Teachers’ Knowledge of the Concept of a Function: A Theoretical Framework

Nyikahadzoyi, Maroni Runesu

doi:10.1007/s10763-013-9486-9

Cited by 28 publications

(47 citation statements)

References 6 publications

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“…Ball (1990) states that, "Examining a specific topic also makes more vivid the contrast between some key characteristics of what pre-service teachers have learned as students and what they need to know as teachers" (p. 451). Functions are central to many topics in mathematics (Dubinsky & Wilson, 2013;Nyikahadzoyi, 2013) and are fundamental to the study of further mathematics and related subjects such as Physics (Even, 1998;Watson & Harel, 2013). However, research has shown that students do not find functions easy (Bloch, 2003;Spyrou & Zagorianakos, 2010), and while they may understand procedures and structures, conceptual insight is scarce.…”

Section: Introductionmentioning

confidence: 99%

Dysfunctional Functions: The Case of Zambian Mathematics Education Students

Malambo

Putten

Botha

et al. 2018

EURASIA J MATH SCI T

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This study investigated student mathematics teachers' ability to recognise and explain their understanding of school level functions. We challenged the assumption that studying advanced mathematics automatically develops an understanding of school mathematics that is sufficient to explain concepts and justify reasoning. This case study tested this assumption by exploring the depth of pre-service mathematics student teachers' understanding of school function concepts at the University of Zambia. The test items required calculation, as well as justification of the answers, and an explanation of the concepts. Of the 22 participants, all final year mathematics education students, 18 student teachers scored below the 50% pass mark. The average mark was 8 out of a possible 28 (27%). The majority of the participants found it difficult to explain and justify their reasoning. This study resulted in the development of a new school mathematics module for prospective mathematics teachers at the University of Zambia.

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Section: Introductionmentioning

confidence: 99%

Dysfunctional Functions: The Case of Zambian Mathematics Education Students

Malambo

Putten

Botha

et al. 2018

EURASIA J MATH SCI T

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“…In this study it was possible to categorise the errors made by students at the rural and urban schools using Dufresne (2012)'s eight categories.  Drawing from the review of related literature (Gardee & Brodie, 2015, Error Pattern Analysis, n.d;Nyikahadzoyi, 2013), errors made by the students in the test could be rectified.…”

Section: Resultsmentioning

confidence: 99%

A Critical Analysis of Errors Made by Rural and Urban Students in ‘O’ Level Mathematics Paper 1 (4008/1) in Shurugwi and Gweru Districts, Zimbabwe

Chirume

2017

AJEEL

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ABSTRACT----This study critically investigated and analysed mathematical errors made by forty rural and urban Zimbabwe Ordinary Level students who wrote a test adopted from the ZIMSEC 2012 past examination paper (4008/1). Twenty students at a rural school in Shurugwi District and twenty students of similar characteristics (except for location or district) at an urban school in Gweru District were randomly sampled. Questions 1 and 7 (arithmetic and algebraic manipulations), 2 and 21 (psychomotor skills-measurement, shading, locus and geometric constructions) and 8 and 15 (word problems) were purposively sampled and students' written and marked scripts were subjected to a critical analysis of errors. The errors were classified into eight categories proposed by Dufresne (2012) and these were error in knowledge, error in skill, error in concept, error in making connections, error in strategy effectiveness, error in convention, error in process and error in format. Mixed methods (QUAL-quan, content and interpretivist) analyses of errors made by the rural students and those made by the urban students were made. The study offers possible strategies that teachers in rural and urban areas can use to rectify students' mathematical errors in the classroom situation and contributes to the body of knowledge on mathematical error analysis.

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“…While the MKT framework was eloborated in this study, Ball et al (2008), Nyikahadzoyi (2015), and Steel et al's (2013) studies were considered. After Ball and her collegues developed the MKT framework, Nyikahadzoyi (2015) and Steel et al (2013) adapted and developed the MKT framework by specializing in the concept of function.…”

Section: Figure 1 Domains Of Mkt Framework (Adapted Frommentioning

confidence: 99%

“…After Ball and her collegues developed the MKT framework, Nyikahadzoyi (2015) and Steel et al (2013) adapted and developed the MKT framework by specializing in the concept of function. Nyikahadzoyi (2013) and Steel et al's (2013) eloborated Ball and her collegues ideas regarding the MKT framework to identify the components of what constitutes teachers' knowledge for teaching of the concept of function.…”

Section: Figure 1 Domains Of Mkt Framework (Adapted Frommentioning

confidence: 99%

“…Nyikahadzoyi (2013) and Steel et al's (2013) eloborated Ball and her collegues ideas regarding the MKT framework to identify the components of what constitutes teachers' knowledge for teaching of the concept of function. For instance, Nyikahadzoyi (2015) indicated that teachers, who have SCK, should know the different definition and representations of a function, be able to choose the neccessary representation for particular purposes and concepts, have a great collection of neat examples, know the importance of the topic in relation to the whole subject and be able to explain this to the students, and conceive a function as a procedure, process, object, or procept (s. 268). While Steele et al (2013) defined the components of SCK, they also focused on the importance of definition, using multiple representation and being able to felxibly move them.…”

Section: Figure 1 Domains Of Mkt Framework (Adapted Frommentioning

confidence: 99%

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Examination of Pre-Service Mathematics Teachers’ Knowledge of Teaching Function Concept

Taşdan¹,

Koyunkaya²

2017

ADN

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Abstract:Teaching of mathematics could be improved with teachers who have a strong mathematical knowledge and have an ability to reflect this knowledge on their teaching. Therefore, it is important to develop mathematics teachers' theoretical and pedagogical knowledge. This study was designed to examine pre-service secondary mathematics teachers' (PSMT) mathematical knowledge for teaching (MKT) in terms of function concept. In order to examine PSMT's MKT regarding function concept, case study design was used in the study. Three PSMTs', who were at the fifth year in the program, were selected as the participants. The data was collected by observing and recording PSMTs' teaching of function concept as well as by examining their lesson plan of the concept. Descriptive and content analysis were used to analyze the collected data. The results revealed that PSMTs' had limited knowledge regarding teaching of function concept. Particularly, they had difficulties to reflect their knowledge of function concept on their teaching. The results also showed that experience is directly related to teaching of function concept, time and classroom management and communication with students. Therefore, it is important to improve both in-service and pre-service teachers' MKT by considering the effect of experience and abilities in teaching.

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Teachers’ Knowledge of the Concept of a Function: A Theoretical Framework

Cited by 28 publications

References 6 publications

Dysfunctional Functions: The Case of Zambian Mathematics Education Students

Dysfunctional Functions: The Case of Zambian Mathematics Education Students

A Critical Analysis of Errors Made by Rural and Urban Students in ‘O’ Level Mathematics Paper 1 (4008/1) in Shurugwi and Gweru Districts, Zimbabwe

Examination of Pre-Service Mathematics Teachers’ Knowledge of Teaching Function Concept

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