Mathematics education and transition
The Mathematics Education strand of the Critical Pedagogies Thematics Research Programme, led by Professor Julian Williams, organises a group of academic researchers and research fellows, post-docs and research students engaged in research projects in the field of mathematics education.
Recent major ESRC funded projects (see individual projects for links) have focused on mathematics in transition (between schools, colleges and universities) and on mathematics problem-solving and modelling curricula, but there is also a long history of work on curriculum and assessment. Indeed, much of this work involves research and evaluation of innovations in school and university mathematics courses, especially where mathematical modelling is concerned.
Mathematics education at Manchester has long had interests in culture, history and mathematics, largely influenced by (now Honorary Reader) George Joseph. Many in the team have strong theoretical interests in socio-cultural theory and have always been mainstays of the sociocultural theory interest group strand led by Etienne Wenger and Julian Williams. This has led particularly to projects involved with mathematical identities, mathematics pedagogy and the culture of mathematics education. This work has led us of new theorisations drawing on Vygotsky, Bakhtin/Volosinov, Bourdieu, and others, and we have been active in all the recent ISCAR conferences.
There have been key projects exploring links between mathematics in and out of school, as well as between mathematics in 'other school subjects' (and hence our work links closely with interdisciplinary science and technology work).
Additionally however, there is a significant strand of quantitative, measurement and statistical methods in our work. The work of the MaLT project involved new techniques for integrating formative assessment and summative assessments, and computer adaptive testing. The creation and validation of new tools for measuring affective learning outcomes have been vital to most of the ESRC projects, including Teleprism’s new methodological approaches in 11-16 schools (Maria Pampaka).
Finally, many us of are also active in the 'Teacher education and lesson study research' strand. Luis Radford has joined the group as visiting professor and is engaged with our research in Primary school lesson study, as well as our sociocultural theory work.
We welcome new research students applications to join an active community of researchers, led by the following academics:
- Julian Williams (organiser/contact)
- Rosa Archer
- Laura Black
- Andy Howes
- Diane Harris
- Graeme Hutcheson
- George Joseph
- Olwen McNamara
- Sian Morgan
- Gary Motteram
- Maria Pampaka
- Pauline Prevett
- Luid Radford (visiting Prof)
- David Swanson
- Michael Omuvwie (RA)
- Lawrence Wo (RA)
PI: Maria Pampaka
This three year ESRC funded project aims to map secondary students’ learning outcomes, attitudes and choices regarding mathematics, together with the teaching they are exposed to. New understandings of how mathematics pedagogy relates to learner engagement and hence outcomes will be important to both mathematics education research, and policy and practice.
The Multiplicative Reasoning (MR) project is a new project funded by the Department for Education (DfE) to provide high quality professional development and curriculum resources in order to improve learning and teaching of this content within Key Stage 3.
It is being run on behalf of the DfE by the NCETM as a response to the phase 3 findings of the recent ICCAMS research. This project is being run on a small scale to begin with and will be completed by July 2014, but if it proves to be successful, it will be replicated, in whole or in part, so that more secondary school teachers can participate and benefit.
The MR content includes developing a deeper understanding of multiplicative structures such as fractions, decimals, percentages and ratios. It has been suggested by research that many pupils (and adults) fail to move on from additive structures and this can lead to many misconceptions and errors in subsequent mathematical study.
PI: Geoff Wake, Julian Williams
This project will synthesise findings from three previous ESRC funded projects undertaken by researchers in mathematics education at the University of Manchester. These projects investigated students’ engagement with, and dispositions towards, mathematics in and across programmes from compulsory school, through college to Higher Education. This research recognised the crucial role that mathematics plays in underpinning careers in Science, Technology, Engineering and Mathematics (STEM), and students’ potential trajectories in STEM were explored.
This project team will work directly in partnership with the HE National STEM Centre, National STEM Centre (schools) and National Centre for Excellence in Teaching Mathematics (NCETM) to use the results of their research to make significant impact on both policy and practitioner audiences. This will be achieved using a range of dissemination channels with case studies, briefing documents, videos etc. developed from the outcomes of the previous research. Policy briefings will be developed with the intention of informing policy advisory groups (for example, ACME and SCORE). Practitioners in-the-field will be advised of practices that take account of the diversity of students’ needs, motivations and aspirations and which have been identified as having the potential of increasing participation in mathematics for STEM.
This HE STEM project "Mathematical Modelling & Problem Solving" aims to equip first year STEM undergraduates with a high level, transferable skill – “the ability to solve problems in science and engineering by setting up mathematical models and using mathematics”
Such skills are highly valued by both employers and researchers:
“The ability to solve physical problems using mathematical modelling and mathematics are invaluable attributes for new undergraduates entering an engineering industry”
Dr Alan Stevens, Rolls Royce, Maths Modelling Group
“A key attribute for engineering graduates is their ability to apply theoretical knowledge to a real problem to create a solution. Modelling skills are key to this process.”
Professor Barry Clarke, President (elect), Institution of Civil Engineers
Thirteen project partners in eight universities
There are currently 13 HE STEM Departments (Physics, Mathematics and Engineering spread across 8 universities who fully recognise the importance of modelling and problem solving skills for STEM undergraduates and are now actively engaged in introducing such skills into their curriculum in ways that are most suitable for their needs. This approach has enabled the 13 departments to implement tailored approaches based on agreed concepts.
There are, in fact, several ways of introducing modelling that are particularly appropriate for engineering, applied mathematics and physics students, of which Newtonian mechanics is just one.
PI: Julian Williams
This project investigated students' transitions from school / college to mathematically demanding degree programmes in Higher Education. Case study data collection in five universities focused on a range of courses including mathematics, engineering and the sciences. The focus was on transitional practices at the boundaries between college and HE with investigation of the effects on learner identities, choices and learning outcomes of different educational contexts and their interaction with students' socio-cultural contexts.
Mathematics learning, identity and educational practice: the transition into post-compulsory education
PI: Paul Hernandez-Martinez
The project aimed to understand how different educational practices in mathematics at School (GCSE) and in transition to College (AS level) impact on students' dispositions and identity, hence influencing their choices and future success in subjects that demand high levels of mathematics.
PI: Julian Williams
This project aimed to better understand how to extend and improve learning in mathematics, especially by those 'on the edge' of further participation. Our study surveyed students by large-scale questionnaire and by a series of interviews as they progressed through their AS year. We also studied contrasting Programmes and pedagogies. We conclude that Programme and pedagogy can make significant differences to learning outcomes for these students, in terms of drop-out and the disposition to continue to study mathematics, sometimes despite injurious policy and institutional influences.
Funder: Hodder Murray
This project developed a new series of age-standardised Mathematics tests but with additional provision for effective on-screen assessment and diagnostic follow-up.