Abstract
The aim of this study is to investigate prospective elementary teachers’ (PsETs) mathematical and didactical knowledge of comparing decimals. Thirty-two fourth-year PsETs from an elementary school teacher education study program in Indonesia participated in this study. Each PsET is asked to solve a mathematical task of comparing decimals presented in the hypothetical teacher task (HTT), and then the PsETs use their mathematical knowledge to build their didactical knowledge collectively (pairs). Their mathematical and didactic knowledge is analyzed based on the anthropological theory of the didactic, especially praxeology. The findings indicate that PsETs have various techniques to solve the comparing decimal task, but some of them find it difficult to explain those techniques.
Highlights
The results from the Program for International Student Assessment (PISA) in 2015 ranked the performance of Indonesian pupils 62 out of 70 countries, and most of the pupils were only able to solve problems directly related to routine procedures(OECD, 2015)
The analysis of answers to the task of type Tm was mainly based on the prospective elementary teachers’ (PsETs)’ written solutions, but we looked at the video transcripts when there were some difficulties in categorizing the mathematical techniques from the written solutions
Almost all mathematical techniques described in the reference models appeared in PsETs’ written answers, but some techniques were more common than others
Summary
The results from the Program for International Student Assessment (PISA) in 2015 ranked the performance of Indonesian pupils 62 out of 70 countries, and most of the pupils were only able to solve problems directly related to routine procedures (mostly at level 1 and 2 on the PISA framework)(OECD, 2015) These results reflect how pupils learn mathematics at school, and how teachers teach mathematics to their pupils. Teacher Education and Development Study in Mathematics (TEDS-M) studied teachers’ knowledge through questionnaires (Tatto, et al 2008; Tatto, et al 2018) They used three question formats: multiple-choice, complex multiple-choice, and open constructed-response. They argued that only the third one allows teachers to demonstrate the depth of their thinking on mathematics knowledge and mathematics
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