Generations have been inspired by Edwin A. Abbott's profound tour of the dimensions in his novella "Flatland: A Romance of Many Dimensions" (1884). This well-known satire is the story of a flat land inhabited by geometric shapes trying to navigate the subtleties of their geometric, social, and political positions. In this article, the authors…

The papers in the monograph address different topics related to mathematics teaching and learning processes which are of great interest to both students and prospective teachers. Some papers open new research questions, some show examples of good practice and others provide more information about earlier findings. The monograph consists of six…

In this experiment we studied the effect of goal setting on the strategies used to perform a block design task called SAMUEL. SAMUEL can measure many indicators, which are then combined to determine the strategies used by participants when solving SAMUEL problems. Two experimental groups were created: one group was given an explicit, difficult…

Does solving subtraction problems with negative answers (e.g., 5-14) require different cognitive processes than solving problems with positive answers (e.g., 14-5)? In a dual-task experiment, young adults (N=39) combined subtraction with two working memory tasks, verbal memory and visual-spatial memory. All of the subtraction problems required…

Directed actions can play a causal role in cognition, shaping thought processes. What drives this cross-talk between action and thought? I investigated the hypothesis that representations in spatial working memory mediate interactions between directed actions and problem solving. Participants attempted to solve an insight problem while…

We live our lives in three-dimensional space and encounter geometrical problems (equipment instructions, maps, etc.) every day. Yet there are not sufficient opportunities for high school students to learn geometry. New teaching methods can help remedy this. Specifically our experience indicates that there is great promise for use of geometry…

The investigation monitored the digital game-playing behaviours of 428 primary-aged students (aged 10-12 years). Chi-square analysis revealed that boys tend to spend more time playing digital games than girls while boys and girls play quite different game genres. Subsequent analysis revealed statistically significant gender differences in terms of…

The purpose of this study was to examine the effects on four-year-olds' knowledge of mathematics by introducing professional development and center-based mathematics activities around four mathematical domains to early educators' teaching in Head Start programs. Because of the need to provide necessary mathematical experiences to young children to…

This article reports a recent case study providing evidence that toddlers explore mathematical concepts in their outdoor play. The play experiences the toddlers engaged in gave rise to seven mathematical categories. In each of these categories examples are given of some of the ways the toddlers displayed their mathematical knowledge and skill.

Certain secondary school subjects, such as geography, contain topics which are based on mathematical concepts. However, some geography teachers either fail to recognize this connection or choose to ignore it when they teach. Instead, they present the subject matter as a collection of facts, which need to be memorized and reproduced by the pupils.…

The purpose of this study was to examine the existence and strength of relationships between students' cognitive skills and mathematical problem-solving performance. Specifically, relationships between students' verbal, spatial, and analytical skills and their problem-solving performance on items that require a verbal response, items…

Using a means-means-ends problem-solving task, this study examined whether 16-month-old walking infants (N = 28) took into account the width of a bridge as a means for crossing a precipice and the location of a handrail as a means for augmenting balance on a narrow bridge. Infants were encouraged to cross from one platform to another over narrow…

Enabling learning through meaningful classroom experiences has always been a challenge for teachers. Bringing about a balance of the "conceptual" and the "hands-on", along with contextual embeddedness in problem-solving situations, broadly characterises the experience of development and trials of three Design and Technology…

Problem solving is a highly valued skill in chemistry. Courses within this discipline place a substantial emphasis on problem-solving performance and tend to weigh such performance heavily in assessments of learning. Researchers have dedicated considerable effort investigating individual factors that influence problem-solving performance. The…

This study examines visual and spatial working memory skills in 35 third to fifth graders with both mathematics learning disabilities (MLD) and poor problem-solving skills and 35 of their peers with typical development (TD) on tasks involving both low and high attentional control. Results revealed that children with MLD, relative to TD children,…