Sixty (35 girls) ninth graders were assessed on measures of algebraic reasoning and usage of visual and symbolic representations (with a prompt for visual use) to solve equations and inequalities. The study grouped visual representations into two categories: arithmetic-visual, which entailed the use of real-world objects to represent specific…

The paper describes the results of a study whose main aim was to find the interrelationship between pupils' school grades in Czech language (native), mathematics, and physics and pupils' cognitive predispositions to problem-solving in science and mathematics diagnosed by the Lawson Classroom Test of Scientific Reasoning and the Culture of Problem…

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…

The literature on the association between reading comprehension and mathematics skills is complicated and conflicting. This study seeks to illuminate the nature of the association between mathematics skills and reading comprehension by incorporating potential moderators, namely components of mathematics skills, domains of content standards in…

As algebra teachers, the authors explore the following question in this article: "How can algebra 1, algebra 2, and precalculus teachers support students to develop algebraic reasoning and understanding of structure that can serve them in day-to-day algebraic computation?" The article shows how the algebraic identity "(a +…

Linear algebra students are typically introduced to the problem of how to convert from one coordinate system to another in a very abstract way. Often, two bases for a given vector space are provided, and students are taught how to determine a transition matrix to be used for changing coordinates. If students are successful in memorizing this…

The Australian Curriculum: Mathematics calls for the concurrent development of mathematical skills and mathematical reasoning. What are the big ideas of mathematical reasoning and is it possible to map their learning trajectories? Using rich assessment tasks designed for middle-years students of mathematics, this symposium reports on the…

The general purpose of the study was to promote the research on effects of physical activity on mathematical performance and brain functions, which is of particular interest regarding children's education as well as for all adults. Several studies have identified an influence of cycling on cognitive processes and brain activity. In the present…

This is a study about the didactical organization of a research based group of activities designed using APOS theory to help university students make constructions, needed to understand and graph two-variable functions, but found to be lacking in previous studies. The model of the "moments of study" of the Anthropological Theory of…

fMRI was used to examine the differential effect of two problem-solving strategies. Participants were trained to use both a pictorial/spatial and a symbolic/algebraic strategy to solve word problems. While these two strategies activated similar cortical regions, a number of differences were noted in the level of activation. These differences…

Middle school teachers realize the value of students playing games in mathematics classes if those games emphasize problem-solving strategies, algebraic reasoning, or spatial sense. This article describes various versions of the traditional game of nim and shows how working backward can be used to find a winning strategy. The link is then made…

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…

Presents a methodology designed to strengthen the cognitive effects of using graphing calculators to solve polynomial equations using pattern matching, searching, and heuristics. Discusses pattern matching as a problem-solving strategy useful in the physical, social, political, and economic worlds of today's students. (DDR)

This article describes the use of commercial games in mathematics to help teach algebraic reasoning, spatial sense, and multistep problem solving. It also provides a description of how one teacher implemented the use of games.

"Everyday Mathematics," published by Wright Group/McGraw-Hill, is a core curriculum for students in kindergarten through grade 6 covering numeration and order, operations, functions and sequences, data and chance, algebra, geometry and spatial sense, measures and measurement, reference frames, and patterns. At each grade level, the…