An APOS study on pre-service teachers’ understanding of injections and surjections

Bansilal, Sarah; Brijlall, Deonarain; Trigueros, María

doi:10.1016/j.jmathb.2017.08.002

Cited by 23 publications

(12 citation statements)

References 14 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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“…Other research focuses on specific aspects of the function concept and not on functions in general. Bansilal, Brijlall and Trigueros (2017) explored pre-service teachers' understanding of injections and surjections through an APOS study. They found that most participants were at the action level.…”

Section: Conceptual Difficulties Of the Function Conceptmentioning

confidence: 99%

Learning the function concept by exploring digital images as functions

Venter¹

2020

Pythagoras

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Despite the function concept being fundamental to mathematics, an adequate understanding of this concept is often lacking. This problem is prevalent at all levels of education and is reported in many countries. This article reports on a new pedagogical strategy based on exploring photographs or digital images as functions. The objective of this study was to determine if the Image Functions Intervention (IFI) could be considered sound and viable with respect to the learning of the function concept. A two-part approach was used. The first part used the Action-Process-Object-Schema (APOS) theory as a theoretical framework for evaluating the IFI. The second part implemented the IFI with a group (n = 27) of undergraduate students, followed by qualitative analysis of questionnaire data in order to look for indications of participants experiencing broadened thinking with respect to the function concept. The theoretical evaluation confirmed the IFI to be sound and providing opportunities for addressing common conceptual difficulties of the function concept. The qualitative analysis provided evidence of the participants’ expanded concept images. It was concluded that the designed intervention, the IFI, is sound and viable and shows promise with respect to increased understanding of the function concept.

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“…Similarly, research demonstrates that pre-service teachers have difficulties in understanding and constructing proofs (Bansilal et al, 2017;Baştürk, 2010;Zeybek, 2015). These results suggest that teacher preparation programs should pay a careful attention to the proof understandings of pre-service mathematics teachers.…”

Section: Introductionmentioning

confidence: 96%

A Phenomenographic Investigation of Middle School Pre-service Mathematics Teachers' Conceptions of Proof

Akkurt

Yıldırım

2021

Necatibey Eğitim Fakültesi Elektronik Fen Ve Matematik Eğitimi Dergisi

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Özet -Öğretmen adaylarının matematiksel akıl yürütmeyi öğretme yetenekleri sahip oldukları ispat kavramlarının kalitesine bağlıdır. Bu nitel çalışma, ortaokul matematik öğretmen adaylarının ispat kavramlarına odaklanmaktadır. Bu amaçla, bu çalışma öğretmen adaylarının ispat deneyimlerindeki farklılıkları belirlemek için fenomenografik bir yaklaşım kullanmıştır. Yarı yapılandırılmış görüşmelerin analizi, niteliksel olarak farklı beş kategori ortaya çıkarmıştır. Buna göre, ispat (a) bir problem çözme yoludur, (b) anlamanın bir aracıdır, (c) düşünmeyi ikna edici bir şekilde açıklamaktır, d) mantıksal argümanlar kullanarak varsayımları doğrulamaktır ve (e) matematiğin keşfi için bir araçtır. Bu çalışma, ispat kavramlarıyla ilgili pedagojik bilgiye katkıda bulunmaktadır. Sonuçlar, matematik öğretmeni hazırlık programlarının kalitesini artırmak için kullanılabilir.

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An APOS study on pre-service teachers’ understanding of injections and surjections

Cited by 23 publications

References 14 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

Learning the function concept by exploring digital images as functions

A Phenomenographic Investigation of Middle School Pre-service Mathematics Teachers' Conceptions of Proof

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