A Study of Calculus Students' Difficulties, Approaches and Ability to Solve Multivariable Optimization Problems

Autor/in	Mkhatshwa, Thembinkosi Peter
Titel	A Study of Calculus Students' Difficulties, Approaches and Ability to Solve Multivariable Optimization Problems
Quelle	In: International Journal of Mathematical Education in Science and Technology, 53 (2022) 11, S.2987-3014 (28 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Mkhatshwa, Thembinkosi Peter)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2021.1927227
Schlagwörter	Mathematics Instruction; Calculus; Mathematical Logic; Problem Solving; Barriers; Undergraduate Students; College Mathematics + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Mathematical logics; Mathematische Logik; Problemlösen
Abstract	This study used task-based interviews to examine students' reasoning about multivariable optimization problems in a volume maximization context. There are four major findings from this study. First, formulating the objective function (i.e. the function whose maximum or minimum value(s) is to be found) in each task came easily for 15 students who participated in the study. Second, most of the students successfully used the Lagrange Multiplier method or the Substitution method (i.e. eliminating one of the variables from the objective function, finding partial derivatives, and solving the simultaneous equations that result) to find the critical points of the objective function in each task. Third, verifying/justifying extrema (i.e. showing that the dimensions students found in each task are dimensions of largest volume object) was problematic for a majority of the students. Fourth, solving systems of nonlinear equations to find critical points of the objective function in each task was particularly challenging for nearly half of the students. This study has characterized students' difficulties when solving multivariable optimization problems. Further research is needed to explore instructional approaches instructors could adopt to help students develop a robust understanding of multivariable optimization problems and the methods used to solve these problems. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01