudenthal Institute dedicated to students at seconday schools (and higher). That is for students from age 12 and up. On the WisWeb-site you will find a wide collection of applets, worksheets, applications for graphing calculators, other software packages, instructional materials not related to technology, publications, and reports and memos about testing and field testing. More than 100 applets with supporting and additional instructional materials are now available on the WisWeb-site.

The WisWeb-site is the result of experimental activities related to the development and research of web-based educational materials. These activities started in the early nineties as a spin-off of other research and development projects, and were officially tied together in the WisWeb-project (2000-2002) and the WELP project (a technology implementation project 2002-2004). The WELP-project focused on the use of applets in the domain of school algebra for students of 13-14 years old. In these projects four secondary schools and PAS-wiskunde (a school counseling organization) participated in the development, testing and implementation of the applets and related educational materials, and the Dutch Association of Math Teachers (NVvW) supported the project as well. In the WELP-project, educational publishers and Texas Instruments joined the team.

Besides the educational and instructional materials (including the applets), various networks have been established:

a network of webmasters of (educational) mathematics websites in The Netherlands.
a network of (commercial) educational publishers
a network of inservice trainers and institutions that provide professional development.

The WELP-project has ended in August 2004, but the WisWeb-site will stay alive and will be frequently updated with new "products".

Supervisor: drs. M. van Reeuwijk l Category: secundary education, l Status: completed
no website

The Wisbaak (Math Oracle) is a design research project aiming at the development of educational materials and theory about language sensitive math education: (second) language learning integrated in the math lessons.
The main purpose of this project is to support math teachers and their students from ethnic minorities as well as native Dutch students with language problems. Lesson designs and web based materials were developed bearing the main characteristics of language sensitive math teaching: comprehensible orientation on math problems, promoting interaction, and providing evaluation for teachers and students on math and language learning.
Wisbaak includes:

Introductory lessons with a strong interactive character in which the teacher can explore what students already know about a subject by offering them motivating problems and can stimulate learning by talking and writing about it.
Interactive applets which supports students understanding of language and math concepts and offers exercises to apply and integrate this knowledge. Interaction is stimulated by having students working in pairs.
Vocabulary tests aimed at formative testing and developing students understanding of math and language concepts.
An electronic dictionary where students can check the meaning of school concepts and math concepts.
A manual providing information about the structure and use of Wisbaak materials, and background information about language sensitive math instruction.

For teachers the website contains ready-to-use lessons and vocabulary tests which can be printed and thus be available for use in the class. Moreover students can work online with the applets and electronic dictionary.
The site will be extended permanently. First materials are developed for class 1 and 2 of secondary education (age 12-14), in 2005 materials will be available for the highest grades of primary education (age 10-12).

Supervisor: mw. dr. C. van den Boer en mw.dr. D. van Eerde l Category: research, primary education, secundary education, l Status: completed
http://www.fi.uu.nl/wisbaak/

Discipline:	all mathematics science
Educational level:	all primary edu secundary edu other
Type:	all research conferences
	66 project(s) found

Projects