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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
Pub Date : 2022-05-31DOI: 10.4102/pythagoras.v43i1.641
Ernest Mahofa, S. Adendorff
{"title":"Novice mentors versus mentees: Mentoring experiences in mathematics at General Education and Training phase","authors":"Ernest Mahofa, S. Adendorff","doi":"10.4102/pythagoras.v43i1.641","DOIUrl":"https://doi.org/10.4102/pythagoras.v43i1.641","url":null,"abstract":"","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46456436","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 : 2022-05-31DOI: 10.4102/pythagoras.v43i1.655
Vuyisile L. Khumalo, S. van Staden, M. Graham
{"title":"Weathering the storm: Learning strategies that promote mathematical resilience","authors":"Vuyisile L. Khumalo, S. van Staden, M. Graham","doi":"10.4102/pythagoras.v43i1.655","DOIUrl":"https://doi.org/10.4102/pythagoras.v43i1.655","url":null,"abstract":"","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46647982","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 : 2022-04-22DOI: 10.4102/pythagoras.v43i1.644
Antonia Makina,Langton Kadzere
The education sector, among others, was severely affected by the coronavirus disease 2019 (COVID-19) pandemic. Because mathematics has always been singled out as a subject that needs more verbal communication and interaction, rapid adjustments had to be made by mathematics lecturers in higher education institutions to try and facilitate normal teaching and learning remotely through emergency open distance methods. Lecturers were forced to examine prevailing practices with a view to creating innovative and workable solutions to the emergency challenges without compromising the quality previously experienced during face-to-face classroom interactions. The article developed through a simple technology a conceptual framework for emergency remote teaching (ERT) in an emergency techno-response pedagogy (ETRP). The key was to demonstrate an innovative instructional strategy for teaching mathematics using a simple technology instead of an advanced or complicated mathematics software in the move from face-to-face to fully online teaching during a crisis. A development qualitative virtual case study was conducted that involved observing live and recorded mathematics lectures and interviewing an innovative lecturer of mathematics in the delivery of complex numbers at a graduate school in South Africa. The facilitation of the lesson through a simple and inexpensive technology (Microsoft OneNote) guided the development of a conceptual framework for ERT within an ETRP. The Context, Input, Process, and Product (CIPP) evaluation model was used as a theoretical framework to guide the analysis and conceptualisation of the lessons. Results provided guidelines through a conceptual framework for ERT that included a unique model of a lesson plan and advantages of using a simple technology in ERT instead of advanced mathematical software. The article contributes to the knowledge base in planning future ERT interventions.
{"title":"Exploring low-tech opportunities for higher education mathematics lecturers in an emergency techno-response pedagogy","authors":"Antonia Makina,Langton Kadzere","doi":"10.4102/pythagoras.v43i1.644","DOIUrl":"https://doi.org/10.4102/pythagoras.v43i1.644","url":null,"abstract":"The education sector, among others, was severely affected by the coronavirus disease 2019 (COVID-19) pandemic. Because mathematics has always been singled out as a subject that needs more verbal communication and interaction, rapid adjustments had to be made by mathematics lecturers in higher education institutions to try and facilitate normal teaching and learning remotely through emergency open distance methods. Lecturers were forced to examine prevailing practices with a view to creating innovative and workable solutions to the emergency challenges without compromising the quality previously experienced during face-to-face classroom interactions. The article developed through a simple technology a conceptual framework for emergency remote teaching (ERT) in an emergency techno-response pedagogy (ETRP). The key was to demonstrate an innovative instructional strategy for teaching mathematics using a simple technology instead of an advanced or complicated mathematics software in the move from face-to-face to fully online teaching during a crisis. A development qualitative virtual case study was conducted that involved observing live and recorded mathematics lectures and interviewing an innovative lecturer of mathematics in the delivery of complex numbers at a graduate school in South Africa. The facilitation of the lesson through a simple and inexpensive technology (Microsoft OneNote) guided the development of a conceptual framework for ERT within an ETRP. The Context, Input, Process, and Product (CIPP) evaluation model was used as a theoretical framework to guide the analysis and conceptualisation of the lessons. Results provided guidelines through a conceptual framework for ERT that included a unique model of a lesson plan and advantages of using a simple technology in ERT instead of advanced mathematical software. The article contributes to the knowledge base in planning future ERT interventions.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138536008","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 : 2022-01-18DOI: 10.4102/pythagoras.v43i1.560
Nkosinathi Mpalami
Mathematics education remains problematic in South Africa’s schools. However, some mathematics educators are deliberately using learners’ home languages in tasks to assist learners to understand mathematics. Research-based evidence shows that learners’ home languages when used as a resource have a potential to enhance learners’ understanding of mathematics. This article addresses the issue of translating mathematics tasks from English to learners’ home languages, a field that is less common in mathematics education studies. The study shows that there are complexities associated with such translation which all stakeholders in education should bear in mind. The article does so by referring to a study where a Grade 11 mathematics educator in a multilingual class tried to use learners’ home languages in tasks with an aim to enhance learners’ understanding of linear programming concepts. The study was conducted in township school in Gauteng province. Ethical clearance was given by the Gauteng Department of Education. Data were collected through observations and were analysed qualitatively. The situated sociocultural perspectives guided the study. The findings show that during the translation process, the educator went as far as translating mathematics technical terms. Such translation distorted the meaning of the original task and therefore made it hard for learners to comprehend concepts as envisioned. The recommendation is that the translation should not be left to individual mathematics educators but rather there should be a broader approach of having mathematics tasks translated from English into other official languages and such tasks be distributed to all schools throughout the country. Professional translators must also be contracted to do such a job.
{"title":"Complexities of translating mathematics tasks from English to learners’ home languages","authors":"Nkosinathi Mpalami","doi":"10.4102/pythagoras.v43i1.560","DOIUrl":"https://doi.org/10.4102/pythagoras.v43i1.560","url":null,"abstract":"Mathematics education remains problematic in South Africa’s schools. However, some mathematics educators are deliberately using learners’ home languages in tasks to assist learners to understand mathematics. Research-based evidence shows that learners’ home languages when used as a resource have a potential to enhance learners’ understanding of mathematics. This article addresses the issue of translating mathematics tasks from English to learners’ home languages, a field that is less common in mathematics education studies. The study shows that there are complexities associated with such translation which all stakeholders in education should bear in mind. The article does so by referring to a study where a Grade 11 mathematics educator in a multilingual class tried to use learners’ home languages in tasks with an aim to enhance learners’ understanding of linear programming concepts. The study was conducted in township school in Gauteng province. Ethical clearance was given by the Gauteng Department of Education. Data were collected through observations and were analysed qualitatively. The situated sociocultural perspectives guided the study. The findings show that during the translation process, the educator went as far as translating mathematics technical terms. Such translation distorted the meaning of the original task and therefore made it hard for learners to comprehend concepts as envisioned. The recommendation is that the translation should not be left to individual mathematics educators but rather there should be a broader approach of having mathematics tasks translated from English into other official languages and such tasks be distributed to all schools throughout the country. Professional translators must also be contracted to do such a job.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138535994","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 : 2021-12-17DOI: 10.4102/pythagoras.v42i1.630
Samah Gamal Ahmed Elbehary
Interpreting phenomena under uncertainty stands as a substantial cognitive activity in our daily life. Furthermore, in probability education research, there is a need for developing a unified model that involves several probabilistic conceptions. From this aspect, a central inquiry has been raised through this study: how do preservice mathematics teachers (PSMTs) reason under uncertainty? A multiple case study design was operated in which a purposive sample of PSMTs was selected to justify their reasoning in two probabilistic contexts while their responses were coded by NVivo, and corresponding categories were developed. As a result, PSMTs’ probabilistic reasoning was classified into mathematical (M), subjective (S), and outcome-oriented (O). Besides, several biases emerged along with these modes of reasoning. While M thinkers shared equiprobability and insensitivity to prior probability, the prediction bias and the belief of Allah’s willingness were yielded among S thinkers. Also, the causal conception spread among O thinkers.
{"title":"Reasoning under uncertainty within the context of probability education: A case study of preservice mathematics teachers","authors":"Samah Gamal Ahmed Elbehary","doi":"10.4102/pythagoras.v42i1.630","DOIUrl":"https://doi.org/10.4102/pythagoras.v42i1.630","url":null,"abstract":"Interpreting phenomena under uncertainty stands as a substantial cognitive activity in our daily life. Furthermore, in probability education research, there is a need for developing a unified model that involves several probabilistic conceptions. From this aspect, a central inquiry has been raised through this study: how do preservice mathematics teachers (PSMTs) reason under uncertainty? A multiple case study design was operated in which a purposive sample of PSMTs was selected to justify their reasoning in two probabilistic contexts while their responses were coded by NVivo, and corresponding categories were developed. As a result, PSMTs’ probabilistic reasoning was classified into mathematical (M), subjective (S), and outcome-oriented (O). Besides, several biases emerged along with these modes of reasoning. While M thinkers shared equiprobability and insensitivity to prior probability, the prediction bias and the belief of Allah’s willingness were yielded among S thinkers. Also, the causal conception spread among O thinkers.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44079929","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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