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A Model for Teaching Mathematical Argument at the Elementary Grades
Deborah Schifter,Susan Jo Russell 대한수학교육학회 2020 수학교육학연구 Vol.- No.특별호
Over years of collaborating with elementary-school teachers to research students’ thinking about the “big ideas” of K-6 mathematics, particular attention was given to generalizations about the operations—addition, subtraction, multiplication, and division—and arguments that explain why these generalizations are true. Through this work, we created a model of five phases that separate different points of focus in the complex process of formulating and proving such generalizations: 1) noticing patterns, 2) articulating conjectures, 3) representing with specific examples, 4) creating representation-based arguments, and 5) comparing and contrasting operations. In this paper, we illustrate the phases with classroom examples as students investigate a set of generalizations. We then present assessment results from classrooms of project teachers who engaged their students in this content.
Traci Higgins,Susan Jo Russell,Deborah Schifter 대한수학교육학회 2022 수학교육학연구 Vol.32 No.3
Through analysis of 108 interviews of students in grades 2 to 5, the research team created a framework consisting of four mathematical dimensions students engage with as they formulate a conjecture about a behavior of an operation. The four dimensions are: attending to the action of the operation, identifying which elements change and how, expressing conditionality, and considering the generality of the claim. This article describes and illustrates what student conjecturing looks like with respect to these dimensions. The framework provides a lens for researchers and practitioners to identify significant aspects of student-generated conjectures as students work to articulate their ideas.