Geometry is one of the highest achievements of our species, but its foundations are obscure. Consistent with longstanding suggestions that geometrical knowledge is rooted in processes guiding navigation, the present study examines potential sources of geometrical knowledge in the navigation processes by which young children establish their sense…

The representation of numerical and non-numerical ordered sequences was investigated in children from preschool to grade 3. The child's conception of how sequence items map onto a spatial scale was tested using the Number-to-Position task (Siegler & Opfer, 2003) and new variants of the task designed to probe the representation of the alphabet…

The contribution of the three core components of working memory (WM) to the development of mathematical skills in young children is poorly understood. The relation between specific WM components and Numerical Operations, which emphasize computation and fact retrieval, and Mathematical Reasoning, which emphasizes verbal problem solving abilities in…

Defines spatial structuring as the mental operation of constructing an organization or form for an object/set of objects. Examines in detail students' structuring and enumeration of two-dimensional rectangular arrays of squares. Concludes that many students do not see row-by-column structure. Describes various levels of sophistication in students'…

Reports the results of a cross-cultural study of the development of five spatial competencies in samples of Thai and Australian children. The pattern of development was found to be similar for seven- and eight-year-olds but different for four- and five-year-olds. (Author/JN)

To study the developmental interrelationships among various aspects of logico-mathematical knowledge, 80 one- to 4-year-olds were individually asked to build "something tall" with 20 blocks. Percentages of new and significant behaviors increased with age and were analyzed in terms of the development of logico-mathematical relationships. It was…

This study examined the relationships between spatial ability, mathematics achievement, and sex for students in grades 2-7. Four spatial tests (embedded figures, serial integration, coordination of viewpoints, and rotation and development of surfaces) were used to measure spatial ability; sex and mathematics achievement, as measured by the Iowa…

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)

Examines preschool children's understanding of the mathematical significance of unit size through problems that involve making judgments about the number of larger objects versus the number of smaller objects. Elicits children's judgments about the effects of object size both before and after the presentation of a series of demonstration trials.…

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,…

Reports that a congenitally blind child, as well as sighted but blindfolded children and adults, can determine the appropriate path between two objects after traveling to each of those objects from a third object. Explores relationships of finding to geometric principles underlyinq innate spatial knowledge and inferential ability. (Author/CS)

Reports a study designed to identify 9 and 11 year olds' ways of drawing nets of solids and to provide opportunities for them to reflect on their models in whole class discussions. Results indicated that children's views of solids' nets progressed from more global and holistic to more quantitative and analytic. (MDH)

The development of young children's internal representations of large space was assessed by asking 15 boys and 15 girls to construct a three-dimensional model of their kindergarten classroom. Three groups of 10 children (ranging in age from 4 years, 8 months to 6 years, 3 months) were tested, two in the spring and one in the fall. One of the…

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)