First, fourth, seventh, and tenth graders were timed when solving simple and complex addition problems, then were presented similar problems in untimed interviews. Manipulation of confusion between addition and multiplication, where multiplication answers were given to addition problems (3 + 4 = 12) indicated an interrelatedness of these…

Building on previous research on the tendency in students of diverse ages to overrely on proportionality in different domains of mathematics (e.g., geometry, probability), this study shows that--when confronted with missing-value word problems--Flemish primary school pupils strongly tend to apply proportional solution strategies, also in cases…

The focus of this study was to investigate mental computation conceptual frameworks that Heirdsfield (2001c) formulated to explain the difference between proficient (accurate and flexible) mental computers and accurate (but not flexible) mental computers. A further aim was to explore the potential for students' developing efficient mental…

Research shows that introducing basic forms of algebraic reasoning in elementary school enhances children's learning of arithmetic. In this guide, a research and a professional development project are described that have taken a practical approach to introducing algebraic reasoning to elementary students in Massachusetts. (Author/SOE)

Computational strategies and estimating abilities of 466 Japanese students were tested and interviews with a subsample of that group were used to compare with a theoretical model based on a sample from the United States. Results of the comparison of computational and estimating abilities are presented. (CW)

Hypothesized that arithmetic calculating procedures and types of problems that necessitate more subproblems will lead to longer solution times. Data from 36 third grade students who mentally computed problems with sums greater than 20 and less than 100, confirmed both hypotheses. (RH)

Self-modeling was studied in three experiments with a total of 148 elementary school children who had experienced difficulties in arithmetic. Observing self-model videotapes raised achievement outcome as well as viewing peer models. Self-model tapes showing skill acquisition were as effective as were tapes showing mastery. (SLD)

It is argued that Australian elementary mathematics curricula have been influenced by earlier British and United States educational movements and theories and are out of touch with current research emphasizing a constructivist approach. A new model of young children's numerical development is offered, and recommendations for improving mathematical…

Many children read mathematics word problems and directly translate them to arithmetic operations. More sophisticated problem solvers transform word problems into object-based or mental models. Subsequent solutions are often qualitatively different because these models differentially support cognitive processing. Based on a conception of problem…

How can it be explained that, aside from inter-individual differences, pupils in certain classes are more responsive than others to the formal aspects of a problem that has been set? The author puts forward the hypothesis that teachers differ in their ability to operate relevant variations in the conception of problems. The differences in…

We examined the relationship between parents' behaviour and children's use of simple arithmetic strategies while playing a board game in contrast to solving arithmetic problems. In a microgenetic study spanning 3 weeks, 5-year-old children who were just beginning kindergarten played a modified game of "Chutes and Ladders" with one of…

This paper presents a framework for understanding conditions of discovery learning in computer-based microworlds. It begins with a short discussion of problems related to a traditional type of microworld--i.e., learning tools for mathematics--using the Dienes Multibase Arithmetic blocks as an example. In this discussion, hypotheses are developed…

This paper looks at the issue of mathematics learning from a developmental perspective. It begins by focusing on the importance for teachers of understanding how mathematical thinking develops. The New Zealand Number Framework is used as an example of a developmental progression that is of particular relevance to the teaching of mathematics. The…

Presented are materials related to the work of the Number and Measure and Rational Numbers working group of the Georgia Center for the Study of the Learning and Teaching of Mathematics. Much of the content reports on attempts to bring constructs from developmental psychology and mathematics to bear in understanding children's ideas of number and…

The study involving 60 learning disabled (LD) and 30 normal achieving seventh through ninth graders was designed to identify adolescents homogeneously defined as exhibiting a "specific learning disability in arithmetic" and to determine if the cognitive processes (visual-spatial, visual-reasoning, and visual-memory) are related to the academic…