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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
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Palatnik, Alik; Koichu, Boris – For the Learning of Mathematics, 2015
The paper presents and analyses a sequence of events that preceded an insight solution to a challenging problem in the context of numerical sequences. A three­week long solution process by a pair of ninth­-grade students is analysed by means of the theory of shifts of attention. The goal for this article is to reveal the potential of this theory…
Descriptors: Attention, Grade 9, Attention Control, Educational Theories
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McMartin, Kimberley; McMaster, Heather – Australian Primary Mathematics Classroom, 2016
As an alternative to looking solely at linear functions, a three-lesson learning progression developed for Year 6 students that incorporates triangular numbers to develop children's algebraic thinking is described and evaluated.
Descriptors: Elementary School Mathematics, Elementary School Students, Mathematics Instruction, Number Concepts
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Wilson, W. Stephen – AASA Journal of Scholarship & Practice, 2009
This article first describes some of the basic skills and knowledge that a solid elementary school mathematics foundation requires. It then elaborates on several points germane to these practices. These are then followed with a discussion and conclude with final comments and suggestions for future research. The article sets out the five…
Descriptors: Elementary School Mathematics, Needs Assessment, Mathematics Skills, Knowledge Level