Pre-service Mathematics Teachers’ Mental Constructions of the Determinant Concept

Ndlovu, Zanele; Brijlall, Deonarain

doi:10.1080/09751122.2016.11890488

Cited by 11 publications

(8 citation statements)

References 1 publication

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“…There were 18 and two students who displayed procedural errors in question 1 and question 2, respectively. The total number of procedural errors was small, and this concurs with Ndlovu and Brijlall (2016) study that the undergraduate student learning is more connected with procedural understanding rather than conceptual understanding. This is in line with Malambo (2021) who also noted that students mastered procedural knowledge without understanding the conceptual connections in relationships.…”

Section: Discussion Of Procedural Errors For Linear Independencesupporting

confidence: 88%

Misconceptions and resulting errors displayed by in service teachers in the learning of linear independence

Mutambara¹,

Bansilal²

2022

INT ELECT J MATH ED

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The aim of this paper is to identify errors and misconceptions that student demonstrated when learning linear independence and linear dependence concepts. A case study is presented involving 73 in-service mathematics teachers at a university in Zimbabwe who were studying for a Bachelor of Science Education Honors Degree in mathematics. Data was generated from a content analysis of the written responses of the participants to two items from a structured activity sheet. Follow up interviews with five participants were used to gain a better understanding of their misconceptions. The study found that the participants had different kinds of misconceptions leading to errors which could be described as procedural, conceptual, and foundational respectively and the distribution of the errors differed across the two problems. For question 1 which was set within the vector space M2×2, students found it harder to move past the first few two steps of formulating the general vector equation and doing scalar multiplication; those who passed those two steps were mostly able to get to a correct solution. For question 2 which was set within ℝ 3 most students went past the first two steps formulating the general vector equation and converting that to an augmented matrix but then made many foundational errors, most of which were related to misinterpretations of the solutions to the system of equations.

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Section: Discussion Of Procedural Errors For Linear Independencesupporting

confidence: 88%

Misconceptions and resulting errors displayed by in service teachers in the learning of linear independence

Mutambara¹,

Bansilal²

2022

INT ELECT J MATH ED

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“…In this study, students demonstrated inroads into EROs as a concept but struggled to apply it in solving SLEs. The use of APOS theory has intension to instructional strategies as understanding the mental constructions that students make when learning a mathematical concept leads to improved practice (Ndlovu & Brijlall, 2016). The mental constructions made by the students concurred with the preliminary concept decompositions for both the concept of EROs and their applications.…”

Section: Discussionmentioning

confidence: 88%

“…To counter this, the authors suggested revising the theoretical decomposition of matrix operations so that students were be able to make the required mental constructions of linear algebra concepts. On the other hand, Ndlovu and Brijlall (2016) investigated students' mental constructions as they learn the concept of determinants but without the application thereof. They discovered that most students conceptualized determinants procedurally and operated on the action or process stages of APOS theory.…”

Section: Literature and Theorymentioning

confidence: 99%

Undergraduate students’ conceptualization of elementary row operations in solving systems of linear equations

Tatira

2023

EURASIA J Math Sci Tech Ed

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The concept of systems of linear equations (SLEs) is fundamental and core in linear algebra, a subject, which has many applications in a number of disciplines. Gaussian elimination is a versatile method, which can be used to solve almost all types of SLEs by using row-reductions. This study focused on exploring undergraduate students’ conceptualizations of elementary row operations (EROs) as a means to solve SLEs. The purpose of this study was to explore undergraduate students’ conceptualizations of row reductions and their applications to the solutions of systems of equations. The perspectives of the action-process-object-schema theoretical framework were used in analyzing data and discussing the findings. To explore the students’ conceptualization of EROs, a descriptive research approach was followed. I considered a case study of 131 students registered for a mathematics for educators course, where linear algebra was one of the topics. The findings revealed that students attained the action conception of reducing a system with unique solutions but had challenges reducing and interpreting solutions to a system with non-unique solutions. The latter row-reduction implored process and object conceptions especially when variable elements in the augmented matrix were involved. As students find the learning of linear algebra difficult, this study contributes to the debate in literature on how to improve its teaching and make suggestions on the ways make more effective the learning of linear algebra.

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“…The findings revealed that, except for the few working at an object stage, many of PMTs operated at the action and process stages. The findings further suggest that though PMTs were able to carry out procedures effectively, several were not able to construct the meaning of the concept (Ndlovu & Brijlall, 2017). An earlier study by Ndlovu and Brijlall (2015) examined the link between the mental constructions of PMTs when learning matrix algebra concepts and their preliminary genetic decomposition (Dubinsky & McDonald, 2001).…”

Section: Pre-service Mathematics Teachers' Mental Construction Of Alg...mentioning

confidence: 92%

Subject competency and teacher knowledge: An exploration of second-year pre-service mathematics teachers’ difficulties in solving logarithmic problems using basic rules for logarithm

Okoye-Ogbalu,

Nnadozie

2024

Journal of Mathematics and Science Teacher

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Pre-service mathematics teachers’ (PMTs) subject competency continues to engage scholars and researchers. Understanding level of knowledge of concepts that PMTs bring to their learning in university is crucial to developing their teacher knowledge. This article examines genetic decomposition of schemas PMTs in one university in South Africa build (to know about rules) for solving logarithmic equations. A mixed methods approach, and the action-process-object-schema (APOS) theory were employed to examine mental construction the 19 purposively selected PMTs that responded to a 90-minute simple logarithm research task (LRT) made while solving problems. Analysis of task scripts using percentage score forms the basis of the qualitative phase of the research. Individual interview was useful to elicit PMTs’ views and perceptions of their encountered difficulties in solving LRT problems. One common difficulty was proving the logarithmic equation. This highlights gaps in PMTs’ prior knowledge of logarithmic concepts and basic rules. Implications of the findings for PMT subject competency were discussed.

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Pre-service Mathematics Teachers’ Mental Constructions of the Determinant Concept

Cited by 11 publications

References 1 publication

Misconceptions and resulting errors displayed by in service teachers in the learning of linear independence

Misconceptions and resulting errors displayed by in service teachers in the learning of linear independence

Undergraduate students’ conceptualization of elementary row operations in solving systems of linear equations

Subject competency and teacher knowledge: An exploration of second-year pre-service mathematics teachers’ difficulties in solving logarithmic problems using basic rules for logarithm

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