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Exploring low-tech opportunities for higher education mathematics lecturers in an emergency techno-response pedagogy Pythagoras Pub Date : 2022-04-22 Antonia Makina,Langton Kadzere
The education sector, among others, was severely affected by the coronavirus disease 2019 (COVID-19) pandemic. Because mathematics has always been singled out as a subject that needs more verbal communication and interaction, rapid adjustments had to be made by mathematics lecturers in higher education institutions to try and facilitate normal teaching and learning remotely through emergency open distance
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Complexities of translating mathematics tasks from English to learners’ home languages Pythagoras Pub Date : 2022-01-18 Nkosinathi Mpalami
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Table of Contents Vol 42, No 1 (2021) Pythagoras Pub Date : 2021-12-30 Editorial Office
No abstract available.
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Reasoning under uncertainty within the context of probability education: A case study of preservice mathematics teachers Pythagoras Pub Date : 2021-12-17 Samah G.A. Elbehary
Interpreting phenomena under uncertainty stands as a substantial cognitive activity in our daily life. Furthermore, in probability education research, there is a need for developing a unified model that involves several probabilistic conceptions. From this aspect, a central inquiry has been raised through this study: how do preservice mathematics teachers (PSMTs) reason under uncertainty? A multiple
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Novice and expert Grade 9 teachers’ responses to unexpected learner offers in the teaching of algebra Pythagoras Pub Date : 2021-12-15 Julian Moodliar,Lawan Abdulhamid
In South Africa, limited studies have been conducted investigating responsive teaching and little is known about how teachers respond to unexpected events ‘in the moment’ that did not form part of their planning. In this article, we report how a Grade 9 novice and expert teacher responded to unexpected learner offers during the teaching of algebra using a qualitative case study approach. Three consecutive
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Constructing mental diagrams during problem-solving in mathematics Pythagoras Pub Date : 2021-11-29 Vimolan Mudaly
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Insights into the reversal error from a study with South African and Spanish prospective primary teachers Pythagoras Pub Date : 2021-11-25 Calos Soneira,Sarah Bansilal,Reginald Govender
This study, using a quantitative approach, examined Spanish and South African pre-service teachers’ responses to translating word problems based on direct proportionality into equations. The participants were 79 South African and 211 Spanish prospective primary school teachers who were in their second year of a Bachelor of Education degree. The study’s general objective was to compare the students’
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Reflecting on dilemmas in digital resource design as a response to COVID-19 for learners in under-resourced contexts Pythagoras Pub Date : 2021-11-09 Pamela Vale,Mellony H. Graven
The coronavirus disease 2019 (COVID-19) pandemic and the resulting school closures in South Africa necessitated a major shift in how to support learners’ ongoing mathematics learning. For 10 weeks learners were strictly confined to their homes with restrictions that prohibited seeing any person outside of their household. The only means to access learners and parents in their homes was to reimagine
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Early career teacher’s approach to fraction equivalence in Grade 4: A dialogic teaching perspective Pythagoras Pub Date : 2021-11-09 Benjamin Shongwe
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Grade 9 learners’ understanding of fraction concepts: Equality of fractions, numerator and denominator Pythagoras Pub Date : 2021-10-21 Methuseli Moyo,France M. Machaba
Our research with Grade 9 learners at a school in Soweto was conducted to explore learners’ understanding of fundamental fraction concepts used in applications required at that level of schooling. The study was based on the theory of constructivism in a bid to understand whether learners’ transition from whole numbers to rational numbers enabled them to deal with the more complex concept of fractions
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Design principles to consider when student teachers are expected to learn mathematical modelling Pythagoras Pub Date : 2021-09-29 Rina Durandt
This article sets out design principles to consider when student mathematics teachers are expected to learn mathematical modelling during their formal education. Blum and Leiß’s modelling cycle provided the theoretical framework to explain the modelling process. Learning to teach mathematical modelling, and learning to solve modelling tasks, while simultaneously fostering positive attitudes, is not
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Professional development for teachers’ mathematical problem-solving pedagogy – what counts? Pythagoras Pub Date : 2021-08-25 Brantina Chirinda
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Bridging powerful knowledge and lived experience: Challenges in teaching mathematics through COVID-19 Pythagoras Pub Date : 2021-08-13 Karin Brodie,Deepa Gopal,Julian Moodliar,Takalani Siala
The coronavirus disease 2019 (COVID-19) pandemic supported an investigation of ongoing challenges as to whether and how to make mathematics relevant to learners’ lifeworlds. Given that COVID-19 created major disruptions in all learners’ lives, we developed and taught tasks that attempted to make links between their experiences of the pandemic and disciplinary mathematical knowledge. We located our
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Flexible teaching of mathematics word problems through multiple means of representation Pythagoras Pub Date : 2021-08-10 Matshidiso M. Moleko,Mogege D. Mosimege
Flexible teaching of mathematics word problems is essential to improve learning. Flexible teaching is vital in terms of providing meaningful learning, creating inclusive learning spaces and making content accessible. As such, teachers need to strive to provide flexible teaching of mathematics word problems in order to optimise and maximise learning. In line with this notion, therefore, the qualitative
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The contribution of online mathematics games to algebra understanding in Grade 8 Pythagoras Pub Date : 2021-07-29 Tichaona Marange,Stanley A. Adendorff
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Table of Contents Vol 41, No 1 (2020) Pythagoras Pub Date : 2020-12-23 Editorial Office
No abstract available.
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Relative difficulty of early grade compare type word problems: Learning from the case of isiXhosa Pythagoras Pub Date : 2020-12-21 Ingrid E. Mostert
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Becoming mathematical: Designing a curriculum for a mathematics club Pythagoras Pub Date : 2020-12-18 Erna Lampen,Karin Brodie
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Evaluation and orientations to Grade 10 mathematics in schools differentiated by social class Pythagoras Pub Date : 2020-12-17 Shaheeda Jaffer
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Investigating the strength of alignment between Senior Phase mathematics content standards and workbook activities on number patterns Pythagoras Pub Date : 2020-12-17 Agnes D. Qhibi,Zwelithini B. Dhlamini,Kabelo Chuene
The investigation of the strength of alignment ensures synergy between curriculum components’ main content standards, classroom instruction and assessment (Polikoff & Porter, 2014; Porter, 2002). The extent of agreement between these curriculum components is referred to as alignment (Roach, Niebling, & Kurz, 2008). The conceptualisation of alignment begins with common understanding of the educational
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University students’ mental construction when learning the Convergence of a Series concept Pythagoras Pub Date : 2020-12-15 Conilius J. Chagwiza,Aneshkumar Maharaj,Deonarain Brijlall
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Postgraduate mathematics education students’ experiences of using digital platforms for learning within the COVID-19 pandemic era Pythagoras Pub Date : 2020-11-30 Jayaluxmi Naidoo
Within the digital era, as global society embraces the fourth industrial revolution, technology is being integrated swiftly within teaching and learning Within the Coronavirus disease (COVID-19) pandemic era, education institutions are preparing robustly for digital pedagogy This article reports on a study focusing on 31 postgraduate mathematics education students' experiences of using digital platforms
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Learner performance in the 2009 to 2014 final Grade 12 mathematics examination: A quantile regression approach Pythagoras Pub Date : 2020-11-30 Nombuso Zondo,Temesgen Zewotir,Delia North
The South African education system bears evidence of fluctuations in the final Grade 12 mathematics marks occurring across different learner profiles. This study reflected on the National Senior Certificate (NSC) mathematics results from the Western Cape Education Department for the years 2009 to 2014, the period just after the introduction of the NSC in 2008 and including the updated NSC introduced
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The effect of graphing calculator use on learners’ achievement and strategies in quadratic inequality problem solving Pythagoras Pub Date : 2020-11-18 Levi Ndlovu,Mdutshekelwa Ndlovu
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Pedagogical narratives in mathematics education in South Africa Pythagoras Pub Date : 2020-09-25 Charles R. Smith
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Learning the function concept by exploring digital images as functions Pythagoras Pub Date : 2020-08-31 Christiaan Venter
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Table of Contents Vol 40, No 1 (2019) Pythagoras Pub Date : 2019-12-19 Editorial Office
No abstract available.
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The professional development of primary school mathematics teachers through a design-based research methodology Pythagoras Pub Date : 2019-12-17 Piera Biccard
This article sets out a professional development programme for primary school mathematics teachers. Clark and Hollingsworth’s model of teacher change provided the theoretical framework necessary to understand teacher change. A design study allowed for increased programme flexibility and participator involvement. Five volunteer primary school teachers teaching at South African state schools were involved
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Book review: International reflections on Realistic Mathematics Education Pythagoras Pub Date : 2019-12-17 Stanley A. Adendorff
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The use of semiotic representations in reasoning about similar triangles in Euclidean geometry Pythagoras Pub Date : 2019-12-13 Ifunanya Ubah,Sarah Bansilal
Mathematics outcomes in South Africa are very low and many researchers and stakeholders have expressed concerns about the poor performance in mathematics at school level, especially in geometry (Luneta, 2015; Mthembu, 2007; Singh, 2006; Van Putten, Stols & Howie, 2010). Euclidean geometry forms part of the core curriculum of mathematics in the Further Education and Training (FET) band in South Africa;
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Using standard setting to promote meaningful use of mathematics assessment data within initial teacher education programmes Pythagoras Pub Date : 2019-12-12 Qetelo M. Moloi,Anil Kanjee,Nicky Roberts
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Mathematics teachers’ levels of technological pedagogical content knowledge and information and communication technology integration barriers Pythagoras Pub Date : 2019-12-11 Gabrielle de Freitas, Erica D. Spangenberg
Technological advances in South Africa over the past two decades have led to information and communication technology (ICT) becoming a significant role player in the educational landscape (Guerrero, 2010). ICTs are more readily available and form part of the general resources in many mathematics classrooms. The effective use of ICTs for teaching and learning adds value to the mathematics curriculum
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Comparison of geometric proof development tasks as set up in the textbook and as implemented by teachers in the classroom Pythagoras Pub Date : 2019-12-10 Lisnet Mwadzaangati
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The standard written algorithm for addition: Whether, when and how to teach it Pythagoras Pub Date : 2019-12-06 Nicky Roberts
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Keeping sites in sight: Conversations with teachers about the design of toolkits peculiar to a continuous professional development initiative Pythagoras Pub Date : 2019-12-05 Faaiz Gierdien,Charles Smith,Cyril Julie
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Towards validation of a rational number instrument: An application of Rasch measurement theory Pythagoras Pub Date : 2019-12-05 Jeremiah Maseko,Kakoma Luneta,Caroline Long
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Erratum: A commognitive perspective on Grade 8 and Grade 9 learner thinking about linear equations Pythagoras Pub Date : 2019-12-05 Anthea Roberts,Kate le Roux
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Social science students’ concept images and concept definitions of anti-derivatives Pythagoras Pub Date : 2019-11-13 Eunice K. Moru, Makomosela Qhobela
Calculus is an important branch of mathematics in a number of social and natural science disciplines. In the social sciences anti-derivatives are required in tackling problems in marginal analysis and optimisation problems. In the natural sciences students need to understand antiderivatives to deal with rates of change for concepts such as velocity, acceleration and rate of flow. However, students
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Webs of development: Professional networks as spaces for learning Pythagoras Pub Date : 2019-06-27 Kenneth Ngcoza, Sue Southwood
The concept of the inter-related structure of social reality, made famous over 50 years ago by Martin Luther King (1967), and scientifically articulated by the likes of Capra (1996), focuses on the complexity of life, the underlying connectedness, the systemic nature of our existence. Conventional linear thought and mechanistic reductionism necessarily yield to ideas of complexity, viewing the world
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Corrigendum: Metacognitive awareness and visualisation in the imagination: The case of the invisible circles Pythagoras Pub Date : 2019-02-13 Divan Jagals,Marthie van der Walt
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Tracking Grade 10 learners’ geometric reasoning through folding back Pythagoras Pub Date : 2018-11-15 Samuel Mabotja,Kabelo Chuene,Satsope Maoto,Israel Kibirige
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‘Eighteen hands high’: A narrative reading of Animal Farm from a mathematical perspective Pythagoras Pub Date : 2018-11-15 Liveness Mwale, Willy Mwakapenda
These excerpts from Animal Farm are examples of the many instances in which mathematical ideas, especially those connected to number, are used in the book. The author used his ‘common’ knowledge of mathematics and his familiar language to present the story of Animal Farm using mathematical ideas explicitly or implicitly. It is possible that the author’s intentions were not to present mathematics or
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Exploring teachers’ use of technology in teaching and learning mathematics in KwaZulu-Natal schools Pythagoras Pub Date : 2018-11-14 Odette Umugiraneza,Sarah Bansilal,Delia North
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Conversations in a professional learning community: An analysis of teacher learning opportunities in mathematics Pythagoras Pub Date : 2018-10-31 Million Chauraya,Karin Brodie
The growing perception of professional learning communities as an effective professional development approach needs to be supported with knowledge of how such communities create learning opportunities for teachers. Activities in professional learning communities are underpinned by collegial conversations that foster learning, and in this article we analysed such conversations for learning opportunities
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Acquiring mathematics as a second language: A theoretical model to illustrate similarities in the acquisition of English as a second language and mathematics Pythagoras Pub Date : 2018-10-29 Maureen Ledibane, Kotie Kaiser, Marthie Van der Walt
Many researchers have described mathematics as a language in itself (Esty, 1992; Setati, 2002). It, therefore, stands to reason that mathematics should be taught by teachers and acquired by learners in the same way as any other second or third language (Garrison & Mora, 1999). In South Africa, where the majority of learners have to learn through the medium of English as a second language, mathematics
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Mathematical sense-making through learner choice Pythagoras Pub Date : 2018-10-24 Piera Biccard
Learners often view learning mathematics as non-sense-making (Dienes, 1971; Schoenfeld, 1991). Non-sense-making is distinct from nonsense (no meaning is possible) and is closer to the term senseless (having no meaning). Schoenfeld (1991, p. 316, 320) coined the phrase ‘suspension of sensemaking’ or ‘significant nonreason in students’ school mathematics’ to describe learners’ disengagement with mathematics
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Students’ understanding of geometry terminology through the lens of Van Hiele theory Pythagoras Pub Date : 2018-10-18 Jogymol Alex,Kuttickattu J. Mammen
After a long six-year lapse, the Curriculum and Assessment Policy Statement introduced in 2012 included geometry as part of the South African Grade 12 Mathematics Paper 2. The first cohort of matriculation students wrote Paper 2 in 2014. This article reports on the understanding of geometry terminology with which a group of 154 first-year mathematics education students entered a rural South African
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Affordances for learning linear functions: A comparative study of two textbooks from South Africa and Germany Pythagoras Pub Date : 2018-09-26 Kathryn Mellor, Robyn Clark, Anthony A. Essien
Mathematics textbooks have been found to have a strong influence on classroom practice (Fan, 2013; Howson, 1995; Stylianides, 2014; Valverde, Bianchi, Wolfe, Schmidt, & Houang, 2002) and the tasks that they include can stimulate different levels of mathematical thinking and learning (Watson, & Ohtani, 2015; Stein, Smith, Henningsen, & Silver, 2000; Sullivan, Clarke, Clarke, & O’Shea, 2010). At a South
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Metacognitive awareness and visualisation in the imagination: The case of the invisible circles Pythagoras Pub Date : 2018-08-13 Divan Jagals,Martha Van der Walt
Awareness of one’s own strengths and weaknesses during visualisation is often initiated by the imagination – the faculty for intuitively visualising and modelling an object. Towards exploring the role of metacognitive awareness and imagination in facilitating visualisation in solving a mathematics task, four secondary schools in the North West province of South Africa were selected for instrumental
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Beyond test scores: A framework for reporting mathematics assessment results to enhance teaching and learning Pythagoras Pub Date : 2018-07-25 Meshack Moloi, Anil Kanjee
National assessment surveys (NAS) have been implemented in South Africa since the abolishment of the apartheid education system in 1996, and have evolved over time, changing in name, purpose, design, scope and frequency (Department of Education [DOE], 2005; Kanjee, 2007). National assessments are defined as ‘regular and systematic measurement exercises designed to determine what students have learned
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The effects of examination-driven teaching on mathematics achievement in Grade 10 school-based high-stakes examinations Pythagoras Pub Date : 2018-06-28 Onyumbe Okitowamba, Cyril Julie, Monde Mbekwa
Underachievement in school mathematics is a concern in most countries in the world. Watson and De Geest (2012) sketch the situation of underachievement in mathematics by drawing attention to ‘identifiable groups of students, such as those with different language backgrounds and those from lower socioeconomic rankings [who] underachieve in national and international tests’ (p. 213). Regarding the situation
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A commognitive perspective on Grade 8 and Grade 9 learner thinking about linear equation Pythagoras Pub Date : 2018-03-28 Anthea Roberts, Kate le Roux
Mathematics education research has, necessarily, focused on different aspects of this complex problem, for example wider socio-economic factors affecting performance (e.g. Setati, 2008; Taylor, 2009), school and classroom management (e.g. Fleisch, 2008; Taylor, 2009), teacher practice and professional development (e.g. Adler, 2011; Gardee & Brodie, 2015; Venkat & Adler, 2012), and learner thinking
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Teachers’ learning and assessing of mathematical processes with emphasis on representations, reasoning and proof Pythagoras Pub Date : 2018-03-19 Satsope Maoto, Kwena Masha, Lekwa Mokwana
This article focuses mainly on two key mathematical processes (representation, and reasoning and proof). Firstly, we observed how teachers learn these processes and subsequently identify what and how to assess learners on the same processes. Secondly, we reviewed one teacher’s attempt to facilitate the learning of the processes in his classroom. Two interrelated questions were pursued: ‘what are the
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Differences in the quality of school-based assessment: Evidence in Grade 9 mathematics achievement Pythagoras Pub Date : 2017-10-31 Surette Van Staden, Puleng Motsamai
This non-experimental, exploratory and descriptive study, using a qualitative case study approach, aims to investigate whether there is evidence of variance in the quality of school-based assessment (SBA) in Grade 9 mathematics. Participants were purposefully selected from five schools in a district in the Northern Cape in South Africa. After questionnaires were completed, individual face-to-face semi-structured
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The quantitative literacy of South African school-leavers who qualify for higher education Pythagoras Pub Date : 2017-10-31 Robert Prince, Vera Frith
There is an articulation gap for many students between the literacy practices developed at school and those demanded by higher education. While the school sector is often well attuned to the school-leaving assessments, it may not be as aware of the implicit quantitative literacy (QL) demands placed on students in higher education. The National Benchmark Test (NBT) in QL provides diagnostic information
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Mentoring as professional development intervention for mathematics teachers: A South African perspective Pythagoras Pub Date : 2017-09-22 Benita Nel, Kakoma Luneta
Only a small percentage of mathematics teacher professional development activities in South Africa include pedagogy and instruction approaches required to teach the content. In the light of the poor mathematics results, it is of pertinent importance that teachers need to be developed in terms of the mathematics they teach and the pedagogical component of it. A teachers’ professional development programme
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Educating Grade 6 students for higher-order thinking and its influence on creativity Pythagoras Pub Date : 2017-08-28 Wajeeh Daher, Amal Tabaja-Kidan, Faaiz Gierdien
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
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How does the grade obtained at school for English and Mathematics affect the probability of graduation at a university? Pythagoras Pub Date : 2017-08-25 Michael Murray
Over half of all students enrolling at a particular university in KwaZulu-Natal fail to complete a degree. This article is wanting to determine to what extent the marks they obtain for English and Mathematics at school impact on their probability of graduation at this university. In addressing this problem, other student specific factors associated with their gender, race and the type of school they
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The application of the percentage change calculation in the context of inflation in Mathematical Literacy Pythagoras Pub Date : 2017-07-31 Sarah Bansilal
The school subject Mathematical Literacy requires application of mathematics procedures in various contextual settings, but not much is known about the ways in which students engage with contextual settings such as inflation. This qualitative study was conducted with in-service Mathematical Literacy teachers in South Africa with the purpose of exploring the extent to which the teachers recognised the