Teacher Guidance In Mathematical Problem-Solving Lessons: Insights From Two Professional Development Programs

When implementing a problem-solving lesson, the teacher needs to provide students appropriate guidance during problem solving. This demanding task requires understanding students' work in progress and giving them necessary help without constraining their thinking. In this article, we share insights from two professional development programs on how teachers guided students' problem solving and how they reflected on these instances. One of the programs included Finnish pre-service teachers, while the other program included US in-service teachers. We analyzed video-recorded problem-solving lessons from 16 Finnish and 2 US teachers in grades 6-9. We found two themes about teacher guidance of student problem-solving activity: focusing students' thinking on something and emphasizing justification. In the first theme, the teachers' ways to guide students differed depending on how much space they allowed for students' thinking and how much their guidance actually helped the students to focus on the targeted issue. In the second theme, we identified two patterns: asking repeatedly for justification and helping to build a justification. The elaboration on the themes is supported with the analysis of the teachers' reflection related to the themes.