We examine a hypothesis implied by Steffe's constructivist model of children's numerical reasoning: a child's "spontaneous" additive strategy may relate to a foundational form of multiplicative reasoning, termed multiplicative double counting (mDC). To this end, we mix quantitative and qualitative analyses of 31 fourth graders' responses…

Unitizing, a cognitive support for number sense, describes how students conceptualize quantities in terms of units. Given the importance of this skill, a formative assessment tool was developed for array multiplication problems, including arrays that model the distributive property found in typical classroom curricula. Video of 77 fourth grade…

Making sense of fractions is critical for building the mathematical competence of upper elementary students with and at-risk for a mathematics learning disability. The primary aim of this study was to investigate the effectiveness of teaching students with and at-risk for learning disabilities an intervention in which they learned to construct…

This study analyzed children's use of mental computation strategies and the standard algorithm on multi-digit subtractions. Fifty-eight Flemish 4th graders of varying mathematical achievement level were individually offered subtractions that either stimulated the use of mental computation strategies or the standard algorithm in one choice and two…

In this study, I examine how using a writers' workshop model in mathematics creates a space for students to write about their mathematical thinking and problem solving and how their writing impacts instruction. This case study of one classroom with one teacher spanned 6 weeks and included 18 implementations of an adapted version of the Writers'…

Proportional reasoning as the capacity to compare situations in relative (multiplicative) rather than absolute (additive) terms is an important outcome of primary school mathematics. Research suggests that students tend to see comparative situations in additive rather than multiplicative terms and this thinking can influence their capacity for…

This paper explored variation of strategy use in pattern generalization across different generalization types and across grade level. A test was designed to assess students' strategy use in pattern generalization tasks. The test was given to a sample of 1232 students from grades 4 to 11 from five schools in Lebanon. The findings of this study…

Recently, the author has been fortunate to be a visitor in a number of classrooms in the United States, England and Europe. On one such visit to an Elementary School in Columbia, Missouri, the teachers accepted him into their normal classrooms for their normal lessons. He moved between three classes: Grade 1, Grade 2 and Grade 4. A snapshot…