Spatial reasoning is identified as a Numeracy general capability in the Australian Curriculum, and more globally as a significant precursor to mathematics proficiency. Currently, the literature surrounding mathematical-spatial relations remains largely removed from classroom practice. This paper provides a reflection on the spatial cognition field…

Bramlett and Drake (2013) suggest that the ability of teachers to teach proof is crucial for students to learn and develop formal and informal proofs. Teachers need to be involved in the process of proving and have a firm understanding of the critical role of proofs in order to effectively engage their students in proving activities. It is…

In the core of computational thinking (CT) practices is problem-solving. However, there is little research on connecting CT with problem solving processes. We developed a computer-based assessment on CT that can log students' problem-solving processes and administered it to a group of fifth graders as a pre- and post- measure of a robotics…

Many students are not good at geometric proofs. One reason for this is that it is possible to memorize the proof procedure explained by the teacher without understanding the structure of a geometric proof. So far, we have developed a web-based application that supports the understanding of the "structure of geometric proofs" in junior…

Visual and analytic strategies are features of students' schemes for spatial tasks. The strategies used by six students to anticipate the folding of nets were investigated. Evidence suggested that visual and analytic strategies were strongly connected in competent performance.

Although the psychological literature has demonstrated that spatial reasoning and mathematics performance are correlated, there is scant research on these relationships in the middle years. The current study examined the commonalities and differences in students' performance on instruments that measured three spatial reasoning constructs and two…

This design-based research project investigated the development of functional thinking in algebra for the upper primary years of schooling. Ten teachers and their students were involved in a sequence of five cycles of collaborative planning, team-teaching, evaluating and revising five lessons on functional thinking for their students over one…

Amongst important and under-researched questions are how introductory lessons can be designed for teaching initial proofs to junior high school students, and how such lessons enrich students' understanding of proofs. With a view to improving the learning situation in the classroom, in this paper we report on the various functions of introductory…

To support university students' understanding of mathematical proofs, pictures accompanying text are frequently used in textbooks as well as in lectures. However, it is unclear if such pictures influence the individual's reading behaviour. By recording the eye movements of eight mathematicians, we investigated whether and how adults with high…

This article argues for a shift in how researchers discuss and examine students' uses of representations during their calculus problem solving. An extension of Zazkis, Dubinsky, and Dautermann's (1996) Visualization/Analysis-framework to include physical modes of reasoning is proposed. An example that details how transitions between visual,…

This paper reports on a series of four studies carried out over a period of four years. These related studies were clinical and qualitative as they investigated middle and high school students' development of geometric thought, particularly as it related to three- dimensional visualization. The studies were carried out in the constructivist…