Proceedings of the New Researchers Day Conference held at the University of Nottingham on Friday 10th June 2022 and the Day Conference held at the University of Nottingham on Saturday 11th June 2022.
Leyton Sixth Form College (LSC)
As participants in the National Centres for Excellence in Mathematics (CFEM) programme, Leyton Sixth Form College (LSC) and our network partners conducted a series of action research projects focused on improving the teaching of GCSE re-sit mathematics.. We developed practice in the classroom using key aspects of teaching Mathematics for engagement and mastery including dialogic learning, representations, blended learning and responsive teaching. We found that students were more able to engage with and articulate mathematical ideas when discussion was scaffolded using conversation structures, talking points, and representations. This led to improvements in their willingness to attempt problem-solving assessment questions. Doing the research supported teachers to experiment with and refine new practice over a full academic year. The result has been improved confidence using the new techniques and longer term changes of practice. In this report I outline 5 projects and give details of how to access the full version.
Sheffield Hallam University
As teachers enter the profession, tensions between their values and beliefs and the expectations of their schools and colleagues are common. This study gains insight into such struggles with these individual and contextual factors, or identity work, by reporting on initial analysis of one early career mathematics teacher’s stories of navigating a tension between herself and a colleague. Using a narrative inquiry approach, stories were elicited through personal written reflections and an exploratory interview. Analysis of these stories demonstrates how interactions with colleagues are emotive experiences which are likely to cause identity shifts and tensions. To help make sense of this, and choose how to navigate the situation, the teacher drew on past experiences as both a teacher and learner of mathematics and was ultimately able to view this experience as an opportunity for professional learning.
It is widely acknowledged that dialogic exchanges facilitate the construction and organisation of mathematical knowledge and challenge power structures. However, the complex nature of interactions mean that students’ experiences are diverse and may differ from the intentions and assumptions of educators. This case study seeks to bring students’ stories to the fore by exploring their perceptions and experiences of discussion, and in particular, the ways in which they experience dialogic characteristics such as collective discussion. Data was collected through interviews with students aged 11 to 16, from classes where discussion is encouraged. The findings show ways in which individualistic narratives can dominate, and how these are linked to aspects of identity. This research brings an important student perspective to the field of dialogic learning and identity at a time when social and economic inequality have created divisions in society and assessment culture has made mathematics into an individualistic pursuit.
Dave Hewitt, Ian Jones
In this paper we focus on the use of a popular App called Stick and Split which has some game-like features. The design of the App is such that mathematics is an intrinsic feature of the game and where success in the game requires multiplicative thinking. We analysed one child’s first encounter with the game using the framework of subordination. Over a relatively short session with the game, we saw a significant shift from additive to multiplicative thinking. This seemed to occur through her seeing the consequences of her actions whilst playing the game, a feature of the framework of subordination, rather than the occasional support offered by the accompanying teaching assistant.
Elizabeth Kimber, Cathy Smith
The Open University
Classroom discourse on gradients develops from gradients of straight lines to gradients of curves and the gradient function. We can then ask: what are particular features of teachers’ language when talking about gradient in public discussions, and what might their role be in developing the discourse on gradient? Systemic Functional Linguistics (SFL) offers tools to analyse teachers’ linguistic choices such as the Thematic and Information structures of teachers’ speech. We report here on SFL analysis of classroom data from a GCSE lesson in which the teacher used the context of speed to introduce the idea of changing gradients of curves. Our analysis revealed use of relational clauses to identify gradient with other concepts and a relationship between the kinematics context and the use of speed in the Information structure of the teacher’s speech.
Stephen Lee1, Iram Hussain2, Jo Deko2
1Mathematics in Education and Industry, 2Tribal Education Ltd
More than 12,000 students in over 650 state schools/colleges now study Level 3 Core Maths. Entries have grown steadily from 2930 in the first year (2016), but there remain barriers for some institutions to offering it. As part of the work of the Advanced Mathematics Support Programme, a study was conducted into all (100) Further Education (FE) Colleges that didn’t have A level Mathematics entries to consider their Core Maths provision. Phase one of the work involved the 15 FE Colleges who did have Core Maths entries and phase two involved the 85 FE Colleges who didn’t. This paper reports on feedback from interviews with 18 institutions and 4 survey responses. Findings from phase one were used in the discussions with FE Colleges in phase two. Timetabling, student recruitment and retention, along with a lack of teacher expertise, familiarity and awareness of Core Maths were the main barriers identified.
Stephen Lee, Kevin Lord
Mathematics in Education and Industry
AS and A level Mathematics and Further Mathematics qualifications were reformed in England for first teaching in 2017 as part of reforms to all A level qualifications. Changes to the assessment, content and educational philosophy to emphasise problem solving and the use of technology were made. Qualifications overall became linear, rather than modular, and achievement at AS no longer counted towards the awarding of an A level grade. Education charity Mathematics in Education and Industry (MEI) have conducted analysis into both the uptake and availability of AS and A level Mathematics and Further Mathematics in schools/colleges in England. There has been a large decrease in entries for AS Mathematics, like for all other subjects, although AS Further Mathematics has done relatively well. An analysis of provision at institutional level, prior to 2017 and after, shows a complete shift from offering both AS and A levels to predominately just A levels.
University of East Anglia
Mentoring has become established as a central feature of initial teacher education (ITE) programmes in the English further education and training sector (FE) yet there is lack of clarity about its purpose and role. The education systems globally had to change when COVID 19 struck and there was no choice but to go online. Mentoring had to go online as well and became what could be referred to as COVID 19 triggered e-mentoring, which was a reaction to the unprecedented situation. In this paper, I report findings of the analysis of ten questionnaire and seven follow up interview responses that included questions about mentoring and hypothetical classroom situation from mentors of mathematics student teachers in FE colleges. Thematic analysis was employed as the analytic tool and key themes – correcting student teachers; observing experienced teachers; discussing generic issues; working mathematics questions and discussing how to teach specific topics – emerged.
Yasin Memis and H. Bahadir Yanik
Anadolu University, Turkey
Among the many factors influencing mathematics teaching, textbooks have crucial potential. They offer an initial pathway on ‘what to teach’ and ‘how’. Integrating the research results for student development in a more dynamic way on the design of textbooks will increase the learning opportunities that they offer. This study compares the extent to which selected textbooks from Turkey, Singapore and Canada (Ontario) are designed to align with the development of proportional reasoning. In order to examine how textbooks deal with students’ thinking developmentally, levels of proportional reasoning and indicators for each level were determined. In the analysis, all questions in the ratio and proportion units were examined sequentially, and timeline dot graphs were created according to the development levels. It was found that there were still gaps between the results of the research carried out on student progress and the contents of the selected math textbooks.
Elena Nardi1, Angeliki Stylianidou1, Lina Kayali1, 2
1University of East Anglia, 2University of Bristol
What may the challenges be that British Sign Language (BSL) interpreters face when assisting hard-of-hearing (HoH) and D/deaf learners in the mathematics classroom? And, if any, how can these be overcome? We report exchanges with BSL interpreters which took the form of a focused group discussion that revolved around two mathematical problems (Platonic Solids, Bridges of Königsberg) designed for a workshop aimed at teachers of mathematics as part of the CAPTeaM project. Discussion zoomed out to broader issues regarding BSL interpreters’ preparedness for supporting the mathematical learning of HoH & D/deaf students. We see sharing these insights as having additional topicality within mathematics lessons and beyond, given that significant steps are finally in progress towards recognising BSL’s official status across the UK.
University College London
The teaching practices associated with formative assessment are widely accepted as improving students’ learning. Wiliam and Thompson proposed a set of strategies that can enhance teachers’ productive formative assessment practices. These strategies, however, give only limited guidance for implementation in specific contexts. My PhD research aims to identify examples of these strategies in the context of multiplicative reasoning in early secondary mathematics and interrogate ways to support teachers in enacting these strategies productively. As the first step, I analysed teacher guides for multiplicative reasoning lessons from five different sets of curriculum materials in the United Kingdom and the United States, adopting Braun and Clarke’s reflexive thematic analysis approach. In this paper, I present the initial findings of this analysis in relation to the strategy of eliciting students’ learning and introduce the future directions of this research.