Developing the use of diagrammatic representations in primary mathematics through professional development

Barmby, Patrick; Bolden, David; Raine, Stephanie; Thompson, Lynn

doi:10.1080/00131881.2013.825164

Cited by 7 publications

(6 citation statements)

References 44 publications

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“…Moreover, Ben spent much time emphasising the links between the verbal and the symbolic representations, helping learners to see concrete examples of the role of the numerator and denominator in the symbolic representation of fraction. This finding was in line with Azuka (2009), Barmby et al (2014), Naidoo (2011), who revealed that the use of representations can be more effective when concrete and semi-concrete aids are used in teaching and learning of mathematics.…”

Section: Discussionsupporting

confidence: 83%

“…Muraka's study (2008) observed that the consistent and coherent use of one type of representation can bridge student understanding over time because of its focus on mathematical relationships and problem-solving processes. Many researchers argue that the use of representations can be more effective and when concrete and semi-concrete aids are used in teaching and learning of mathematics, the conceptual understanding is improved (Azuka 2009;Barmby et al 2014;Naidoo 2011). Representations commonly used in the early years of schooling include concrete materials, diagrams or pictures, symbols, spoken language and experiences and are used to present mathematical idea with the aim of making it accessible to learners (Green & Hall 1997).…”

Section: Literature Reviewmentioning

confidence: 99%

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The impact of different approaches to the teaching of Grade 5 fraction by three experienced teachers

Ubah

2021

South African Journal of Childhood Education

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Background: Many teachers for different reasons recognise the teaching of fraction as a challenge. This research explored the teaching of fraction in Grade 5 by three experienced teachers (Ben, Greg and Will) in KwaZulu-Natal province, South Africa.Aim: The purpose of this study was to investigate the impact of different approaches to the teaching of Grade 5 fraction by three experienced teachers.Method: Three teachers and 177 learners were purposively sampled for this study. Classroom observations, interview and fraction achievement test (FAT) were instruments used for data collection. Hence, this study employed a mixed method, where both quantitative and qualitative data sets were collected at the same time, and the data were analysed at the same time in order to discuss the findings.Results: The quantitative data were analysed using descriptive statistics and analysis of covariance (ANCOVA), whilst the qualitative data were analysed in themes. The results showed that learners of teacher Ben performed significantly better than those of teachers Will and Greg. The findings revealed that a combination of good practices and appropriate use of multiple representations by teacher Ben improved his learners’ achievement in addition of fraction more than other learners taught by the other two teachers.Conclusion: The study recommends that mathematics teachers should endeavour to facilitate learners’ conceptual knowledge of fraction by using appropriate teaching approach in their instruction, namely, learner-centred approach, activity-based learning, use of mother tongue for clarity and use of multiple representations. This recommendation will improve learners’ knowledge and conceptual understanding of fraction and algebra in its entity.

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Section: Discussionsupporting

confidence: 83%

Section: Literature Reviewmentioning

confidence: 99%

The impact of different approaches to the teaching of Grade 5 fraction by three experienced teachers

Ubah

2021

South African Journal of Childhood Education

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“…Visual representations (VRs) enable children to make connections between their existing experiences and mathematical concepts (Barmby et al, 2013). Additionally, VRs help students gain insight into more abstract ideas and support the problem-solving process (Gersten et al, 2009).…”

Section: Conceptual Understanding Through Visual Representationsmentioning

confidence: 99%

Use of Visual Representations to Support English Learners' Math Talk

Falomir¹

2019

Proceedings of the 2019 AERA Annual Meeting

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Visual representations (VRs) support problem solving skills by helping students clarify ideas, support reasoning, and build concept understanding. VRs should be paired with meaningful discussions and conversations to fully achieve students' conceptual understanding and provide language opportunities (Murata & Stewart, 2017;Bond & Wasik, 2009).Quantitative analysis examined the frequency of types of VRs and their associated purposes.Qualitative analysis explored the patterns in interactive, inferential, student-teacher talk integrating VRs. Results indicated that teachers: (a) frequently incorporated different types of VRs; (2) initiated and led classroom conversations; and (3) focused conversations on content around VRs using a literal or decontextualized level of language abstraction.

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“…The importance of pupils' understanding and the use of different representations is widely noted in the mathematics education literature [76]. However, there is mixed evidence for efficacy [77].…”

Section: Models and Representationsmentioning

confidence: 99%

“…For example, greater use may or may not lead to changes in how representations are used in terms of classroom activity, but may change classroom talk. The increased use is also sensitive to forms of professional development [76].…”

Section: Models and Representationsmentioning

confidence: 99%

The Mathematics Teacher Exchange and ‘Mastery’ in England: The Evidence for the Efficacy of Component Practices

et al. 2018

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‘Mastery’ is central to current policy in mathematics education in England, influenced by East Asian success in transnational assessments. We scrutinise the prospects for mastery pedagogies to improve pupil attainment in English primary schools. The Mathematics Teacher Exchange (MTE)—an element of the mastery innovation—involves teachers visiting Shanghai and then hosting Shanghai teachers in their schools. Informed by programme evaluation, core component practices are analysed, which were implemented by schools belonging to the first cohort of MTE schools. These consist of: varied and interactive teaching; meaningful and coherent mathematical activity; and full curriculum access for all. These elements are supported, optimally, by collaborative, embedded, and mathematically focused professional development. Details of the implemented pedagogy and forms of professional development are reported. Differences from prevailing practice in primary mathematics in England are highlighted. Evidence is reviewed from quasi-experimental trials, reviews and meta-analyses, and rigorous observational studies of the efficacy of practices similar to the MTE mastery pedagogy components in order to assess the prospects for increases in pupil attainment. The analysis suggests that many of the specific practices, if considered individually, have the potential to improve attainment, though overall policy ambitions may not be realised. Based on the review, component practices are identified for which existing evidence justifies immediate implementation by schools and teachers. In addition, practices that would benefit from further testing and evaluation are highlighted.

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Developing the use of diagrammatic representations in primary mathematics through professional development

Cited by 7 publications

References 44 publications

The impact of different approaches to the teaching of Grade 5 fraction by three experienced teachers

The impact of different approaches to the teaching of Grade 5 fraction by three experienced teachers

Use of Visual Representations to Support English Learners' Math Talk

The Mathematics Teacher Exchange and ‘Mastery’ in England: The Evidence for the Efficacy of Component Practices

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