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Weber, Eric; Thompson, Patrick W. – Educational Studies in Mathematics, 2014
This paper presents a conceptual analysis for students' images of graphs and their extension to graphs of two-variable functions. We use the conceptual analysis, based on quantitative and covariational reasoning, to construct a hypothetical learning trajectory (HLT) for how students might generalize their understanding of graphs of…
Descriptors: Visual Aids, Abstract Reasoning, Learning Processes, Mathematics Instruction
Dorko, Allison; Weber, Eric – North American Chapter of the International Group for the Psychology of Mathematics Education, 2014
The purpose of this paper is to describe (a) multivariable calculus students' meanings for the domain and range of single and multivariable functions and (b) how they generalize their meanings for domain and range from single-variable to multivariable functions. We first describe how students think about domain and range of multivariable functions…
Descriptors: Calculus, Mathematics Instruction, Generalization, Learning Processes