Roles and characteristics of problem solving in the mathematics curriculum: a review

Abstract

Since problem solving became one of the foci of mathematics education, numerous studies have been performed to improve its teaching, develop students’ higher-level skills, and evaluate its learning. While these studies usually study specific aspects of problem solving, further research is needed to understand how to address problem solving from a more comprehensive perspective, especially in the curriculum. We therefore ask two questions: What characteristics should problem solving have at each stage of the curriculum enactment process to ensure successful implementation? What role should problem solving have from a global curriculum perspective? To answer these questions, we perform a literature review to identify the roles and characteristics of problem solving that facilitate its successful implementation. Based on qualitative analysis of the data, we organize the results into the following categories: conditions of the education system, curriculum structure, characteristics of the planned curriculum and instructional design, types of problems in the intended curriculum and instructional materials, characteristics of the tasks implemented, classroom management, evaluation, student-related considerations, and teachers’ roles during problem solving. We also identify five principles to implement problem solving in teaching mathematics: understanding, reasoning, autonomy, collaboration and affective factors.

Since problem solving became one of the foci of mathematics education, numerous studies have been performed to improve its teaching, develop students’ higher-level skills, and evaluate its learning. While these studies usually study specific aspects of problem solving, further research is needed to understand how to address problem solving from a more comprehensive perspective, especially in the curriculum. We therefore ask two questions: What characteristics should problem solving have at each stage of the curriculum enactment process to ensure successful implementation? What role should problem solving have from a global curriculum perspective? To answer these questions, we perform a literature review to identify the roles and characteristics of problem solving that facilitate its successful implementation. Based on qualitative analysis of the data, we organize the results into the following categories: conditions of the education system, curriculum structure, characteristics of the planned curriculum and instructional design, types of problems in the intended curriculum and instructional materials, characteristics of the tasks implemented, classroom management, evaluation, student-related considerations, and teachers’ roles during problem solving. We also identify five principles to implement problem solving in teaching mathematics: understanding, reasoning, autonomy, collaboration and affective factors.