Opportunities for learning: the use of variation to analyse examples of a paradigm shift in teaching primary mathematics in England

Al-Murani, Thabit; Kilhamn, Cecilia; Morgan, Debbie; Watson, Anne

doi:10.1080/14794802.2018.1511460

Cited by 11 publications

(9 citation statements)

References 11 publications

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“…In recent years, international comparison studies have drawn attention to the role of variation in understanding curriculum design and the analysis of classroom practice (e.g. Al-Murani et al, 2019;Huang & Li, 2017;Sun, 2011). While earlier research often focussed on understanding Chinese mathematics classrooms, analysis from a perspective of variation theory has now been undertaken in a wide range of settings (Huang & Li, 2017), including Japanese problem-solving lessons (Hino, 2017).…”

Section: The Analytical Lens: Variation Theorymentioning

confidence: 99%

The use of carefully planned board work to support the productive discussion of multiple student responses in a Japanese problem-solving lesson

Baldry

Mann

Horsman³

et al. 2022

J Math Teacher Educ

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In this paper, we analyse a grade 8 (age 13–14) Japanese problem-solving lesson involving angles associated with parallel lines, taught by a highly regarded, expert Japanese mathematics teacher. The focus of our observation was on how the teacher used carefully planned board work to support a rich and extensive plenary discussion (neriage) in which he shifted the focus from individual mathematical solutions to generalised properties. By comparing the teacher’s detailed prior planning of the board work (bansho) with that which he produced during the lesson, we distinguish between aspects of the lesson that he considered essential and those he treated as contingent. Our analysis reveals how the careful planning of the board work enabled the teacher to be free to explore with the students the multiple alternative solution methods that they had produced, while at the same time having a clear overall purpose relating to how angle properties can be used to find additional solution methods. We outline how these findings from within the strong tradition of the Japanese problem-solving lesson might inform research and teaching practice outside of Japan, where a deep heritage of bansho and neriage is not present. In particular, we highlight three prominent features of this teacher’s practice: the detailed lesson planning in which particular solutions were prioritised for discussion; the considerable amount of time given over to student generation and comparison of alternative solutions; and the ways in which the teacher’s use of the board was seen to support the richness of the mathematical discussions.

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Section: The Analytical Lens: Variation Theorymentioning

confidence: 99%

The use of carefully planned board work to support the productive discussion of multiple student responses in a Japanese problem-solving lesson

Baldry

Mann

Horsman³

et al. 2022

J Math Teacher Educ

View full text Add to dashboard Cite

show abstract

“…Variation theory is a general theory of learning that has been applied specifically to learning mathematics. A central notion within variation theory is that in order to discern one aspect of a phenomenon, that aspect needs to be varied while other aspects remain unchanged (Al-Murani, Kilhamn, Morgan, & Watson, 2019). The aspect of the phenomenon that varies is called the 'dimension of variation'.…”

Section: Language Of Variationmentioning

confidence: 99%

Relative difficulty of early grade compare type word problems: Learning from the case of isiXhosa

Mostert

2020

Pythagoras

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to English, such isiXhosa, one of South Africa's nine official African languages.This study contributes to the limited research on early grade word problems in languages other than English by examining compare type word problems in isiXhosa. The study offers a sub-typology for compare type (difference unknown) problems, both in English and in isiXhosa. The relative difficulty of the problems in the isiXhosa sub-typology is then empirically tested using data collected from an adapted early grade mathematics assessment (EGMA).The following two research questions are answered in this study:• Are certain types of isiXhosa compare type problem easier for learners to solve than others? • If so, is the relative difficulty influenced by:ß the formulation of the comparative question ß the problem situation? Theoretical and methodological perspectivesThis article is informed by theoretical perspectives and methodological tools from linguistics that have proved helpful for research into the way different languages express mathematical concepts, as proposed in a recent paper by Edmonds-Wathen (2019). This article also draws on theoretical perspectives from variation theory, a general theory of learning largely developed by Marton and Booth (1997) and later extended by Watson and Mason (2005) in relation to mathematics learning.Edmonds-Wathen (2019) proposes using a typological framing for research on the diversity of mathematical expression in different languages and using interlinear morphemic glossing to present examples in different languages. These perspectives and methodologies are particularly pertinent for studies done by a researcher not fluent in the language that is being studied. Edmonds-Wathen points out that linguists often work with languages that they are unfamiliar with, either by working with translated texts or by working closely with bilingual speakers. She argues that mathematics education researchers can, and do, work in similar ways, with this study being a case in point. This study was undertaken by an English speaker with an emergent understanding of isiXhosa. The researcher worked very closely with a number of isiXhosa speakers to deepen her understanding of isiXhosa, particularly in relation to compare type problems.

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“…It is important to bear in mind that it is not uncommon to use phenomenography and VT as tools for the analysis of data materials that were generated for other purposes (e.g. Al-Murani et al, 2019;Baillie et al, 2001;Marton, 2006;Marton & Häggström, 2017). Further, in both Marton and Booth (1997) and Marton (2015) a vast number of the re-analyzed studies where not originally designed with VT-analyses in mind.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Enrichment in school principals’ ways of seeing mathematics

Innabi

Emanuelsson

2020

International Journal of Mathematical Education in Science and

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This study presents a case of a problem that did not originate in theory but rather ended in theory. It addresses the issue of the prevalent, traditional public view of the nature of mathematics and that of its teaching and learning that might hamper mathematics reform. In this study, we present a five-day professional development programme that was designed and conducted within the context of practice-oriented research to help elementary school principals to enrich their views of mathematics in order to see mathematics in a different way, more aligned with mathematics reform. Data was generated before, during, and at the end of this programme, and results showed significant enrichment in participants' views of mathematics. By using the Variation Theory of Learning, this study aimed to understand how this programme of short duration can make a difference. The core tenet of Variation Theory is that people learn through experiencing differences and similarities (in this order). The Variation Theory of Learning is used as a lens to see the programme's framework, its activities, and outcomes. The analysis clarified that principals' ways of seeing mathematics were enriched when they experienced patterns of variations and invariance, in particular, the pattern of contrast.

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Opportunities for learning: the use of variation to analyse examples of a paradigm shift in teaching primary mathematics in England

Cited by 11 publications

References 11 publications

The use of carefully planned board work to support the productive discussion of multiple student responses in a Japanese problem-solving lesson

The use of carefully planned board work to support the productive discussion of multiple student responses in a Japanese problem-solving lesson

Relative difficulty of early grade compare type word problems: Learning from the case of isiXhosa

Enrichment in school principals’ ways of seeing mathematics

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