High school learners' mental construction during solving optimisation problems in Calculus: a South African case study

dc.creator	Deonarain Brijlall
dc.creator	Zanele Ndlovu
dc.date	2013-01-01T00:00:00Z
dc.date.accessioned	2015-07-20T22:14:12Z
dc.date.available	2015-07-20T22:14:12Z
dc.identifier	0256-0100
dc.identifier	2076-3433
dc.identifier	https://doaj.org/article/d2409b5f93254d8cb2f6bf78b2d32f36
dc.identifier.uri	http://evidence.thinkportal.org/handle/123456789/16649
dc.description	This qualitative case study in a rural school in Umgungundlovu District in KwaZulu-Natal, South Africa, explored Grade 12 learners' mental constructions of mathematical knowledge during engagement with optimisation problems. Ten Grade 12 learners who do pure Mathematics participated, and data were collected through structured activity sheets and semi-structured interviews. Structured activity sheets with three tasks were given to learners; these tasks were done in groups, and the group leaders were interviewed. It was found that learners tended to do well with routine-type questions, implying that they were functioning at an action level. From the interviews it appeared that learners might have the correct answer, but lacked conceptual understanding. Exploring learners' mental constructions via their responses to activity sheets and interviews enabled common errors and misconceptions to be identified. Themes that emerged were that learners: 1) lacked the understanding of notation dy/dx, 2) had not constructed the derivative and minima/maxima schema, 3) had some difficulty in modelling problems, 4) preferred rules and formulas, and 5) applied algebraic notions incorrectly. Inferences are drawn for curriculum developers and teachers. This study also formulated itemised genetic decompositions for particular tasks, which contribute to APOS theory.
dc.language	English
dc.publisher	Education Association of South Africa (EASA)
dc.relation	http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0256-01002013000200002
dc.relation	https://doaj.org/toc/0256-0100
dc.relation	https://doaj.org/toc/2076-3433
dc.source	South African Journal of Education, Vol 33, Iss 2, Pp 1-18 (2013)
dc.subject	APOS theory
dc.subject	Calculus
dc.subject	genetic decomposition
dc.subject	optimisation
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.title	High school learners' mental construction during solving optimisation problems in Calculus: a South African case study
dc.type	article