Three teaching principles for fostering students’ thinking about modelling: An experimental teaching program for 9th grade students in Japan

摘要

This study reports on an experimental teaching program to foster students’ thinking to promote modelling which consisted of nine lessons for Japanese 9th grade students. In this program, the following three teaching principles were emphasized;(TP1) Conflicting Situations: The teacher presents meaningful conflicting situations arising from particular modelling problem so that students can derive key ideas from these situations, (TP2) Repeated Connections: he teacher makes repeated connections between students’ thinking that promotes modelling and (TP3) Spiral Reflections: The teacher encourages students to reflect on their thinking throughout the series of nine lessons. As a pre- and post-test, the (PISA) Heartbeat problem and a general question on modelling were used before and after the teaching program to examine what transfigurations or shifts in students’ knowledge of modelling can be observed. This general question had the following sub-questions: What processes are required to build up a functional model? What ideas are important for developing an effective functional model? A graduated coding analysis was applied to assess students’ responses to the Specific (Heartbeat) question and to the General question. A graduated coding analysis was applied to assess students’ responses to the Specific (Heartbeat) question and to the General question. Significant gains in students` post-test codes/scores on both questions were obtained. This and the resulting discussion provide strong evidence that a teaching program based on the above three teaching principles is substantially effective in fostering students’ thinking to promote modelling.