Pub Date : 2020-12-17DOI: 10.4102/pythagoras.v41i1.578
S. Jaffer
{"title":"Evaluation and orientations to Grade 10 mathematics in schools differentiated by social class","authors":"S. Jaffer","doi":"10.4102/pythagoras.v41i1.578","DOIUrl":"https://doi.org/10.4102/pythagoras.v41i1.578","url":null,"abstract":"","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44217883","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 : 2020-12-17DOI: 10.4102/pythagoras.v41i1.569
Agnes D. Qhibi, Zwelithini Bongani Dhlamini, K. 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 components used in this discourse, content standards, classroom instruction and assessment. Kurtz, Elliott, Wehby and Smithson (2010) refer to these as follows: (1) the intended curriculum is reflective of the content standards as specified in the Curriculum and Assessment Policy Statement (CAPS) (Department of Basic Education [DBE], 2011); (2) the enacted curriculum refers to the content of instruction taught by teachers in classrooms; (3) the assessed curriculum is depicted by the content measured by the various forms of assessment or tests during the academic year. Hence, the conceptualisation between these three aspects of the curriculum in the alignment discourse is: the intended curriculum specifies content for instruction; the content taught by teachers during instruction portrays the enacted curriculum; the assessed curriculum depicts the assessed content that gauges levels of students’ achievement. The investigation of the strength of alignment normally begins with the determination of the content, the cognitive levels and representations of each of the documents (Porter, 2002; Webb, 1997). Frequent studies on alignment are necessary to improve the agreement of curricula expectations, classroom instruction and assessment (Russell & Moncaleano, 2020). Alignment is both horizontal and vertical. Horizontal is between curricula (intended and assessed) and assessments while vertical is between learning materials, classroom instruction, professional development and learner outcomes (enacted curriculum) (Webb, 1997). Hence, alignment has the potential to strengthen the connections between what is taught, what is tested and what is intended by the curriculum (Martone & Sireci, 2009).
{"title":"Investigating the strength of alignment between Senior Phase mathematics content standards and workbook activities on number patterns","authors":"Agnes D. Qhibi, Zwelithini Bongani Dhlamini, K. Chuene","doi":"10.4102/pythagoras.v41i1.569","DOIUrl":"https://doi.org/10.4102/pythagoras.v41i1.569","url":null,"abstract":"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 components used in this discourse, content standards, classroom instruction and assessment. Kurtz, Elliott, Wehby and Smithson (2010) refer to these as follows: (1) the intended curriculum is reflective of the content standards as specified in the Curriculum and Assessment Policy Statement (CAPS) (Department of Basic Education [DBE], 2011); (2) the enacted curriculum refers to the content of instruction taught by teachers in classrooms; (3) the assessed curriculum is depicted by the content measured by the various forms of assessment or tests during the academic year. Hence, the conceptualisation between these three aspects of the curriculum in the alignment discourse is: the intended curriculum specifies content for instruction; the content taught by teachers during instruction portrays the enacted curriculum; the assessed curriculum depicts the assessed content that gauges levels of students’ achievement. The investigation of the strength of alignment normally begins with the determination of the content, the cognitive levels and representations of each of the documents (Porter, 2002; Webb, 1997). Frequent studies on alignment are necessary to improve the agreement of curricula expectations, classroom instruction and assessment (Russell & Moncaleano, 2020). Alignment is both horizontal and vertical. Horizontal is between curricula (intended and assessed) and assessments while vertical is between learning materials, classroom instruction, professional development and learner outcomes (enacted curriculum) (Webb, 1997). Hence, alignment has the potential to strengthen the connections between what is taught, what is tested and what is intended by the curriculum (Martone & Sireci, 2009).","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46225649","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 : 2020-12-15DOI: 10.4102/pythagoras.v41i1.567
Conilius J. Chagwia, Aneshkumar Maharaj, D. Brijlall
Many mathematical concepts in calculus and other courses depend heavily on the limit concept, like the definite integral as the limit of Riemann sums, Taylor series and the differential in multivariate calculus. Convergent partial sums of a sequence may be used to define the limit of an infinite series. The limit of an infinite series can be defined as the limit (as n → ∞) of the sequence of partial sums. Infinite series development was motivated by the approximation of unknown areas and for the approximation of the value of π (Hartman, 2008). In about 1350, Suiseth indicated
{"title":"University students’ mental construction when learning the Convergence of a Series concept","authors":"Conilius J. Chagwia, Aneshkumar Maharaj, D. Brijlall","doi":"10.4102/pythagoras.v41i1.567","DOIUrl":"https://doi.org/10.4102/pythagoras.v41i1.567","url":null,"abstract":"Many mathematical concepts in calculus and other courses depend heavily on the limit concept, like the definite integral as the limit of Riemann sums, Taylor series and the differential in multivariate calculus. Convergent partial sums of a sequence may be used to define the limit of an infinite series. The limit of an infinite series can be defined as the limit (as n → ∞) of the sequence of partial sums. Infinite series development was motivated by the approximation of unknown areas and for the approximation of the value of π (Hartman, 2008). In about 1350, Suiseth indicated","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42805930","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 : 2020-09-28DOI: 10.4102/PYTHAGORAS.V41I1.520
Abigail Roberts, E. Spangenberg
. This qualitative article utilised pre-and post-interviews as data collection instruments. Ten of the best-performing Grade 12 learners at an ex-model C school in Gauteng province in South Africa were purposively selected to participate in the research. The findings revealed that peer tutors view their role to motivate learners to learn mathematics peculiar to seven positions, which can inform future research on intervention strategies to improve mathematics performance. This article introduces research on an adapted use of the ARCS model of motivation in motivating learners to learn mathematics, which is a novel way of bringing new perspectives to research on motivation in mathematics at secondary school level.
{"title":"Peer tutors’ views on their role in motivating learners to learn mathematics","authors":"Abigail Roberts, E. Spangenberg","doi":"10.4102/PYTHAGORAS.V41I1.520","DOIUrl":"https://doi.org/10.4102/PYTHAGORAS.V41I1.520","url":null,"abstract":". This qualitative article utilised pre-and post-interviews as data collection instruments. Ten of the best-performing Grade 12 learners at an ex-model C school in Gauteng province in South Africa were purposively selected to participate in the research. The findings revealed that peer tutors view their role to motivate learners to learn mathematics peculiar to seven positions, which can inform future research on intervention strategies to improve mathematics performance. This article introduces research on an adapted use of the ARCS model of motivation in motivating learners to learn mathematics, which is a novel way of bringing new perspectives to research on motivation in mathematics at secondary school level.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2020-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47426995","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 : 2020-09-25DOI: 10.4102/pythagoras.v41i1.573
Charles R. Smith
{"title":"Pedagogical narratives in mathematics education in South Africa","authors":"Charles R. Smith","doi":"10.4102/pythagoras.v41i1.573","DOIUrl":"https://doi.org/10.4102/pythagoras.v41i1.573","url":null,"abstract":"","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":"5 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2020-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138535988","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 : 2020-08-31DOI: 10.4102/pythagoras.v41i1.568
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 for learning during the COVID-19 pandemic era The study was located at one teacher education institution in KwaZulu-Natal, South Africa The research process encompassed three interactive online workshops and two online discussion forums, which were conducted via different digital platforms (Zoom, Moodle and WhatsApp) The study was framed using the theory of Communities of Practice, which denotes a group of people who share an interest which is enhanced as group members support and interact with each other Qualitative data generated during the interactive online workshops and discussion forums were analysed thematically The results exhibit challenges and strengths of using digital platforms as experienced by the participants The results of this study suggest that before using digital platforms for mathematics learning, it is important for students to be encouraged to practise and engage collaboratively within digital platforms The study adds to the developing knowledge in the field concerning using digital platforms for learning mathematics within the COVID-19 pandemic era
{"title":"Postgraduate mathematics education students’ experiences of using digital platforms for learning within the COVID-19 pandemic era","authors":"Jayaluxmi Naidoo","doi":"10.4102/pythagoras.v41i1.568","DOIUrl":"https://doi.org/10.4102/pythagoras.v41i1.568","url":null,"abstract":"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 for learning during the COVID-19 pandemic era The study was located at one teacher education institution in KwaZulu-Natal, South Africa The research process encompassed three interactive online workshops and two online discussion forums, which were conducted via different digital platforms (Zoom, Moodle and WhatsApp) The study was framed using the theory of Communities of Practice, which denotes a group of people who share an interest which is enhanced as group members support and interact with each other Qualitative data generated during the interactive online workshops and discussion forums were analysed thematically The results exhibit challenges and strengths of using digital platforms as experienced by the participants The results of this study suggest that before using digital platforms for mathematics learning, it is important for students to be encouraged to practise and engage collaboratively within digital platforms The study adds to the developing knowledge in the field concerning using digital platforms for learning mathematics within the COVID-19 pandemic era","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46620036","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 : 2019-12-12DOI: 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":"1 1","pages":""},"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":"223 1","pages":""},"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":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4102/pythagoras.v40i1.441","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}
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