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All Journal Journal of Research and Advances in Mathematics Education JRAMathEdu (Journal of Research and Advances in Mathematics Education)
Malambo, Priestly
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Education Mathematics

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Pre-service mathematics teachers’ nature of understanding of the tangent function Malambo, Priestly
JRAMathEdu (Journal of Research and Advances in Mathematics Education) Volume 5 Issue 2 June 2020
Publisher : Department of Mathematics Education, Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/jramathedu.v5i2.10638

Abstract

Mathematics teachers’ ability to translate and make connections between representations of functions requires investigation. Consequently, this qualitative case study article focuses on pre-service mathematics teachers’ nature of understanding of the tangent function; a function bearing unique characteristics compared with the sine and cosine functions. Twenty-two finalist pre-service teachers were conveniently selected and assessed concerning the ability to translate a tangent function to the graphical representation. Likewise, participants’ abilities to correctly explain this function and provide appropriate justifications for espoused perspectives were investigated. Although the teachers learned higher mathematics, their assessment was school mathematics-based. Descriptive analyses showed that only one teacher (5%) accurately completed the task. Eleven teachers (50%) did not provide graphs; suggesting a lack of knowledge required to change representation. Ten (45%) drew flawed graphs depicting a lack of understanding of discontinuity of the tangent function at certain angles and the role of a domain. Essentially, these demonstrated mere memorization of the appearance of the tangent graph. A purposive sub-sample of size six then participated in exploratory semi-structured interviews. The interviews allowed participants to elucidate their answers to the initial task. Content analysis of the transcripts corroborated the earlier finding as the interviewees could not coherently explain the tangent function, and failed to justify their reasoning. The teachers demonstrated a superficial understanding despite having studied advanced mathematics. This reinforces the view that studying advanced mathematics does not assure a relational understanding of school mathematics. Therefore, it is necessary for trainee teachers to explore school mathematics.
Consequential implications of mathematics student teachers’ definitions of the function concept Malambo, Priestly
JRAMathEdu (Journal of Research and Advances in Mathematics Education) Volume 7 Issue 4 October 2022
Publisher : Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/jramathedu.v7i4.17146

Abstract

This article reports consequential implications of mathematics student teachers’ definitions of the function concept. The implications emanated from scrutiny of written definitions, and exploration of demonstrated ability to identify functions and translate them into different representations. A qualitative study characterized by a case study design was conducted. Four student teachers of mathematics education at a public university constitute the sample. Whereas the study site was conveniently chosen, the participants were a sub-sample in the principal study selected using extreme case strategy. Data were collected through semi-structured interviews preceded by student teachers’ written definitions of the function concept. Explorations of the written work and interview transcripts suggest that the student teachers’ definitions of a function were dominated by a narrow view that all functions are one-to-one relations. Notwithstanding, the participants’ conception of one-to-one functions was superficial. The student teachers’ flawed definitions of a function influenced their inability to correctly identify functions. Likewise, those definitions were consistent with the student teachers’ incapacity to translate functions accurately from one kind of representation into another. These findings underscore the necessity for mathematics teacher educators to facilitate student teachers’ development of correct definitions and appropriate concept images of the function concept.
Pre-service mathematics teachers’ nature of understanding of the tangent function Malambo, Priestly
JRAMathEdu (Journal of Research and Advances in Mathematics Education) Volume 5 Issue 2 June 2020
Publisher : Lembaga Pengembangan Publikasi Ilmiah dan Buku Ajar, Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/jramathedu.v5i2.10638

Abstract

Mathematics teachers’ ability to translate and make connections between representations of functions requires investigation. Consequently, this qualitative case study article focuses on pre-service mathematics teachers’ nature of understanding of the tangent function; a function bearing unique characteristics compared with the sine and cosine functions. Twenty-two finalist pre-service teachers were conveniently selected and assessed concerning the ability to translate a tangent function to the graphical representation. Likewise, participants’ abilities to correctly explain this function and provide appropriate justifications for espoused perspectives were investigated. Although the teachers learned higher mathematics, their assessment was school mathematicsbased. Descriptive analyses showed that only one teacher (5%) accurately completed the task. Eleven teachers (50%) did not provide graphs; suggesting a lack of knowledge required to change representation. Ten (45%) drew flawed graphs depicting a lack of understanding of discontinuity of the tangent function at certain angles and the role of a domain. Essentially, these demonstrated mere memorization of the appearance of the tangent graph. A purposive subsample of size six then participated in exploratory semi-structured interviews. The interviews allowed participants to elucidate their answers to the initial task. Content analysis of the transcripts corroborated the earlier finding as the interviewees could not coherently explain the tangent function, and failed to justify their reasoning. The teachers demonstrated a superficial understanding despite having studied advanced mathematics. This reinforces the view that studying advanced mathematics does not assure a relational understanding of school mathematics. Therefore, it is necessary for trainee teachers to explore school mathematics.
Consequential implications of mathematics student teachers’ definitions of the function concept Malambo, Priestly
JRAMathEdu (Journal of Research and Advances in Mathematics Education) Volume 7 Issue 4 October 2022
Publisher : Lembaga Pengembangan Publikasi Ilmiah dan Buku Ajar, Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/jramathedu.v7i4.17146

Abstract

This article reports consequential implications of mathematics student teachers’ definitions of the function concept. The implications emanated from scrutiny of written definitions, and exploration of demonstrated ability to identify functions and translate them into different representations. A qualitative study characterized by a case study design was conducted. Four student teachers of mathematics education at a public university constitute the sample. Whereas the study site was conveniently chosen, the participants were a sub-sample in the principal study selected using extreme case strategy. Data were collected through semi-structured interviews preceded by student teachers’ written definitions of the function concept. Explorations of the written work and interview transcripts suggest that the student teachers’ definitions of a function were dominated by a narrow view that all functions are one-toone relations. Notwithstanding, the participants’ conception of one-toone functions was superficial. The student teachers’ flawed definitions of a function influenced their inability to correctly identify functions. Likewise, those definitions were consistent with the student teachers’ incapacity to translate functions accurately from one kind of representation into another. These findings underscore the necessity for mathematics teacher educators to facilitate student teachers’ development of correct definitions and appropriate concept images of the function concept.
Consequential implications of mathematics student teachers’ definitions of the function concept Malambo, Priestly
JRAMathEdu (Journal of Research and Advances in Mathematics Education) Volume 7 Issue 4 October 2022
Publisher : Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/jramathedu.v7i4.17146

Abstract

This article reports consequential implications of mathematics student teachers’ definitions of the function concept. The implications emanated from scrutiny of written definitions, and exploration of demonstrated ability to identify functions and translate them into different representations. A qualitative study characterized by a case study design was conducted. Four student teachers of mathematics education at a public university constitute the sample. Whereas the study site was conveniently chosen, the participants were a sub-sample in the principal study selected using extreme case strategy. Data were collected through semi-structured interviews preceded by student teachers’ written definitions of the function concept. Explorations of the written work and interview transcripts suggest that the student teachers’ definitions of a function were dominated by a narrow view that all functions are one-to-one relations. Notwithstanding, the participants’ conception of one-to-one functions was superficial. The student teachers’ flawed definitions of a function influenced their inability to correctly identify functions. Likewise, those definitions were consistent with the student teachers’ incapacity to translate functions accurately from one kind of representation into another. These findings underscore the necessity for mathematics teacher educators to facilitate student teachers’ development of correct definitions and appropriate concept images of the function concept.
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