# PDM - PROBLEM SOLVING

## Introduction

Often, people stumble upon numeracy problems in their daily lives in very concrete real-life situations. Their aim is not to improve their mathematical competences or to solve mathematical word problems, but to find a concrete solution to a specific problem. Typically, a whole mix of situation perception, problem solving techniques, content knowledge and skills, (self-)believes and possibly computational procedures play a role in such a solution.

## Relation to Common European Numeracy Framework

## Key issues

In mathematics education problem solving is a well-researched topic. Since the groundbreaking publication by George Pólya in the 1945 “How to solve it“, it is one of the major issues in current mathematics education. However, many of these theories refer to textbook problems. Much less literature can be found on how people actual solve problems in real-life quantitative situations.

## Suggestions for PD meetings

## Self study

The booklet How to Solve it is still available and very readable for those who are interested in steps involved in problem solving in mathematics and numeracy.

## Resources

Realistic Mathematics Education Short Introduction

Stella Dudzic introduces the teaching ideas behind the Making Sense of Maths materials, developed by MEI and Manchester Metropolitan University (MMU) in this 3 minute long video. This provides some insight and background into the development of the teaching materials, which in turn were developed into the textbook series. Note that the first few seconds refer to GCSE but the rest is generic.

## Literature

*Csapó, B., & Funke, J. (2017). The nature of problem solving. Using research to inspire 21st century learning. **https://doi.org/10.1787/9789264273955-en*

*Schoenfeld, A. H. (2007). Problem solving in the United States, 1970–2008: research and theory, practice and politics. ZDM, 39(5–6), 537–551. https://doi.org/10.1007/s11858-007-0038-z*

*Jones, I., & Inglis, M. (2015). The problem of assessing problem solving: can comparative judgement help? Educational Studies in Mathematics, 89(3), 337–355. https://doi.org/10.1007/s10649-015-9607-1*

*OECD. (2012). PISA 2012 Results : Creative Problem Solving: Vol. V.*

*J. Rogers (2007)*

**:**Adult Learning. Problem based learning, Coaching S. 160 – 197*Problem-based learning: Reflective coaching for teacher educators. C Basile, F Olson, S Nathenson-MejL´ a – Reflective Practice, 2003 – Taylor & Francis*

*Kaiser, H. (2011). Vorbereiten auf das Prozentrechnen im Beruf. Praxis der Mathematik in der Schule, 53(41), 37-44.*

*Marja Van den Heuvel-Panhuizen and Paul Drijvers (2014): Realistic Mathematics Education; Freudenthal Institute for Science and Mathematics Education, Faculty of Science & Faculty of Social and Behavioural Sciences, Utrecht University, Utrecht, The Netherlands*

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