Abstract
ABSTRACT Mathematical coherence is a goal within the Common Core State Standards for Mathematics. One aspect of this coherence is how student mathematical thinking is developed across concepts. Unfortunately, mathematics is often taught as isolated ideas across grades. The multiplicative field is an area of study that needs to be examined as a space to develop connections across concepts. This paper uses a case study of mathematical thinking from one 5th-grade student over a school year to demonstrate the connections in his thinking across whole numbers, fractions, and graphing work. Analyzing his solution strategies with three frameworks detailing multiplicative, proportional, and functional thinking, his strategies show a developing understanding of proportional reasoning, and functional thinking as he is building his multiplicative thinking and connections from whole numbers to fraction problem-solving strategies to graphing. Examining this student’s mathematical thinking points to the opportunity for connections across the multiplicative field through teaching mathematics in a manner more responsive to student sense-making.
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