Pre-service mathematics teachers’ mental constructions when using Cramer’s rule

Ndlovu, Zanele; Brijlall, Deonarain

doi:10.15700/saje.v39n1a1550

Cited by 9 publications

(6 citation statements)

References 12 publications

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“…This showed that these students understood the concepts as isolated facts and just memorized some rules which were not connected. This hampered the development of the required schema as mentioned by Ndlovu and Brijlall (2019) that university students only master a collection of algorithms which does not lead to a deeper understanding of the concepts.…”

Section: 𝑐 𝑑mentioning

confidence: 99%

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: 𝑐 𝑑mentioning

confidence: 99%

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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“…This represents a gap in literature which this study sought to fill. However, APOS studies were conducted in students' learning other concepts, for example, the Cramer's rule (Ndlovu & Brijlall, 2019), eigenvectors (Salgado & Trigueros, 2015), derivatives (Maharaj, 2013;Moru, 2020), trigonometric ratios and their inverses (Martínez-Planell & Delgado, 2016), the inverse matrix method (Kazunga & Bansilal, 2020), and others.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The main issue in this paper is how undergraduate students conceptualise learning of the Binomial series expansion. Students' mental structures are a key determinant of the extent to which they learn specified topics in mathematics (Ndlovu & Brijlall, 2019). I assume that a fully developed schema in a given topic has the potential to assist students to answer any given question in that topic and to apply what they would have learnt to unfamiliar contexts.…”

Section: Introductionmentioning

confidence: 99%

Mathematics Education Students’ Understanding of Binomial Series Expansion Based on the APOS Theory

Tatira

2021

EURASIA J Math Sci Tech Ed

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Undergraduate students study the topic of binomial series expansion as part of their Calculus course. The purpose of this study was to explore the mental constructions of binomial series expansion of a class of 159 students. Data were collected through a written assessment task by each member of the class. A convenient sample of eleven students from the class was selected to undertake semi-structured interviews. The Action-Process-Object-Schema theory which was used depicts development of understanding of mathematics concepts through the hierarchical growth of mental constructions. Students in the study coped well with questions requiring action-level engagements but grappled with those calling for higher-level mental constructions, namely, processes and objects. Developing an object conception for a mathematical concept is the pinnacle for all teaching but also the most difficult to develop. Thus, this study underlines the significance of helping students construct object conceptions in binomial series expansion.

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“…As a teaching method, the theory is used to design activities for the teaching of a mathematical concept and to examine the mental structures of students after the implementation of these activities (Trigueros & Martinez-Planell, 2010). As seen in the related literature, although the APOS Theory is mostly used for data analysis (Bansilal, 2011;Brijlall & Maharaj, 2015;Brijlall & Ndlazi, 2019;Chimhande, Naidoo, & Stols, 2017;Martinez-Planell, Gaisman, & McGee, 2017) and as a teaching method (Martin, Loch, Cooley, Dexter, & Vidakovic, 2010;Possani, Trigueros, Preciado, & Lozano, 2010), it is also possible to find studies in which the APOS Theory was used for both purposes (Figueroa, Possani, & Trigueros, 2018;Maharaj, 2013;Moon, 2019;Ndlovu & Brijlall, 2019;Trigueros & Possani, 2013). In summary, the APOS Theory can be used for data analysis, as a teaching method, or both.…”

Section: The Purpose Of Using the Apos Theorymentioning

confidence: 99%

Content Analysis of the APOS Theory Studies on Mathematics Education Conducted in Turkey and Internationally: A Meta-Synthesis Study

ŞEFİK

UZUN

Dost

2021

Necatibey Eğitim Fakültesi Elektronik Fen Ve Matematik Eğitimi Dergisi

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This study aimed to review the APOS Theory, which was developed within the context of conceptual understanding as one of the main aims of mathematics education, studies in the field of mathematics education.The studies with Turkey and international samples related to the APOS Theory were subjected to descriptive content analysis, and a systematic summary was presented. As a result of the analysis, three themes, namely the purpose of using the theory, the use of genetic decomposition, and the aim of the study were identified. There are descriptive studies (39%) in the literature that determine the mental structures and mechanisms rather than the structure of mathematical concepts. Such studies are weak in terms of the theory's aim of reinforcing conceptual understanding.

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Pre-service mathematics teachers’ mental constructions when using Cramer’s rule

Cited by 9 publications

References 12 publications

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

Mathematics Education Students’ Understanding of Binomial Series Expansion Based on the APOS Theory

Content Analysis of the APOS Theory Studies on Mathematics Education Conducted in Turkey and Internationally: A Meta-Synthesis Study

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