Repeating patterning proficiency predicts students' later mathematical proficiency. A comparative multi-case design enabled the present study to compare patterning success and strategy use for repeating patterns of 75 Norwegian 6-year-old grade 1 students. We provided the students with duplicate, extend, transfer, and unit isolation activities in…

In two parallel one-year studies, solution strategies for subtraction number facts and achievement patterns of matched groups of first graders in two different instructional programs were examined. Significant differences between groups were found favoring the strategy approach. (Author/CW)

Investigated was the learning of the mathematical uses of "more,""fewer," and "less" at a very early stage in the development of ideas. (CW)

An understanding of fraction addition can be thought to involve two quantitative ideas: (1) the understanding that adding to an original quantity increases its size, and (2) a sense of how much increase occurs. Both of these ideas should underlie or inform a child's approach to problems involving fraction addition and thereby constrain the class…

Identified is research related to concept formation; the chronology of identity and equivalence conservations; the relationship of mental age to performance on number concept tasks; perceptual, attentional, linguistic, and social factors; and the potential use of cognitive developmental criteria as measures of ability for both normal and retarded…

Learning to teach mathematics for understanding is not easy. First, practice itself is complex. Second, many teachers' traditional experiences with and orientations to mathematics and its pedagogy are additional hindrances. This paper examines teaching practices and reviews some of what is known about prospective and experienced elementary…

The contrast between the teaching of reading and mathematics is drawn. A new set of learning conditions for mathematics is presented based on a model of reading instruction. Immersion, demonstration, engagement, expectations, responsibility, use approximation, response, refinement, and outcomes are discussed. (CW)

This paper describes the BUD project which surveyed childrens' conceptions of division, and of fractions and decimals. The lack of connection between counting skills and conceptual understanding is discussed. The expectations for new algorithms and the basic idea in planning the BUD project are summarized. Some previous studies on counting, the…

This paper uses a structural model with a large random sample of urban children to explain children's competence in math concepts and computation at the time they begin first grade. These two aspects of math ability respond differently to environmental resources, with math concepts much more responsive to family factors before formal schooling…

It is generally accepted that mathematical reasoning, like language acquisition, is part of normal cognitive development. This paper proposes that other variables must be considered when explaining the differences in the acquisition of mathematical reasoning skills in young children. Considered is some of the evidence that suggests that certain…

This handbook has been structured to provide teachers (K-2) with the most recent research on problem solving. It contains information and practical applications which deal with the key concepts of problem solving in mathematics. The handbook consists of four sections. The first section establishes the background and gives the purposes of the…