Pub Date : 2021-07-29DOI: 10.4102/pythagoras.v42i1.586
T. Marange, S. Adendorff
{"title":"The contribution of online mathematics games to algebra understanding in Grade 8","authors":"T. Marange, S. Adendorff","doi":"10.4102/pythagoras.v42i1.586","DOIUrl":"https://doi.org/10.4102/pythagoras.v42i1.586","url":null,"abstract":"","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45159883","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 : 2020-12-21DOI: 10.4102/pythagoras.v41i1.538
I. Mostert
Word problems are a central, yet hard-to-teach, aspect of early grade mathematics. For example, in South Africa word problems have been identified as a recurring weakness in the South African Annual National Assessments (ANAs) (Department of Basic Education, 2012, 2014, 2015). Research has shown that the relative difficulty of word problems differs: learners are more likely to solve certain types of word problems than others. For additive relation word problems, in other words any word problems involving addition and subtraction, compare type problems have been shown to be the most difficult for learners to solve. Compare type problems are of the form ‘Sbu has eight bananas and Sive has five bananas. How many more bananas does Sbu have than Sive?’ While there has been some research into early grade word problems in South Africa (e.g. Petersen, McAuliffe, & Vermeulen, 2017), and some research into word problems and African languages in higher grades (e.g. Sepeng, 2013), there has been little research into early grade word problems in African languages. This is problematic as more than 75% of learners are taught mathematics in an indigenous African language in the first four years of formal schooling (Spaull, 2016).
{"title":"Relative difficulty of early grade compare type word problems: Learning from the case of isiXhosa","authors":"I. Mostert","doi":"10.4102/pythagoras.v41i1.538","DOIUrl":"https://doi.org/10.4102/pythagoras.v41i1.538","url":null,"abstract":"Word problems are a central, yet hard-to-teach, aspect of early grade mathematics. For example, in South Africa word problems have been identified as a recurring weakness in the South African Annual National Assessments (ANAs) (Department of Basic Education, 2012, 2014, 2015). Research has shown that the relative difficulty of word problems differs: learners are more likely to solve certain types of word problems than others. For additive relation word problems, in other words any word problems involving addition and subtraction, compare type problems have been shown to be the most difficult for learners to solve. Compare type problems are of the form ‘Sbu has eight bananas and Sive has five bananas. How many more bananas does Sbu have than Sive?’ While there has been some research into early grade word problems in South Africa (e.g. Petersen, McAuliffe, & Vermeulen, 2017), and some research into word problems and African languages in higher grades (e.g. Sepeng, 2013), there has been little research into early grade word problems in African languages. This is problematic as more than 75% of learners are taught mathematics in an indigenous African language in the first four years of formal schooling (Spaull, 2016).","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2020-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45360463","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 : 2020-12-18DOI: 10.4102/pythagoras.v41i1.572
Erna Lampen, K. Brodie
becoming mathematical about mathematics, (3) being mathematical and making mathematics, and (4) mathematics. We argue that through such a curriculum, we can develop mathematical reasoning on the basis of learners’ everyday reasoning in ways that support their mathematical proficiency, identities and agency.
{"title":"Becoming mathematical: Designing a curriculum for a mathematics club","authors":"Erna Lampen, K. Brodie","doi":"10.4102/pythagoras.v41i1.572","DOIUrl":"https://doi.org/10.4102/pythagoras.v41i1.572","url":null,"abstract":"becoming mathematical about mathematics, (3) being mathematical and making mathematics, and (4) mathematics. We argue that through such a curriculum, we can develop mathematical reasoning on the basis of learners’ everyday reasoning in ways that support their mathematical proficiency, identities and agency.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2020-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44650932","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.v41i1.578
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
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