Pre-service Teachers’ Mental Constructions of Concepts in Matrix Algebra

Ndlovu, Zanele; Brijlall, Deonarain

doi:10.1080/10288457.2015.1028717

Cited by 19 publications

(13 citation statements)

References 10 publications

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“…APOS studies have been conducted on pre-service high school Mathematics teachers' understanding of various concepts, but none on primary school teachers' knowledge (e.g. Bansilal, Brijlall & Trigueros 2017;Ndlovu & Brijlall 2015). In this article we will consider pre-service teachers' misconceptions that permeate from addition and subtraction of fractions using APOS theory.…”

Section: Introductionmentioning

confidence: 99%

Pre-service primary Mathematics teachers’ understanding of fractions: An action–process–object–schema perspective

Ubah

Bansilal

2018

South African Journal of Childhood Education

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This study was set up to apply Action-Process-Object-Schema theory to study primary teachers' understanding of addition and subtraction of fractions. Setting:The participants of this study comprised 60 undergraduate full-time students, studying to become teachers. The participants were enrolled in a foundational course in Mathematics because they had not passed Mathematics at Grade 12 level. This course was intended to help deepen their understanding of basic numeracy, allowing them to continue with further courses if they wanted to specialise in teaching primary mathematics Methods: Data were collected using written responses of the pre-service students to two tasks that focused on operations with fractions. Ten students volunteered to be interviewed of which three are drawn upon in this article.Results: Many of the pre-service teachers coped well with addition and subtraction of common fractions with the same denominator. However, more than 52% struggled to carry out these operations on common fractions with different denominators, showing that their conceptions had not developed into object-level structures. Conclusion:It is evident that the incorrect procedures have become embedded in the students mental schema. It is crucial that programmes for upgrading pre-service teachers should include opportunities for teachers to interrogate their personal understandings of the basic mathematics concepts.

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Section: Introductionmentioning

confidence: 99%

Pre-service primary Mathematics teachers’ understanding of fractions: An action–process–object–schema perspective

Ubah

Bansilal

2018

South African Journal of Childhood Education

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“…The interiorization in the action process was to imagine the solving stages implicitly [18]. It was in line with [41]. The study found that solving process was still inside of the mind.…”

Section: Resultsmentioning

confidence: 80%

The spatial thinking process of the field-dependent students in reconstructing the geometrical concept

Bintoro

Sukestiyarno²,

Mulyono³

et al. 2022

IJERE

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<p><span lang="EN-US">Reconstructing geometrical concepts requires a spatial thinking process, so the spatial thinking process will be correct and complete. The phenomena of cognitive style differences cause different perceptions and thinking activities to solve geometric problems. This qualitative-explorative research describes the spatial thinking process of students with field-dependent cognitive styles in reconstructing the concept of spatial geometry based on the theory of Action-Process-Object-Schema (APOS). The research subjects were 27 students and obtained five students with field-dependent cognitive styles. The researchers used a purposive sampling technique from the subjects with a certain consideration. The researchers selected a student that met the three elements of spatial thinking and the five indicators of spatial ability. This research collected the data with interviews, documentation, and group embedded figure test (GEFT). The analyzing techniques used data collection, data reduction, data presentation, and concluding. The spatial thinking process of the field-dependent students had a spatial category with three indications: i) Inaccuracy in the elements of representational thinking; ii) The inaccuracy of spatial perception indicators; and iii) Not using de-encapsulation mental mechanisms.</span></p>

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“…Figure 1 illustrates the proposed preliminary genetic decomposition of the concept of the quadratic equations according to APOS theory. If the differences in students' performance cannot be explained by the genetic decomposition that would imply that the genetic decomposition needs revision (Ndlovu & Brijlall, 2015).…”

Section: Genetic Decompositionmentioning

confidence: 99%

“…According to (Dubinsky and Harel, 1992), Ten is operating at Pre-function level. This level is not contained in the preliminary genetic decomposition, hence the need to come up with a modified genetic decomposition as substantiated by Ndlovu and Brijlall (2015). Ndlovu and Brijlall propounded that if differences in student performance cannot be explained by the genetic decomposition, then that would be implying that the genetic decomposition needs revision.…”

Section: Vertex Form Of a Quadratic Functionmentioning

confidence: 99%

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Exploring the Conceptual Understanding of the Quadratic Function Concept in Teachers’ Colleges in Zimbabwe

Mutambara

Tendere²,

Chagwiza

2019

EURASIA J MATH SCI T

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This paper reports on an exploration of preservice teachers' understanding of the quadratic function concept in Zimbabwe. These concepts were taught to preservice teachers studying for a diploma in Education wishing to specialize in the teaching of Ordinary level mathematics. Concerns about high Mathematics failure rate in Zimbabwean Secondary Schools have prompted this investigation into finding out if teachers' understanding of quadratic function concept could be the cause. The study adopted the APOS (action-process-object-schema) to investigate their conceptual understanding of the concepts. Data were generated from students' responses to a written task and follow up interviews were used to solicit information from the preservice teachers. A designed genetic decomposition for quadratic concepts was used as an analysis tool. The findings of the study also revealed majority of the preservice teachers seemed to be operating at the action level of understanding, with very few teachers who have reached the object level. It was noted that the preliminary genetic decomposition failed to accommodate all students' responses which lead to the development of a modified genetic decomposition.

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Pre-service Teachers’ Mental Constructions of Concepts in Matrix Algebra

Cited by 19 publications

References 10 publications

Pre-service primary Mathematics teachers’ understanding of fractions: An action–process–object–schema perspective

Pre-service primary Mathematics teachers’ understanding of fractions: An action–process–object–schema perspective

The spatial thinking process of the field-dependent students in reconstructing the geometrical concept

Exploring the Conceptual Understanding of the Quadratic Function Concept in Teachers’ Colleges in Zimbabwe

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