Pub Date : 2019-12-05DOI: 10.4102/pythagoras.v40i1.519
Anthea Roberts, Kate le Roux
be shifted. This is an opportunity for teacher professional development and further research.
被转移。这是一个教师专业发展和进一步研究的机会。
{"title":"Erratum: A commognitive perspective on Grade 8 and Grade 9 learner thinking about linear equations","authors":"Anthea Roberts, Kate le Roux","doi":"10.4102/pythagoras.v40i1.519","DOIUrl":"https://doi.org/10.4102/pythagoras.v40i1.519","url":null,"abstract":"be shifted. This is an opportunity for teacher professional development and further research.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4102/pythagoras.v40i1.519","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41894043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-01DOI: 10.4102/pythagoras.v40i1.431
Gabriel De Freitas, E. 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 and is associated with improved learner understanding (Nkula & Krauss, 2014). The incorporation of ICTs in the mathematics classroom may also have important implications for mathematics performance in South Africa, which is viewed as under-performing and below international standards (McCarthy & Oliphant, 2013).
{"title":"Mathematics teachers’ levels of technological pedagogical content knowledge and information and communication technology integration barriers","authors":"Gabriel De Freitas, E. Spangenberg","doi":"10.4102/pythagoras.v40i1.431","DOIUrl":"https://doi.org/10.4102/pythagoras.v40i1.431","url":null,"abstract":"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 and is associated with improved learner understanding (Nkula & Krauss, 2014). The incorporation of ICTs in the mathematics classroom may also have important implications for mathematics performance in South Africa, which is viewed as under-performing and below international standards (McCarthy & Oliphant, 2013).","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4102/pythagoras.v40i1.431","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42426740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-13DOI: 10.4102/pythagoras.v40i1.484
E. K. Moru, Makomosela Qhobela
The purpose of the reported study was to investigate the social science students’ concept images and concept definitions of anti-derivatives. Data were collected through asking students to answer 10 questions related to anti-derivatives and also by interviewing them. The theory of concept image and concept definition was used for data analysis. The results of the study show that the students’ definitions of anti-derivatives were personal reconstructions of the formal definition. Their concept images were coherent only to a certain extent as there were some conceptions of some ideas that were at variance with those of the mathematical community. These were more evident when students solved problems in the algebraic representation. Some students did not know which integration or differentiation methods they should apply in solving the problems. The significance of such findings is to enable the mathematics educators to pay attention not only to the use of signs and symbols representing mathematical concepts but also to their semantics.
{"title":"Social science students’ concept images and concept definitions of anti-derivatives","authors":"E. K. Moru, Makomosela Qhobela","doi":"10.4102/pythagoras.v40i1.484","DOIUrl":"https://doi.org/10.4102/pythagoras.v40i1.484","url":null,"abstract":"The purpose of the reported study was to investigate the social science students’ concept images and concept definitions of anti-derivatives. Data were collected through asking students to answer 10 questions related to anti-derivatives and also by interviewing them. The theory of concept image and concept definition was used for data analysis. The results of the study show that the students’ definitions of anti-derivatives were personal reconstructions of the formal definition. Their concept images were coherent only to a certain extent as there were some conceptions of some ideas that were at variance with those of the mathematical community. These were more evident when students solved problems in the algebraic representation. Some students did not know which integration or differentiation methods they should apply in solving the problems. The significance of such findings is to enable the mathematics educators to pay attention not only to the use of signs and symbols representing mathematical concepts but also to their semantics.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4102/pythagoras.v40i1.484","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41476301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-27DOI: 10.4102/PYTHAGORAS.V40I1.409
K. Ngcoza, S. 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 as a systemic organism. Rather than studying parts to understand the whole, understanding of the whole is attempted through analysis of the relationships and connections making up the whole. Yet, the way in which we approach life is so often to deny this complexity. For instance, there is a tendency to split life into compartments or boxes, give them labels, and even give those who work in them labels, and then proceed to operate within those boxes, often ignoring and thereby negating the relationships and connections between them (Katz & Earl, 2010). The discipline-fragmented curriculum in most educational institutions is evidence of this. As Breen points out in his article on dilemmas of change, we ‘zoom’ in, ‘fixing’ one part, negating the ‘complexity of the phenomenon’. We deal with ‘the complicated rather than the complex and so only a part and never the whole’ (Breen, 2005).
{"title":"Webs of development: Professional networks as spaces for learning","authors":"K. Ngcoza, S. Southwood","doi":"10.4102/PYTHAGORAS.V40I1.409","DOIUrl":"https://doi.org/10.4102/PYTHAGORAS.V40I1.409","url":null,"abstract":"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 as a systemic organism. Rather than studying parts to understand the whole, understanding of the whole is attempted through analysis of the relationships and connections making up the whole. Yet, the way in which we approach life is so often to deny this complexity. For instance, there is a tendency to split life into compartments or boxes, give them labels, and even give those who work in them labels, and then proceed to operate within those boxes, often ignoring and thereby negating the relationships and connections between them (Katz & Earl, 2010). The discipline-fragmented curriculum in most educational institutions is evidence of this. As Breen points out in his article on dilemmas of change, we ‘zoom’ in, ‘fixing’ one part, negating the ‘complexity of the phenomenon’. We deal with ‘the complicated rather than the complex and so only a part and never the whole’ (Breen, 2005).","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4102/PYTHAGORAS.V40I1.409","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46882694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-02-13DOI: 10.4102/pythagoras.v40i1.464
D. Jagals, M. V. D. Walt
{"title":"Corrigendum: Metacognitive awareness and visualisation in the imagination: The case of the invisible circles","authors":"D. Jagals, M. V. D. Walt","doi":"10.4102/pythagoras.v40i1.464","DOIUrl":"https://doi.org/10.4102/pythagoras.v40i1.464","url":null,"abstract":"","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4102/pythagoras.v40i1.464","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42057398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-11-15DOI: 10.4102/PYTHAGORAS.V39I1.403
Liveness Mwale, W. 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 mathematical ideas, but because some storylines needed the use of mathematical language, he could not do so without using mathematics. This article emerges from a study that assessed learners’ abilities to interpret what they read and in particular, to ‘see’ mathematical aspects in the book Animal Farm. The study sought to find out learners’ abilities to read mathematically since mathematics is a specialised language that requires a specialised domain of practice. Animal Farm was one of the English Home Language literature books for high school learners in Grades 10–12 in South Africa in the 2015 academic year. According to the Department of Basic Education (2014), other novels for English Home Language were The Great Gatsby (Fitzgerald, 2008) and Pride and Prejudice (Austen, 2008). Learners were presented with excerpts from Animal Farm such as the ones quoted above. They were required to identify the mathematics part of the excerpts and to interpret what the excerpts meant. In the first excerpt, the mathematics part is ‘eighteen hands high’. According to conversion rates one adult hand is approximately 0.1016 m long. Therefore, Boxer’s height in metres was approximately 1.83 m. It was important for learners to understand this mathematical aspect in order to make sense of the extract. Without this understanding, the statement: ‘eighteen hands high’, does not make sense as one reads it in the printed media. Understanding what one is reading and how one needs to read is a critical skill required in relation to learning and achievement in education generally and mathematics education specifically.
{"title":"‘Eighteen hands high’: A narrative reading of Animal Farm from a mathematical perspective","authors":"Liveness Mwale, W. Mwakapenda","doi":"10.4102/PYTHAGORAS.V39I1.403","DOIUrl":"https://doi.org/10.4102/PYTHAGORAS.V39I1.403","url":null,"abstract":"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 mathematical ideas, but because some storylines needed the use of mathematical language, he could not do so without using mathematics. This article emerges from a study that assessed learners’ abilities to interpret what they read and in particular, to ‘see’ mathematical aspects in the book Animal Farm. The study sought to find out learners’ abilities to read mathematically since mathematics is a specialised language that requires a specialised domain of practice. Animal Farm was one of the English Home Language literature books for high school learners in Grades 10–12 in South Africa in the 2015 academic year. According to the Department of Basic Education (2014), other novels for English Home Language were The Great Gatsby (Fitzgerald, 2008) and Pride and Prejudice (Austen, 2008). Learners were presented with excerpts from Animal Farm such as the ones quoted above. They were required to identify the mathematics part of the excerpts and to interpret what the excerpts meant. In the first excerpt, the mathematics part is ‘eighteen hands high’. According to conversion rates one adult hand is approximately 0.1016 m long. Therefore, Boxer’s height in metres was approximately 1.83 m. It was important for learners to understand this mathematical aspect in order to make sense of the extract. Without this understanding, the statement: ‘eighteen hands high’, does not make sense as one reads it in the printed media. Understanding what one is reading and how one needs to read is a critical skill required in relation to learning and achievement in education generally and mathematics education specifically.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2018-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4102/PYTHAGORAS.V39I1.403","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45824218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-11-15DOI: 10.4102/PYTHAGORAS.V39I1.371
Sam Mabotja, K. Chuene, S. Maoto, Israel Kibirige
{"title":"Tracking Grade 10 learners’ geometric reasoning through folding back","authors":"Sam Mabotja, K. Chuene, S. Maoto, Israel Kibirige","doi":"10.4102/PYTHAGORAS.V39I1.371","DOIUrl":"https://doi.org/10.4102/PYTHAGORAS.V39I1.371","url":null,"abstract":"","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2018-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4102/PYTHAGORAS.V39I1.371","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70234629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-11-14DOI: 10.4102/PYTHAGORAS.V39I1.342
Odette Umugiraneza, S. Bansilal, D. North
{"title":"Exploring teachers’ use of technology in teaching and learning mathematics in KwaZulu-Natal schools","authors":"Odette Umugiraneza, S. Bansilal, D. North","doi":"10.4102/PYTHAGORAS.V39I1.342","DOIUrl":"https://doi.org/10.4102/PYTHAGORAS.V39I1.342","url":null,"abstract":"","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2018-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4102/PYTHAGORAS.V39I1.342","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45261302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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 in one professional learning community of mathematics teachers. Data consisted of audio-recorded community conversations. The focus of the conversations was to understand the thinking behind learners’ errors, and teachers engaged in a number of activities related to learner errors and learner reasoning. Our analyses show how opportunities for learning were created in identifying the origins of learners’ errors as well as learners’ thinking underlying their errors. Results also showed that the teachers had opportunities for learning how to identify learners’ learning needs and in turn the teachers’ own learning needs. The teachers also had opportunities for deepening their own understanding of the conceptual meaning of ratio. The learning opportunities were supported by the following: having a learning focus, patterns of engagement that were characterised by facilitator questioning, teacher responses and explanations, and sharing knowledge. Such mutual engagement practices in professional learning communities resulted in new and shared meanings about teachers’ classroom practices. Our findings also show the critical role of a facilitator for teacher learning in professional learning communities.
{"title":"Conversations in a professional learning community: An analysis of teacher learning opportunities in mathematics","authors":"M. Chauraya, K. Brodie","doi":"10.4102/PYTHAGORAS.","DOIUrl":"https://doi.org/10.4102/PYTHAGORAS.","url":null,"abstract":"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 in one professional learning community of mathematics teachers. Data consisted of audio-recorded community conversations. The focus of the conversations was to understand the thinking behind learners’ errors, and teachers engaged in a number of activities related to learner errors and learner reasoning. Our analyses show how opportunities for learning were created in identifying the origins of learners’ errors as well as learners’ thinking underlying their errors. Results also showed that the teachers had opportunities for learning how to identify learners’ learning needs and in turn the teachers’ own learning needs. The teachers also had opportunities for deepening their own understanding of the conceptual meaning of ratio. The learning opportunities were supported by the following: having a learning focus, patterns of engagement that were characterised by facilitator questioning, teacher responses and explanations, and sharing knowledge. Such mutual engagement practices in professional learning communities resulted in new and shared meanings about teachers’ classroom practices. Our findings also show the critical role of a facilitator for teacher learning in professional learning communities.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2018-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43839331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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