Pub Date : 2019-12-12DOI: 10.4102/pythagoras.v40i1.493
Qetelo Moloi, A. Kanjee, Nicky Roberts
{"title":"Using standard setting to promote meaningful use of mathematics assessment data within initial teacher education programmes","authors":"Qetelo Moloi, A. Kanjee, Nicky Roberts","doi":"10.4102/pythagoras.v40i1.493","DOIUrl":"https://doi.org/10.4102/pythagoras.v40i1.493","url":null,"abstract":"","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4102/pythagoras.v40i1.493","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41470127","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 : 2019-12-10DOI: 10.4102/pythagoras.v40i1.458
Lisnet Mwadzaangati
One of the aims of teaching secondary school mathematics in Malawi is to promote learners’ logical reasoning, problem-solving and critical thinking skills (Ministry of Education, Science and Technology [MEST], 2013). Euclidean geometry is regarded as the main area of mathematics that is a key source for teaching mathematical argumentation and proof, developing learners’ deductive reasoning and critical thinking (Kunimune, Fujita, & Jones, 2010). But the Malawi National Examinations Board (MANEB) chief examiners’ reports indicate that secondary school learners fail to develop geometric proofs at national examinations (MANEB, 2013). Poor teaching practices are highlighted as a major cause of learners’ inability to understand geometric proof development (MANEB, 2013). The reports emphasise that due to lack of both content knowledge and pedagogical knowledge, the teachers are not creative in conducting effective lessons to support learners’ understanding of geometric proof development. Studies conducted in different parts of the world also indicate that despite the importance of reasoning and proving in learners’ learning, many learners face serious challenges in proof development (Kunimune et al., 2010; Otten, Males & Gibertson, 2014; Stylianides, 2014). These studies support MANEB’s by arguing that learners’ challenges in proof development should be attributed more to classroom inappropriate practices that mainly emphasise rules of verification and devalue or omit exploration. As a result, the learners memorise the rules without understanding the process of proof development; hence, they are able to reproduce similar proofs but cannot apply the principles to develop a different proof (Ding & Jones, 2009). Use of exploratory teaching strategies is suggested as one way of helping learners to understand geometric proof development (Ding & Jones, 2009; Jones et al., 2009). This implies that the solution for improving classroom practices for enhancing learners’ understanding of geometric proof development lies in teacher professional development and teacher education.
{"title":"Comparison of geometric proof development tasks as set up in the textbook and as implemented by teachers in the classroom","authors":"Lisnet Mwadzaangati","doi":"10.4102/pythagoras.v40i1.458","DOIUrl":"https://doi.org/10.4102/pythagoras.v40i1.458","url":null,"abstract":"One of the aims of teaching secondary school mathematics in Malawi is to promote learners’ logical reasoning, problem-solving and critical thinking skills (Ministry of Education, Science and Technology [MEST], 2013). Euclidean geometry is regarded as the main area of mathematics that is a key source for teaching mathematical argumentation and proof, developing learners’ deductive reasoning and critical thinking (Kunimune, Fujita, & Jones, 2010). But the Malawi National Examinations Board (MANEB) chief examiners’ reports indicate that secondary school learners fail to develop geometric proofs at national examinations (MANEB, 2013). Poor teaching practices are highlighted as a major cause of learners’ inability to understand geometric proof development (MANEB, 2013). The reports emphasise that due to lack of both content knowledge and pedagogical knowledge, the teachers are not creative in conducting effective lessons to support learners’ understanding of geometric proof development. Studies conducted in different parts of the world also indicate that despite the importance of reasoning and proving in learners’ learning, many learners face serious challenges in proof development (Kunimune et al., 2010; Otten, Males & Gibertson, 2014; Stylianides, 2014). These studies support MANEB’s by arguing that learners’ challenges in proof development should be attributed more to classroom inappropriate practices that mainly emphasise rules of verification and devalue or omit exploration. As a result, the learners memorise the rules without understanding the process of proof development; hence, they are able to reproduce similar proofs but cannot apply the principles to develop a different proof (Ding & Jones, 2009). Use of exploratory teaching strategies is suggested as one way of helping learners to understand geometric proof development (Ding & Jones, 2009; Jones et al., 2009). This implies that the solution for improving classroom practices for enhancing learners’ understanding of geometric proof development lies in teacher professional development and teacher education.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4102/pythagoras.v40i1.458","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70234746","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 : 2019-12-05DOI: 10.4102/pythagoras.v40i1.441
J. Maseko, K. Luneta, Caroline Long
Venkat and Spaull (2015) reported that 79% of 401 South African Grade 6 mathematics teachers showed proficiency of content knowledge below Grade 6–7 level in a Southern and East African Consortium for Monitoring Educational Quality (SACMEQ) 2007 mathematics teacher test. Universities recruit and receive students from some of these school where these teachers are teaching. In the previous years of teaching first-year students in the mathematics module in the Foundation Phase teacher development programme, we noticed that each cohort of prospective teachers come with knowledge bases that are at different levels. These classes, of students’ with varied mathematics knowledge, are difficult to teach unless you have some idea of their conceptual and procedural gaps. This varied knowledge base is greatly magnified in the domain of rational numbers in which they are expected to be knowledgeable and confident in order to teach and lay a good foundation in future teaching. An instrument, functioning as a diagnostic and baseline test for the 2015 first-year Foundation Phase cohort, was constructed at the university level in the fractions-decimals-percentages triad. This instrument aimed at gauging the level of students’ cognitive understanding of rational numbers as well as evaluating the validity of the instrument that was used to elicit their mathematical cognition. All the participants admitted into the Foundation Phase teacher training programme were tested on 93 items comprising multiple choice, short answer and constructed response formats. That elicited both conceptual and procedural understanding.
{"title":"Towards validation of a rational number instrument: An application of Rasch measurement theory","authors":"J. Maseko, K. Luneta, Caroline Long","doi":"10.4102/pythagoras.v40i1.441","DOIUrl":"https://doi.org/10.4102/pythagoras.v40i1.441","url":null,"abstract":"Venkat and Spaull (2015) reported that 79% of 401 South African Grade 6 mathematics teachers showed proficiency of content knowledge below Grade 6–7 level in a Southern and East African Consortium for Monitoring Educational Quality (SACMEQ) 2007 mathematics teacher test. Universities recruit and receive students from some of these school where these teachers are teaching. In the previous years of teaching first-year students in the mathematics module in the Foundation Phase teacher development programme, we noticed that each cohort of prospective teachers come with knowledge bases that are at different levels. These classes, of students’ with varied mathematics knowledge, are difficult to teach unless you have some idea of their conceptual and procedural gaps. This varied knowledge base is greatly magnified in the domain of rational numbers in which they are expected to be knowledgeable and confident in order to teach and lay a good foundation in future teaching. An instrument, functioning as a diagnostic and baseline test for the 2015 first-year Foundation Phase cohort, was constructed at the university level in the fractions-decimals-percentages triad. This instrument aimed at gauging the level of students’ cognitive understanding of rational numbers as well as evaluating the validity of the instrument that was used to elicit their mathematical cognition. All the participants admitted into the Foundation Phase teacher training programme were tested on 93 items comprising multiple choice, short answer and constructed response formats. That elicited both conceptual and procedural understanding.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4102/pythagoras.v40i1.441","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44421799","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 : 2019-12-05DOI: 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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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 : 2018-12-24DOI: 10.4102/pythagoras.v39i1.466
Editorial Office
{"title":"Table of Contents Vol 39, No 1 (2018)","authors":"Editorial Office","doi":"10.4102/pythagoras.v39i1.466","DOIUrl":"https://doi.org/10.4102/pythagoras.v39i1.466","url":null,"abstract":"","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2018-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138535987","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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