Cambridge Mathematics Education Project: Developing a Framework For Students ‘Deep’ Understanding in Key Stage 5 Mathematics

Author(s):

Tatiana Rostovtseva(presenting / submitting)Sharon Walker(presenting)

Conference:

ECER 2016

Network:

24. Mathematics Education Research

Format:

Video

Session Information

24 SES 08 A, Mathematics Teachers Training (Part 2)

Paper/Video Session continued from 24 SES 07

Time:

2016-08-25

09:00-10:30

Room:

Vet-Theatre 114

Chair:

Nadia Ferreira

Contribution

The Cambridge Mathematics Education Project (CMEP), a five-year project launched in October 2012, develops online resources to support the teaching and learning of Key Stage 5 (KS5) mathematics. Funded by the UK Department for Education (DfE), CMEP aims to provide creative resources that help to make KS5 mathematics a richer, more coherent and more stimulating experience for students and teachers alike.

This research is an evaluation of the implementation of CMEP resources in classrooms, as well as an investigation of the types of learning environments and experiences the resources aim to promote.

The research questions are:

1. How is CMEP being implemented in KS5 classrooms?

2. What kind of environments and experiences promote mathematical thinking in classrooms informed by CMEP?

Influential to the development of the research are social constructivist views of learning that emphasise the importance of society, culture, language, and social interaction in the construction of new knowledge (Vygotsky, 1978). By adopting a social constructivist view, the research acknowledges the collaborative nature of mathematical classrooms in the construction of knowledge and draws attention to students as active agents in their cognitive development. The research also draws on the work of scholars in mathematics education such as Boaler (2010), Mason, Burton, and Stacey (2010), and Swan (2006), as it frames the outcome of deeper understanding in mathematics in terms of the development of students’ mathematical thinking. It is also cognisant of the role of classroom dialogue in the development of students’ thinking and reasoning in mathematics (see Howe and Abedin, 2013).

Data collection and analysis are supported by an evaluation framework developed by the research team following an initial analysis of data. It is also assisted by a tool developed by researchers in the UK, Spain, and Mexico – The Cam-UNAM Scheme for Educational Dialogue Analysis (SEDA) – to analyse pupil-teacher dialogic interactions in classrooms (Hennessey, et al., 2016).

The evaluation aims to investigate implementation through analysis of student and teacher dialogue, as the Project perceives mathematics to be inherently dialogic and collaborative. The framework also focuses on two categories: classroom ‘environments’ and ‘experiences’. This reflects an understanding by CMEP that student learning will be enhanced as a result of exposure to certain classroom experiences and environments. 'Environments' refers to the physical environment in the mathematics classrooms observed, and to the teaching and learning atmosphere, for example, a supportive (or unsupportive) atmosphere and classroom language (e.g. discursive versus didactic). 'Experiences' is defined as those learning experiences, which help students to develop their mathematical thinking. The framework includes subcategories under each heading:

Environments

Authority
Questions

Experiences

Collaboration
Making connections
Reflection

The SEDA research tool will be employed to provide an in-depth analysis of the categories and subcategories. Developed over a three-year period by a cross-national research team from the University of Cambridge, UK, and the National Autonomous University of Mexico, with contributions from the University of Deusto in Spain, and funded through a grant from the British Academy (2013-2015), the SEDA tool makes available a coding scheme to systematically analyse classroom dialogue across a range of educational settings (Hennessey et al., 2016). By adopting the tool, the case study research situates itself in the wider cross-cultural exploration of classroom dialogue. The tool has already been applied in educational contexts in Mexico and Chile with further plans of use in the UK primary school sector. CMEP research aims to take forward a wider international application of the tool by applying it to KS5 mathematics classrooms in UK schools.

Method

The research employs a mixed-method multiple-case study approach and adopts an exploratory non-experimental design. Each case is defined as a single KS5 mathematics classroom. The sample has been selected from a range of schools and teachers, both those new to CMEP and from a pool of existing users. Two types of case studies are being conducted: 1) SOW – focusing on existing users who are in the process of integrating CMEP activities in their schemes of work; and 2) New User – focusing on new users arriving at CMEP through a paired-days CPD delivered by the Mathematics in Education and Industry (MEI). The sample of SOW teachers was self-selected from all teachers who contacted the Project to say they would be integrating CMEP tasks into their schemes of work in 2015-2016. There are four SOW classrooms participating in research activities from September 2015. The sample of New User cases was selected from MEI CPD attendees who participated in the CPD course between October-December 2015. Schools were stratified on key characteristics using data from the DfE public database, including free school meal (FSM) status and mathematics cohort size (to ensure that at least some schools have cohorts of 20+ students enrolled in KS5 mathematics) and randomly selected from each strata. Although the chosen schools will not be representative, due to sample size, exploration of potentially different classroom settings will inform the Project on possible future questions and future research design. It is hoped that at least four schools from the New User case study type will participate in research activities between January-July 2016. Data collection will involve classroom visits and remote data collection through surveys and diaries. Researchers visit each classroom two to three times termly and conduct the following: Classroom observations – using a pre-designed template developed by the research team Video and audio recordings – of whole class and small group discussions/interactions Teacher interviews and student focus groups – conducted termly Examples of students’ work – video recordings and images of students work, gathered opportunistically Quantitative survey data – pre-task teacher survey at the planning stage of using a CMEP task; post-task survey following use of the task; student post-task survey Teacher diary - a diary of teachers’ reflections on using individual CMEP tasks. This activity is encouraged rather than prescribed.

Expected Outcomes

The case study research design is exploratory and aims to “develop pertinent hypotheses and propositions for further enquiry” in 2016-2017 and beyond (Yin, 2014, p.10). These hypotheses and propositions will address issues such as resource design and the type of learning environments and experiences best suited to support ‘deep’ understanding in mathematics. Research findings will be discussed and reported under the categories of ‘environments’ and ‘experiences’ and their subcategories, e.g. Authority and Reflection. Evaluation reports on each of the subcategories will be created for different audiences – teacher practitioners, policy-makers and educational researchers. It is expected that findings will inform the future development of CMEP resources but, more importantly, provide insights and learning on the design and implementation of rich mathematical tasks in classrooms. Primarily, it is envisaged that findings will contribute to discussions and learning on the promotion of students’ mathematical thinking skills and rich engagement with mathematical knowledge. Findings will additionally contribute to cross-cultural learning on classroom dialogue in the construction of knowledge from the perspective of post-16 mathematics. A review of the efficacy of the SEDA tool, in this context, will be offered to contribute to the continued use of the research tool. Finally, it is anticipated that findings will highlight issues relevant to teacher support and pedagogical development in the effective use of rich mathematical tasks, as well as teacher support in the context of content delivered online (see Major, Watson & Kimber, 2015, for a discussion on instructional and pedagogical design to support and enhance mathematics education). Although teacher support is not the primary focus of the current case studies, we expect to tease out promising classroom practices, as they relate to the subcategories of classroom environments and experiences, to help build teacher capacity in implementing rich mathematical tasks.

References

Boaler, J. (2010). The elephant in the classroom: helping children learn and love maths. London: Souvenir. Feng, W.Y. & Kimber, E. (2014). Evaluating the Cambridge Mathematics Education Project. In Proceedings of British Society for Research into Learning Mathematics (BSRLM), 34(2), 19-24. Hennessy, S., Rojas-Drummond, S., Higham, R., Márquez, A.M., Maine, F., Ríos, R.M.,...Barrera, M.J. (2016). Developing a coding scheme for analysing classroom dialogue across educational contexts. Learning, Culture and Social Interaction, in press Howe, C. & Abedin, M. (2013). Classroom dialogue: a systematic review across four decades of research. Cambridge Journal of Education, 43(3), 325–356. Major, L., Watson, S. & Kimber, E. (2015). Developing instructional and pedagogical design for the Cambridge Mathematics Education Project: A Design-based research approach. In Proceedings of British Society for Research into Learning Mathematics (BSRLM), 35(2) Mason, J., Burton, L. & Stacey, K. (2010). Thinking Mathematically. Harlow: Pearson. Swan, M. (2006). Collaborative learning in mathematics: a challenge to our beliefs and practices. London: Leicester: NRDC ; NIACE. Vygotsky, L. (1978). Interaction between learning and development. In M. Gauvain & M. Cole (Eds.), Readings on the Development of Children (pp, 29–35). New York: W.H. Freeman and Company. Yin, R.K. (2014). Case study research: Design and Methods. London: Sage.

Author Information

Tatiana Rostovtseva (presenting / submitting)

Cambridge Mathematics Education Project

Cambridge

Sharon Walker (presenting)

University of Cambridge

Department of Pure Mathematics and Mathematical Statistics

Hertford

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