Over half a century has passed since Bruner suggested his three-stage enactive-iconic-symbolic model of instruction. In more recent research, predominantly in educational psychology, Bruner's model has been reformulated into the theory of instruction known as concreteness fading (CF). In a recent constructivist teaching experiment investigating…

The use of manipulatives to develop conceptual understanding appears to be a prevalent practice in many mathematical learning experiences, particularly in the early years of schooling. This study evaluates the impact of mathematical manipulatives on young children's attitudes towards mathematics (YCATM). The modified three-dimensional model of…

This study explored students' mathematics-related beliefs and the relationship between the beliefs and their strategies for solving non-routine mathematical problems. The study was guided by Daskalogianni and Simpson's 2001 belief systems categories and strategies for non-routine mathematical problems. The participants were 625 grade 11 students…

The purpose of this study was to investigate the understanding of prospective elementary mathematics teachers of the formal definition of the limit of a sequence. The participants were 32 prospective mathematics teachers (8 male and 24 female) who were in their third year of study in a four-year mathematics teacher preparation programme Istanbul…

There exist many studies on modeling competencies and their promotion; however, there is a need to investigate what modeling competencies are and how they vary in lower and higher-achieving groups of students in mathematics within the current modeling literature domain. This study examined how mathematical modeling competencies were displayed in…

Using simulation-based inference (SBI), such as randomization tests, as the primary vehicle for introducing students to the logic and scope of statistical inference has been advocated with the potential of improving student understanding of statistical inference and the statistical investigative process. Moving beyond the individual class…

Practical problem solving is not common in many mathematical classes in Malaysian upper secondary schools. Usually, students receive the mathematical concepts through abstract materials (students cannot see some of them in their daily life). Thus some students believe that 'mathematics is not necessary for human life'. In this article, the…

Proportional reasoning is a key topic both at school and in everyday life. However, students are often misled by their preconceptions regarding proportions. Our hypothesis is that these limitations can be mitigated by working on alternative ways of categorizing situations that enable more adequate inferences. Multiple categorization triggers…

Introducing the distributivity property of multiplication over addition is a well-known challenge in mathematics education, especially in primary school. As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation and evaluation of a modelling activity in which 2nd-grade students are…

The purpose of this paper is to follow the reasoning of high school students when asked to explain the standard trigonometric limit lim/[theta][right arrow] sin[theta]/[theta]. An observational study was conducted in four different phases in order to investigate if visualization, by means of an interactive technology environment (Geogebra), can…

An inequality concept has an important role; even in advanced mathematics, inequality assists in analysis and proof. However, students' understanding of inequality is not satisfying. The fact shows that students experience difficulties and errors in solving inequality problems. These difficulties and errors are not intentional or do not result…

The paper addresses concept formation processes of students in the field of geometry. More precisely, the paper deals with the questions of what knowledge do students activate about triangles in different contexts with different (digital) tools and furthermore what content-related meaning do they give to the concept of triangles? Methodologically,…

One challenge facing the fields of mathematics education and special education is how to design instruction on fraction concepts that can meet the needs of diverse learners. An innovation that shows promise is to base instructional design upon well-established trajectories of students' fraction learning. However, little research has been done to…

Off You Go is a PK-12 mathematical routine that leverages children's home resources and assets to help students take a concept with which they have initial or informal understanding and explore and test its boundaries to support defining or estimating with precision. The authors provide a guide for how to adapt this routine to engage students at…

Purpose: The purpose of this action research was to identify students' errors in solving fraction number line and word problems. It also explored the effectiveness of Tik-Tok short videos in improving students' fraction understanding. Methods: The sample for this research consisted of 48 students from Form 1 at SMK SANZAC. In this study, a Check…