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…

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

Traditional methods of teaching addition include algorithms that involve right-to-left procedures. This article describes efficient procedures for left-to-right addition and subtraction involving computation and computational estimation that reflect children's natural behaviors observed during activities with unifix cubes. (MDH)

Presents an analysis of young students' development of multiplication and division concepts based on a multimodal Structure of the Observed Learning Outcome (SOLO) model. Describes a SOLO developmental model for multiplication and division in terms of developing structure and associated counting and calculation strategies. Contains 48 references.…

Discusses various research findings aimed at helping teachers provide a classroom climate which leads students to develop better number sense. Focuses on number and symbol meaning, including number size, place value, and fractions, as well as computation and computational estimation. (MKR)

Examined the effects of intervention in the instruction of 12 male seventh-grade students for the purpose of developing number sense. Results indicate that after instruction students were more likely to use strategies to solve number magnitude, mental computation, and computational estimation problems that reflected number sense. (Contains 50…

Mathematical concepts presented within disciplines outside mathematics are either assumed to be already familiar to the students, or else, they are regarded as being peripheral to the appreciation of the content of the nonmathematical lesson. Because it is routinely included without regard for possible students' interpretations, the mathematical…

Describes a method of teaching the order of mathematical operations based upon the psychological theory of conceptual generalization. (MDH)

The major idea in this paper is the formulation of a theory of three distinct but interrelated worlds of mathematical thinking each with its own sequence of development of sophistication, and its own sequence of developing warrants for truth, that in total spans the range of growth from the mathematics of new-born babies to the mathematics of…

A study with 29 preschoolers showed that a statistically significant number of them successfully reassigned tags in counting (ordinality) but failed to predict that differently ordered counts would produce the same outcome (cardinality). Results indicated that children may not entirely understand implications of their counting actions. (Contains…

Arguing that cognitive development involves both conceptual and semiotic achievements, the authors emphasize the distinctness of semiotic issues and develop a differentiated appreciation of semiotic aspects of cognition, particularly in elementary mathematics cognition. Semiotic analyses are provided of differences between counting, adding, and…

Research conducted in several countries has shown consistent patterns of performance on "change,""combine," and "compare" word problems involving addition and subtraction. These findings are interpreted within a theoretical framework which emphasizes development of levels of word problem-solving ability related to…

Pre-experimental interviews conducted with three children to investigate three aspects of the nature of counting are detailed. Sixteen findings related to the counting of perceptual items are summarized. (MP)

Provides the instructions to build a homemade calculator that can be used as a reinforcement device to assist primary students in memorizing their addition facts. (MDH)

Discusses the use of middle-school students' natural understanding of large numbers to introduce the concept of infinity. Presents activities that investigate infinite sets by demonstrating a one-to-one correspondence between the counting numbers and the given set. Examples include prime numbers, Fibonacci numbers, fractions, even and odd numbers,…