Analysing engineering students’ understanding of integration to propose a genetic decomposition

Brijlall, Deonarain; Ndlazi, Nokwethemba Jubilee

doi:10.1016/j.jmathb.2019.01.006

Cited by 15 publications

(12 citation statements)

References 13 publications

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“…Responses at N level (no response): ST13 did not attempt question 1c (i) which is an indication that he operated at the N level. The student could have faced trouble with limit and series notation (Brijlall & Ndlazi, 2019;Earls, 2017). Specifically, the student did not appear to think of the limit of a series as a limit of partial sums.…”

Section: Rmentioning

confidence: 99%

“…This contribution to the field of the learning of undergraduate mathematics is one of the strong traits of APOS theory. Similar studies effectively formulated the modified GDs: Brijlall & Ndlazi (2017) explored preservice teachers' mental constructions of the concepts of injections, surjections and bijections and in another study (Brijlall & Ndlazi, 2019) presented a modified GD for integration techniques.…”

Section: Introductionmentioning

confidence: 99%

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University students’ mental construction when learning the Convergence of a Series concept

2020

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Section: Rmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

University students’ mental construction when learning the Convergence of a Series concept

2020

Self Cite

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“…Integral is one of the most important concepts of calculus. It is a prerequisite concept for other mathematics concepts and even for other subjects (Brijlall & Ndlaz, 2019;Saepuzaman et al, 2017;Jones, 2013). However, most undergraduate students find that integral is the most difficult concept to learn (Moru & Qhobela, 2019;Hashemi et al, 2019a;Wagner, 2018;Jones et al, 2017;Nursyahidah & Albab, 2017;Li et al, 2017;Sealey, 2014;Tarmizi, 2010;Metaxas, 2007).…”

Section: 10 Introductionmentioning

confidence: 99%

“…According to researchers such as Metaxas (2007) and Tall (1993) conceptual understanding does not happen sufficiently and completely in the learning of integral because instructors and students focus on the symbolic aspect rather than graphical (Brijlall & Ndlaz, 2019;Moru & Qhobela, 2019;Wagner, 2018;Li et al, 2017;Tatar & Zengin, 2016), Moreover, there is no connection and relationship between graphical aspect and symbolical aspect through the learning of integral. Hence, students have difficulties in solving problems in integral because they do not use a framework or plan to solve the problems (Brijlall & Ndlaz, 2019;Nursyahidah & Albab, 2017;Li et al, 2017). In addition, they also have difficulties in using their previous knowledge and information in new areas (Villers & Garner, 2008;Mason, 2010;Tarmizi, 2010).…”

Section: 10 Introductionmentioning

confidence: 99%

The Emphasis on Generalization Strategies in Teaching Integral: Calculus Lesson Plans

Hashemi

Kashefi

Abu

2020

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Although integral is one of the important concepts in mathematics, most students have problems learning it. A well-designed lesson plan consisting generalization and its related activities can play an important role to overcome the students’ difficulties in the learning process. In this study, generalization means going from particular to something general by looking at common things and expanding their domains of validity. The main goal of this study is to investigate the rate of using generalization by mathematics instructors in teaching of integral concepts based on lesson plans. Thus, the instructors were interviewed on what generalization means to them and to find the reasons of emphasis on generalization or lack of it in their lesson plans. Findings revealed that most instructors did not emphasise the teaching of generalization in their lesson plans. Although most of the instructors expressed that generalization can be used to extend the theorems, the interview clarified that majority of the instructors did not know about the important applications of generalization in the teaching of integral. The results demonstrated that instructors have oppressed generalization in the integral teaching process.

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“…As they suggest, understanding a mathematical concept involves forming the concept image of it. Brijlall and Ndlazi (2019) have suggested developing the genetic decomposition of a concept (that is suggesting ways of how the concept might be learnt) so that instructors may organise their teaching of the concept for learning to take such a route. The current study was therefore conducted with the purpose of documenting university students' concept images and concept definitions of anti-derivatives, an important idea, applicable in the social sciences.…”

Section: Introductionmentioning

confidence: 99%

Social science students’ concept images and concept definitions of anti-derivatives

Moru

Qhobela

2019

Pythagoras

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The purpose of the reported study was to investigate the social science students’ concept images and concept definitions of anti-derivatives. Data were collected through asking students to answer 10 questions related to anti-derivatives and also by interviewing them. The theory of concept image and concept definition was used for data analysis. The results of the study show that the students’ definitions of anti-derivatives were personal reconstructions of the formal definition. Their concept images were coherent only to a certain extent as there were some conceptions of some ideas that were at variance with those of the mathematical community. These were more evident when students solved problems in the algebraic representation. Some students did not know which integration or differentiation methods they should apply in solving the problems. The significance of such findings is to enable the mathematics educators to pay attention not only to the use of signs and symbols representing mathematical concepts but also to their semantics.

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Analysing engineering students’ understanding of integration to propose a genetic decomposition

Cited by 15 publications

References 13 publications

University students’ mental construction when learning the Convergence of a Series concept

University students’ mental construction when learning the Convergence of a Series concept

The Emphasis on Generalization Strategies in Teaching Integral: Calculus Lesson Plans

Social science students’ concept images and concept definitions of anti-derivatives

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