Mathematics teaching and learning in secondary schools: the impact of pedagogical practices on important learning outcomes

Lead Research Organisation: University of Manchester
Department Name: Environment, Education and Development

Abstract

Abstracts are not currently available in GtR for all funded research. This is normally because the abstract was not required at the time of proposal submission, but may be because it included sensitive information such as personal details.
 
Description The study aimed to map secondary students' learning outcomes and choices including dispositions and attitudes together with the teaching they are exposed to. The project was designed to capture the five years of students' progression in Secondary Education (Year 7 to 11) in about one year of data collection (from 10/2011 to 12/2012). The most significant achievements from the grant so far are listed below:
- We collected data from longitudinal surveys with students in 40 Secondary Schools about their attitudes to mathematics, confidence at various mathematical topics, future aspirations, and their perceptions of the teaching they encounter. The latter was also captured through a survey administered to their mathematics teachers. Our aim was to match these datasets, along with extra information provided by the schools (e.g. schools attainment) and the National Pupil Database. This has been achieved, but as expected with such designs we had missing data in various patterns, as well as a huge challenge in maintaining linkage in the datasets, which we initially underestimated in regards to time. Despite the challenges, however, we have achieved a new rich dataset of more than 13000 students in about 660 classes in 40 schools, and a linked teacher-class level dataset (from over 130 teachers). This sample is comparable to the national picture in regards to main descriptors such as free school meals, ethnicity and language, but differs in female students' concentration. In addition we have also conducted 2 intensive case studies with observations and interviews. Thus we also have 170 transcripts from interviews from over 100 students and their teachers.
- We designed and validated various instruments. In particular, our instrument capturing students' mathematics attitudes was found to be two-dimensional, capturing 'mathematics dispositions' and 'mathematics identity'. In regards to measuring perceptions of teaching practices, our analysis confirmed a second dimension, of what we call 'teaching variation', in addition to our previously established 'transmissionist' teaching. This finding applies to both students' as well as their teachers' reported perceptions. Additional validated measures include students' perception of parental support, and mathematics self-efficacy. For the latter, we have gone beyond our intended aims and also associated with actual students' scores on an equivalent test administered in one school.
- Our (multilevel) statistical modelling found evidence of an association between students' declining mathematics dispositions and their perception of the teaching they received (transmissionist teaching was found to negatively affect dispositions, whereas more variation in teaching is positively associated). We also found significant gender and ethnicity effects. It should also be noted that class and school effects account for a significant proportion of the variance in maths dispositions.
- We also addressed the challenge of linking the 5 different year group cohorts of this accelerated longitudinal design with multilevel growth curve models which capture the progression of students' (dropping) dispositions, at least from Year 7 till the start of Year 11.
Off course the wealth of this dataset along with the involved challenges gave rise to new applications and questions we are currently exploring.
Exploitation Route The new understandings of how mathematics pedagogy relates to learner engagement and hence outcomes should be important to both mathematics education practitioners and researcher, and policy and practice. In fact, our preliminary findings have also been picked up by the media, and we have already contributed to policy debates based on our findings. Our instruments have already been used by other researchers for other studies. There are definitely more to come regarding policy implications, teaching practices as well as research innovations. We are already in touch with colleagues across the globe for potential duplication or comparative work based on this study.
Sectors Education,Other

URL http://www.teleprism.com
 
Description The project's impact, to date, has been through the development of understandings of the association between teaching practices in secondary schools and declining students' mathematics dispositions, and how policy and practice might be changed accordingly to ameliorate this. The research, in brief, has raised awareness of the complexity of this relationship and confirmed that traditional, teaching-to-the-test approaches turn off students from maths. Our main impacts have been and will continue to be disseminated at national (e.g. BERA, BSRLM) and international educational and methodological (e.g. ECER, PME, ECM) conferences, and relevant journal papers are being developed from these. Conclusions from preliminary findings of the project have reached the national news after a press release during BERA 2012 conference. The validated instruments from this work have already been used for an MEI evaluation study, are currently being developed further for use within new studies (e.g. EEF ICAMMS evaluation) and are included as tools in ongoing (ERC, ERSC and Nuffield) research proposals. This work, has also created opportunities for networking and collaboration with colleagues nationally and internationally; some of these collaborations have already come to fruition (e.g. use of the pedagogical instruments in an intervention study sponsored by London Schools Excellence Fund, use of the adapted maths attitudes instruments with parents in a local school aiming to improve learning outcomes). We have also contributed with school reports and presentations to practitioners (e.g. teachers) and relevant policy makers. The partner schools were invited to the Maths and Sciences Teachers Conference (University of Manchester, June 2014) where we also disseminated some of the project's findings as part of the information fair, through briefings developed for teachers (accessible on our website). We also presented some relevant results under a session titled "Ethnicity and Inequalities in Education" at Policy week 2014 (organised by the University of Manchester) an event widely attended by various stakeholders. The project's impact had also reached Parliament as evidenced by an invitation to present the findings issued by the then minister Truss. However, further outputs are also in preparation, including several journal articles and a book chapter. We aim to continue dissemination and website updates to reach higher impact. The resulting datasets have only recently been archived and we have already been contacted by a colleague interested in using this research resource to investigate post-secondary outcomes (e.g. nurses' numeracy confidence/skills), which indicates a promising impact potential.
First Year Of Impact 2012
Sector Education
Impact Types Societal,Economic

 
Description Engineering skills for the future
Geographic Reach National 
Policy Influence Type Citation in other policy documents
URL https://www.raeng.org.uk/publications/reports/engineering-skills-for-the-future
 
Description Survey Advisory Group for Greater Manchester Police/Safety Survey
Geographic Reach Local/Municipal/Regional 
Policy Influence Type Participation in a advisory committee
 
Description Systematic Review on Maths Anxiety
Geographic Reach Europe 
Policy Influence Type Membership of a guideline committee
 
Description ESRC Impact Accelerator Account
Amount £19,870 (GBP)
Organisation Economic and Social Research Council 
Sector Public
Country United Kingdom
Start 04/2018 
End 06/2019
 
Description Evaluation of the ICCAMS Maths Intervention
Amount £180,792 (GBP)
Organisation Education Endowment Foundation 
Sector Charity/Non Profit
Country United Kingdom
Start 08/2015 
End 03/2019
 
Description HEFCE Learning Gain Pilot
Amount £95,000 (GBP)
Organisation Higher Education Funding Council for England 
Sector Public
Country United Kingdom
Start 09/2015 
End 09/2018
 
Description Research Simulation Fund
Amount £4,969 (GBP)
Organisation University of Manchester 
Sector Academic/University
Country United Kingdom
Start 12/2014 
End 07/2015
 
Description SEED Rapid response impact fund
Amount £963 (GBP)
Organisation University of Manchester 
Sector Academic/University
Country United Kingdom
Start 05/2017 
End 07/2017
 
Description Special Research Projects
Amount £158,494 (GBP)
Funding ID SR160026 
Organisation The British Academy 
Sector Academic/University
Country United Kingdom
Start 04/2016 
End 09/2017
 
Title Dynamic Models 
Description This involves some work in progress, partly funded by some internal funding from the University of Manchester, which allowed us to develop our theoretical work on dynamical models. This preliminary work involves a visualisation of our attemprs to locate nonlinear patterns in the dynamic development of the relationships between students' dispositions, attainment and teaching practices. 
Type Of Material Computer model/algorithm 
Provided To Others? No  
Impact This is still work in progress and the impact is within our team members. We keep the updates in this website: http://www.teleprism.com/complexity/ 
URL http://teleprism.com/nonlinear/
 
Title Qualitative datasets 
Description We conducted more than 170 interviews with over 100 students and their teachers in two schools. The transcripts of these interviews have been anonymised and are ready to be shared with others. Unique ids are used to match between students interviews at two different occasions, and when possible to also match with their survey responses. 
Type Of Material Database/Collection of data 
Provided To Others? No  
Impact The interview data are analysed both separately (see work in progress) as well as in support of the quantitative findings from the survey datasets. 
 
Title Quantitative Database 
Description This database includes four different but link-able datasets: The student-level dataset includes data from longitudinal surveys (3 time points) with students in 40 Secondary Schools about their attitudes to mathematics, confidence at various mathematical topics, future aspirations, and their perceptions of the teaching they encounter. It is presented in the 'long format', thus it contains more than 30000 cases, which consist of repeated measurements (maximum 3) of more than 13000 students in years 7 to 11. Unique ids are included for students, their classes, and their teachers in order to allow the linkage of this dataset with the other three datasets. The Teacher-class level dataset includes the data collected from the teachers' surveys for each of the classes they teach separately, and for each of the two timepoints they were asked to complete the survey (in order to link with students' dataset). It mainly consists of the teachers' responses to questions about their teaching practices with each of these classes at different time points in the academic year 2011-2012 (the timing of completion is also recorded). The teacher-level dataset includes background information (e.g. gender, ethnicity, age, teaching experience, qualifications) for each of the teacher (130+) who responded in the survey. The class-level dataset includes the information provided by the teacher about some class characteristics (e.g. set, mixed ability, etc) when available. 
Type Of Material Database/Collection of data 
Provided To Others? No  
Impact The datasets are the main tools that gave rise to all the results and impact we report on other sections of the outcomes. 
 
Description AEON Engineering 
Organisation AEON Engineering Ltd
PI Contribution IAA-ESRC - to organise events with partners to discuss findings from previous studies and help change practice in relation to gender and engineering primarily and participation more broadly
Collaborator Contribution intend to: provide personnel to participate in workshops and meetings, access to company HR data and insight into policy and impact
Impact ongoing
Start Year 2018
 
Description Cansu Ayan 
Organisation Ankara University
Country Turkey 
Sector Academic/University 
PI Contribution A research assistant and PhD student in the department of Measurement and Evaluation in the Faculty of Education Science at Ankara University, Turkey, expressed interest in joining my group as a visiting scholar to work on mathematics attitudes and anxiety including measurement models as well.
Collaborator Contribution The visit is being currently organised for this Spring/Summer
Impact TBC
Start Year 2018
 
Description Eindhoven University of Technology in The Netherlands 
Organisation Eindhoven University of Technology
Country Netherlands 
Sector Academic/University 
PI Contribution shared instruments from teleprism and transmaths projects for use in the Netherlands
Collaborator Contribution to share data and results
Impact ongoing
Start Year 2017
 
Description GCRF Kenya 
Organisation Research Councils UK (RCUK)
Country United Kingdom 
Sector Public 
PI Contribution Have been invited to attend the Nairobi networking meeting funded by GCRF RCUK (January 2018).
Collaborator Contribution Partnerships are being explored from the contacts made during this event.
Impact ongoing
Start Year 2018
 
Description IBM UK 
Organisation IBM
Department IBM UK Ltd
Country United Kingdom 
Sector Private 
PI Contribution As part of IAA ESRC - to organise events with partners to discuss findings from previous studies and help change practice in relation to gender and engineering primarily and participation more broadly
Collaborator Contribution To be discussed at the start of the project
Impact ongoing
Start Year 2018
 
Description Jaquar Land Rover 
Organisation Jaguar Land Rover
Country United Kingdom 
Sector Private 
PI Contribution As partner in IAA ESRC awarded project. We will organise events with partners to discuss findings from previous studies and help change practice in relation to gender and engineering primarily and participation more broadly
Collaborator Contribution intend to: (a) host a forum with industry and academics, b) provide personnel to participate as Steering Group members and co-researchers. c) access to company HR data, and (d) insight to existing policy and policy impacts
Impact ongoing
Start Year 2018
 
Description Nottingham University - Instrument adoptation 
Organisation University of Nottingham
Country United Kingdom 
Sector Academic/University 
PI Contribution I have been asked by colleagues in Nottingham for potential use of our developed questionnaires in other projects run by researchers and practitioners in their groups. In particular, Geoff Wake (Geoffrey.Wake@nottingham.ac.uk) got me in touch with Matt Lewis (mattdlewis@gmail.com) who subsequently adopted our teaching practice instrument, for use with teachers in his study. Later on I got another request for use of the Mathematics Self Efficacy Instrument (from our student surveys). The first implementation with Matt gave some preliminary data which I helped with analysis drawing on my measurement expertise. There is definitely potential for collaborative outputs here. The second request I need to follow up in regards to progress.
Collaborator Contribution One of the partners in this collaboration (Matt) shared data which can be potentially useful for extending on our work and increasing impact (e.g. in regards to teachers' professional development and training). This resulted in a report
Impact This resulted in a report for the evaluation which drew on the results based on instruments borrowed from Teleprism study. The evaluation's website where the report can be found, after validated, is: http://project-oracle.com/projects/info/high-challenge-for-high-achievement/
Start Year 2014
 
Description Primary Science Evaluation (funded by Wellcome Trust) 
Organisation CFE (Research And Consulting) Limited
Country United Kingdom 
Sector Private 
PI Contribution I am consulting the evaluation team especially in regards to the development of their instruments which also built on the teleprism student and teacher surveys. This work is at its preliminary stages.
Collaborator Contribution The CFE are actually leading on this work, and our team from the University of Manchester provides consulting and advice on the methods and other aspects of the evaluation.
Impact Not available yet
Start Year 2016
 
Description Science Manchester Group (Andy Howes and others) 
Organisation University of Manchester
Country United Kingdom 
Sector Academic/University 
PI Contribution I have supported through the provision of the teachers and student questionnaires their instrument development. Collaboration with Andy Howes, Robert Buck and Zahra Aijah More details are provided below as quoted from Andy's overview.
Collaborator Contribution By Andy Howes (15 March 2017) We have adapted the questionnaire on teachers' practices in maths education, with minimal adaptation, in order to use it to build a picture of current practice in science classrooms from the point of view of the science teacher. We asked teachers to rate possible elements of their practice in relation to different KS3 year groups (years 7, 8, 9). Our intention is to use this with teachers at various stages in their careers as part of a project investigating current practice and the rationale for it, along with associated challenges and tensions. So far we have piloted the questionnaire with 60 PGCE science trainees at a point halfway through their initial teacher education year, and we are currently analysing the results.
Impact A teacher questionnaire
Start Year 2014
 
Description Secondary School Implementation of Instrument with Parents 
Organisation University of Manchester
Country United Kingdom 
Sector Academic/University 
PI Contribution I collaborated as an advisor/consultant with a particular school taking part in the coalition of research schools: in their efforts to increase students' learning outcomes they decided to implement an adaptation of our students' maths attitudes instrument (which we helped them developed) into an instrument for parents. I had also helped with analysis of the data they got, as well as disseminating some results with them to present in a local event (as part of the coalition of research schools project).
Collaborator Contribution Shared data and provided feedback on generic school reports for higher impact with teachers.
Impact A report of findings was sent to the involved school.
Start Year 2013
 
Description Women in Engineering 
Organisation The Women's Engineering Society
PI Contribution for project which starts in April 2018:Project title: 'Futures in Engineering: Informing policy and practice and developing future research agendas via existing research' Investigators: Dr Maria Pampaka and Dr Diane Harris to organise events with partners to discuss findings from previous studies and help change practice in relation to gender and engineering primarily and participation more broadly
Collaborator Contribution the intention as per letter of support is: to Support sharing of insights, data and case studies, for example through participation of WES trustees and other senior WES members on advisory panels and as presenters • Promote opportunities for collaboration to WES partners and other supporters through our monthly e-newsletter and social media • Disseminate the output through our journal The Woman Engineer and on our website.
Impact ongoing
Start Year 2018
 
Description BBC breakfast - 5 March 2018 
Form Of Engagement Activity A press release, press conference or response to a media enquiry/interview
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Media (as a channel to the public)
Results and Impact Talked to BBC reporters on work related to maths attitudes and anxiety based on current and previous work and mentioned during BBC Breakfast on 5th March 2018
Year(s) Of Engagement Activity 2018
URL https://www.bbc.co.uk/iplayer/episode/b09tm2m9/breakfast-05032018
 
Description Big Issue - October 2018 
Form Of Engagement Activity A magazine, newsletter or online publication
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Public/other audiences
Results and Impact I have been invited by a colleague to collaborate in writing an article about school inequalities, which was then published in the Big Issue.
Year(s) Of Engagement Activity 2018
URL https://www.bigissuenorth.com/comment/2018/09/dont-just-ensure-children-well-school/
 
Description Blog for Evidence into Education 
Form Of Engagement Activity Engagement focused website, blog or social media channel
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Mathematics Anxiety: What we found out in a recent review of research and wider evidence. We have presented some findings from our review focusing on teachers and their practices.
Year(s) Of Engagement Activity 2018
URL http://blogging2.humanities.manchester.ac.uk/miebee/mathematics-anxiety-what-we-found-out-in-a-recen...
 
Description British Academic - Open Day (22 June 2018) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Schools
Results and Impact I have been invited to organise and deliver a workshop for school aged children as part of the British Academy's Summer Show Case 2018. The aim of the talk was to inspire young people and get them to see why our subject is an inspiring, exciting subject. We have presented interactive activities of the uses of maths and statistics to around 50 students and their teachers. The idea behind the activity was that GCSE aged children who are selecting their A-level's which will affect their University choices might feel inspired by something they hear or encounter during their visit, and choose this subject to study later on.
Year(s) Of Engagement Activity 2018
URL https://www.thebritishacademy.ac.uk/events/summershowcase/2018
 
Description CCSR Newsletter 2012 
Form Of Engagement Activity A magazine, newsletter or online publication
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact This was a brief outline of the project as part of CCSR newsletter, in which I presented the project as well as some preliminary findings.

I got a few emails from researchers and practitioners around the country after this newsletter.
Year(s) Of Engagement Activity 2012
 
Description Debate on Learning Gain at Milton Keynes (November 2018) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact I have been invited to take part in a debate in relation to a pilot study on exploring measurement of learning gain at university hosted by the Open University.
During the debate we got a chance to discuss emerging findings in front of an audience of around 30-50 people (professionals, students and public). This opportunity opened the doors to a potential upcoming collaborative publication.
The work presented indirectly relates to the award and more directly relates to the project funded by HEFCE following this particular awar.
Year(s) Of Engagement Activity 2018
URL https://abclearninggains.com/
 
Description Embracing Change in Engineering (Dec 2018 - Manchester) 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact With support from the ESRC Impact Accelerator Account funding we have hosted a full day of presentations and discussions providing a forum for reflection and discussion between academics, researchers, professionals and policy makers around various challenges in relation to engineering as evidenced by findings from our previous projects.
Participants engaged with discussions and one of the conclusions of the date was that we need more spaces like that were social scientists and engineering academics and professionals can share knowledge to help improve the field.
Year(s) Of Engagement Activity 2018
URL http://www.researchingfuturesinengineering.com/
 
Description Engineering Education Systems that are Fit for the Future Conference (September 2018) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact We have been invited to present during a session on 'Enhancing leaning teaching and training' as part of a the two day conference on Engineering Education systems that are Fit for the Future hosted by the Royal Academy of Engineering at Prince Philip House, London. The conference convened awardees from its international programmes, Industry Academia Partnership Programme (IAPP), Higher Education Partnerships in sub-Saharan Africa Programme (HEP SSA) and GCRF Africa Catalyst, alongside the Academy's UK partners, funders and networks.
Year(s) Of Engagement Activity 2018
URL https://www.raeng.org.uk/grants-and-prizes/international-research-and-collaborations/higher-educatio...
 
Description Engineering Professors Council - working group 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Invitation to attend the Engineering Professors' Council (EPC) Recruitment and Admissions Working Group Conference (in 2017 and 2018). The EPC have invited 2 members of the team (Pampaka and Harris) to a workshop as part of their Recruitment and Admissions Working Group Conference in November. Two areas of concern will be worked on at the conference and one will be worked up into a green paper to inform Government. It is proposed that the decisions made at the conference will be taken up by Government and will appear as a white paper.
Year(s) Of Engagement Activity 2017,2018
 
Description Learning Gain: An Agenda for Change (27th September 2018) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact I have been invited to present and take part on the final LEGACY event on the piloting of alternative learning gain outcomes (for learning at Higher education). The event held at Woburn House, London on Thursday 27th September 2018, brought together practitioners and policy makers to discuss the future of learning gain measurement in higher education. The insightful debate during the day considered the methodological and conceptual challenges for those working to research and implement learning gain measures.
Year(s) Of Engagement Activity 2018
URL https://warwick.ac.uk/services/aro/dar/quality/legacy/events/agendaforchange/
 
Description MEC-Loughborough Presentation February 2016 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Professional Practitioners
Results and Impact Title: Falling in (or out of) Love with Maths: Does teaching matter? (A measurement and modelling story).
I have presented to a mainly academic research group results from the project focusing both on substantive findings as well as measurement challenges. There were between 15 and 20 attendants. The presentation sparked questions and discussions afterwards and there were at least 2 participants who followed up the conversation via email and requested the instruments we have developed as part of this work.
Year(s) Of Engagement Activity 2016
URL http://www.lboro.ac.uk/media/wwwlboroacuk/content/mathematicseducationcentre/downloads/workshopsched...
 
Description Manchester Policy Blog 
Form Of Engagement Activity Engagement focused website, blog or social media channel
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Media (as a channel to the public)
Results and Impact We have written a blog on the reasons engineering must embrace change. As a result of this publication we have been invited to submit a proposal in response to a call to explore young people's aspirations to study (or not) engineering. This has been successful and we are now commissioned by EngineeringUK and the Institution of Mechanical Engineers to provide more evidence on the matter.
Year(s) Of Engagement Activity 2018
URL http://blog.policy.manchester.ac.uk/posts/2018/07/why-engineering-in-the-uk-must-embrace-change/
 
Description OfS national conference on learning gain (March 2019) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Policymakers/politicians
Results and Impact I have been invited to present on this event as part of a breakout session on learning gain and the student participation and progression. Around 30 professionals/colleagues from universities across the country attended my talk and some of the attendants expressed interest in how universities could embed the measures we have been suggesting as well as asked for further use of our developed instruments. The impact of this work is still ongoing.
Year(s) Of Engagement Activity 2019
URL https://www.officeforstudents.org.uk/news-blog-and-events/events/ofs-national-conference-on-learning...
 
Description Policy at Manchester 2014 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Professional Practitioners
Results and Impact The presentation along with the others in the theme sparkled discussion around ethnicity issues regarding students' subject choices (focusing on STEM topics).
Year(s) Of Engagement Activity 2014
URL https://www.policy.manchester.ac.uk/connect/policy-week/pw-2014/
 
Description Women in Technology Interconnect (April 2018) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact The theme for this event was 'Press for Progress', borrowing from this year's International Women's Day theme. We have been invited to present findings from our studies in relation to the barriers to engineering.
Year(s) Of Engagement Activity 2018
URL http://www.researchingfuturesinengineering.com/files/Engineering%20-%20The%20Barriers.pdf