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The purpose of this study was to identify affordances and limitations of using order and value comparison tasks versus number placement tasks to infer students’ negative integer understanding and growth in understanding…
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This study is a case of using second-order models of students’ mathematical thinking to differentiate instruction, and it reveals that inquiring into research-based knowledge and inquiring responsively into students’…
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The give-n task is widely used in developmental psychology to indicate young children’s knowledge or use of the cardinality principle (CP): the last number word used in the counting process indicates the total number of…
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In this study, we explored second and fifth graders’ noticing of negative signs and incorporation of them into their strategies when solving integer addition problems. For both grade levels, the order of the numerals, the…
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Language can affect cognition, but through what mechanism? Substantial past research has focused on how labeling can elicit categorical representation during online processing. We focus here on a particularly powerful type…
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The author describes an innovative approach to assessment that aims to blend the productive characteristics of both summative and formative assessment. The resulting assessment system is accountable to students and…