The Reciprocal Relationship between Conceptual and Procedural Knowledge--A Case Study of Two Calculus Problems

Autor/inn/en	Hechter, J.; Stols, G.; Combrinck, C.
Titel	The Reciprocal Relationship between Conceptual and Procedural Knowledge--A Case Study of Two Calculus Problems
Quelle	In: African Journal of Research in Mathematics, Science and Technology Education, 26 (2022) 2, S.111-124 (14 Seiten) PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Hechter, J.)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1029-8457
DOI	10.1080/18117295.2022.2101271
Schlagwörter	Calculus; Mathematics Instruction; Teaching Methods; Problem Solving; Correlation; Case Studies; Concept Formation; Mathematical Concepts; Engineering Education; Undergraduate Students; Foreign Countries; South Africa + Suchen Sie Ihr Suchwort? Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Mathematics lessons; Mathematikunterricht; Teaching method; Lehrmethode; Unterrichtsmethode; Problemlösen; Korrelation; Case study; Fallstudie; Case Study; Concept learning; Begriffsbildung; Ingenieurausbildung; Ausland; Südafrika; Süd-Afrika; Republik Südafrika; Südafrikanische Republik
Abstract	The literature describes different stances concerning the focus on how mathematics should be taught, with some preferring a conceptual knowledge approach and others a procedural knowledge approach. The current study investigated the relationship between students' conceptual and procedural knowledge in a calculus context. To better understand the relationship between students' conceptual and procedural knowledge, we conducted a content analysis of the solution approaches of three subject specialists, as well as student responses to two mathematical problems. The students (n =192) were enrolled for a first-year mathematics module which forms part of an extended engineering degree in South Africa. The solutions to the two problems were analysed based on the number and nature (conceptual or procedural) of experts' and students' steps to solve each problem. Each step in the solution was categorised based on the approaches used to solve the problem. The study found that solutions are not unique and could follow more than one approach. More importantly, the study found that the relationship between conceptual and procedural knowledge is complex and integrated as solutions require both procedural and conceptual knowledge. The findings reveal that calculus problems cannot be uniquely described as mainly conceptual or procedural. Both procedural and conceptual thinking is required to solve calculus problems and is often iterative. Student techniques to solve the calculus problems included algebraic, graphical and unexpected approaches. The analyses of student solutions suggest that lecturers and teachers should compare and discuss multiple solution strategies with their students to enhance mathematical proficiency and understanding. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01