The study aims to define the processes of pre-service mathematics teachers in reaching spatial visualisation generalisations within the context of drawing surface nets of solids. Two theories, Polya's problem-solving steps and novice-to-expert problem-solving schemas, were used as reference frameworks to describe the participants' spatial…

In this research study, I investigated the relationships between preferences for solution methods, task difficulty, gender, and high school students' geometry performance. Data were collected from 161 geometry students at six high schools at a county located in the southeastern region of the USA at the time of the 2013-2014 school year. The result…

Previous research has demonstrated that cognitive offloading (i.e., externalizing mental processes) is useful for immediate problem solving. However, long-term effects of cognitive offloading on subsequent problem solving without offloading are remarkably understudied. Our main goal was to investigate the effects of representation control (i.e.,…

Spatial visualization--the ability to mentally imagine and manipulate objects--has frequently been measured using the Paper Folding Test (PFT). In this task, participants view diagrams of a paper being folded and a hole being punched. They then identify the resulting punch pattern. Although task instructions promote mentally unfolding the paper,…

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…

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of…

Problem-solving and collaboration are regarded as an essential part of 21st Century Skills. This study describes a task-focused approach to network analysis of trace data from collaborative problem-solving in a digital learning environment. The analysis framework builds and expands upon previous analyses of social ties as well as discourse…

This inquiry presents two fine-grained case studies of students demonstrating different levels of cognitive functioning in relation to bilateral symmetry and reflection. The two students were asked to solve four sets of tasks and articulate their reasoning in task-based interviews. The first participant, Brittany, focused essentially on three…

We examined the effectiveness of (a) a working memory (WM) training program and (b) a combination program involving both WM training and direct instruction for students with geometry difficulties (GD). Four students with GD participated. A multiple-baseline design across participants was employed. During the Phase 1, students received six sessions…

Co-thought gestures are hand movements produced in silent, noncommunicative, problem-solving situations. In the study, we investigated whether and how such gestures enhance performance in spatial visualization tasks such as a mental rotation task and a paper folding task. We found that participants gestured more often when they had difficulties…

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 research team has developed a learning trajectory on 3D visualization for elementary children. This paper focuses on the interchange among the three Spatial Operational Capacity framework representations, namely, 3D models, 2D conventional diagrams, and semiotic abstract representations, and the critical role of a dynamic computer interface…

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…

This study assesses the effects of visual and verbal rehearsal on the problem solving efficiency of preschool children. The study examines the use of stimulus pretraining designed to induce verbal rehearsal and compares the effectiveness of induced verbal rehearsal with the effectiveness of induced visual rehearsal. Fifty-four middle class…