Pub Date : 2023-11-06DOI: 10.4102/pythagoras.v44i1.767
Rose Maoto
{"title":"Mathematics education for relevance, responsiveness, and viability in Africa within the Fourth Industrial Revolution era","authors":"Rose Maoto","doi":"10.4102/pythagoras.v44i1.767","DOIUrl":"https://doi.org/10.4102/pythagoras.v44i1.767","url":null,"abstract":"","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135584200","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 : 2023-10-11DOI: 10.4102/pythagoras.v44i1.647
Brian Chihodzi, Willy Mwakapenda, Beatrice Ngulube
Ticks and crosses (TCs) are a common aspect of teachers’ classroom practice in relation to assessment in many learning areas including mathematics. Putting TCs in learners’ written work is a strategy of feedback. Even though these TCs are frequently used in different types of mathematics assessments, there is limited research in relation to what they actually stand for and what functions they are designed for and especially what purpose they eventually serve in practice. This article emerged from a broader study that aimed at exploring classroom formative assessment practices of Grades 4–6 mathematics teachers, a learning goals and documentary analysis. Since this study was qualitative in nature, we used qualitative, non-probability sampling to recruit respondents according to pre-selected criteria relevant to our research questions. The study participants were 43 qualified and experienced Intermediate Phase mathematics teachers and 95 Grades 4–6 learners from the Tshwane South district, where a phenomenon of low achievement was of great concern. We engaged in document analysis of all the 95 learners’ mathematics workbooks. Questionnaires were administered to the 43 teachers. We report on an analysis of teachers’ assessment practices of Grades 4–6 learners’ mathematics work. We narrate the extent of the use of TCs among teachers from selected schools in Tshwane South district in Gauteng, South Africa. Our analysis shows that while there is prevalent use of TCs among teachers, there are critical gaps in relation to knowledge of TCs in assessing mathematics. We present a qualitative and quantitative data analysis to illustrate how these were used in connection with assessment of learners’ mathematics work linked to the concepts of numerical, geometric, and graphical relationships. We use our analysis of the vignettes to explore and argue that teachers use TCs without adequate understanding of what these actually mean in relation to assessment broadly and assessment intended at collecting and clarifying goals for mathematical learning specifically. Despite teachers having mathematical qualifications and a repertoire of experience for teaching, the majority of teachers grappled with understanding mathematical concepts as evidence in how they marked learners’ mathematics work. The study also found that teachers’ understandings of assessment of mathematics were diverse and largely inconsistent with the formal definitions of mathematics.Contribution: This study indicated that there are critical gaps in relation to knowledge of TCs in assessing mathematics. A clear-cut marking policy will guide teachers to provide effective marking using TCs.
{"title":"Ticks and crosses in primary mathematics assessments: What purpose do they serve?","authors":"Brian Chihodzi, Willy Mwakapenda, Beatrice Ngulube","doi":"10.4102/pythagoras.v44i1.647","DOIUrl":"https://doi.org/10.4102/pythagoras.v44i1.647","url":null,"abstract":"Ticks and crosses (TCs) are a common aspect of teachers’ classroom practice in relation to assessment in many learning areas including mathematics. Putting TCs in learners’ written work is a strategy of feedback. Even though these TCs are frequently used in different types of mathematics assessments, there is limited research in relation to what they actually stand for and what functions they are designed for and especially what purpose they eventually serve in practice. This article emerged from a broader study that aimed at exploring classroom formative assessment practices of Grades 4–6 mathematics teachers, a learning goals and documentary analysis. Since this study was qualitative in nature, we used qualitative, non-probability sampling to recruit respondents according to pre-selected criteria relevant to our research questions. The study participants were 43 qualified and experienced Intermediate Phase mathematics teachers and 95 Grades 4–6 learners from the Tshwane South district, where a phenomenon of low achievement was of great concern. We engaged in document analysis of all the 95 learners’ mathematics workbooks. Questionnaires were administered to the 43 teachers. We report on an analysis of teachers’ assessment practices of Grades 4–6 learners’ mathematics work. We narrate the extent of the use of TCs among teachers from selected schools in Tshwane South district in Gauteng, South Africa. Our analysis shows that while there is prevalent use of TCs among teachers, there are critical gaps in relation to knowledge of TCs in assessing mathematics. We present a qualitative and quantitative data analysis to illustrate how these were used in connection with assessment of learners’ mathematics work linked to the concepts of numerical, geometric, and graphical relationships. We use our analysis of the vignettes to explore and argue that teachers use TCs without adequate understanding of what these actually mean in relation to assessment broadly and assessment intended at collecting and clarifying goals for mathematical learning specifically. Despite teachers having mathematical qualifications and a repertoire of experience for teaching, the majority of teachers grappled with understanding mathematical concepts as evidence in how they marked learners’ mathematics work. The study also found that teachers’ understandings of assessment of mathematics were diverse and largely inconsistent with the formal definitions of mathematics.Contribution: This study indicated that there are critical gaps in relation to knowledge of TCs in assessing mathematics. A clear-cut marking policy will guide teachers to provide effective marking using TCs.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136098176","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 : 2023-07-07DOI: 10.4102/pythagoras.v44i1.686
K. Luneta, Mekonnen Y. Legesse
School algebra serves as the language of mathematics and a foundational subject for learning advanced mathematics courses. This makes developing learners’ proficiency in algebra the most desirable instructional goal of school mathematics. Despite having such importance emphasis, however, studies indicate that the vast majority of learners are characterised by inadequate mathematics proficiency levels in general and in the algebra syllabus topics in particular. Consequently, this quasi-experimental study attempted to investigate the efficacy of using discourse-based instruction as an instructional approach to developing proficiency in algebra unit topics. One hundred and six (N = 106) Grade 11 learners participated in the study and were randomly grouped into an experimental group (n = 52) and a control group (n = 54). Using a test instrument that consisted of 24 Rasch-validated items, both pre-test and post-test data were collected from both groups under similar conditions. The Mann-Whitney U statistical analysis of the pre-test data revealed no significant difference between the control and experimental groups. The Mann-Whitney U analysis performed on the post-test data demonstrated that the experimental group scored significantly higher in the post-test scores when compared to the control group after the intervention. The study findings provided evidence of the efficacy of discourse-based instruction over teacher-centred instruction for developing learners’ algebra proficiency.Contribution: The study has contributed to the conceptual and practical understanding of how discourse-based instruction can be used to concretise learners’ proficiency in basic algebra.
{"title":"Discourse-based mathematics instruction on Grade 11 learners’ mathematical proficiency in algebra topics","authors":"K. Luneta, Mekonnen Y. Legesse","doi":"10.4102/pythagoras.v44i1.686","DOIUrl":"https://doi.org/10.4102/pythagoras.v44i1.686","url":null,"abstract":"School algebra serves as the language of mathematics and a foundational subject for learning advanced mathematics courses. This makes developing learners’ proficiency in algebra the most desirable instructional goal of school mathematics. Despite having such importance emphasis, however, studies indicate that the vast majority of learners are characterised by inadequate mathematics proficiency levels in general and in the algebra syllabus topics in particular. Consequently, this quasi-experimental study attempted to investigate the efficacy of using discourse-based instruction as an instructional approach to developing proficiency in algebra unit topics. One hundred and six (N = 106) Grade 11 learners participated in the study and were randomly grouped into an experimental group (n = 52) and a control group (n = 54). Using a test instrument that consisted of 24 Rasch-validated items, both pre-test and post-test data were collected from both groups under similar conditions. The Mann-Whitney U statistical analysis of the pre-test data revealed no significant difference between the control and experimental groups. The Mann-Whitney U analysis performed on the post-test data demonstrated that the experimental group scored significantly higher in the post-test scores when compared to the control group after the intervention. The study findings provided evidence of the efficacy of discourse-based instruction over teacher-centred instruction for developing learners’ algebra proficiency.Contribution: The study has contributed to the conceptual and practical understanding of how discourse-based instruction can be used to concretise learners’ proficiency in basic algebra.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48641924","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 : 2023-06-21DOI: 10.4102/pythagoras.v44i1.678
Samukeliso Chikiwa, Mellony Graven
{"title":"Exploring the development of South African pre-service teachers’ reflective practice","authors":"Samukeliso Chikiwa, Mellony Graven","doi":"10.4102/pythagoras.v44i1.678","DOIUrl":"https://doi.org/10.4102/pythagoras.v44i1.678","url":null,"abstract":"","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45488120","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 : 2023-05-31DOI: 10.4102/pythagoras.v44i1.716
Mark Jacobs, F. George, Daniel Anga’ama
{"title":"Online learning and peer support: Exploring the use of WhatsApp in first-year mathematics","authors":"Mark Jacobs, F. George, Daniel Anga’ama","doi":"10.4102/pythagoras.v44i1.716","DOIUrl":"https://doi.org/10.4102/pythagoras.v44i1.716","url":null,"abstract":"","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70234840","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 : 2022-12-15DOI: 10.4102/pythagoras.v43i1.714
Rajendran Govender
No abstract available.
没有可用的摘要。
{"title":"Research Resilience in the COVID era","authors":"Rajendran Govender","doi":"10.4102/pythagoras.v43i1.714","DOIUrl":"https://doi.org/10.4102/pythagoras.v43i1.714","url":null,"abstract":"No abstract available.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45677093","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 : 2022-11-17DOI: 10.4102/pythagoras.v43i1.647
Brian Chihodzi, W. Mwakapenda, B. Ngulube
Ticks and crosses (TCs) are a common aspect of teachers’ classroom practice in relation to assessment in many learning areas including mathematics. Putting TCs in learners’ written work is a strategy of feedback. Even though these TCs are frequently used in different types of mathematics assessments, there is limited research in relation to what they actually stand for and what functions they are designed for and especially what purpose they eventually serve in practice. This article emerged from a broader study that aimed at exploring classroom formative assessment practices of Grades 4–6 mathematics teachers, a learning goals and documentary analysis. Since this study was qualitative in nature, we used qualitative, non-probability sampling to recruit respondents according to pre-selected criteria relevant to our research questions. The study participants were 43 qualified and experienced Intermediate Phase mathematics teachers and 95 Grades 4–6 learners from the Tshwane South district, where a phenomenon of low achievement was of great concern. We engaged in document analysis of all the 95 learners’ mathematics workbooks. Questionnaires were administered to the 43 teachers. We report on an analysis of teachers’ assessment practices of Grades 4–6 learners’ mathematics work. We narrate the extent of the use of TCs among teachers from selected schools in Tshwane South district in Gauteng, South Africa. Our analysis shows that while there is prevalent use of TCs among teachers, there are critical gaps in relation to knowledge of TCs in assessing mathematics. We present a qualitative and quantitative data analysis to illustrate how these were used in connection with assessment of learners’ mathematics work linked to the concepts of numerical, geometric, and graphical relationships. We use our analysis of the vignettes to explore and argue that teachers use TCs without adequate understanding of what these actually mean in relation to assessment broadly and assessment intended at collecting and clarifying goals for mathematical learning specifically. Despite teachers having mathematical qualifications and a repertoire of experience for teaching, the majority of teachers grappled with understanding mathematical concepts as evidence in how they marked learners’ mathematics work. The study also found that teachers’ understandings of assessment of mathematics were diverse and largely inconsistent with the formal definitions of mathematics.Contribution: This study indicated that there are critical gaps in relation to knowledge of TCs in assessing mathematics. A clear-cut marking policy will guide teachers to provide effective marking using TCs.
{"title":"Ticks and crosses in primary mathematics assessments: What purpose do they serve?","authors":"Brian Chihodzi, W. Mwakapenda, B. Ngulube","doi":"10.4102/pythagoras.v43i1.647","DOIUrl":"https://doi.org/10.4102/pythagoras.v43i1.647","url":null,"abstract":"Ticks and crosses (TCs) are a common aspect of teachers’ classroom practice in relation to assessment in many learning areas including mathematics. Putting TCs in learners’ written work is a strategy of feedback. Even though these TCs are frequently used in different types of mathematics assessments, there is limited research in relation to what they actually stand for and what functions they are designed for and especially what purpose they eventually serve in practice. This article emerged from a broader study that aimed at exploring classroom formative assessment practices of Grades 4–6 mathematics teachers, a learning goals and documentary analysis. Since this study was qualitative in nature, we used qualitative, non-probability sampling to recruit respondents according to pre-selected criteria relevant to our research questions. The study participants were 43 qualified and experienced Intermediate Phase mathematics teachers and 95 Grades 4–6 learners from the Tshwane South district, where a phenomenon of low achievement was of great concern. We engaged in document analysis of all the 95 learners’ mathematics workbooks. Questionnaires were administered to the 43 teachers. We report on an analysis of teachers’ assessment practices of Grades 4–6 learners’ mathematics work. We narrate the extent of the use of TCs among teachers from selected schools in Tshwane South district in Gauteng, South Africa. Our analysis shows that while there is prevalent use of TCs among teachers, there are critical gaps in relation to knowledge of TCs in assessing mathematics. We present a qualitative and quantitative data analysis to illustrate how these were used in connection with assessment of learners’ mathematics work linked to the concepts of numerical, geometric, and graphical relationships. We use our analysis of the vignettes to explore and argue that teachers use TCs without adequate understanding of what these actually mean in relation to assessment broadly and assessment intended at collecting and clarifying goals for mathematical learning specifically. Despite teachers having mathematical qualifications and a repertoire of experience for teaching, the majority of teachers grappled with understanding mathematical concepts as evidence in how they marked learners’ mathematics work. The study also found that teachers’ understandings of assessment of mathematics were diverse and largely inconsistent with the formal definitions of mathematics.Contribution: This study indicated that there are critical gaps in relation to knowledge of TCs in assessing mathematics. A clear-cut marking policy will guide teachers to provide effective marking using TCs.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44591255","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 : 2022-11-04DOI: 10.4102/pythagoras.v43i1.691
S. Tesfamicael
{"title":"Prospective teachers’ cognitive engagement during virtual teaching using GeoGebra and Desmos","authors":"S. Tesfamicael","doi":"10.4102/pythagoras.v43i1.691","DOIUrl":"https://doi.org/10.4102/pythagoras.v43i1.691","url":null,"abstract":"","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44456644","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 : 2022-09-15DOI: 10.4102/pythagoras.v43i1.677
George Ekol, Simphiwe Mlotshwa
This case study carried out during the 2020 coronavirus disease of 2019 (COVID-19) lockdown used online data collection means to investigate the distribution of cognitive demand levels of probability and counting principles (PCP) learning tasks in a popular online Grade 12 mathematics textbook, based on the PCP teachers’ rating. The teachers’ cognitive demand ratings were categorised following Stein’s mathematical task framework. Five mathematics teachers from four secondary schools in two provinces in South Africa participated in the study by filling in an online questionnaire. We developed a rating framework named the mean cognitive demand rating (MCDR) to help us interpret the teachers’ perception of the tasks in terms of cognitive demand to the learners. Data from the teachers’ ratings revealed nearly 65% of the PCP learning tasks in the online textbook were rated as high. Analysis of secondary data from Department of Basic Education diagnostic reports from 2014 to 2020, however, suggests no association between teachers’ rating of learning tasks and learner performance. Contribution: This study draws attention to a long-standing underperformance in the topic of probability and suggests classroom-based study that focuses on the learners’ rating of the learning tasks themselves to understand clearly how best to support them.
{"title":"Investigating the cognitive demand levels in probability and counting principles learning tasks from an online mathematics textbook","authors":"George Ekol, Simphiwe Mlotshwa","doi":"10.4102/pythagoras.v43i1.677","DOIUrl":"https://doi.org/10.4102/pythagoras.v43i1.677","url":null,"abstract":"This case study carried out during the 2020 coronavirus disease of 2019 (COVID-19) lockdown used online data collection means to investigate the distribution of cognitive demand levels of probability and counting principles (PCP) learning tasks in a popular online Grade 12 mathematics textbook, based on the PCP teachers’ rating. The teachers’ cognitive demand ratings were categorised following Stein’s mathematical task framework. Five mathematics teachers from four secondary schools in two provinces in South Africa participated in the study by filling in an online questionnaire. We developed a rating framework named the mean cognitive demand rating (MCDR) to help us interpret the teachers’ perception of the tasks in terms of cognitive demand to the learners. Data from the teachers’ ratings revealed nearly 65% of the PCP learning tasks in the online textbook were rated as high. Analysis of secondary data from Department of Basic Education diagnostic reports from 2014 to 2020, however, suggests no association between teachers’ rating of learning tasks and learner performance. Contribution: This study draws attention to a long-standing underperformance in the topic of probability and suggests classroom-based study that focuses on the learners’ rating of the learning tasks themselves to understand clearly how best to support them.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44403535","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 : 2022-08-29DOI: 10.4102/pythagoras.v43i1.696
H. Mbhiza
{"title":"Grade 10 teachers’ example selection, sequencing and variation during functions lessons","authors":"H. Mbhiza","doi":"10.4102/pythagoras.v43i1.696","DOIUrl":"https://doi.org/10.4102/pythagoras.v43i1.696","url":null,"abstract":"","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44254176","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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