<p>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.</p>

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.

The purpose of this study is to examine problem solving in teaching materials. Problem solving should, according to Lgr 11, have a central role in the teaching of mathematics. In a teaching that is dominated by textbooks it is important that the textbook give students the possibility to continuously develop their problem solving skills. This study investigates the extent to which teaching material address problem solving and if our textbooks challenge students to perform rich problems. In order to fulfill this purpose, the textbooks have been analyzed based on Eva Taflin's model for defining problems and rich problems. The textbooks used in the study are textbooks from primary school, which continuously work with problem solving and are based on Lgr 11. The data collection method chosen was a quantitative content analysis. It showed that teaching materials more or less address problem solving. The study also shows that it is difficult for the teaching materials to fulfill certain requirements needed for a problem to be classified as a rich problem. / Syftet med denna studie är att undersöka problemlösning i läromedel. Problemlösning ska enligt Lgr 11 ha en central roll i matematikundervisningen. I en läromedelsdominerande undervisning är det viktigt att våra läromedel ger elever möjlighet att kontinuerligt utveckla sin problemlösningsförmåga. Denna studie undersöker i vilken omfattning läromedel behandlar problemlösning samt om våra läromedel utmanar elever att utföra rika problem. För att uppfylla syftet har läromedlen analyserat utifrån Eva Taflins modell för att definiera problem och rika problem. Läromedlen som används i studien är läromedel från årskurs 1–3 som uttrycker att de arbetar kontinuerligt med problemlösning och utifrån Lgr 11. Den valda datainsamlingsmetoden blev en kvantitativ innehållsanalys där det framgick att läromedel från Matematik eldorado, Favorit matematik samt Koll på matematik i olika utsträckning behandlar problemlösning. Studien visar även att det är svårt för läromedlen att uppfylla vissa krav som behövs för att det ska klassas som ett rikt problem.

This study measures the effect of a model of explicit instruction (EMIT) on the: 1) physics graduate teaching assistants’ adherence to reformed teaching methods, 2) impact of the instructional model on GTAs’ beliefs about the nature of physics and physics problem solving and 3) undergraduate physics students’ understanding and performance in an introductory calculus-based physics course. Methods included explicit modeling for the treatment group GTAs of the Reformed Teaching Observation Protocol (RTOP) and assessment of treatment and control GTAs and their students throughout the semester. Students’ understanding was measured using the Force Concept Inventory (FCI) and Flash-mediated Force and Motion Concept Inventory (FM2CA). Students were surveyed about performance of GTAs using the Student Survey (SS). Results indicated changes were tied to individual GTAs’ beliefs about the nature of physics. Student conceptual understanding reflected a two-fold Hake gain compared to the control group. General application of the EMIT model presupposes explicit instruction of the model for GTAs.

This study measures the effect of a model of explicit instruction (EMIT) on the: 1) physics graduate teaching assistants’ adherence to reformed teaching methods, 2) impact of the instructional model on GTAs’ beliefs about the nature of physics and physics problem solving and 3) undergraduate physics students’ understanding and performance in an introductory calculus-based physics course. Methods included explicit modeling for the treatment group GTAs of the Reformed Teaching Observation Protocol (RTOP) and assessment of treatment and control GTAs and their students throughout the semester. Students’ understanding was measured using the Force Concept Inventory (FCI) and Flash-mediated Force and Motion Concept Inventory (FM2CA). Students were surveyed about performance of GTAs using the Student Survey (SS). Results indicated changes were tied to individual GTAs’ beliefs about the nature of physics. Student conceptual understanding reflected a two-fold Hake gain compared to the control group. General application of the EMIT model presupposes explicit instruction of the model for GTAs.