Pythagoras最新文献

{"title":"Developing undergraduate engineering mathematics students’ conceptual and procedural knowledge of complex numbers using GeoGebra","authors":"Philemon M. Seloane, Sam Ramaila, Mdutshekelwa Ndlovu","doi":"10.4102/pythagoras.v44i1.763","DOIUrl":"https://doi.org/10.4102/pythagoras.v44i1.763","url":null,"abstract":"This study explored the utilisation of GeoGebra as a modelling tool to develop undergraduate engineering mathematics students’ conceptual and procedural knowledge of complex numbers. This mission was accomplished by implementing GeoGebra-enriched activities, which provided carefully designed representational support to mediate between students’ initially developed conceptual and procedural knowledge gains. The rectangular and polar forms of the complex number were connected and merged using GeoGebra’s computer algebra systems and dynamic geometric systems platforms. Despite the centrality of complex numbers to the undergraduate mathematics curriculum, students tend to experience conceptual and procedural obstacles in mathematics-dependent physics engineering topics such as mechanical vector analysis and electric-circuit theory. The study adopted an exploratory sequential mixed methods design and involved purposively selected first-year engineering mathematics students at a South African university. The constructivist approach and Realistic Mathematical Education underpinned the empirical investigation. Data were collected from students’ scripts. Implementing GeoGebra-enriched activities and providing carefully designed representational support sought to enhance students’ conceptual and procedural knowledge of complex numbers and problem representational competence. The intervention additionally helped students to conceptualise and visualise a complex rectangular number. Implications for technology-enhanced pedagogy are discussed.Contribution: The article provides exploratory insights into the development of undergraduate engineering mathematics students’ conceptual and procedural knowledge of complex numbers using GeoGebra as a dynamic digital tool. Key findings from the study demonstrated that GeoGebra appears to be an effective modelling tool that can be harnessed to demystify the complexity of mathematics students’ conceptual and procedural knowledge of complex numbers.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":"82 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138951307","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}

{"title":"Ascertaining Grade 10 learners’ levels of mathematical modelling competency through solving simultaneous equations word problems","authors":"Rajendran Govender, Dzivaidzo Machingura","doi":"10.4102/pythagoras.v44i1.728","DOIUrl":"https://doi.org/10.4102/pythagoras.v44i1.728","url":null,"abstract":"Possessing mathematical competence is a pre requisite for independently comprehending, understanding and applying all features of mathematical modelling in a particular setting. This research study thus explores the mathematical modelling competencies that Grade 10 learners exhibit while solving contextual problems in a mathematics learning and teaching context, with specific reference to using mathematical modelling. Since mathematical modelling is a fairly new teaching strategy used in mathematics teaching some teachers may be ignorant of the skills and competencies required for learners to solve problems efficiently. A mixed-methods approach to this study was decided upon and a case study design used within an interpretative paradigm in an effort to ascertain the levels of mathematical modelling competencies of a non-random sample of 20 Grade 10 learners. Participant learners who attended a Western Cape school were requested to solve a set of word problems involving the use of simultaneous equations. Task based activities and observations were used as a means to collect data, as well as semi-structured interviews to gauge participating learners’ views and experiences. Qualitative content analysis methods were employed together with basic descriptive statistical methods.Contribution: Research findings reveal the limited competence and abilities of the participating Grade 10 learners to make sense of, understand or constructively progress in solving contextual problems, and the challenges they experience to progress through particular stages of the modelling process, such as building and solving models and interpreting the solutions thereof.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":"30 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138589162","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}

{"title":"Solving quadratic equations by completing the square: Applying Newman’s Error Analysis Model to analyse Grade 11 errors","authors":"T. Makgakga","doi":"10.4102/pythagoras.v44i1.742","DOIUrl":"https://doi.org/10.4102/pythagoras.v44i1.742","url":null,"abstract":"Error analysis is an instructional strategy that can assist teachers to identify learners’ areas of weakness in mathematics and that can point to remediation of those errors. This article explores the errors learners exhibit when solving quadratic equations by completing the square using Newman’s Error Analysis Model. A research study explored the errors learners exhibit when solving quadratic equations by completing the square. Newman’s Error Analysis Model provided the analytic framework for the qualitative approach that was used to explore those errors. A diagnostic test with five test items was administered to 35 learners in one secondary school in Limpopo province of South Africa. Subsequently, 12 learners whose scripts featured common mistakes were identified; these learners participated in a semi-structured interview to diagnose the errors. The findings revealed that learners commit comprehension, transformation and process errors. The findings suggest that if the errors that learners make are exposed and made explicit, the errors can be remediated and thereby enhance understanding and learning. The findings of this study indicate that for teachers to understand the types of errors learners commit when solving quadratic equations by completing the square it is vital for them (errors) to be addressed. Mathematics teachers should also consider diagnosing why learners commit those errors, as they would know the strategies to be employed to teach this topic and subsequent topics.Contribution: The findings of this article add value to the current literature by providing empirical knowledge on learner challenges when solving quadratic equations by completing the square. This study provides opportunities for mathematics teachers to focus more on the strategies that would assist learners to understand this topic.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":"45 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138592165","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}

{"title":"The impact of artificial intelligence and the future of ChatGPT for mathematics teaching and learning in schools and higher education","authors":"Rajendran Govender","doi":"10.4102/pythagoras.v44i1.787","DOIUrl":"https://doi.org/10.4102/pythagoras.v44i1.787","url":null,"abstract":"No abstract available.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":"48 6","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138602079","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}

{"title":"Conversations reflecting boundary-objects-related details of a teacher’s local practices with spreadsheet algebra programs on variables","authors":"M. Gierdien, Wajeeh M. Daher, Awni M. Abu-Saman","doi":"10.4102/pythagoras.v44i1.756","DOIUrl":"https://doi.org/10.4102/pythagoras.v44i1.756","url":null,"abstract":"The ways teachers converse about their work in relation to information and communications technologies (ICTs) are worth studying. We analyse how a teacher converses about her local practices in relation to two spreadsheet algebra programs (SAPs) on variables. During the conversations we noticed that the teacher keeps different policy documents – boundary objects – firmly in view, in relation to the design of the two other boundary objects, namely the two SAPs. The policy documents provide details on the operative curricula which entail the intended, implemented and examined curricula. Of these curricula, the teacher regarded the examined curriculum and associated examinations as most important. Also, she conversed about how she intends to align the design features of the two SAPs with particular policy documents, especially in the context of the South African high-stakes National Senior Certificate examinations and the attendant examination pressure. Our results confirm current professional development (PD) literature suggestions that emphasise fostering coherence, for example between policy boundary objects details and what university-based PD providers do when they interact with school teachers.Contribution: The results provide guidelines for university-based PD providers to integrate SAPs or other ICTs related to algebra and variables by keeping teachers’ local practices in view. These providers should note that different policy-related boundary objects shape the ways teachers understand and converse about their local practices, namely their work at the classroom level.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":"48 30","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139203776","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}

{"title":"Talk that supports learners’ folding back for growth in understanding geometry","authors":"K. Chuene, Koena Mabotja, S. Maoto","doi":"10.4102/pythagoras.v44i1.711","DOIUrl":"https://doi.org/10.4102/pythagoras.v44i1.711","url":null,"abstract":"In this article, we argue that folding back is successful when the learners engage in exploratory talk. To support our argument, we sourced data from a Grade 10 mathematics classroom of 54 learners who participated in a four-week teaching experiment conducted by the second author. We mainly focused on talks in two groups of learners to address the silence of literature on folding back that alludes to the kind of talk that learners engage in. Data were captured through video recording of learners’ interactions as they worked on the tasks in different sessions. We present these data as transcribed extracts of talks that the learners held and synthesise them into stories through Polkinghorne’s narrative mode of data analysis, also using a process that Kim referred to as narrative smoothing. Pirie and Kieren’s conception of folding back and Wegerif and Mercer’s three ways of talking and thinking among learners were used as a heuristic device for synthesising the stories. The narratives illustrate that exploratory talk promotes folding back, where learners build on each other’s ideas to develop geometry understanding. Therefore, the significance of this article is that for classrooms that wish to promote growth in understanding through folding back, the type of talk that should be normative is exploratory talk.Contribution: Our search of the literature databases has yet to reveal an empirical study that draws attention to exploratory talk’s role in developing learners’ understanding of geometry in South Africa. However, this study is one of those that allude to the support of exploratory talk on folding back in developing geometry understanding. Our findings imply that mathematics classrooms should consider incorporating exploratory talk as part of teaching and learning geometry. Furthermore, studies on engendering exploratory talk in teaching mathematics are recommended.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":"60 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139198489","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}

{"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":"93 5","pages":"0"},"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}

{"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":"48 1","pages":"0"},"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}

{"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":" ","pages":""},"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}

{"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":"1 1","pages":""},"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}