2026-05-22T08:42:38Zhttps://keep.lib.asu.edu/oai/request

oai:keep.lib.asu.edu:node-2003532025-04-16T15:44:30Zoai_pmh:repo_items

200353 https://hdl.handle.net/2286/R.2.N.200353 http://rightsstatements.org/vocab/InC/1.0/ http://creativecommons.org/licenses/by-nc-sa/4.0 2025-05 2025-10-16T05:00:00 47 pages McFarland, Lauren Carlson, Marilyn Lock, Kayla Barrett, The Honors College School of Mathematical and Statistical Sciences School of International Letters and Cultures This study investigates how students conceptualize the idea of the derivative through a small-scale teaching experiment rooted in covariational reasoning. Drawing on the Covariation Framework and conventions such as speaking with meaning, emergent shape thinking, and emergent symbol meaning, the research explores how students transition from understanding average rate of change to a formal conception of derivative as an instantaneous rate of change (rate of change at a moment). Three students from a university calculus course were individually interviewed through a sequenced investigation, with their reasoning analyzed across five phases. Findings reveal varied levels of mental action (MA1–MA5) among students, particularly in their use of function notation, understanding of limit processes, and ability to conceptualize the derivative as a function. The results underscore the importance of emphasizing variable relationships, ratio-as-measure thinking, and formal definitions to support students in developing a precise and meaningful understanding of the derivative. Mathematics Derivative Math Education Conceptualizing Math Concepts Pre-Calculus Rate of Change Average Rate of Change Covariational Reasoning Function Notation Limit Investigating Student Understanding and Learning of the Idea of Derivative