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…

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…

External number representations are commonly used throughout the first years of instruction. The twenty-frame is a grid that contains two rows of 10 dots each, and within each row, dots are organized in two groups of five. The assumption is that children can make use of these structures for enumerating the dots, rather than relying on one-by-one…

Analyzed students' reasoning with fractions. Found that skilled students applied strategies specifically tailored to restricted classes of fractions and produced reliable solutions with a minimum of computation effort. Results suggest that competent reasoning depends on a knowledge base that includes numerically specific and invented strategies,…

Focuses on a single case study of a mentally handicapped child to examine directly the relation between the development of number-after rules and a counting-on from the larger addend (COL) strategy. Examines the development of children's proficiency with n+ and 1+n combinations and the evolution of their counting-on strategies over time. (AA)