The Evolution of Students' Learning from Calculus to Analysis: How Students Solve Analysis Tasks That Look Like Calculus Tasks

Autor/inn/en	Broley, Laura; Hardy, Nadia
Titel	The Evolution of Students' Learning from Calculus to Analysis: How Students Solve Analysis Tasks That Look Like Calculus Tasks
Quelle	In: International Journal of Research in Undergraduate Mathematics Education, 8 (2022) 2, S.269-292 (24 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2198-9745
DOI	10.1007/s40753-022-00171-2
Schlagwörter	Calculus; Mathematics Instruction; Teaching Methods; Task Analysis; Barriers; Undergraduate Students; Validity; Mathematical Logic; Introductory Courses; Learning Processes; Educational Anthropology; Models; Learning Theories; Student Evaluation + Suchen Sie Ihr Suchwort? Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Mathematics lessons; Mathematikunterricht; Teaching method; Lehrmethode; Unterrichtsmethode; Aufgabenanalyse; Gültigkeit; Mathematical logics; Mathematische Logik; Einführungskurs; Learning process; Lernprozess; Pädagogische Anthropologie; Analogiemodell; Learning theory; Lerntheorie; Schulnote; Studentische Bewertung
Abstract	Research using the Anthropological Theory of the Didactic suggests different models of how student learning may evolve in the progression of undergraduate mathematics coursework: from elementary courses in Calculus to more advanced courses in Analysis. An ideal model suggests that the theory-driven learning in the latter serves as a natural complement and extension to the primarily procedural focus of the former. A contrasting model points to a potential didactic obstacle to the ideal evolution of students' knowledge: When the types of tasks in Analysis courses (e.g., "prove a specified limit") resemble those in Calculus courses (e.g., "find a specified limit"). To gain insight into the actual evolution experienced by students, we contributed an exploratory study of one introductory Analysis course, including an analysis of assessment activities provided in the course and task-based interviews with 15 students shortly after they passed the course. Results suggest that when faced with "Analysis tasks" that look like "Calculus tasks," most students do not mobilize the proof-based knowledge that was expected to be learned in Analysis. Moreover, this could be linked not only to the non-empty intersection of students' Calculus and Analysis courses, but also to the place of Calculus and Analysis in the intersection of their differing future professional institutions. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01