Using lesson study to help mathematics teachers enhance students’ problem-solving skills with teaching through problem solving

Abstract

As a central objective, problem-solving skills are important in the mathematics curricula of many countries. However, such skills tend to receive limited and rarely systematic attention in mathematics lessons, including in the Netherlands. To address this gap, the authors adopt a specific approach that defines problem solving as integral to mathematics: Teaching mathematics Through Problem solving (TTP). In Japan, teachers often learn about TTP by performing Lesson Study (LS), an approach in which teachers work in teams to design and conduct a research lesson that allows them to learn collectively about students’ learning processes. TTP offers a promising, structured, didactical approach to introducing problem solving in mathematics lessons, and LS appears to represent an effective means for teachers to learn about TTP. To test this proposition, the current study entails a TTP- and LS-based intervention implemented in two secondary schools in the Netherlands, with an explicit focus on problem-solving skills. The central research objective for this study is to determine whether this TTP-LS-intervention helps mathematics teachers incorporate problem-solving skills into their lessons and how design characteristics and mechanisms of the intervention affect the outcomes. Interviews with teachers provide insights into which characteristics of the TTP-LS intervention fostered the implementation of problem solving in their teaching practice, as well as which did not. The collected data show that the teachers regard TTP as a valuable pedagogy to teaching mathematical problem solving. They report that the joint development, implementation, and evaluation of TTP lessons in the LS cycles, and especially observations of students, has given them more tools for applying TTP pedagogy and that they use these tools to promote problem-solving skills. Elements of the TTP lessons that the teachers perceived as difficult were the lesson phases that featured discussions on solution strategies rather than finding the “right” answers. Teachers regarded LS as a suitable approach for learning about TTP. Some points for improvement also emerged from the data. For example, more support should be given to TTP-LS-teams to explain the problem-solving skills they want to target in their lessons, and to practice especially the classroom discussion and summary phase.