Browsing by Author "Gierdien, Faaiz"

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    Educating Grade 6 students for higher-order thinking and its influence on creativity
    (AOSIS Publishing, 2017) Daher, Wajeeh; Tabaja-Kidan, Amal; Gierdien, Faaiz
    Educating students for higher-order thinking provides them with tools that turn them into more critical thinkers. This supports them in overcoming life problems that they encounter, as well as becoming an integral part of the society. This students’ education is attended to by educational organisations that emphasise the positive consequences of educating students for higher-order thinking, including creative thinking. One way to do that is through educational programmes that educate for higher-order thinking. One such programme is the Cognitive Research Trust (CoRT) thinking programme. The present research intended to examine the effect of the participation of Grade 6 students in a CoRT programme on their creative thinking. Fifty-three students participated in the research; 27 participated in a CoRT programme, while 26 did not participate in such programme. The ANCOVA test showed that the students who participated in the CoRT programme outperformed significantly, in creative thinking, the students who did not. Moreover, the students in the CoRT programme whose achievement scores were between 86 and 100 outperformed significantly the other achievement groups of students. Furthermore, students with reported high ability outperformed significantly the other ability groups of students. The results did not show statistically significant differences in students’ creativity attributed to gender.
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    From ‘proofs without words’ to ‘proofs that explain’ in secondary mathematics
    (AOSIS Publishing, 2007-06) Gierdien, Faaiz
    The purpose of this paper is to explore an epistemic role for visualisation with respect to proofs without words in secondary mathematics in the current South African education policy context. Visualisation as process and product can be a means to examining proofs without words by turning them into proofs that explain. In this way students can develop insights and explanations for the mathematics they encounter in the secondary curriculum. The proofs without words chosen are those that show analytic and visual representations of series and sequences. In the secondary curriculum series and sequences are mainly represented analytically. It will be shown that a thoughtful interpretation and explanation through visualisation of such proofs without words connects different strands in the bureaucratically stated secondary curriculum found in the policy document (Department of Education, 2003). There is more mathematics embedded and ‘unseen’ in these proofs without words.
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    Keeping sites in sight : conversations with teachers about the design of toolkits peculiar to a continuous professional development initiative
    (AOSIS, 2019-03) Gierdien, Faaiz; Smith, Charles Raymond; Julie, Cyril
    The aim of this article is to shift the notion of ‘sites’ as places of work peculiar to continuous professional development (CPD) to a theoretical level, independent of, yet intimately connected to, their physical meanings, for example universities and schools. Most CPD initiatives have to contend with at least one of these two sites, in which university-based mathematics educators and school teachers can have different and at times overlapping ways of talking about the same mathematics. Using research on number and operations, non-visually salient rules in algebra and algebraic fractions, and analytic tools and notions peculiar to conversation analysis and ethnomethodology, the authors identify and analyse site-related issues in the design of particular problem sets in Grade 8 and Grade 9 toolkits and related conversations between a mathematics educator and participating teachers. The article concludes with the implications of ‘keeping in sight’ ways in which universities and schools talk and work when it comes to designing and discussing toolkits.
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    On the use of spreadsheet algebra programmes in the professional development of teachers from selected township high schools
    (Taylor & Francis, 2014) Gierdien, Faaiz
    This paper reports on the initial stages of a small-scale project involving the use of ‘spreadsheet algebra programmes’ (SAPs) in the professional development of eight teachers from three township high schools. In terms of the education context, the paper draws on social practice theory. It then details what is meant by spreadsheet algebra. An analysis of teacher conversations and artefacts generated during an in-service workshop is conducted which takes into account the education context and two practices – the teachers’ pencil-paper algebra and the mathematics teacher educator’s spreadsheet algebra. Implications for professional development are considered, especially the teachers’ strategies with respect to the ‘top down’ imposition of the curriculum in terms of patterns and functions.
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    Pre-service teachers’ views about their mathematics teacher education modules
    (AOSIS Publishing, 2012-07) Gierdien, Faaiz
    This article reports on the views of intermediate and senior phase pre-service teachers (PSTs) enrolled in mathematics education modules that attempt to teach both content and pedagogy. The PSTs are students in a four-year Bachelor of Education (BEd) model located in a faculty of education. Findings were analysed by means of an analytic framework that takes into account the university–school divide. Findings indicate that the PSTs position themselves in different ways with regard to their preparation for school mathematics teaching. Implications are considered, especially the PSTs’ affective views such as their anxiety and apprehension related to the discursive differences between the content in the university modules and school mathematics.
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    Self study as a mechanism to foster hopeful teaching
    (SUN MeDIA, 2012) Gierdien, Faaiz
    Teaching mathematics education to pre-service teachers (PSTs) enrolled at university is problematic, due to their lack of agreement about the extent to which they are prepared for teaching school mathematics. Pre-service preparation in South Africa currently occurs in the university, which impacts on the teaching of mathematics education. Noting such a context for teacher education, with its attendant dilemmas, this chapter attempts to present and explore a theoretical basis for helping us to understand what it means to teach mathematics education in such a context. I argue that such a theoretical basis is useful, providing perspectives on the practices of mathematics educators in the light of calls for teaching for the public good. The chapter takes the form of an analysis of selected excerpts of PSTs’ views of my teaching of mathematics education in a four-year Bachelor of Education (B.Ed) programme. There are a growing number of university-based science and mathematics educators who study their teaching; ie they engage in selfstudy. The question considered is: what might teaching for the public good of mathematics education in pre-service preparation at a university be like?
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    Self-efficacy in creativity and curiosity as predicting creative emotions
    (Universitas Muhammadiyah Surakarta, 2021) Daher, Wajeeh; Gierdien, Faaiz; Anabousy, Ahlam
    Self-efficacy constructs could predict students’ practices and affect in learning the sciences. Researchers have pointed at such constructs as predictors of students’ mathematics achievement and performance. Self-efficacy was also studied as predictor of emotions in learning mathematics, though little research has done so regarding self-efficacy as predictor of creative emotions. Another predictor of creative emotions could be curiosity. The present study has a regression-based modelling design, where it examined whether a set of constructs of self-efficacy in creativity or/and a set of constructs of curiosity predict significantly creative emotions in mathematical problem solving. Five hundred Grade 8-10 students participated in the study. Data were collected using three self-report questionnaires that measured the research constructs. Data analysis used SPSS 21. Results from multiple regression indicated that the set of constructs of self-efficacy in creativity explained significantly 29.6% of the variance in creative emotions. Moreover, the set of constructs of curiosity explained 17.8% of the variance in creative emotions. Furthermore, three of the five independent variables had best prediction of creative emotions, explaining 32.9% of the variance in creative emotions. The results of the stepwise regression showed that self-efficacy in originality and stretching curiosity were the first two variables in a set of three variables that best explained the variance in creative emotions. The research results lead to the recommendation of developing the previous two constructs in classroom setting to cultivate students’ creative emotions and thus their creative practices.
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    Use of Language By generative AI Tools in Mathematical Problem Solving: The Case of ChatGPT
    (Taylor & Francis, 2024-08-18) Daher, Wajeeh; Gierdien, Faaiz
    Texts generated by artificial intelligence agents have been suggested as tools supporting students’ learning. The present research analyses the language of texts generated by ChatGPT when solving mathematical problems related to the quadratic equation. We use the functional grammar theoretical framework that includes three meta-functions: the ideational meta-function, the interpersonal meta-function and the textual meta-function. The results indicated that in at least one of six problem-solving tasks ChatGPT provided a mathematically incorrect answer. The processes appearing in ChatGPT texts, aiming at developing students’ understanding of mathematical concepts, included verbal, mental, existential, relational and behavioural processes but no material processes. Specifically, ChatGPT performed a mathematically incorrect existential process. ChatGPT generally used the first plural pronoun ‘we’ when describing the processes of solving mathematical problems, while it generally used the first-person singular pronoun when taking responsibility for a specific mistake or when expressing happiness for the actions of the user. Moreover, generally the text of the solution did not include direct imperatives but used ‘let us do’. The advancement of the ChatGPT textual solution was made usually through steps like ‘first’, ‘second’, etc. The research results indicated that the way ChatGPT responded to the mathematical problems would be useful in supporting learners’ understanding of ways to solve quadratic equations, but only if the teacher critically accompanies the student in the problem-solving process. Self-study with ChatGPT could lead to or confirm students’ mathematical misconceptions.