Teacher’s instruction in the reflection phase of the problem solving process
Mathematical problem solving has a key part in developing students’ mathematical thinking. Yet in the Finnish primary school classrooms mathematics lessons are very traditional and have little room for problem solving and mathematical discussions. Although problem solving has been a part of the Finnish curriculum for a few decades, it is the teachers who seem to choose not to include problem solving in the classroom on a regular basis. In this article I take a look at three Finnish fifth grade teachers who took part in a study on problem solving. They each incorporated problem solving in their mathematics lessons approximately once a month, and in this study I focused on one of the problems – an open problem called “The Labyrinth”. In each lesson I chose to focus on the teachers’ instruction in the reflection phase of the problem solving process. When instructing individual students in the reflection phase and during whole-classroom discussions, the teacher has an opportunity to point out the important parts of the problem solving process, help the students make connections and recall key moments of the process. In the reflection phase there is an opportunity to reflect, review and analyze one’s solutions and make generalizations. In the Labyrinth problem the teacher’s own understanding of the solution was an important factor during the instruction and the whole-classroom discussion. If the teacher’s instruction was purely led by the students’ own discoveries and insights, some important points were left unexplored. The teacher can even lead the students to the wrong direction, if he or she hasn’t carefully thought through the solution of the problem beforehand. The problem solving lesson is not just about finding a suitable problem and presenting it to the students, but guiding the students in the process.