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":"1 1","pages":""},"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 : 2022-11-17DOI: 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":" ","pages":""},"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":" ","pages":""},"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":" ","pages":""},"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":" ","pages":""},"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}
Pub Date : 2022-08-16DOI: 10.4102/pythagoras.v43i1.666
L. O. Adesanya, M. Graham
A well-designed assessment construct is critical for improving all aspects of quality education and validating the achievement of educational reform. The global prevalence of how teachers communicate learning intentions (LIs) and success criteria (SC) has been of great concern, particularly in the South African context. This study investigates how Meaning Equivalence Reusable Learning Objects (MERLO) pedagogy effectively transforms Senior Phase mathematics teachers’ daily practice in the classroom. The study adopted qualitative participatory action research to frame the evolution of teachers’ praxeologies such as teachers’ meta-didactical and didactical praxeologies, to improve teachers’ beliefs and practices to integrate MERLO pedagogy as assessment activities. Twelve Senior Phase teachers were purposively selected in Gauteng, South Africa. The methods used for data generation were interviews, classroom observation, document analysis, field notes and training sessions. Thematic analysis was used to obtain insight into teachers’ beliefs and practice of effectively communicating LIs and SC in the classroom. At the initial stage, teachers were examined with regard to their beliefs and practices of assessment practices in the classroom, which informed MERLO intervention. In the second stage, teachers were asked to learn about MERLO items by reading the MERLO handout provided to them, participating in the workshop and sharing their opinions and views with others. In the third stage, teachers had to design MERLO assessment items on their own to assess learners’ level of understanding of the mathematical concepts in Senior Phase. The findings revealed that the participating teachers acquired adequate knowledge and skills on MERLO techniques that allowed them to structure and integrate the lesson plan of assessment activities into their mathematics classrooms. This study contributes to the body of knowledge by introducing MERLO pedagogy to Senior Phase South African mathematical teachers as an assessment strategy. COVID-19 caused some teachers to drop out of the study after the pre-MERLO participation phase and, accordingly, future research suggests that more teachers be included in similar studies.
{"title":"Effective communication of learning intentions and success criteria in the mathematics classroom: MERLO pedagogy for Senior Phase South African schools","authors":"L. O. Adesanya, M. Graham","doi":"10.4102/pythagoras.v43i1.666","DOIUrl":"https://doi.org/10.4102/pythagoras.v43i1.666","url":null,"abstract":"A well-designed assessment construct is critical for improving all aspects of quality education and validating the achievement of educational reform. The global prevalence of how teachers communicate learning intentions (LIs) and success criteria (SC) has been of great concern, particularly in the South African context. This study investigates how Meaning Equivalence Reusable Learning Objects (MERLO) pedagogy effectively transforms Senior Phase mathematics teachers’ daily practice in the classroom. The study adopted qualitative participatory action research to frame the evolution of teachers’ praxeologies such as teachers’ meta-didactical and didactical praxeologies, to improve teachers’ beliefs and practices to integrate MERLO pedagogy as assessment activities. Twelve Senior Phase teachers were purposively selected in Gauteng, South Africa. The methods used for data generation were interviews, classroom observation, document analysis, field notes and training sessions. Thematic analysis was used to obtain insight into teachers’ beliefs and practice of effectively communicating LIs and SC in the classroom. At the initial stage, teachers were examined with regard to their beliefs and practices of assessment practices in the classroom, which informed MERLO intervention. In the second stage, teachers were asked to learn about MERLO items by reading the MERLO handout provided to them, participating in the workshop and sharing their opinions and views with others. In the third stage, teachers had to design MERLO assessment items on their own to assess learners’ level of understanding of the mathematical concepts in Senior Phase. The findings revealed that the participating teachers acquired adequate knowledge and skills on MERLO techniques that allowed them to structure and integrate the lesson plan of assessment activities into their mathematics classrooms. This study contributes to the body of knowledge by introducing MERLO pedagogy to Senior Phase South African mathematical teachers as an assessment strategy. COVID-19 caused some teachers to drop out of the study after the pre-MERLO participation phase and, accordingly, future research suggests that more teachers be included in similar studies.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43340079","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 : 2022-08-05DOI: 10.4102/pythagoras.v43i1.646
Hanrie S. Bezuidenhout, E. Henning
{"title":"The intersect of early numeracy, vocabulary, executive functions and logical reasoning in Grade R","authors":"Hanrie S. Bezuidenhout, E. Henning","doi":"10.4102/pythagoras.v43i1.646","DOIUrl":"https://doi.org/10.4102/pythagoras.v43i1.646","url":null,"abstract":"","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49348880","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 : 2022-07-29DOI: 10.4102/pythagoras.v43i1.659
S. C. Mahlaba, Vimolan Mudaly
This article is an advanced theoretical study as a result of a chapter from the first author’s PhD study. The aim of the article is to discuss the relationship between commognition and the Van Hiele theory for studying discourse during Euclidean geometry problem-solving. Commognition is a theoretical framework that can be used in mathematics education to explain mathematical thinking through one’s discourse during problem-solving. Commognition uses four elements that characterise mathematical discourse and the difference between ritualistic and explorative discourses to explain how one displays mastery of mathematical problem-solving. On the other hand, the Van Hiele theory characterises five levels of geometrical thinking during one’s geometry learning and development. These five levels are fixed and mastery of one level leads to the next, and there is no success in the next level without mastering the previous level. However, for the purpose of the Curriculum and Assessment Policy Statement (CAPS) we only focused on the first four Van Hiele levels. Findings from this theoretical review revealed that progress in the Van Hiele levels of geometrical thinking depends mainly on the discourse participation of the preservice teachers when solving geometry problems. In particular, an explorative discourse is required for the development in these four levels of geometrical thinking as compared to a ritualistic discourse participation.
{"title":"Exploring the relationship between commognition and the Van Hiele theory for studying problem-solving discourse in Euclidean geometry education","authors":"S. C. Mahlaba, Vimolan Mudaly","doi":"10.4102/pythagoras.v43i1.659","DOIUrl":"https://doi.org/10.4102/pythagoras.v43i1.659","url":null,"abstract":"This article is an advanced theoretical study as a result of a chapter from the first author’s PhD study. The aim of the article is to discuss the relationship between commognition and the Van Hiele theory for studying discourse during Euclidean geometry problem-solving. Commognition is a theoretical framework that can be used in mathematics education to explain mathematical thinking through one’s discourse during problem-solving. Commognition uses four elements that characterise mathematical discourse and the difference between ritualistic and explorative discourses to explain how one displays mastery of mathematical problem-solving. On the other hand, the Van Hiele theory characterises five levels of geometrical thinking during one’s geometry learning and development. These five levels are fixed and mastery of one level leads to the next, and there is no success in the next level without mastering the previous level. However, for the purpose of the Curriculum and Assessment Policy Statement (CAPS) we only focused on the first four Van Hiele levels. Findings from this theoretical review revealed that progress in the Van Hiele levels of geometrical thinking depends mainly on the discourse participation of the preservice teachers when solving geometry problems. In particular, an explorative discourse is required for the development in these four levels of geometrical thinking as compared to a ritualistic discourse participation.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48993610","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 : 2022-07-25DOI: 10.4102/pythagoras.v43i1.669
Kathryn McLachlan, Anthony A Essien
{"title":"Language and multilingualism in the teaching and learning of mathematics in South Africa: A review of literature in Pythagoras from 1994 to 2021","authors":"Kathryn McLachlan, Anthony A Essien","doi":"10.4102/pythagoras.v43i1.669","DOIUrl":"https://doi.org/10.4102/pythagoras.v43i1.669","url":null,"abstract":"","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48741898","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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