Mathematical representations are 'visible productions' that embody mathematical ideas. The author guides teachers with suggestions for the use of representations in mathematical problem solving with students. Representations can be used to help make abstract mathematical ideas accessible, allowing teachers and students to interpret, communicate,…

The exploration of children's drawings as mathematical representations is a current focus in early years mathematics education research. This paper presents a qualitative analysis of 72 kindergarten to Grade 3 (5 to 8 years old) children's drawings produced during problem-solving tasks centred on multiplicative strategies. Existing frameworks for…

Learners in general struggle when working with word problems. South African learners in particular have an added barrier owing to the many official languages that have been legislated. The South African Department of Basic Education, through its curriculum statements, envisages that problem solving will play a fundamental part in mathematics…

Both sketching and self-explanation are widely believed to be effective for problem-solving in science learning. However, it is unclear which aspects of these strategies promote learning and how they might interact. Compared to a read-only baseline, we examined the impact of instructing 11-year-old students to solve science problems to sketch,…

The purpose of this study is to develop a hand-drawing curriculum to promote the students' creativity for Vocational College, so as to study its implementation effect. The participants were 40 students were sampled by cluster random sampling method majoring in interior design from the Guangxi Electrical Polytechnic Institute in Nanning, Guangxi in…

Mathematization is a critical competency in the modelling process. This study aims to elicit prospective mathematics teachers' mathematizing through the analysis of their solution approaches to a modelling problem related to the bales of straw. This study was conducted with 75 fourth-year prospective mathematics teachers (PMTs) enrolled in a…

Although student covariation reasoning has been explored in depth to improve understanding of the correspondence between variables, research has focused on studying existing reasoning about variables in Cartesian representations. The working method had a qualitative approach, with a descriptive exploratory scope, the spontaneous representations…

The study aims to define the processes of pre-service mathematics teachers in reaching spatial visualisation generalisations within the context of drawing surface nets of solids. Two theories, Polya's problem-solving steps and novice-to-expert problem-solving schemas, were used as reference frameworks to describe the participants' spatial…

Drawing bar diagrams has been shown to improve performance on mathematical word problems wherein the relational keyword is consistent with the required arithmetic operation. This study extends this by testing the effectiveness of bar diagram drawing for word problems with an inconsistent keyword-arithmetic operation mapping. Seventy-five fifth…

This study aims to reveal the profile of open-start problem-solving with ethnomathematics regarding student learning styles. This research is a qualitative research study on 3 out of 31 students of Junior High School of 3 Magetan taken by purposive sampling. The three students carried out four stages: understanding the problem, planning…

Making drawings can help students avoid and overcome difficulties they encounter when solving real-world (or modeling) problems. However, many students do not make drawings spontaneously. In the present study, 132 students in Grades 9 and 10 were randomly assigned to the experimental conditions "with situational or mathematical drawing…

The aim of the study is to find out the problem-solving strategies used by primary school 3rd and 4th-graders in solving non-routine problems. The basic qualitative research design, one of the qualitative research approaches, was used in the research. The participants of the research consisted of 216 students, 104 of them in the third-grade and…

Non-optimal use of teaching materials and learning techniques impacts students' low skills, especially problem-solving abilities and learning independence. The study aims to develop a flipped classroom-based e-module that is feasible, practical, and effective in improving students' problem-solving skills and learning independence. This research…

This study enquires into the embodied processes of children in solving multiplication tasks, considering how such processes can expand access to spatial reasoning skills and simultaneously develop students' understanding of multiplication. The analysis focused on four Year 2 students as they completed two embodied tasks. The aim was to understand…

In collaborative design settings, designers communicate and explicate their ideas visually and verbally in order to reach a shared understanding. The verbal exchanges of group members engaged in a joint design task provide rich data regarding the design activities being undertaken by the group members. In addition, sketching and modelling are…