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Direct linkNorton, Anderson; Ulrich, Catherine; Kerrigan, Sarah – Journal for Research in Mathematics Education, 2023
This article introduces unit transformation graphs (UTGs) as a tool for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We report findings from a study in which we identified patterns in the ways preservice elementary school teachers relied on working memory to coordinate mental actions when operating in…
Descriptors: Graphs, Fractions, Short Term Memory, Preservice Teachers
Download full textStryker, Rachael; Kokushkin, Vladislav; Norton, Anderson; Kerrigan, Sarah – North American Chapter of the International Group for the Psychology of Mathematics Education, 2022
This study examined the role of student generated drawings to offload cognitive demands of a mathematical problem. We used Unit Transformation Graphs to compare students' thought processes when they had to solve the problem mentally, and when they were allowed to use pen and paper. The results indicated that the possibility to rely on drawings…
Descriptors: Freehand Drawing, Mathematics Instruction, Problem Solving, Mathematical Logic
Norton, Anderson; Ulrich, Catherine; Kerrigan, Sarah – North American Chapter of the International Group for the Psychology of Mathematics Education, 2020
We introduce a methodology for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We studied 12 pre-service teachers as they solved a set of fractions tasks, ranked by cognitive demand. We present the unit transformation graphs for one of those pre-service teachers, to illustrate how she experienced and met…
Descriptors: Mathematics Education, Problem Solving, Preservice Teachers, Preservice Teacher Education
