# Problem Solving (Algemeen)

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 Versie op 3 jan 2018 06:10 (brontekst bekijken)Mas ← Oudere bewerking Versie op 3 jan 2018 06:17 (brontekst bekijken)Mas Nieuwere bewerking → Regel 14: Regel 14: - ===Blum & Miss 1991=== + ===Blum & Niss 1991=== "The following way of describing the interplay between the real world and mathematics is well-known and is by no means our invention ... The starting point is an applied problem or, as we also call it, a real problem situation. This situation has to be simplified, idealized, structured, subjected to appropriate conditions and assumptions, and to be made more precise by the "'problem solver" according to his/her interests. This leads to a real model of the original situation which on the one hand still contains essential features of the original situation, but is on the other hand already so schematized that (if at all possible) it allows for an approach with mathematical means. The real model has to be mathematized, i.e. its data, concepts, relations, conditions and assumptions are to be translated into mathematics. Thus, a mathematical model of the original situation results. Such a model consists essentially of certain mathematical objects, corresponding to the "basic elements" of the original situation or the real model, and of certain relations between these objects, again corresponding to relations between those basic elements." "The following way of describing the interplay between the real world and mathematics is well-known and is by no means our invention ... The starting point is an applied problem or, as we also call it, a real problem situation. This situation has to be simplified, idealized, structured, subjected to appropriate conditions and assumptions, and to be made more precise by the "'problem solver" according to his/her interests. This leads to a real model of the original situation which on the one hand still contains essential features of the original situation, but is on the other hand already so schematized that (if at all possible) it allows for an approach with mathematical means. The real model has to be mathematized, i.e. its data, concepts, relations, conditions and assumptions are to be translated into mathematics. Thus, a mathematical model of the original situation results. Such a model consists essentially of certain mathematical objects, corresponding to the "basic elements" of the original situation or the real model, and of certain relations between these objects, again corresponding to relations between those basic elements." Regel 58: Regel 58: * [[Mathematical literacy]] * [[Mathematical literacy]] * Pisa (2003). {{refworks3|The PISA 2003 Assessment Framework|3565|http://www.oecd.org/edu/school/programmeforinternationalstudentassessmentpisa/33694881.pdf}}. Paris: OECD. * Pisa (2003). {{refworks3|The PISA 2003 Assessment Framework|3565|http://www.oecd.org/edu/school/programmeforinternationalstudentassessmentpisa/33694881.pdf}}. Paris: OECD. + * PISA 2015 draft mathematics framework. (2013). Paris: OECD. https://www.oecd.org/pisa/pisaproducts/Draft%20PISA%202015%20Mathematics%20Framework%20.pdf * [[POPO-project]] * [[POPO-project]] * [[POPO-promotieonderzoek]] * [[POPO-promotieonderzoek]]

## Algemeen

• Probleemoplossen (problem solving in het Engels) is meer dan alleen het oplossen van een probleem.
• Ook wel genoemd als een van de 21ste eeuwse vaardigheden

## Achtergrond

Met probleemoplossen doelt men meer op het proces dat leidt tot het oplossen van het probleem dan op het vinden van de oplossing zelf. Bij probleemoplossen zijn het kunnen hanteren van heuristieken en het hebben van een wiskundige houding van belang. Over het algemeen kunnen bij probleemoplossen een aantal fasen worden onderscheiden:

1. beschrijf het probleem;
2. maak een plan om het probleem op te lossen;
3. los het probleem op;
4. blik terug op wat je precies gedaan hebt.

### Blum & Niss 1991

"The following way of describing the interplay between the real world and mathematics is well-known and is by no means our invention ... The starting point is an applied problem or, as we also call it, a real problem situation. This situation has to be simplified, idealized, structured, subjected to appropriate conditions and assumptions, and to be made more precise by the "'problem solver" according to his/her interests. This leads to a real model of the original situation which on the one hand still contains essential features of the original situation, but is on the other hand already so schematized that (if at all possible) it allows for an approach with mathematical means. The real model has to be mathematized, i.e. its data, concepts, relations, conditions and assumptions are to be translated into mathematics. Thus, a mathematical model of the original situation results. Such a model consists essentially of certain mathematical objects, corresponding to the "basic elements" of the original situation or the real model, and of certain relations between these objects, again corresponding to relations between those basic elements."

Bron (1991) Blum, W., & Niss, M. (p. 38)

### Pisa 2003

Bron: (2003). The PISA 2003 Assessment Framework (klik voor een uitvergroting)

### Blomhøj 2003

Bron: (2003). Blomhøj, M., & Jensen, T. H. (2003). (klik voor een uitvergroting)

### Blum 2009

Bron: Blum, W. and Borromeo Ferri, R. (2009) (klik voor een uitvergroting)

### Pisa 2013

Bron: PISA 2015 draft mathematics framework. (klik voor een uitvergroting)