Problem posing is commonly perceived as a cognitive activity that emerges in the process solving a problem but appears less commonly in the process of classroom instruction. The creation and reformulation of mathematics problems engages students' thinking and their inquisitiveness in mathematical learning. This dissertation consists of three articles that explore the potential of problem posing for improving the teaching and learning of mathematics.
This dissertation study begins with a meta-analytic study of research findings on classroom instruction based on problem posing activities. The Hedges' g effect size is utilized to measure the effect of the problem posing instruction from 13 published studies. Four learning outcomes are identified from the studies: mathematics achievement, problem solving skills, levels of problems posed, and attitudes toward mathematics.
The second article focuses on finding the relationship between problem posing and problem solving. Fifty one middle school preservice teachers participated in this study and completed two tasks related to problem posing and problem solving. Rubrics were developed to assess the written responses that revealed participants' abilities in solving and posing mathematical problems.
A fully mixed methods research design is utilized in article three for examining the effect of a fraction instruction on the level of elementary preservice teachers' content knowledge, pedagogical content knowledge, and attitudes towards fractions. The instruction focused on using concrete models, problem solving, and problem posing activities for developing elementary preservice teachers' knowledge of teaching fractions.
The results from these studies revealed that problem posing is an effective approach as an inquiry-based instruction for improving students' learning in mathematics. Research efforts are needed to further the type of studies that can provide teachers with specific approaches in developing and using problem posing strategies in the mathematics classroom.
