This secondary analysis of data from a randomized control trial of an early mathematics intervention, ROOTS, explored whether patterns of intervention response were best categorized by the typical response/non-response binary or a more complex framework with additional response profiles. Participants included kindergarten students at risk for…

Children start preschool with large individual differences in their early numerical abilities. Little is known about the importance of heterogeneous patterns that exist within these individual differences. A person-centered analytic approach might be helpful to unravel these patterns and the cognitive and environmental factors that are associated…

The goal of the current study is to develop a more complete understanding of the early "home math environment," encompassing both numeracy and non-numeracy aspects of that environment. Parents of preschoolers (n = 63) were surveyed about their support of three components of early mathematics knowledge (i.e., numeracy, spatial, and…

This paper presents the results of a study of the structural development of young students' drawings of arrays, and in particular, the significance of using lines instead of drawing individual squares. Students' array drawings were classified on basis of numerical properties, and perceived structural similarities that reflected the spatial…

A review of work related to the topological primacy thesis and a critique of some aspects of it are presented. On the basis of the psychological research, it is concluded that topological concepts ought to be taught. (MP)

In this study with four sections of preservice teachers, both spatial visualization and cognitive development correlated significantly with achievement. However, in an analysis of variance, only cognitive development was significant, and no interaction was found. Spatial visualization was greater at the end of the geometry course than at the…

Several critical questions concerning the topological primacy thesis were raised in an extensive literature survey (SE 531 428). Three points related to this criticism are discussed and reinforced, including a reexamination of Laurendeau and Pinard's data (showing that they do not support the hypothesis of topological primacy in children's…

Some geometric activities are described that teachers can use to give their students experiences that will influence their spatial abilities. It is noted that the goal is to improve spatial abilities, not to increase knowledge, so individual pupil responses should not be used to judge student achievement. (MP)

The document opens with an editorial comment discussing the role of mathematics in teaching and learning. Then, 13 reports related to mathematics education are abstracted and analyzed. Three of the reports deal with problem solving, and another three look at aspects of cognitive development. There are two each on mathematics instruction,…

Uses manipulative materials to build and examine geometric models that simulate the self-similarity properties of fractals. Examples are discussed in two dimensions, three dimensions, and the fractal dimension. Discusses how models can be misleading. (Contains 10 references.) (MDH)

Noting that assumptions about the teaching and learning of early childhood mathematics have changed substantially since the 1970s, this chapter examines recent research that may inform curriculum development in early childhood mathematics. The chapter begins with a consideration of the theoretical perspectives for defining an appropriate…

This is volume 4 of the series of translations of books from the Soviet literature on research in the psychology of mathematics instruction and on teaching methods influenced by the research. The introduction to this English language translation highlights the fact that significant advances have been made in the understanding of both the…

Virtual Reality (VR) is a computer generated, multi-dimensional, inclusive environment that can build axioms of algebra into the behavior of the world. This paper discusses the use of VR to represent part of the algebra curriculum in order to improve students' classroom experiences in learning algebra. Students learn to construct their knowledge…

Several studies that were directed towards examining the influence of cognitive factors in sex-related differences in mathematics achievement are reported. Specifically, two lines of research were pursued examining: (1) the relationship between different types of visual-spatial skill and mathematics achievement, and (2) the trainability of…

Describes five skills underpinning the understanding of geometry for primary and lower secondary mathematics students. Skill categories identified include (1) visual; (2) verbal; (3) drawing; (4) logical; and (5) application. Gives examples of skills appropriate for Van Hiele levels 1-3. (MDH)