Research has highlighted the important role that the senses play in mathematics thinking and learning, particularly in the area of visualisation, but also in relation to physical movement. Recent scholarship suggests that sensory experiences are not limited to the five cardinal senses but involve a range of other specific senses as well as…

Within educational research, dyslexia and other disabilities are typically conceptualized as deficits. The theory of neurodiversity encourages researchers to conceptualize cognitive differences as natural forms of human diversity with unique sets of challenges and strengths. Using neurodiversity as our theoretical framework, we analyze the…

This study assessed the effectiveness of a spatialized mathematics intervention on the mathematical performance and spatial visualization skills of students from an underprivileged Indonesian community. Grade 8 students (N = 407) were assigned to one of twelve experimental classes, receiving the spatial mathematics intervention, or one of seven…

An important approach for developing children's algebraic thinking involves introducing them to generalized arithmetic at the time they are learning arithmetic. Our aim in this study was to investigate children's attention to and expression of generality with the subtraction-compensation property, as evidence of a type of algebraic thinking known…

A concept map is a visualisation of a group of related concepts with their relationships identified by directed arrows, which can be viewed as an externalisation of a schema encoded in a learner's long-term memory. Concept maps have become popular learning tools in various educational settings. However, the existing research has not fully explored…

Teachers whose mathematical meanings support understanding across different contexts are likely to convey them in productive ways for coherent student learning. This exploratory study sought to elicit 67 secondary mathematics pre-service teachers' (PSTs) meanings for quadratics with growing pattern creation and multiple translation tasks. A…

We examine teachers' use of resources as they prepare to teach the topic of numerical series of real numbers, in order to identify how their "personal relationship" with mathematical content--and its teaching--interacts with their use of a commonly used textbook. We describe this interplay between textbook and personal relationship, a…

This paper contributes to research on the material dimensions of teaching and learning mathematics, arguing that perception is not sensory integration or synthesis of multi-modal information, but rather a speculative investment in specific material encounters. This approach entails sociopolitical consequences for how we work with dis/ability in…

Currently, instruction pays little attention to the development of students' sampling variability reasoning in relation to statistical inference. In this paper, we briefly discuss the especially designed sampling variability learning experiences students aged about 15 engaged in as part of a research project. We examine assessment and…

Recently, a new cognitive style approach was introduced, which refers to two types of visualizers. This approach is based on neuropsychological evidence and neuroimaging results, which suggest the existence of two distinct imagery subsystems, the object and the spatial imagery subsystems. The goal of the study was twofold: first to examine a…

A teaching experiment-using Mathematica to investigate the convergence of sequence of functions visually as a sequence of objects (graphs) converging onto a fixed object (the graph of the limit function)-is here used to analyze how the approach can support the dynamic blending of visual and symbolic representations that has the potential to lead…

It is our presupposition that there is still a need for more research about how classroom practices can exploit the use and power of visualization in mathematics education. The aim of this article is to contribute in this direction, investigating how visual representations can structure geometry activity in the classroom and discussing teaching…

There are many studies on the role of images in understanding the concept of limit. However, relatively few studies have been conducted on how students' understanding of the rigorous definition of limit is influenced by the images of limit that the students have constructed through their previous learning. This study explored how calculus…

Proposes a developmental model involving four response levels concerning how students arrange pictures to represent data in a pictograph, how they interpret these pictographs, and how they make predictions based on these pictographs. The model is exemplified by responses from three related interview-based studies. Discusses educational…

Spatial tests involving the comparison of diagrams of interlaced ropes or knots at varying orientations were given to (n=21) subjects, mostly English college undergraduates, to determine an ordering in terms of complexity of tasks involving the mental manipulation of the knots. Certain knot shapes were processed faster than others and greater…