The aim of this study is to investigate Danish pre-service teachers' (PSTs) mathematical and didactical knowledge of operations with rational numbers. This knowledge is studied through their collaborative activities to certain tasks related to the teaching of operations with rational numbers. An explicit model of the teachers' mathematical and…

This study aims to analyze the effectiveness of learning materials based on realistic mathematics education approach, as well as improving mathematical problem solving ability and student self-efficacy. Learning materials that developed were lesson plan, student book, student worksheet, mathematical problem solving ability test and self-efficacy…

Circle, ellipse, parabola, hyperbolic curves are defined as conic sections from the intersection of a coni with a plane at different angles. These curves can be found in different positions depending on the different angles. In this case, rotation transformation can be applied to the curves so that their major axes are brought to the horizontal…

The introduction of auxiliary elements as a method of solving problems in high-school geometry is considered here from two perspectives: first, to elicit recalling some known result or concretizing a definition and, second, as a means of shifting the focus and structure of the students' attention. We present and compare various examples of how…

This study aimed to determine the relationship between routine/non-routine problem-solving achievements and self-regulation skills of seventh-grade students who are educated in Turkey. For this purpose, in the 2016-2017 academic year, 133 seventh-grade students who were randomly selected in Denizli and Bursa provinces were studied. In the scope of…

Mathematical reasoning is a key proficiency in mathematics, however primary school teachers may have trouble noticing students' mathematical reasoning mid-lesson. In this study, students' mathematical reasoning has been analysed using video data collected as one grade of Year 5 and 6 students worked through the 'Painted Cube' task. Analysis…

Determining the most effective ways to support student-to-student talk requires some negotiating from a responsive teacher. This paper reports on a case study of two emergent multilingual students in Grade 3 (seven to eight-year-olds) who explained their strategies to each other. The transcript of their conversation was analysed using Chan and…

Teachers have difficulty integrating proof in their mathematics instruction due to both narrow beliefs about proofs and limited understanding of proofs. Indirect proofs seem to be a particular cause for concern. In this exploratory study, we contribute to the research area by reporting on an empirical study of Norwegian pre-service teachers'…

This case study was undertaken to characterise the interventions made by a kindergarten teacher during a multiplicative structure problem-solving lesson. The study findings show that when she realised the children were having difficulty, she provided assistance to enable them to find the right answer. When the children gave an incorrect response,…

Teaching is a process for which its plan should contain reflection onto previous experience. With that in mind, teaching situations should be continuously researched and improved in accordance with the research results. Led by this thought and the fact that students are uncritically using visualization to solve mathematical problems, we defined…

This qualitative document analysis study reports on opportunities to learn provided by textbooks for mathematics content courses for pre-service elementary teachers. Specifically, the study examined opportunities to engage in problem posing and quantitative reasoning, in the context of fractions, provided by six textbooks commonly used in the…

This article proposes an in-depth mathematics analysis of simple and compound interest through an exploration of the mathematical structures underlying these concepts. Financial numeracy concepts (simple and compound interest, interest rates, interest period, present and future value, etc.) have been added to the mathematics curriculum of the…

Using game-based learning (GBL) and digital game-based learning (DGBL) as a teaching and learning environment can be a pedagogical resource and a good strategy in the classroom to support mathematical learning (Santos et al., 2023). Even though primary school teachers are demonstrating strong preferences for using non-digital games instead of…

The Cell Phone modeling task centers on a Fermi real-world estimation question. The task and rubric can be used at different grade levels to focus on the modeling process and classroom community. Finding time and space to engage students, especially novice modelers, in mathematical modeling can be a challenge, yet the benefits of modeling are…

Pattern recognition is an aspect of computational thinking and a vital competency for solving mathematical problems. By recognizing patterns, one can develop possible solutions. This paper aims to describe the pattern recognition of prospective mathematics teachers in solving mathematical problems from a semiotic perspective. This study based on a…