A method to overcome the double discontinuity of pre-service mathematics teachers: Focusing on didactic transpositions

Pre-service mathematics teachers who entered the College of Education experienced a disconnection between higher mathematics and school mathematics. Moreover, in-service mathematics teachers also experienced the disconnections in teaching school mathematics after graduating the university. These disconnections have been recognized as an issue for a very long time since Klein called it as double discontinuity in 1908. This study attempted a pedagogical approach to overcome the double discontinuity problem of pre-service mathematics teachers. According to the results of this study, pre-service mathematics teachers basically tried didactic transpositions based on textbooks in the pre-assignment. After the project, pre-service mathematics teachers attempted to make additional didactic transpositions based on the differences they recognized through project activities comparing the content between university mathematics and school mathematics. In addition, through teachers' impressions, it was confirmed that this project helped resolve the double disconnection that teachers were experiencing. Implications based on the findings were discussed.