Didactic transposition from scholarly knowledge of mathematics to school mathematics on sets theory

Abstract

A study was conducted to analyze the didactic transposition process on sets theory. Specifically, this study aimed to analyze the transposition of knowledge on sets theory from scholarly mathematics to school mathematics. This study was a phenomenology study. Abstract algebra textbooks, the 2013 curriculum and school mathematics textbooks were sources of data in this study. The analysis of didactic transposition process used descriptive analysis. The results of this study show that there was a transposition of knowledge in the concept of the set from scholarly mathematics to school mathematics. The transposition of knowledge occurs in the structure and form, and context, but not in sequences. In context, the transposition of knowledge to the concept of the set can be seen from how the concept of the set is built. In scholarly mathematics, the concept of sets is built from abstract formulas. Whereas in school mathematics, the concept of a set is built from concrete formulas, to later obtain semi-concrete and abstract formulas. Structurally and formally, the transposition of knowledge can be seen from the presentation of concepts. Whereas in sequence, there was no transposition of knowledge to the concept of sets.

Didactical Transposition within Reflective Practice of an Indonesian Mathematics Teacher Community: A Case in Proving the Pythagorean Theorem Topic

“…Knowledge to be taught is a scholarly knowledge process resulting in curriculum-based knowledge (Bosch, & Gascón, 2006). Knowledge to be taught can be acquired through a literature review from textbooks (Jamilah, et al, 2020). In this research, the teacher trainer employed textbooks published by the teacher competency development institution in Indonesia.…”

“…Didactical transposition also enables the teaching practitioners to analyse whether teachers' knowledge on learning materials is associated with scholarly knowledge (Arzarello et al, 2014). If mathematical knowledge acquired by students and teachers has been justified to be in accordance with scholarly knowledge and curriculum, it is expected that the obstacles and difficulties of students' learning affected by learning materials can be reduced (Jamilah, Suryadi & Priatna, 2020).…”

“…Meanwhile, Shinno and Yanagimoto (2020) elaborated on the affirmative values of collaboration between pre-service and in-service teachers. Hausberger (2017) investigated the homomorphism concept in didactical transposition performed in university whereas Jamilah et al (2020), scrutinised the didactical transposition within the education of mathematics pre-service teacher.…”