It is well known that students benefit from opportunities to interpret and create different representations (e.g., diagrams, graphs, tables, symbols) of mathematical ideas. Employing Marton's Variation theory as a lens, I argue for an expansion of the use of multiple representations in task design for graphs: Incorporate two different forms of the…

Students often look to the standard algorithm, which requires rewriting the task, regrouping tens to create enough ones to subtract, and other opportunities to make errors. However, when the authors apply structural thinking, the resultant strategy is an efficient and elegant shortcut and even brings a positive connotation to the word…

The proposed revisions to the "Australian Curriculum: Mathematics" highlight the importance of learning to mathematise, problem-solve and reason in real world contexts, including financial contexts. Through the Economics + Maths = Financial Capability research project, the authors have been imagining fresh ideas for connecting the…

Media for children reflects societal views about appropriate childhoods in that the content has been chosen based on adults' views of what is appropriate for children to engage with. In this article, the mathematics in puzzles and handicrafts in a selection of Danish children's magazines from 1925 to 1930 are analysed to understand the childhoods…

This conceptual paper proposes a model to describe the quality of student dialogue during participative collaborative problem solving. Drawing on the participation metaphor of learning, we argue that the construct of mathematical sophistication is useful to describe the quality. We then present two frameworks, mathematical competencies and…

Inhibitory control--the ability to ignore salient but unhelpful stimuli and responses--seems to be important for learning mathematics. For instance there is now robust evidence that performance on classic measures of inhibition, such as the Stroop Task, correlate with school-level mathematics achievement. At the same time, a great deal of…

We report here on students' views of example generation tasks assigned to them in two first year undergraduate Calculus courses. The design and use of such tasks was undertaken as part of a project which aimed to afford students opportunities to develop their thinking skills and their conceptual understanding. In interviews with 10 students, we…

It is widely accepted in the mathematics education community that pedagogies oriented toward inquiry are aligned with a constructivist theory of learning, and that these pedagogies effectively support students' learning of mathematics. In order to promote such an orientation, we first separate the idea of inquiry from its conception as a…

Individual differences in inhibitory control have been shown to relate to general mathematics achievement, but whether this relation varies for specific areas within mathematics is a question that remains open. Here, we evaluate if inhibitory processes play a specific role in the particular case of fraction comparison, where learners must ignore…

Mathematical skills are becoming increasingly critical for achieving academic and professional success. Developmental dyscalculia (DD) is a childhood-onset disorder characterized by the presence of abnormalities in the acquisition of arithmetic skills affecting approximately 5% of school age children. Diagnosing students with possible dyscalculia…

The belief that studying mathematics improves reasoning skills, known as the Theory of Formal Discipline (TFD), has been held since the time of Plato. Research evidence supports this idea, at least in the context of students who had chosen to study post-compulsory mathematics. Here we examined the development of reasoning skills in 16- to…

The authors used a multiple-probe, across-tasks design to evaluate the effects of a classwide, multicomponent intervention on first-grade students' addition-fact fluency. Intervention components included "cover, copy, and compare," a 2-min math sprint, and a weekly group reward. Results showed that classwide digits correct per minute averages…

The purpose of this study was to examine the effects of grade-aligned math instruction on math skill acquisition of four middle schools with moderate intellectual disability. Teachers were trained to follow a task analysis to teach grade-aligned math to middle school students using adapted math problem stories and graphic organizers. The teacher…

This article examines the role of working memory, attention shifting, and inhibitory control executive cognitive functions in the development of mathematics knowledge and ability in children. It suggests that an examination of the executive cognitive demand of mathematical thinking can complement procedural and conceptual knowledge-based…

Passive and active visuospatial working memory (VSWM) were investigated in relation to maths performance. The mental rotation task was employed as a measure of active VSWM whereas passive VSWM was investigated using a modified Corsi Blocks task and a matrix pattern task. The Raven Progressive Matrices Test measured fluid intelligence. A total of…