Pythagoras最新文献_第4页

Novice and expert Grade 9 teachers’ responses to unexpected learner offers in the teaching of algebra 初教和专教九年级教师在代数教学中对意外学习者的反应

IF 1.2

Pythagoras Pub Date : 2021-12-15 DOI: 10.4102/pythagoras.v42i1.624

Julian Moodliar, Lawan Abdulhamid

{"title":"Novice and expert Grade 9 teachers’ responses to unexpected learner offers in the teaching of algebra","authors":"Julian Moodliar, Lawan Abdulhamid","doi":"10.4102/pythagoras.v42i1.624","DOIUrl":"https://doi.org/10.4102/pythagoras.v42i1.624","url":null,"abstract":"In South Africa, limited studies have been conducted investigating responsive teaching and little is known about how teachers respond to unexpected events ‘in the moment’ that did not form part of their planning. In this article, we report how a Grade 9 novice and expert teacher responded to unexpected learner offers during the teaching of algebra using a qualitative case study approach. Three consecutive lessons for each teacher were video recorded, transcribed and analysed. Our units of analysis for episodes were teachers’ responses to unexpected learner offers and we coded the responses as ‘appropriate’ or ‘inappropriate’. Indicators used to highlight the degree of quality of the response were ‘minimum’, ‘middle’ and ‘maximum’ if a response was coded as appropriate to a learner’s offer. Once lessons were analysed, the first author conducted video-stimulated recall interviews with each participant to gain insight into the two teachers’ thoughts and decision-making when responding to unexpected learner offers. The findings from this study illustrated that the novice teacher failed to press learners when their thinking was unclear, chose to ignore or provided an incorrect answer when faced with an unexpected learner offer. Conversely, the expert teacher continuously interrogated learner offers by pressing if a learner offer was unclear or if she wanted learners to explain their thinking. This suggests that the expert teacher’s responses were highly supportive of emergent mathematics learning in the collective classroom space.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43684210","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: 3

Constructing mental diagrams during problem-solving in mathematics 在数学问题解决过程中构建心理图

IF 1.2

Pythagoras Pub Date : 2021-11-29 DOI: 10.4102/pythagoras.v42i1.633

Vimolan Mudaly

{"title":"Constructing mental diagrams during problem-solving in mathematics","authors":"Vimolan Mudaly","doi":"10.4102/pythagoras.v42i1.633","DOIUrl":"https://doi.org/10.4102/pythagoras.v42i1.633","url":null,"abstract":"In mathematics, problem-solving can be considered to be one of the most important skills students need to develop, because it allows them to deal with increasingly intricate mathematical and real-life issues. Often, teachers attempt to try to link a problem with a drawn diagram or picture. Despite these diagrams, whether given or constructed, the student still individually engages in a private discourse about the problem and its solution. These discourses are strongly influenced by their a priori knowledge and the given information in the problem itself. This article explores first-year pre-service teachers’ mental problem-solving skills. The emphasis was not on whether they solved the problems, but rather on their natural instincts during the problem-solving process. The research shows that some students were naturally drawn to construct mental images during the problem-solving process while others were content to simply leave the question blank. The data were collected from 35 first-year volunteer students attending a second semester geometry module. The data were collected using task sheets on Google Forms and interviews, which were based on responses to the questions. An interpretive qualitative analysis was conducted in order to produce deeper meaning (insight). The findings point to the fact that teachers could try to influence how students think during the problem-solving process by encouraging them to engage with mental images.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46321796","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: 2

Insights into the reversal error from a study with South African and Spanish prospective primary teachers 一项针对南非和西班牙未来小学教师的研究对逆转错误的见解

IF 1.2

Pythagoras Pub Date : 2021-11-25 DOI: 10.4102/pythagoras.v42i1.613

Calos Soneira, S. Bansilal, Reginald Gerald Govender

{"title":"Insights into the reversal error from a study with South African and Spanish prospective primary teachers","authors":"Calos Soneira, S. Bansilal, Reginald Gerald Govender","doi":"10.4102/pythagoras.v42i1.613","DOIUrl":"https://doi.org/10.4102/pythagoras.v42i1.613","url":null,"abstract":"This study, using a quantitative approach, examined Spanish and South African pre-service teachers’ responses to translating word problems based on direct proportionality into equations. The participants were 79 South African and 211 Spanish prospective primary school teachers who were in their second year of a Bachelor of Education degree. The study’s general objective was to compare the students’ proficiency in expressing direct proportionality word problems as equations, with a particular focus on the extent of the reversal error among the students’ responses. Furthermore, the study sought to test the explanatory power of word order matching and the static comparison as causes of the reversal error in the two contexts. The study found that South African students had a higher proportion of correct responses across all the items. While nearly all the errors made by Spanish students were reversals, the South African group barely committed reversal errors. However, a subgroup of the South African students made errors consisting of equations that do not make sense in the situation, suggesting that they had poor foundational knowledge of the multiplicative comparison relation and did not understand the functioning of the algebraic language. The study also found that the word order matching strategy has some explanatory power for the reversal error in both contexts. However, the static comparison strategy offers explanatory power only in the Spanish context, suggesting that there may be a difference in curriculum and instructional approaches in the middle and secondary years of schooling, which is when equations are taught.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46122748","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

Reflecting on dilemmas in digital resource design as a response to COVID-19 for learners in under-resourced contexts 在资源不足的背景下，反思数字资源设计中的困境，以应对新冠肺炎

IF 1.2

Pythagoras Pub Date : 2021-11-09 DOI: 10.4102/pythagoras.v42i1.599

Pamela Vale, Mellony Graven

{"title":"Reflecting on dilemmas in digital resource design as a response to COVID-19 for learners in under-resourced contexts","authors":"Pamela Vale, Mellony Graven","doi":"10.4102/pythagoras.v42i1.599","DOIUrl":"https://doi.org/10.4102/pythagoras.v42i1.599","url":null,"abstract":"The coronavirus disease 2019 (COVID-19) pandemic and the resulting school closures in South Africa necessitated a major shift in how to support learners’ ongoing mathematics learning. For 10 weeks learners were strictly confined to their homes with restrictions that prohibited seeing any person outside of their household. The only means to access learners and parents in their homes was to reimagine our South African Numeracy Chair Project work and transform it from predominantly face-to-face interventions to digital modalities. As a result, we initiated a project of digital resource development and distribution, particularly focused on our local community in the Eastern Cape. Twenty-two existing resources and 36 purpose-designed resources were shared via Facebook. Through in-depth post hoc reflection of the rapid digitalisation of our materials and ways of working we address these questions: (1) In relation to learners’ new ‘ecology of learning’ during lockdown what digital access modality and platforms were most fit-for-purpose in sharing mathematics learning resources? (2) What principles informed resource design and adaptation for digital distribution and use? (3) What dilemmas were confronted in making decisions about resource design and distribution?. These questions are answered through a document review and post hoc reflections on the noted dilemmas. We share some feedback received and discuss implications of our work and the dilemmas confronted for the provision of quality digital resources for supporting mathematics learning in historically disadvantaged and under-resourced communities in a post pandemic world.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49121914","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: 1

Early career teacher’s approach to fraction equivalence in Grade 4: A dialogic teaching perspective 对话教学视角下初任教师四年级分数等值的探索

IF 1.2

Pythagoras Pub Date : 2021-11-09 DOI: 10.4102/pythagoras.v42i1.623

Benjamin Shongwe

引用次数: 2

Grade 9 learners’ understanding of fraction concepts: Equality of fractions, numerator and denominator 九年级学生对分数概念的理解：分数、分子和分母相等

IF 1.2

Pythagoras Pub Date : 2021-10-21 DOI: 10.4102/pythagoras.v42i1.602

Methuseli Moyo, F. Machaba

{"title":"Grade 9 learners’ understanding of fraction concepts: Equality of fractions, numerator and denominator","authors":"Methuseli Moyo, F. Machaba","doi":"10.4102/pythagoras.v42i1.602","DOIUrl":"https://doi.org/10.4102/pythagoras.v42i1.602","url":null,"abstract":"Our research with Grade 9 learners at a school in Soweto was conducted to explore learners’ understanding of fundamental fraction concepts used in applications required at that level of schooling. The study was based on the theory of constructivism in a bid to understand whether learners’ transition from whole numbers to rational numbers enabled them to deal with the more complex concept of fractions. A qualitative case study approach was followed. A test was administered to 40 learners. Based on their written responses, eight learners were purposefully selected for an interview. The findings revealed that learners’ definitions of fraction were neither complete nor precise. Particularly pertinent were challenges related to the concept of equivalent fractions that include fraction elements, namely the numerator and denominator in the phase of rational number. These gaps in understanding may have originated in the early stages of schooling when learners first conceptualised fractions during the late concrete learning phase. For this reason, we suggest a developmental intervention using physical manipulatives to promote understanding of fractions before inductively guiding learners to construct algorithms and transition to the more abstract applications of fractions required in Grade 9.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47011133","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: 4

Design principles to consider when student teachers are expected to learn mathematical modelling 学生教师学习数学建模时要考虑的设计原则

IF 1.2

Pythagoras Pub Date : 2021-09-29 DOI: 10.4102/pythagoras.v42i1.618

R. Durandt

{"title":"Design principles to consider when student teachers are expected to learn mathematical modelling","authors":"R. Durandt","doi":"10.4102/pythagoras.v42i1.618","DOIUrl":"https://doi.org/10.4102/pythagoras.v42i1.618","url":null,"abstract":"This article sets out design principles to consider when student mathematics teachers are expected to learn mathematical modelling during their formal education. Blum and Leiß’s modelling cycle provided the theoretical framework to explain the modelling process. Learning to teach mathematical modelling, and learning to solve modelling tasks, while simultaneously fostering positive attitudes, is not easy to achieve. The inclusion of real-life examples and applications is regarded as an essential component in mathematics curricula worldwide, but it largely depends on mathematics teachers who are well prepared to teach modelling. The cyclic process of design-based research was implemented to identify key elements that ought to be considered when mathematical modelling is incorporated in formal education. Fifty-five third-year student teachers from a public university in South Africa participated in the study. Three phases were implemented, focusing firstly on relevance (guided by a needs analysis), secondly on consistency and practicality via the design and implementation of two iterations, and lastly on effectiveness by means of reflective analysis and evaluation. Mixed data were collected via a selection of qualitative instruments, and the Attitudes Towards Mathematical Modelling Inventory. Through content analyses students’ progress was monitored. Results analysed through SPSS showed significant positive changes in their enjoyment and motivation towards mathematical modelling. Student teachers require sufficient resources and opportunities through their formal education to participate regularly in mathematical modelling activities, to develop competence in solving modelling tasks, and to augment positive attitudes. This study adds value to the global discussion related to teachers’ professional development regarding mathematical modelling.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48404415","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: 2

Professional development for teachers’ mathematical problem-solving pedagogy – what counts? 教师数学问题解决教学法的专业发展——什么重要?

IF 1.2

Pythagoras Pub Date : 2021-08-25 DOI: 10.4102/pythagoras.v42i1.532

Brantina Chirinda

引用次数: 3

Bridging powerful knowledge and lived experience: Challenges in teaching mathematics through COVID-19 衔接强大的知识和实际经验:2019冠状病毒病期间数学教学面临的挑战

IF 1.2

Pythagoras Pub Date : 2021-08-13 DOI: 10.4102/pythagoras.v42i1.593

K. Brodie, Deepa Gopal, Julian Moodliar, Takalani Siala

{"title":"Bridging powerful knowledge and lived experience: Challenges in teaching mathematics through COVID-19","authors":"K. Brodie, Deepa Gopal, Julian Moodliar, Takalani Siala","doi":"10.4102/pythagoras.v42i1.593","DOIUrl":"https://doi.org/10.4102/pythagoras.v42i1.593","url":null,"abstract":"The coronavirus disease 2019 (COVID-19) pandemic supported an investigation of ongoing challenges as to whether and how to make mathematics relevant to learners’ lifeworlds. Given that COVID-19 created major disruptions in all learners’ lives, we developed and taught tasks that attempted to make links between their experiences of the pandemic and disciplinary mathematical knowledge. We located our investigation in current debates about the extent to which disciplinary knowledge can be linked to learners’ out-of-school experiences. We developed and analysed two tasks about COVID-19 that could support link-making and productive disciplinary engagement, and analysed one Grade 10 teacher teaching these tasks. We found that linking mathematics to learners’ lifeworlds is both possible and extremely difficult in relation to task design and how the teacher mediates the tasks. In relation to task design, we argue that teachers cannot do it alone;they need to be supported by the curriculum and textbooks. In relation to mediation, we saw that teacher practices are difficult to shift, even in the best of circumstances. We articulate the complexities and nuances involved in bridging powerful knowledge and lived experience and thus contribute to debates on how to teach powerful knowledge in relation to learners’ lifeworlds.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41472779","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: 2

Flexible teaching of mathematics word problems through multiple means of representation 运用多种表征手段灵活教学数学题

IF 1.2

Pythagoras Pub Date : 2021-08-10 DOI: 10.4102/pythagoras.v42i1.575

M. M. Moleko, M. Mosimege

{"title":"Flexible teaching of mathematics word problems through multiple means of representation","authors":"M. M. Moleko, M. Mosimege","doi":"10.4102/pythagoras.v42i1.575","DOIUrl":"https://doi.org/10.4102/pythagoras.v42i1.575","url":null,"abstract":"Flexible teaching of mathematics word problems is essential to improve learning. Flexible teaching is vital in terms of providing meaningful learning, creating inclusive learning spaces and making content accessible. As such, teachers need to strive to provide flexible teaching of mathematics word problems in order to optimise and maximise learning. In line with this notion, therefore, the qualitative case study reported in this article aimed to explore the implementation of one aspect of universal design for learning (UDL), namely multiple means of representation (MMR), to guide flexible teaching of mathematics word problems. Data were collected using focus group discussions, reflection and observation sessions in which five high school mathematics teachers and a Head of Department were involved. The teachers participated in a mini-workshop on the application of the UDL principles which was organised to introduce and induct them to the approach. The study showed that MMR can be used to help guide flexible teaching of mathematics word problems by providing varied options for comprehension: options for language, mathematical expressions and symbols, as well as options for perception. The findings of the study recommend the need for teachers to adapt their teaching by considering the application of the MMR principle to guide and promote flexible teaching of mathematics word problems.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49663618","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: 3