IF 0.3

Pythagoras Pub Date : 2024-07-10 DOI: 10.4102/pythagoras.v45i1.762

Atteeq Razzak

{"title":"A graphical user interface tool to teach plane curves in pandemic situations through a flipped classroom","authors":"Atteeq Razzak","doi":"10.4102/pythagoras.v45i1.762","DOIUrl":"https://doi.org/10.4102/pythagoras.v45i1.762","url":null,"abstract":"During the pandemic and lockdown situations of the last few years, we transitioned to online, physical, and hybrid education approaches at various times. We had difficulty teaching multiple calculus and analytical geometry units online. In light of the current situation, a graphical user interface (GUI) teaching tool has been developed to teach university students many plane curve modules through a flipped classroom. With a few inputs and a single click as output, these executable spreadsheets can assist physics and mathematics students in practising several principles of analytical geometry. Spreadsheets can readily draw planes in three-dimensional geometry due to their widespread use. Some online vector GUIs present the results; however, this GUI conveniently illustrates the plot. The well-designed user interface also helps create new questions with answer keys and gives access to the teachers of physics and mathematics, which can make online teaching very easy. The effectiveness of this GUI was checked through Kolmogorov-Smirnov and Shapiro-Wilk tests, and a good agreement has been found in the results.Contribution: This article contributes to Mathematics teaching through GUIs.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141659164","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}

引用次数: 0

Simplifying algebraic expressions with brackets: Insights into Grade 10 learners’ structure sense through a study of their errors 用括号简化代数表达式：通过研究 10 年级学生的错误，了解他们的结构意识

IF 1.2

Pythagoras Pub Date : 2024-05-13 DOI: 10.4102/pythagoras.v45i1.783

Nadia M. Theba, Craig Pournara, Shikha Takker

{"title":"Simplifying algebraic expressions with brackets: Insights into Grade 10 learners’ structure sense through a study of their errors","authors":"Nadia M. Theba, Craig Pournara, Shikha Takker","doi":"10.4102/pythagoras.v45i1.783","DOIUrl":"https://doi.org/10.4102/pythagoras.v45i1.783","url":null,"abstract":"Developing structure sense is an important part of learning algebra. We investigated learners’ structure sense of algebraic expressions involving brackets. This led us to propose the constructs surface structure sense and systemic structure sense. Using a random sample of 58 Grade 10 learners scoring above 40% in a test, we coded incorrect responses for surface and systemic structure errors. The initial analysis revealed that the presence of more brackets supports surface structure sense. However, learners overgeneralised the presence of brackets to represent multiplication in situations involving subtraction. The arrangement of brackets also led to errors in the order of operations. Further analysis suggested that regular application of procedures on familiar algebraic structures may give the illusion of systemic structure sense. We recommend that the teaching of algebraic expressions must emphasise what the arrangement of an expression means before focusing on how to operate on the expression.Contribution: The research contributes to mathematics teaching by suggesting teaching strategies to improve on learners’ understanding of the role of brackets in algebraic expressions, by considering the arrangement of the components in structures.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140983242","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}

引用次数: 0

Comparing the finite and infinite limits of sequences and functions: A mathematical and phenomenological analysis and its implications in Spanish textbooks 比较序列和函数的有限极限和无限极限：数学和现象学分析及其对西班牙语教科书的影响

IF 1.2

Pythagoras Pub Date : 2024-03-29 DOI: 10.4102/pythagoras.v45i1.774

Mónica Arnal-Palacián, Francisco J. Claros-Mellado, M. T. Sánchez-Compaña

引用次数: 0

Relating motivation and learning strategies to algebra course results in a foundation programme 在基础课程中将学习动机和学习策略与代数课程成绩联系起来

IF 1.2

Pythagoras Pub Date : 2024-01-29 DOI: 10.4102/pythagoras.v45i1.781

W. Baumgartner, Erica D. Spangenberg, Geoffrey V. Lautenbach

引用次数: 0

Developing undergraduate engineering mathematics students’ conceptual and procedural knowledge of complex numbers using GeoGebra 使用 GeoGebra 开发本科工程数学学生的复数概念和程序知识

IF 1.2

Pythagoras Pub Date : 2023-12-21 DOI: 10.4102/pythagoras.v44i1.763

Philemon M. Seloane, Sam Ramaila, Mdutshekelwa Ndlovu

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

引用次数: 0

Ascertaining Grade 10 learners’ levels of mathematical modelling competency through solving simultaneous equations word problems 通过解决同步方程文字题确定十年级学生的数学建模能力水平

IF 1.2

Pythagoras Pub Date : 2023-12-08 DOI: 10.4102/pythagoras.v44i1.728

Rajendran Govender, Dzivaidzo Machingura

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

引用次数: 0

Solving quadratic equations by completing the square: Applying Newman’s Error Analysis Model to analyse Grade 11 errors 通过完成平方来解一元二次方程：应用纽曼错误分析模型分析 11 年级错误

IF 1.2

Pythagoras Pub Date : 2023-12-07 DOI: 10.4102/pythagoras.v44i1.742

T. Makgakga

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

引用次数: 0

The impact of artificial intelligence and the future of ChatGPT for mathematics teaching and learning in schools and higher education 人工智能的影响以及 ChatGPT 在学校和高等教育数学教学中的前景

IF 1.2

Pythagoras Pub Date : 2023-12-04 DOI: 10.4102/pythagoras.v44i1.787

Rajendran Govender

引用次数: 0

Conversations reflecting boundary-objects-related details of a teacher’s local practices with spreadsheet algebra programs on variables 反映教师在当地使用电子表格变量代数程序时与边界对象有关的细节的对话

IF 1.2

Pythagoras Pub Date : 2023-11-30 DOI: 10.4102/pythagoras.v44i1.756

M. Gierdien, Wajeeh M. Daher, Awni M. Abu-Saman

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

引用次数: 0

Talk that supports learners’ folding back for growth in understanding geometry 支持学习者折返的谈话，促进对几何知识的理解

IF 1.2

Pythagoras Pub Date : 2023-11-30 DOI: 10.4102/pythagoras.v44i1.711

K. Chuene, Koena Mabotja, S. Maoto

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

引用次数: 0

Pythagoras最新文献