This study aims to evaluate Indonesian in-service elementary teachers’ knowledge on fraction by their responses to contextual problems on multiplication of a fraction by a whole number (O1) and multiplication of a fraction by a fraction (O2). Fifty Indonesian in-service elementary teachers from Elementary School for Teacher Education study program, University of Riau, participated in this research in 2015. This research is based on anthropological theory of the didactic (ATD), in particular praxeology, as a framework to analyse the data. The result showed that only 22% of Indonesian in-service elementary teachers have a satisfactory relation to O1 and 64% of them have succeeded on the problems related to O2.

This paper presents a framework of a PhD research of the first author about a comparative study of pre-service elementary teachers’ knowledge of rational numbers between Indonesia and Denmark. To obtain the data, the authors design a series of hypothetical teacher tasks (HTTs), inspired by a paper of Durand-Guerrier, Winsløw, and Yoshida (2010). Subjects in this research are pre-service elementary teachers from a selection of different University Colleges in Denmark and from the elementary school teacher education study program, Riau University, in Indonesia. The praxeological reference models and the levels of didactic codetermination are used as tools to analyse the result.

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Coronavirus disease (COVID-19) outbreaks have changed learning models from face-to-face to online learning. This change has an impact on students' readiness in participating in learning. To deal with this situation, this study aims to investigate prospective elementary teachers’ perspective on online mathematics learning. Thirty-eight prospective elementary teachers from a public teacher institution in Pekanbaru, Riau, Indonesia, participated in this study. The informants were asked to answer an open question at the end of the course related to their views on online mathematics learning during COVID-19 pandemic. The findings showed that the online course was less effective due to poor internet connection and limited internet quota. Those problems affected their performance on understanding the mathematics contents, interacting with the teacher and other students, and doing assignments. However, few prospective teachers provided positive attitude toward online mathematics learning. An implication for this study was the government must intervene and provide support for online learning success.

The present study aims to introduce the notion of praxeological change, developed based on the Anthropological Theory of the Didactic, to describe a necessity of changing mathematical praxeologies when passing from natural to rational numbers. It is applied to study and compare Danish and Indonesian pre-service teachers' (PSTs) knowledge of the density of rational numbers. They work in pairs to solve and discuss a hypothetical teacher task, which involves both mathematical and didactical tasks, related to the density of rational numbers. The findings highlight significant differences of the mathematical and didactical knowledge which are shared by the Danish and Indonesian PSTs. In particular, the Danish PSTs are more successful than the Indonesian PSTs in proposing didactical praxeologies to support pupils' praxeological change. They use the mathematical idea of converting fractions into decimals or vice versa and representing fractions and decimals on the same number line, while the Indonesian pairs tend to suggest pupils to order fractions and decimals based on the ordering properties of natural numbers.

This study aims to determine the feasibility of a math picture book (MPB) on the properties of 2-D shapes designed for primary students, and to find out how it can stimulate primary students' understanding about the properties of 2-D shapes. The method used in this research is design research based on Plomp’s development model. The development research was carried out from designing MPB, validating with two experts, and testing with primary students in two stages, namely one-to-one and small group experiments. Based on experts’ reviews, the designed MPB met very valid criteria, and the students and teachers also provided positive responses to the quality of designed MPBs. From experimenting it to six primary students in the experiment, it shows that students could explain the properties of 2-D shapes after reading the MPB. Therefore, the developed MPB had a positive impact on students’ understand the properties of 2-D shapes.

This study aims to improve the mental model of prospective primary school teacher related to the concept of boiling through the implementation of the conceptual development-oriented instruction (CDOI) model assisted by multimode visualization. This research was conducted using the pre-experimental method with the design of one group pretest-posttest. The subjects of the study were 36 the prospective primary school teachers, consisting of 20 female and 16 males. The research location is one of the universities in Riau province. The instrument used for collecting data is the conceptual understanding level test related to the concept of boiling in the form of open-ended that cover three parts of the question, which has previously been validated and tested for its reliability. The results of this study indicate that the implementation of the CDOI model assisted by multimode visualization has high effectiveness in facilitating the achievement of the scientific mental model, and no gender bias on achieving scientific mental models by the prospective primary school teacher.

This study aims to investigate pre-service elementary teachers’ knowledge on representing fraction operations by rectangle models. The subjects of this study are 64 pre-service elementary teachers from elementary school techer training study program, faculty of teacher training and education, University of Riau. The research method used is quantitative descriptive by giving a test related to the representations of fraction operations by rectangle models. The result shows that 82,81% pre-service elementary teachers were success representing addition of fractions, and 67,19% of them for subtraction of fractions. Meanwhile, 44,53% pre-service elementary teachers were success representing multiplication of fractions and 24,22% of them for divison of fractions. Then, they were still get difficulty in representing multiplication and division of fractions using rectangle models than addition and subtraction of fractions.