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Direct linkMarmur, Ofer; Zazkis, Rina – Educational Studies in Mathematics, 2021
We investigate how students make sense of irrational exponents. The data comprise 32 interviews with university students, which revolved around a task designed to examine students' sensemaking processes involved in predicting and subsequently interpreting the shape of the graph of f(x)=x[superscript square root of 2]. The task design and data…
Descriptors: College Students, Comprehension, Graphs, Task Analysis
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
