This study investigated how students reason about the partial derivative and the directional derivative of a multivariable function at a given point, using different graphical representations for the function in the problem statement. Questions were formulated to be as isomorphic as possible in both mathematics and physics contexts and were given…

This study aims to reveal the mathematical reasoning process of 8th-grade students and the reasoning indicators they use in this process. The study was carried out in line with the data obtained from the Mathematical Reasoning Test (MRT) administered to 292 8th-grade students. The mathematical reasoning performances of the participants were…

The retention of foundational knowledge is crucial in learning and teaching mathematics. However, a significant part of university students do not achieve long-term knowledge and problem-solving skills. A possible tool to increase further retention is testing, the strategic use of retrieval to enhance memory. In this study, the effect of a special…

This study aims to investigate the relationship between learning styles and the efficacy of routine and non-routine problem solving. It also compares these relationships with respect to routine and non-routine problem types. The study sample consisted of 356 eighth-grade students in four different schools. In this study, correlational and…

Mathematics teaching and learning goes beyond computations and procedures; it rather includes complex problem-solving and critical thinking. Kilpatrick, Swafford, and Findell (2001) identify five mathematical competencies that are present in mathematics learning: conceptual understanding, procedural fluency, adaptive reasoning, strategic…

Generalisation is a key feature of learning algebra, requiring all four proficiency strands of the Australian Curriculum: Mathematics (AC:M): Understanding, Fluency, Problem Solving and Reasoning. From a review of the literature, we propose a learning progression for algebraic generalisation consisting of five levels. Our learning progression is…

The purpose of this study is to investigate a mathematically gifted student's self-regulation behaviours while constructing and consolidating mathematical knowledge. However, the objective is to determine which self-regulation strategies influence this student's mathematical abstraction process. The case study method was used in the research. As…

We explored the mediating role of prior knowledge on the relation between intelligence and learning proportional reasoning. What students gain from formal instruction may depend on their intelligence, as well as on prior encounters with proportional concepts. We investigated whether a basic curriculum unit on the concept of density promoted…

A theoretical model describing young students' (Grades 1-3) functional-thinking modes was formulated and validated empirically (n = 345), hypothesizing that young students' functional-thinking modes consist of recursive patterning, covariational thinking, correspondence-particular, and correspondence-general factors. Data analysis suggested that…

Scientific reasoning refers to the thinking skills involved in conceiving and conducting an investigation. This study examined how proficiency in performing these skills develops during the upper-elementary school years. A sample of 157 children (age 7-10) took a performance-based scientific reasoning test in three consecutive years. Four distinct…

The capacity to recognise, represent, and reason about relationships between different quantities, that is, to think multiplicatively, has long been recognised as critical to success in school mathematics in the middle years and beyond. Building on recent research that found a strong link between multiplicative thinking and algebraic, geometrical,…

Background: Key to optimizing Computational Thinking (CT) instruction is a precise understanding of the underlying cognitive skills. Román-González et al. (2017) reported unique contributions of spatial abilities and reasoning, whereas arithmetic was not significantly related to CT. Disentangling the influence of spatial and numerical skills on CT…

In the context of an analytical geometry, this study considers the mathematical understanding and activity of seven students analyzed simultaneously through two knowledge frameworks: (1) the Van Hiele levels (Van Hiele, 1986, 1999) and register and domain knowledge (Hibert, 1988); and (2) three action frameworks: the SOLO taxonomy (Biggs, 1999;…

We present study findings that depict the natural and fractional number knowledge of one third grade student with learning disabilities (LDs) in seven experimental sessions. We utilize qualitative analysis methods to illustrate how this student evidenced her knowledge of natural number and fractions through her interactions with varied learning…

This article describes part of a study in which researchers designed lesson sequences based around using a string number line to help teachers support children's development of relative thinking and understanding of linear scale. In the first year of the study, eight teachers of Years 3-5 participated in four one-day professional development…