BSRLM Proceedings: Vol 41 No 1 held Online on Saturday 6 th March 2021
Proceedings of the Day Conference held Online on Saturday 6th March 2021.
University of Oxford
Drawing from cognitive load theory, the worked example effect details how studying worked examples allow for greater learning gains than traditional problem-solving practices for novice students or those of low prior knowledge. A classroom-based intervention was conducted with 223 students between the ages of 14-15 years old, and their teachers from two schools of different socioeconomic standing in South Africa. Faded worked examples were used as the medium of instruction. In contrast to the pre-test results, female students outperformed males in the post-test. Female students and those from a low socioeconomic background also found faded worked examples significantly more beneficial for their learning than male students and those from a higher socioeconomic status. Consequently, the use of faded worked examples may improve the mathematics performance for female students and those of low socioeconomic status and highlight that the worked example effect may be more prevalent among these groups of students.
University of Stirling
This paper reports on the engagement of a small number of Scottish secondary mathematics teachers, with an online subject specific professional learning module, offered by a Development Education Centre. The responses suggest the teachers had to reconcile their activity with the hegemonic priorities of teaching the standard curriculum and of preparing learners to be tested. The teachers drew on limited professional and pedagogic courage and further work is needed to identify how these resources might be developed and activated. These early findings from the project point to implications for initial and continuing teacher education if Scotland is to achieve its aspirations for ‘Learning for Sustainability.’
Peter Kwamina Awortwe and Geoff Wake
University of Nottingham
This paper reports new ways of constructing geometric figures used with beginning teachers working with dynamic geometry software. The research aims to understand how we might improve teacher education in this area. The research question considers how explorative tasks support beginning teachers and how researchers can develop insight into new ways of constructing geometric figures. Methodologically, design-based research was adopted for the study. The traditional method of teaching geometry, based on deductive approaches rather than the inductive approaches used in the research, results in beginning teachers becoming used to procedural approaches for constructing geometric figures with little understanding. In this paper, we present a modern way of using dynamic software to teach geometric constructions, that centrally involves inductive approaches and pedagogies that aims to support a deeper understanding of geometry. We present data that provides evidence and insight into how the approaches used are potentially successful in realising our aims.
Sally Bamber1 and Christian Bokhove2
1University of Chester, 2University of Southampton
In the Erasmus+ Research in Teacher Education (RiTE) project, student teachers are stimulated to use evidence from educational and scientific research to experiment and innovate their teaching and learning processes. In two case studies we use Engestrom’s expansive learning cycle. The first case study reports on the design and implementation of materials designed to enhance student teachers’ critical review of literature in the context of the post-graduate study that is incorporated within their teacher education. The second case study presents the design of collaborative lesson research that aims to foster authentic connections between school-based learning (teaching practice) and research that informs mathematics teaching and learning. We discuss the aims of research-informed mathematics teacher education at each site, demonstrate some of the approaches used and discuss tensions within the design and early implementation of the projects.
Ellen Barrow1, Jennie Golding2, Grace Grima1
1Pearson UK, 2UCL Institute of Education
We report Autumn 2020 findings from a 2019-2021 study of impact and use of a ‘mastery’-oriented primary (ages 4-11) mathematics resource, ‘Power Maths’. The study follows 40 classes of primary children and their teachers, in 20 schools, over two years. Following earlier pandemic evidence, more recent data show schools and teachers responding to Autumn ‘mathematics recovery’ challenges in very different ways, with a range of creativity, of solution-focus, and of alignment with the Power Maths-promoted ‘mastery’ approaches, although more complex mathematical processes commonly remained marginalised. Teachers reported that new classroom guidelines severely restricted ‘carpet’ and group work and use of manipulatives. They pervasively referenced identification and addressing of gaps in children’s prior learning. While most teachers expressed concern about the continuing impact on mathematical development, and reduction in confidence, they reported children usually still responding positively to mathematical opportunities to learn, and confidence slowly returning.
Cosette Crisan, Nicola Bretscher, Alison Clark-Wilson and Eirini Geraniou
UCL Institute of Education, University College London
This new working group (WG) was created to discuss the theoretical and methodological challenges faced by the mathematics education field when the prevailing boundaries of the classroom shifted; alongside the changed nature of the classroom interactions between the humans (teachers and students) and the chosen technologies. Starting with the assumption that technology resources are being used, the WG explored the nature of these tools and their affordances for the mathematical teaching and learning. The work was framed by the following three pedagogic activities, which are proving to be particularly challenging: introducing and developing understanding of new mathematical topics; managing interaction and communication in mathematics; and assessing mathematics, both formatively and summatively. Three case studies of teachers’ practices were presented to initiate discussions with respect to these challenges and to highlight some existing theoretical and methodological frames.
University of Tasmania
Algebra involves various activities including transformational activities that are mainly about solving equations. Fluency (or flexibility) in these activities is important. Several researchers have proposed conceptualisations of flexibility in equation solving. This paper makes a reflection about flexibility in equation solving that contributes to the extension of Star and Seifert’s operationalisation. Examples are used as context for the reflection. The need for another property of flexibility, namely making connections, is suggested to deepen investigations of students’ flexibility in equation solving and its provision in teaching.
University of Bristol
For students who are labelled as low attaining in mathematics, stories about their identity work are often interpreted through the lens of others. However, the positionality of the researcher can impact on how these stories are analyzed. This report discusses the using of a Social Identity Map as a device to explicitly examine my positionality as part of a small-scale project in the context of post-16 mathematics. By acknowledging the impact of my assumptions and subjectivities, as facets of positionality, I was able to listen in new ways to the student’s data and hear a counter narrative of finally able with regard to the teaching and learning of mathematics.
Jenni Ingram and Kyla Smith
University of Oxford
Mathematics is a coherent and connected discipline, but for many learners it can be a set of disparate concepts, procedures, and representations. One role of teaching is to support students in making these connections, whether these connections are between representations, between topics, or between contexts. This paper explores the connections that teachers made when teaching quadratic equations, using data from the eight countries/economies that participated in the OECD’s TALIS Video Study.
‘Ability’ grouping, almost universal in English secondary mathematics classrooms nowadays, limits access to the subject for many children. Thus, it is a social justice issue. Here, I draw on my doctoral thesis, a small-scale qualitative study, using interviews, into all attainment teaching in secondary mathematics departments. Here I focus in particular on my findings in relation to the question: How do mathematics teachers introduce, develop and maintain all attainment teaching in the current educational environment?
Sue Johnston-Wilder1and Kate Mackrell2
1Warwick University, 2Independent researcher
We bring together Self-Determination Theory (SDT) and mathematical resilience (MR) to address mathematics anxiety. The focus of SDT on meeting basic psychological needs to enhance wellbeing and prevent harm provides grounding for much good practice in mathematics education, including work in MR. We illustrate this with the case of an adult learner. MR goes beyond what is currently proposed in SDT; we illustrate how MR tools can specifically facilitate learner emotion regulation, by developing mathematical learning competence, leading to greater wellbeing, learning, and a release from mathematics anxiety.
University of Cambridge
Underpinned by the classical writing of the pedagogy of the oppressed, this case study seeks to evaluate student mental imageries of power dynamics in the classroom. These were assessed with the help of a classroom drawing activity which was conducted with 60 male and female 13-year old students, who all study mathematics at the same Egyptian school and are governed by the national framework for mathematics instruction. The mixed methods analysis was underpinned by the Draw a Science Teacher Test (DAST) drawing filtration framework. Findings revealed a distant relationship between teacher and student, a subtle sense of student inferiority that over the years seems to have been normalised.
Elena Nardi1, Irene Biza1, Bruna Moustapha-Corrêa2, Evi Papadaki1, Athina Thoma1
1University of East Anglia, 2Universidade Federal do Estado do Rio de Janeiro
Commognitive studies offer a nuanced lens on datasets that evidence micro-level accounts of mathematical experience – and are now starting to explore the theory’s capacity to support the design, tracing and dissecting of discursive shifts in medium/long term interventions. Here, we focus on two university mathematics education (UME) examples of such interventions. The Norway-based study engaged biology students with biology-themed Mathematical Modelling activities to challenge deficit narratives about the role of mathematics in their discipline and about their mathematical competence and confidence. The Brazil-based study engaged teachers with activities which feature mathematical practices from the past and in today’s mathematics classrooms to trigger changes in teachers’ narratives about how mathematics comes to be and how its emergence can be negotiated in the mathematics classroom. We show how the discursive shifts orchestrated by these interventions generate new narratives about mathematics and its pedagogy, de-ritualised participation in mathematical routines and, ultimately, meta-level learning.
David Young1, John Reilly2 and Sue Pope3
1University of Strathclyde, 2Education Scotland, 3Scottish Qualifications Authority
In Scotland, numeracy is a key area of the Curriculum for Excellence so learners develop essential analytic, problem-solving and decision-making skills. The SQA Higher Applications of Mathematics was developed for young people to learn these skills, with statistics as one third of the curriculum. The emphasis is on the application of statistics to real-life data, and interpretation of results. Ensuring learners are confident in statistical literacy requires teachers’ sound knowledge and understanding of how data can be managed and processed in a meaningful way, as real-world data rarely conform to textbook assumptions for analysis. In collaboration with the Scottish Funding Council, the University of Strathclyde has developed an SCQF level 7 award in statistics. It covers the Higher curriculum and the use of both software packages, so teachers have the statistical skills to teach this new and innovative qualification in Scotland.