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Tzur, Ron; Johnson, Heather Lynn; Norton, Anderson; Davis, Alan; Wang, Xin; Ferrara, Michael; Harrington, Cody; Hodkowski, Nicola Mercedes – Cognition and Instruction, 2021
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…
Descriptors: Constructivism (Learning), Mathematics Skills, Elementary School Students, Grade 4
Whitacre, Ian – Cognition and Instruction, 2018
I present a viable learning trajectory for prospective elementary teachers' number sense development with a focus on whole-number place value, addition, and subtraction. I document a chronology of classroom mathematical practices in a Number and Operations course. The findings provide insights into prospective elementary teachers' number sense…
Descriptors: Preservice Teachers, Elementary School Teachers, Mathematics Activities, Mathematics
Whitacre, Ian; Rumsey, Chepina – Cognition and Instruction, 2018
This article contributes to the research literature concerning prospective elementary teachers' mathematical thinking and learning with a focus on flexibility. We present a case study of a prospective elementary teachers' development of flexibility in mental addition and subtraction during a Number and Operations course. Building upon the…
Descriptors: Mathematics Instruction, Social Influences, Preservice Teachers, Elementary Education
van Galen, Mirte S.; Reitsma, Pieter – Cognition and Instruction, 2011
Predictions of the Identical Elements (IE) model of arithmetic fact representation (Rickard, 2005; Rickard & Bourne, 1996) about transfer between arithmetic facts were tested in primary school children. The aim of the study was to test whether the IE model, constructed to explain adult performance, also applies to children. The IE model…
Descriptors: Transfer of Training, Multiplication, Recall (Psychology), Arithmetic