The Janet Duffin Fund administers a generous gift made to the British Society for Research into Learning Mathematics (BSRLM) by Bill Duffin, in memory of his wife Janet, a longstanding and active member of the Society. The Fund covers the costs of the Janet Duffin Award and Lecture. It is managed by the BSRLM Executive.
To find out more about Janet Duffin, read this tribute which describes her contributions towards mathematics education research and towards cultivating a love of mathematics and numeracy among students of all ages:
Remembering Janet Duffin
The Janet Duffin Award is made annually by the Society to the author (or authors) of what is judged to be the most significant contribution – either research paper or essay review – published in the Society’s journal, Research in Mathematics Education [RME], during the preceding calendar year. All research papers or essay reviews published in RME during the calendar year in question are considered for the award.
The winner of the award is decided by inviting all BSRLM members to participate in a poll and to vote for the article they have read (from those above) which they consider had the most significance for them.
The author (or the nominee of multiple authors) is invited to attend one of the Society’s day conferences to receive the award, and to deliver the Janet Duffin Lecture. The Fund will meet the expenses (including travel and accommodation) incurred in giving the Lecture, and in providing a token of the award. Where it proves possible within its indicative budget, the Fund will endeavour to cover the costs of all authors attending.
Janet Duffin Award Winners
Hunter, J. (2022). Challenging and disrupting deficit discourses in mathematics education: Positioning young diverse learners to document and share their mathematical funds of knowledge. Research in Mathematics Education, 24(2), 187–201. https://doi.org/10.1080/14794802.2022.2088607
Barclay, N. (2021). Valid and valuable: lower attaining pupils’ contributions to mixed attainment mathematics in primary schools. Research in Mathematics Education, 23(2), 208-225. https://doi.org/10.1080/14794802.2021.1897035
Marie-Josée Bisson, Camilla Gilmore, Matthew Inglis and Ian Jones
An ongoing debate concerns whether novel mathematical concepts are better learned using contextualised or decontextualised representations. A barrier to resolving this debate, and therefore to progress in the discipline, has been the paucity of validated methods of measuring students’ understanding of mathematical concepts. We developed an innovative and efficient method for measuring, in experimental settings, students’ understanding of any mathematical concept using comparative judgement. We demonstrate the method by applying it to the comparison of learning outcomes from two teaching conditions. Participants (260 15–16 year olds across six schools) were introduced to differential calculus using contextualised or decontextualised representations. We then assessed participants’ comparative conceptual understanding of derivatives. We found evidence that contextualised and decontextualised representations were equally effective at promoting student learning in this context. The assessment method yielded valid and reliable results, suggesting that it offers a robust and efficient approach for the problem of assessing conceptual understanding in experimental or other comparative settings.
The 2019 Janet Duffin Award has been awarded to TWO teams of researchers.
Mathematical reasoning requires perseverance to overcome the cognitive and affective difficulties encountered whilst pursuing a reasoned line of enquiry. The aims of the study were: to understand how children’s perseverance in mathematical reasoning (PiMR) manifests in reasoning activities, and to examine how PiMR can be facilitated through a focus on children’s active goals. The article reports on children aged 10–11 from two English schools, purposively selected for their limited PiMR. Data relating to their cognitive and affective responses and the focus of their attention, a conative component, were collected by observation and interview. The study defines the construct perseverance in mathematical reasoning. Conative characteristics of PiMR were used to analyse the cognitive–affective interplay during reasoning. It revealed the role that children’s active goals play in restricting and enabling PiMR. The article offers new approaches to designing pedagogic interventions and collecting and analysing data relating to perseverance in vivo.
Diana Zakaryan & Miguel Ribeiro
Recognising teachers’ knowledge as one of the main factors influencing their practices and student learning, we aim to contribute to obtaining a better and deeper understanding of the specificities of teachers’ mathematical knowledge. A case study involving one 8th-grade Chilean mathematics teacher is presented in the context of rational numbers. Using video and audio recordings of classroom practices, questionnaires, and an interview, we sought to characterise, and better understand the content of the Knowledge of Topics from the perspective of the Mathematics Teachers’ Specialized Knowledge (MTSK) theoretical framework. The results reveal some critical aspects that teacher education should focus on, while also identifying lost opportunities and examples of “good” practices, thus contributing to the refinement of the MTSK conceptualisation. The conclusions can be considered in a broader perspective, with implications for teacher education in other contexts.
Julie Alderton and Sue Gifford
The 2018 Janet Duffin Award has been awarded to Julie Alderton and Sue Gifford for their paper Teaching mathematics to lower attainers: dilemmas and discourses. Research in Mathematics Education 20(1), 53-69.
This article draws on Foucault’s concepts of power and discourse to explore the issues of teaching mathematics to low attainers in primary schools in England. We analyse a data set of interviews, from a larger study, with the mathematics teachers of one child across three years, showing how accountability practices, discourses of ability and inclusion policies interrelate to regulate both teachers and student. We demonstrate the impact of neoliberal policy discourses on teachers’ practices and how they are caught up in conflicting ways by an accountability regime that subverts inclusive pedagogies, requiring teachers to monitor, label and assign within-child deficits. In spite of these regulatory technologies we identify contradictory fault lines between mathematics education policy discourses which we argue provide the potential for developing critical awareness of accepted practices and opportunities for change.
The 2017 Janet Duffin Award has been awarded to Susan Staats for her paper The poetics of argumentation: the relevance of conversational repetition for two theories of emergent mathematical reasoning. Research in Mathematics Education 19(3), 276-292.
Poetic structures emerge in spoken language when speakers repeat grammatical phrases that were spoken before. They create the potential to amend or comment on previous speech, and to convey meaning through the structure of discourse. This paper considers the ways in which poetic structure analysis contributes to two perspectives on emergent mathematical reasoning: Toulmin’s model of argumentation and Martin, Towers, & Pirie’s theory of collaborative coactions in multi-speaker discourse. Poetic structures appear in varied argument types and at varied educational levels. They appear to facilitate speakers’ expression of warrants, backings, qualifications, and coactions.
Note that a there is a video available of the Janet Duffin Lecture given by Susan Staats at the BSRLM 2019 Spring Conference.
Click here for the link.
Julian Williams and Sophina Choudry
The 2016 Janet Duffin Award has been awarded to Julian Williams and Sophina Choudry for their paper Mathematics capital in the educational field: Bourdieu and beyond. Research in Mathematics Education 18(1), 3-21.
Mathematics education needs a better appreciation of the dominant power structures in the educational field: Bourdieu’s theory of capital provides a good starting point. We argue from Bourdieu’s perspective that school mathematics provides capital that is finely tuned to generationally reproduce the social structures that serve to keep the powerful in power, while ensuring that less powerful groups are led to accept their own failure in mathematics. Bourdieu’s perspective thereby highlights theoretical inadequacies in much mathematics education research, insofar as it presumes a consensus about a ‘what works agenda’ for improving achievement for all. Drawing on one case where we manufactured awkward facts, we illustrate a Bourdieusian interpretation of mathematics capital as reproductive, and the crucial role of its cultural arbitrary. We then criticise the Bourdieusian concept of ‘mathematical capital’ as the value of mathematical competence in practice and propose to extend his tools to include the contradictory ‘use’ and ‘exchange’ values of mathematics instead: we will show how this conceptualisation goes ‘beyond Bourdieu’ and helps explain how teaching-learning might (ideally) produce ‘cultural use value’ in mathematical competence, while still recognising the contradictions teachers and learners face. Finally, we suggest how critical education research generally can benefit from this theoretical framework: (1) in exposing the interest of the dominant classes; but also (2) in researching critical pedagogic alternatives that challenge orthodoxy in educational policy and practice both in mathematics education and more generally.
Christine Howe, Stefanie Luthman, Kenneth Ruthven, Neil Mercer, Riikka Hofmann, Sonia Ilie & Paula Guardia
The 2015 Janet Duffin Award has been awarded by the editorial boards to Christine Howe for her paper (with co-authors Stefanie Luthman, Kenneth Ruthven, Neil Mercer, Riikka Hofmann, Sonia Ilie & Paula Guardia) Rational number and proportional reasoning in early secondary school: towards principled improvement in mathematics. Research in Mathematics Education 17(1), 38-56.
Reflecting concerns about student attainment and participation in mathematics and science, the Effecting Principled Improvement in STEM Education (epiSTEMe) project attempted to support pedagogical advancement in these two disciplines. Using principles identified as effective in the research literature (and combining these in a novel fashion), the project developed topic modules for early secondary-school teaching in the UK, arranged for their implementation in classrooms, and evaluated the results. This article reports the development, implementation and evaluation of the epiSTEMe mathematics module entitled Fractions, Ratios and Proportions. The module covers aspects of rational number and proportional reasoning relevant to the early secondary curriculum, and was developed in collaboration with teachers, implemented in 11 classrooms, and evaluated through comparison with 16 control classrooms where the topic was addressed using established methods. Students who used the epiSTEMe materials made significantly greater progress than control students as regards topic mastery, while holding positive opinions about their teaching and learning experiences.
The 2014 Janet Duffin Award has been awarded by the editorial boards to Rachel Marks for her paper Educational triage and ability-grouping in primary mathematics: a case-study of the impacts on low-attaining pupils. Research in Mathematics Education 16(1), 38-53.
This case-study, drawing on an unanticipated theme arising from a wider study of ability-grouping in primary mathematics, documents some of the consequences of educational triage in the final year of one primary school. The paper discusses how a process of educational triage, as a response to accountability pressures, is justified by teachers on the basis of shared theories about ability and potential. Attainment gains show that some practices associated with the triaging process work for the school, pushing selected pupils to achieve the Government target for the end of primary school. However, other practices appear to coincide with reduced mathematical gains for the lowest attaining pupils and a widening of the attainment gap. This case-study examines the mechanisms behind this, focusing on resource allocation, and assumptions about learners and their potential. The paper suggests a need to create dissonance, challenging shared assumptions, such as fixed-ability, which currently support triage processes.
Carole Torgerson, Andy Wiggins, David Torgerson, Hannah Ainsworth and Catherine Hewitt
The 2013 Janet Duffin Award has been awarded by the editorial boards to Carole Torgerson, Andy Wiggins, David Torgerson, Hannah Ainsworth and Catherine Hewitt for their paper Every Child Counts: testing policy effectiveness using a randomised controlled trial, designed, conducted and reported to CONSORT standards. Research in Mathematics Education 15(2), 141-153.
This paper reported a randomised controlled trial evaluation of an intensive one-to-one numeracy programme, Numbers Count, which formed part of the previous government’s numeracy policy intervention Every Child Counts. The authors rigorously designed and conducted the trial to CONSORT guidelines. They used a pragmatic waiting list design to evaluate the intervention in real life settings in diverse geographical areas across England, to increase the ecological validity of the results. Children were randomly allocated within schools to either the intervention (Numbers Count in addition to normal classroom practice) or the control group (normal classroom practice alone). The primary outcome assessment was the Progress in Maths (PIM) 6 test from GL Assessment. Independent administration ensured that outcome ascertainment was undertaken blind to group allocation. The secondary outcome measure was the Sandwell test, which was not undertaken and marked blind to group allocation. At post-test the effect size (standardised mean difference between intervention and control group) on the PIM6 was d = 0.33, indicating strong evidence of a difference between the two groups. The effect size for the secondary outcome (Sandwell test) was d = 1.11. The results demonstrate a statistically significant effect of Numbers Count on the primary, independently marked, mathematics test. Like many trials, the study had both strengths and limitations. However, due to the a priori decision to report these in an explicit manner, as advocated by the CONSORT guidelines, that the study could maximise rigour (e.g., by using blinded independent testing) and report potential problems (e.g., attrition rates). The study demonstrated that it is feasible to conduct an educational trial using the rigorous methodological techniques required by the CONSORT statement.
Aron Samkoff, Yvonne Lai, and Keith Weber
The 2012 Janet Duffin Award has been awarded by the editorial boards to Aron Samkoff, Yvonne Lai, and Keith Weber for their paper How mathematicians use diagrams to construct proofs. Research in Mathematics Education 14(1), 49-67.
The processes by which individuals can construct proofs based on visual arguments are poorly understood. We investigated this issue by presenting eight mathematicians with a task that invited the construction of a diagram, and examined how they used this diagram to produce a formal proof. The main findings were that participants varied in the extent of their diagram usage, it was not trivial for participants to translate an intuitive argument into a formal proof, and participants’ reasons for using diagrams included noticing mathematical properties, verifying logical deductions, representing ideas or assertions, and suggesting proof approaches.
The 2011 Janet Duffin Award has been awarded by the editorial boards to Tom Lowrie for his paper ‘If this was real’: Tensions between using genuine artefacts and collaborative learning in mathematics tasks. Research in Mathematics Education 13(1), 1-16.
This investigation identified the interactions and discourse employed by students (11–12 years old) when challenged to solve a realistic mathematics problem in a collaborative group situation. The students were asked to use genuine artefacts (including brochures, menus, bus timetables and photographs) to complete an open-ended task in small groups. Although most students were able to establish their own sense of authenticity by aligning the problem to their personal experiences and understandings, it was also the case that the majority found it difficult to establish meaningful, realistic understandings in the group situation. The students were unable to regulate the collective ideas of the group because too much emphasis was placed on personalising the task.
The 2010 Janet Duffin Award has been awarded by the editorial boards to Cathy Smith for her paper Choosing more mathematics: happiness through work. Research in Mathematics Education 12(2), 99-116.
This paper examines how A-level students construct relationships between work and happiness in their accounts of choosing mathematics and further mathematics A-level. I develop a theoretical framework that positions work and happiness as opposed, managed and working on the self and use this to examine students’ dual engagement with individual practices of the self and institutional practices of school mathematics. Interviews with students acknowledge four imperatives that they use as discursive resources to position themselves as successful/unsuccessful students: you have to work, you have to not work, you have to be happy, you have to work at being happy. Tensions in these positions lead students to rework their identities or drop further mathematics. I then identify the practices of mathematics teaching that students use to explain un/happiness in work, and show how dependable mathematics and working together are constructed as ‘happy objects’ for students, who develop strategies for claiming control over these shapers of happiness.
The 2009 Janet Duffin Award has been awarded by the editorial boards to Andrew Noyes for his paper Exploring social patterns of participation in university-entrance level mathematics in England. Research in Mathematics Education 11(2), 167-18.
In recent years in England, considerable attention has been given to a range of apparent crises in mathematics education, one of which has been the long term decline of participation in university-entrance level (Advanced or A level) mathematics. Given the negative impact upon mathematics participation of a national reform of Advanced level qualifications, commonly known as Curriculum 2000, together with the government’s emphasis on science, technology engineering and mathematics (STEM), the political intent to increase participation in Advanced level mathematics is clear. This paper uses the National Pupil Database (NPD) to develop a descriptive statistical account of how completion of Advanced level mathematics varies along the social axes of socioeconomic status, ethnicity and gender. The process of working with the NPD is discussed in some depth in order to clarify the processes involved in this type of quantitative analysis and then to illustrate how such analyses can be used to raise questions about who is studying mathematics in the post-16 age-range.
Nathalie Sinclair and Violeta Yurita
The 2008 Janet Duffin Award has been awarded by the editorial boards to Nathalie Sinclair and Violeta Yurita for their paper To be or to become: How dynamic geometry changes discourse. Research in Mathematics Education. 10(2), 135-150.
In this article, we investigate the impact of the introduction of a dynamic geometry environment on mathematical thinking by identifying changes in discourse engendered by its introduction in a high school geometry class. Our focus is on the teacher, and we find significant differences between static and dynamic geometry in terms of the ways in which the teacher talks about geometric objects, makes use of visual artifacts and models geometric reasoning. Even though these changes have major implications for the geometry being studied, they are made only very implicitly in the classroom.