Collapsing dimensions, physical limitation, and other student metaphors for limit concepts : an instrumentalist investigation into calculus students' spontaneous reasoning

By M. Oehrtman. 2009

137 citations recorded by the source corpus.

Subfields: Developmental and Educational Psychology, Education

View Paper: https://www.semanticscholar.org/paper/e5be8474f3479ef3abb8e64c7d62e50b04c415c8

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In Developmental and Educational Psychology

In Education

Citations in the corpus

Ideas foundational to calculus learning and their links to students’ difficulties (2021, background): “Other common concept images students construct for the concept of limit identified by Oehrtman (2009) include the proximity image (as x gets closer to y, f(x) gets closer f(y)), infinity-is-a-very-big-number image, and physical limitation image (a smallest positive number exists).”
THE CONCEPT OF ACCUMULATION IN CALCULUS (2008, background): “We located only two empirical studies that addressed students’ reasoning about limit in the context of integration (Oehrtman, 2002; P. W. Thompson, 1994a).”
Students’ images and their understanding of definitions of the limit of a sequence (2008, background): “However, the words used in expressing the dynamic imagery of limits, such as “approaching” or “getting close to,” do not precisely convey the mathematical meaning of the concept of limit (Oehrtman 2002; Tall and Vinner 1981; Williams 1991).”
A Study of Students’ Readiness to Learn Calculus (2015, background): “output values of a function change together they are able to distinguish between different function types, explain the meaning of a concave up graph and conceptualize the covarying quantities related by trigonometric functions in precalculus (Moore 2012, 2014) and the Fundamental Theorem of Calculus”
Lectures in Advanced Mathematics: Why Students Might Not Understand What the Mathematics Professor Is Trying to Convey. (2016, methodology): “A was asserting when he discussed the method of the proof, in part because they did not understand what he meant by small and they did not view his discussion of smallness as being important to the message he was conveying, a phenomenon also observed by Oehrtman (2009).”
The Precalculus Concept Assessment: A Tool for Assessing Students’ Reasoning Abilities and Understandings (2010, background): “Other studies have also revealed that covariational reasoning is a foundational reasoning ability needed for understanding concepts of limit (Monk, 1987; Oehrtman, 2008b), derivative (Zandieh, 2000), related rate problems (Engelke, 2007), accumulation (Carlson et al.”