Abstract
This study aims to present a detailed analysis of didactic transposition of rational numbers from knowledge to be taught into taught knowledge occurring in a teacher education institution. The knowledge to be taught of rational numbers is analysed from the mathematics textbook used by prospective elementary teachers in a mathematics education course. The analysis focuses on mathematical praxeology, especially the type of task and technique. Then, the taught knowledge is investigated from 32 prospective elementary teachers’ collaborative work on two hypothetical teacher tasks (HTT) related to operations with rational numbers.
Highlights
Previous studies on mathematics education have focused on teachers’ knowledge and their learning and teaching of rational numbers
An hypothetical teacher tasks (HTT) is a task based on a teaching situation that may arise at school and allows teachers to use their relevant mathematical and didactic knowledge to act appropriately
The second part presents prospective elementary teachers’ collaborative work on HTTs concerning the mathematical and didactical praxeology being discussed in pairs
Summary
Previous studies on mathematics education have focused on teachers’ knowledge and their learning and teaching of rational numbers Teachers tend to instruct students based on a standard procedure without knowing the underlying meaning (Putra, 2018; Sembiring, Hadi, & Dolk, 2008). An HTT is a task based on a teaching situation that may arise at school and allows teachers to use their relevant mathematical and didactic knowledge to act appropriately. Putra (2018) found that most prospective elementary teachers employed a standard technique to solve the mathematical tasks, such as the standard procedure for adding two fractions. The prospective elementary teachers mostly considered those as the only way to teach students about rational numbers. With more advanced tasks, such as the division of fractions, many prospective elementary teachers were unaware of the concept behind the standard procedure. With more advanced tasks, such as the division of fractions, many prospective elementary teachers were unaware of the concept behind the standard procedure. Ma (1999) found that only few U.S elementary teachers realised the meaning of division of fractions, and many of them could not explain why the divisor has to be inverted to perform the standard procedure of fraction division
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