Geometry learning has a long history with the connection to human cognitive development. The ability to mentally or physically orient 2D shapes or 3D objects in space is believed to support achievement in science, technology, engineering, and mathematics (STEM) disciplines. Thus, geometry by its description is characterised by space; hence its…

Finding teaching methods that foster students' development of geometric thinking and visualization skills is still a current challenge. This study analyses the effects of the combined use of paper folding and dynamic geometry on high school students' geometric thinking and visualization skills. A quasi-experimental study pretest/post-test design…

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…

The present study is a part of design research in local instructional theory in a pre-algebraic lesson using the Realistic Mathematics Education (RME) approach. The article will focus on recommendations for the type of pre-algebra class that supports elementary school students' algebraic thinking. As design research study, it followed the three…

A key aspect of young children's development of algebraic reasoning is the process of visualising and identifying structures to both abstract and generalise. There has been a growing body of research focused on how students form generalisations, this article adds to the existing body of research by examining how young culturally diverse students…

The overarching goal of this 2-phase study was to investigate the contributions of relational reasoning to mathematical thinking and performance for 790 primary and middle-school Chinese students. Phase I of the study was undertaken to establish the reliability and validity of the Test of Relational Reasoning-Junior (TORRjr), a 32-item measure…

In this paper we probe prospective mathematics teachers' thinking as displayed in their solutions to a geometry content knowledge-based task. Geometry content knowledge is examined in terms of connections made by these prospective teachers between the geometric configurations and the geometric principles established through visualization and…

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…

Over three decades of research has shown that spatial reasoning and mathematics performance are highly correlated. Spatial visualization, in particular, has been found to predict mathematics performance in primary and middle school children. This research sought to determine the effectiveness of a spatial visualization intervention program on…

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.

In this study, it was aimed to determine the views of graduate students on mathematics learning with dynamic mathematics software GeoGebra. Case study method was used in qualitative research patterns. The study group consists of 7 graduate students who were doing their degrees at the Education Faculty of a state university in Turkey. Data were…

The longitudinal relations of domain-general and numerical skills at ages 6-7 years to 3 cognitive domains of arithmetic learning, namely knowing (written computation), applying (arithmetic word problems), and reasoning (arithmetic reasoning) at age 11, were examined for a representative sample of 378 Finnish children. The results showed that…

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…

Geometry belongs to branches of mathematics that develop students' visualisation, intuition, critical thinking, problem solving, deductive reasoning, logical argument and proof (Jones, 2002). It provides the basis for the development of spatial sense and plays an important role in acquiring advanced knowledge in science, technology, engineering,…

In this article, John West explores student misconceptions relating to division. A range of activities that promote the understanding of divisibility rules are provided.