1,720,957 research outputs found
Using diffusion of innovation theory to understand how technology is adopted in mathematics at a South African higher education institution
No full textThe issue of students enrolling who are ill prepared in mathematics for university studies has been an area of concern for some time in South Africa. Various universities tried different interventions to address this problem. One example is the establishment of a bridging programme at an institution of higher learning. Technology has been discussed as support that can be provided to students. This study therefore sought to understand the adoption of technology in the teaching of mathematics at an institution of higher education in South Africa. Using Roger's diffusion of innovation theory, this study sought to understand how technology is adopted by mathematics teachers in the bridging programme. Whilst the results of the study show that some teachers have adopted technology at different scales to provide access, to supplement instruction and to encourage interaction, the results also show that some teachers are uncertain of the benefits that technology has to teaching and learning in the programme. The current talk and chalk method is seen as being essential as it is tried and tested. The study also showed that teachers did not receive support from the institution resulting in them seeking assistance from outside of the university. The study recommends that higher education institutions should provide instructional design support to ensure that teachers are not overburdened with developing technology interventions where they have little or no expertise in
High-school students' productive struggles during the simplification of trigonometrical expressions and the proving of trigonometrical identities
Get PDFThis study is an investigation into school students' productive struggles in the simplification of trigonometric expressions and proving of trigonometric identities. Although studies have been published on the teaching and learning of trigonometrical concepts in schools and teacher education, there is a lack of published research into students' productive struggles in the simplification of trigonometric expressions and proving of trigonometric identities. To fill this gap in the literature, this study used a sample of 16- and 17-year-old students at a rural high school in South Carolina in the United States of America to conduct a study on the use of productive struggles in the simplification of trigonometric expressions and the proving of trigonometric identities. The study used the Anthropological Theory of the Didactic by Chevallard (1992) as the main theoretical framework. However, this main framework was supported by other frameworks. The Anthropological Theory of the Didactic contends that mathematical activities such as simplifying trigonometric expressions and proving trigonometric identities must be interpreted as a human activity rather than seeing these mathematical activities as a language, the creation of concepts (for example, “simplification” or “proof”) or a cognitive process. A praxeology consists of two parts, namely (in Greek) the praxis, or “know how”, and the logos, or “know why”. The praxis is commonly known as the practical block, and the logos the theoretical block. This means that the Anthropological Theory of the Didactic can be used to describe how certain actions regarding the simplification of trigonometric expressions and proving of trigonometric identities take place, and why these actions take place. The exercises in the activities were obtained and adapted from the students' prescribed textbook. These activity questions were sequenced using the Development Cognitive Abilities Test (DCAT). The DCAT reflects Bloom's (1956) hierarchy of cognitive abilities. This means that the exercises were organised in three groups of increasing complexity, i.e., easy, medium, and difficult. The easy exercises related to the DCAT's Basic Cognitive Abilities, referred to as DCAT 1; the medium exercises related to Application Abilities, referred to as DCAT 2; and the difficult exercises related to Critical Thinking Abilities, referred to as DCAT 3. The data in this study consists of video recordings from classroom observations in real time transcribed verbatim, documentary analysis of students' assessments, and audio-recorded focus group interviews. The focus group interviews were also transcribed verbatim. Each transcription focused on a different aspect of the students' productive struggles in the simplification of trigonometric expression and the proving of trigonometric identities. Errors made by the students in written assessments were analysed using the Newman Error Analysis framework. By using Newman Error Analysis, this study could investigate and compare how the errors on the assessments were related to the students' struggles as observed during the teaching and learning of the activity questions. Due to Co-Vid 19 restrictions that resulted in logistical difficulties, only one class of 15 students participated in this study. After listening to the focus group recordings numerous times and reading the transcripts, common patterns were noted that had emerged, either from paraphrasing or from direct quotes. The primary research question is: What is the nature of the productive struggles experienced by high-school students during the simplification of trigonometric expressions and proving of trigonometric identities and how do these productive struggles influence the learning and teaching of trigonometry? The study findings were that the students struggled with “carrying out known mathematical processes” such as manipulating equations, knowing under what conditions cancellation of terms can be applied, adding and subtracting algebraic fractions involving trigonometric expressions, and factorisation of trigonometric expressions. In addition, there were misconceptions about the concept of “simplification”. Delayed impasse struggles occurred; this is when a student does not initially struggle to get started with a question, but the struggling becomes apparent as the student progresses with the question. The students committed fewer Newman errors in proving trigonometric identities than in the simplification of trigonometric expressions. Subsequently, students performed better at proving trigonometric identities than at simplifying trigonometric expressions. It could well be that through productive struggles, the students developed some of their own strategies from the simplification of trigonometric expressions. Alternatively, proving identities could be seen as “easier”, since the students already know what the “answer” should be. Nonetheless, students still struggled to carry out common mathematical processes such as factorisation and the manipulation of algebraic fractions. Regarding factorisation and manipulation of algebraic fractions, students compartmentalised knowledge. For example, most students knew how to factorise algebraic expressions, but failed to see the resemblance between algebraic expressions and trigonometric expressions (and consequently, how to factorise trigonometric expressions). Although there was a decrease in the number of Newman errors from the simplification of trigonometric expressions to the proving of trigonometric identities, there was an increase at the comprehension hierarchy, which may be attributed to the fact that the students might have struggled with the concept of “proof”. Additionally, students in this study struggled with the concept of “simpler”. Some students thought that the solution to a simplification question should be more complex than the original question. Nonetheless, with both the simplification of trigonometric expressions and the proving of trigonometric identities it remained a challenge for the students to apply prior knowledge in a new mathematical context such as trigonometry. The significance of the study's findings is that they suggest that teachers re-evaluate how to instruct known mathematical processes and procedures, so as not to compartmentalise mathematical knowledge. Productive struggles may not always produce correct answers; but given sufficient time and appropriate intervention by their teacher, students can build their own knowledge and become independent thinkers who can apply prior knowledge in new contexts such as the simplification of trigonometric expressions and the proving of trigonometric identities. In future research, productive struggles in the simplification of trigonometric expressions and the proving of trigonometric identities should be explored with a bigger, more diverse group of students, taught by more than one teacher at more than one school. In addition, to investigate the long-term effects of productive struggles a study lasting more than six months could be carried out
School-based mathematics teacher professional learning: A theoretical position on the lesson study approach
Get PDFThis theoretical paper focuses on how school-based continuous professional development (CPD) for mathematics teachers in schools located in disadvantaged areas can be carried out using the lesson study approach. School-based CPD is based on the notion that teachers need real-time and on-site professional training tailored to improve the instructional practices unique to their school and classroom contexts. The paper seeks to address the research question: How can a lesson study [or research lesson] be used in the school-based CPD of mathematics teachers in schools located in disadvantaged areas? Empirical evidence from lesson study research suggests that it is an effective tool for CPD activities because it is school-centred, focuses on learner learning, and draws on the collective and collaborative experiences of teachers working in the same school mathematics department. Therefore, this paper significantly contributes to theoretical and practical debates on school-based CPD activities in schools located in disadvantaged areas, using lesson study. Further research would necessitate a focus on understanding how the social learning processes within school-based CPD can be linked to school contexts.Keywords: continuous professional development; lesson study; mathematics noticing; research lesso
Teaching Grade 10 girls concepts of the sine trigonometric function using ChatGPT and GeoGebra
Get PDFThis research investigates how ChatGPT, a generative AI tool, and GeoGebra, an interactive mathematical software, can be employed to enhance Grade 10 girls' learning experience and comprehension of sine trigonometric function concepts. The study seeks to address the main research question – “How can the use of ChatGPT and GeoGebra as instructional tools enhance the teaching of sine trigonometric function concepts in a Grade 10 mathematics class?”. The study is grounded in the socio-constructivist approach, which emphasizes active student centred learning, and positions teachers as facilitators that promote student engagement during teaching and learning. Trigonometry, particularly concepts related to trigonometric functions, presents significant challenges for South African Grade 12 students. Traditional, teacher centred methods, often based on lectures, may contribute to this limited understanding. A design-based research methodology, utilizing iterative cycles of design, implementation, and refinement was adopted to facilitate the data collection and analyses from the three lessons used. The research sample consisted of 20 Grade 10 girls. Data was gathered through video recordings, worksheets, focus group interviews of students, and teacher interviews. Thematic analysis was conducted to analyze the qualitative data from the data collection instruments. The main findings indicate that GeoGebra enhanced explorative learning and significantly boosted student engagement. ChatGPT was perceived as most effective when it offered step by-step guidance for problem-solving or methods to achieve specific outcomes. Both students and the teacher expressed a preference for using ChatGPT and GeoGebra in tandem, seamlessly switching between the two rather than using each tool in isolation. The simultaneous integration of ChatGPT and GeoGebra in teaching sine trigonometric function concepts promoted independent exploration and critical thinking among students. This study underscores the potential benefits of using both ChatGPT and GeoGebra software in the classroom for teaching sine trigonometric function concepts. The findings highlight the pedagogical value of employing ChatGPT and GeoGebra in teaching sine trigonometric functions, which can be insightful for teacher educators, curriculum advisors involved in professional development for in-service teachers, and mathematics teachers. A limitation of the study is its reliance on a small sample from a single school. Future research could address this by repeating the study with a larger sample that includes students from diverse educational and cultural backgrounds
A comparative study of the FET phase mathematical literacy and mathematics curriculum
No full textThis article is based on a study that compared the FET (further education and training) phase mathematics literacy curriculum and mathematics curriculum. The study looked into how the conceptualization of a mathematical literacy curriculum enhanced the acquisition of mathematical concepts among the learners. In order to carry out this comparison between the two curricula, views of 355 participants comprising of mathematics and mathematical literacy teachers, mathematics and mathematical literacy subject advisors and heads of departments at the MST (mathematics, science and technology) units were sought. The findings of the study revealed that both curricula have similar learning outcomes, but different assessment standards. Factors that hinder the learning and teaching of mathematics in both curricula, such as lack of qualified mathematics teachers, lack of parental support, negative societal attitudes towards mathematics and lack of support from the Department of Education among others, were identified by the study. Intervention mechanisms, such as the use of information technology as an instructional tool, contextualized teaching and learning materials for mathematics, recruiting and training mathematics teachers and continuous professional development, were suggested. Further research is necessary for exploring the benefits of cross-curriculum teaching and learning of mathematical literacy as a way of enhancing the acquisition of mathematical skills at the FET phase
Information technology as an instructional tool in the teaching of mathematics in secondary schools : perceptions of educators and learners in the North West Province
No full text(M.Ed.) North-West University, Mafikeng Campus, 2003The title of this research study is: Information technology as an instructional tool in the teaching of mathematics in secondary schools: Perceptions of educators and learners in the North West Province of the Republic of South Africa. This research study was intended to study the role played by information technology as an instructional tool in high schools and the challenges associated with the integration of information technology in the teaching and learning of mathematics in high schools:
The research study sought to investigate the following research questions:
Is information technology an effective instructional tool to teach secondary school mathematics?
What are the perceptions of educators and learners regarding the use of computers in
mathematics lessons?
What are the challenges faced by educators and learners when using Information
technology in the teaching and learning of mathematics?
This research study drew its population from all high schools in the Mafikeng, Zeerust and
Lichtenburg Districts of the North West Province, which used computers in teaching. A sample of eight high schools was used; two in the Zeerust District, two in the Lichtenburg District and four in the Mafikeng District. This research sample was made up of mathematics and computer studies educators and learners from the chosen secondary schools. Two questionnaires were used for the purposes of data collection. One of the questionnaires was intended to study the perceptions of learners on the use of information technology in teaching and learning mathematics and the other was intended to study the perceptions of educators on the use of information technology in mathematics education.
Both quantitative and qualitative techniques were used to analyse the research. The main
findings of the research study were that:
The majority of educators (76%) regarded information technology as an effective
instructional too.] in the teaching and learning of secondary school mathematics . ,
Educators were generally not well trained to use information technology as an
instructional tool and that there was a shortage of hardware and software due to financial
constraints in high schools. I have recommended that: The Department of Education, in conjunction with the Faculty of Education of the North West University should organise in-service programmes on the use of information technology as an instructional tool in the teaching and learning of mathematics.
More research studies are required in the development of relevant and appropriate
software for use in the teaching and learning of mathematics.
In conclusion, the researcher hopes that the use of Information technology will go a long way in enhancing the learning and teaching of mathematics in high schools throughout the North West Province of the Republic of South Africa.Master
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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