Matematikproblem i skolan : för att skapa tillfällen till lärande

• Main Author: Taflin, Eva
• Format: Doctoral Thesis
• Language: Swedish
• Published: Umeå universitet, Matematik och matematisk statistik 2007
• Subjects: Mathematics; problem-solving; rich problem; teacher; instruction; learning; mathematical ideas; occasions; MATHEMATICS; MATEMATIK
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-1384; http://nbn-resolving.de/urn:isbn:978-91-7264-397-0

The general purpose of this dissertation is to define and explore what mathematical problem solving entails. Seven criteria for rich problems will also be formulated. Rich problems are defined as problems which are especially constructed for mathematics education in a school context. The first part of the dissertation presents a sketch of what mathematical problem solving can entail in the teaching and learning process. The second part of the dissertation is a presentation and analysis of two ´rich´ problems. The analysis points out where mathematical ideas - concepts, procedures, conventions, strategies and formulae – appear in a problem solving process. The dissertation concludes with examples of the ways in which pupils and teachers together create occasions to utilize accepted mathematical ideas as well as the new range of ideas they devise in order to solve the problems. The concept of ´rich problems´ enables pupils with different mathematical backgrounds and capabilities to work with the same problem and solve it with various mathematical ideas. Research methods have included video- and audio recordings, stimulated recall with pupils and teachers, interviews and pupils drawings.