I am a Senior Lecturer in the Mathematics Education Centre at Loughborough University and a Fellow of the Higher Education Academy.

I was a Senior Research Fellow funded by a Royal Society Shuttleworth Education Research Fellowship.

I lecture mathematics and research mathematics education and assessment. I obtained my PhD in Mathematics Education at the University of Warwick and worked as a Research Fellow at the University of Nottingham before moving to Loughborough University as a Senior Research Fellow funded by the Royal Society. Prior to this I worked as a Research Assistant on many projects at several universities, and was a school teacher for ten years.

### Other roles

I lead on the *Modelling with Mathematics and Statistics* and *Studies in Science and Mathematics* modules. My other teaching duties include developing STACK assessments for use in modules across the university. I edit the Research Update newsletter for teachers interested in engaging with mathematics education research. I am the Departmental Enterprise Coordinator for the MEC and the Mental Health First Aider for the Schofield Building. I am also a member of Loughborough University's UCU committee with the portfolio of Personal Case Work Coordinator.

### Recent grants

- 2017-2020. Higher Education Academy.
*Enabling better online assessment in mathematics.*With Tim Lowe Hunt and Tim Hunt (Open University) and Chris Sangwn (University of Edinburgh). - 2017-2019. British Academy.
*The role of teacher knowledge and classroom resources in understanding equivalence relations in mathematics*. With Şimşek, Iro Xenidou-Dervou and Jodie Hunter (Massey University, New Zealand). - 2013-2016. Nuffield Foundation.
*Measuring conceptual understanding: The case of teaching with abstract and concrete representations.*With Matthew Inglis and Camilla Gilmore. [project page] - 2014-2015. No More Marking Ltd.
*Developing secondary education progress measures in Mathematics and English.* - 2009-2014. Royal Society Shuttleworth Education Research Fellowship.
*Removing the mismatch between intentions and outcomes in GCSE mathematics.* - 2013. AQA.
*Investigating standards across A-level mathematics syllabuses.*With Matthew Inglis. - 2012. Mapping University Mathematics Assessment Practices project.
*Summative peer assessment of undergraduate calculus using Adaptive Comparative Judgement.*With Lara Alcock. - 2012. Higher Education Academy.
*Diversifying practice in assessing the mathematical needs of undergraduate students.* - 2011-2012. Nuffield Foundation.
*Improving the quality of GCSE mathematics examinations.*With Matthew Inglis. - 2010-2010. Nuffield Foundation.
*Investigating validity and reliability in GCSE mathematics examinations.* - 2009-2010. Esmée Fairbairn Foundation.
*How should the equals sign be taught?*With Matthew Inglis and Camilla Gilmore.

### Research areas

- Students' understanding of symbolic equivalence.
- Algebraic thinking.
- Conceptual and procedural understanding of mathematics.
- Improving the quality and validity of mathematics summative assessment.
- Standards and validity in examinations.

### Research interests

My interest is in improving the quality of assessment at all levels of education using Comparative Judgement and STACK.

Comparative Judgement involves no mark schemes and no marking. It is instead based on expert pairwise judgement of student work. My research has explored the potential of Comparative Judgement for

- Improving the validity of assessment in mathematics and other subjects
- Enabling the use of expert judgement without loss of reliability
- Comparing standards of achievement over time and across institutions
- Measuring conceptual understanding quickly and efficiently
- Improving the validity and reliability of peer assessment

STACK provides online mathematics assessments for undergraduates. Uniquely, STACK enables personalised feedback based on student responses. This feature enables the detection of, and directed feedback on, common misconceptions and other patterns of errors made by students.

I am also interested in the transition from arithmetic to algebra when pupils move from primary to secondary school, and in particular the role that understanding mathematical equivalence has to play.

### Recent publications

#### Journal Papers

- Simsek, E., Xenidou-Dervou, I., Karedeniz, I. and Jones, I. (accepted). The conception of substitution of the equals sign plays a unique role in students’ algebra performance.
*Journal of Numerical Cognition*. - Jones I. and Sirl, D. (2017). Peer assessment of mathematical understanding using comparative judgement.
*NOMAD: Nordic Studies in Mathematics Education*, 22, 147-164. [repository] [official] - Sangwin, C. and Jones, I. (2016). Asymmetry in student achievement on multiple-choice and constructed-response items in reversible mathematics processes.
*Educational Studies in Mathematics*, doi:10.1007/s10649-016-9725-4. [repository] [preprint (pdf)] [official] - Jones, I., Humphries, S., Wheadon, C. und Inglis, M. (2016). Wie vergleicht man den Anspruch mathematischer Prüfungen? Die A levels in England, Wales und Nordirland.
*Mitteilungen der Deutschen Mathematiker-Vereinigung, 24*, 100-103. [official] - Alcock, L., Ansari, D., Batchelor, S., Bisson, M., De Smedt, B., Gilmore, C., Gbel, S., Hannula- Sormunen, M., Hodgen, H., Inglis, M., Jones, I., Mazzocco, M., McNeil, N., Schneider, M., Simms, V., and Weber, K. (2016). Challenges in mathematical cognition: A collaboratively-derived research agenda.
*Journal of Numerical Cognition, 2*, 20-41 [official] - Bisson, M., Gilmore, C., Inglis, M. and Jones, I. (2016). Measuring conceptual understanding using comparative judgement.
*International Journal of Research in Undergraduate Mathematics Education, 2*, 141-164. [repository] [preprint (pdf)] [official] - Jones, I., Humphries, S., Wheadon, C. and Inglis, M. (2016). Fifty years of A-level Mathematics: Have standards changed?
*British Educational Research Journal, 42*, 543–560. [repository] [preprint (pdf)] [official] - Jones, I. and Wheadon, C. (2015). Peer assessment using comparative and absolute judgement.
*Studies in Educational Evaluation, 47*, 93-101. [repository] [preprint (pdf)] [official] - Jones, I. (2015). Building bridges that are functional and structural.
*Constructivist Foundations, 10*, 332–333. [repository] [official] - Jones, I. and Inglis, M. (2015). The problem of assessing problem solving: Can comparative judgement help?
*Educational Studies in Mathematics, 89*, 337-355. [repository] [preprint (pdf)] [official] - McMahon, S. and Jones, I. (2014). A comparative judgement approach to teacher assessment.
*Assessment in Education: Principles, Policy & Practice, 22*, 368-389. [repository] [official] - Jones, I., Swan M. and Pollitt, A. (2014). Assessing mathematical problem solving using comparative judgement.
*International Journal of Science and Mathematics Education, 13*, 151-177. [repository] [official] - Adesina, A., Stone, R., Batmaz, F. and Jones, I. (2014). Touch Arithmetic: A process-based Computer-Aided Assessment approach for capture of problem solving steps in the context of elementary mathematics.
*Computers & Education, 78*, 333-343. [repository] [official] - Jones, I. and Alcock, L. (2014). Peer assessment without assessment criteria.
*Studies in Higher Education, 39*, 1774-1787. [repository][official] - Jones, I., Inglis, M., Gilmore, C. and Evans, R. (2013). Teaching the substitutive conception of the equals sign.
*Research in Mathematics Education, 15*, 34-49. [repository] [official] - Jones, I., Inglis, M., Gilmore, C. and Dowens, M. (2012). Substitution and sameness: Two components of a relational conception of the equals sign.
*Journal of Experimental Child Psychology, 113*, 166–176. [repository] [official] - Black, P., Burkhardt, H., Daro, P., Jones, I., Lappan, G., and Pead, D., and Stephens, M. (2012). High-stakes examinations to support policy: design, development and implementation.
*Educational Designer, 5*(2), 1-31. [official]

#### Book reviews

- Jones, I. (2015). Review of "Algebra teaching around the world" edited by Frederick Koon Shing Leung, Kyungmee Park, Derek Holton and David Clarke.
*Educational Studies in Mathematics*. [repository] [preprint (pdf)] [official] - Jones, I. (2012). Review of "Early algebraization: a global dialogue from multiple perspectives" edited by Jinfa Cai and Eric Knuth.
*Research in Mathematics Education, 14*, 301-308. [preprint (pdf)] [official]

#### Book chapters

- Jones, I. (2014). The fitness and impact of GCSE mathematics examinations. In Mendick, H. and Leslie, D. (Eds.)
*Debates in Mathematics Education*, pp. 186-195. London: Routledge. - Jones, I. and Alcock, L. (2012). Summative peer assessment of undergraduate calculus using Adaptive Comparative Judgement. In Iannone, P. and Simpson, A. (Eds.)
*Mapping University Mathematics Assessment Practices*, pp. 63-74. Norwich: University of East Anglia. [pdf]

#### Recent Refereed Conference Papers

- Hunter, J. and Jones, I. (2018). Free-response tasks in primary mathematics: a window on students thinking.
*Proceedings of the 41st Annual Conference of the Mathematics Education Research Group of Australasia*. (Vol. 41, pp. 400-407). Auckland, New Zealand. - Jones, I. and Karadeniz, I. (2016). An alternative approach to assessing achievement.
*The 40th Conference of the International Group for the Psychology of Mathematics Education*. (Vol. 3, pp. 51-58). Szeged, Hungary. [repository] - Hunter, J. and Jones, I. (2015). Measuring teacher awareness of children’s understanding of equivalence.
*Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education*. (Vol. 3, pp. 81-88). Tasmania. [repository] - Adesina, A., Stone, R., Batmaz, F. and Jones, I. (2015). A Semi-Automatic Computer-Aided Assesment Approach for Marking and Providing Feedback Comments.
*7th International Conference on Computer Supported Education*. Lisbon, Portugal. [repository] - Evans, S., Jones, I. and Dawson, C. (2014). Do subject specialists produce more useful feedback than non-specialists when observing mathematics lessons?
*Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education*. (Vol. 3, pp. 33-40). Vancouver, Canada. [repository] - Jones, I., Inglis, M., Gilmore, C, and Hodgen, J. (2013). Measuring conceptual understanding: The case of fractions. In A. M. Lindmeier and A. Heinze (Eds.),
*Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education*. (Vol. 3, pp. 113-120). Kiel, Germany. [repository] - Adesina, A., Stone, R., Batmaz, F. and Jones, I. (2013). Use of multi-touch gestures for capturing solution steps in arithmetic word problems.
*5th International Conference on Computer Supported Education*(pp. 210-215). Aachen, Germany. [repository]

#### Recent Professional Journals

- Jones, I. (2015). It's easy to judge.
*Mathematics Teaching, 248*, 39-41. - Jones, I. and Inglis, M. (2013). Judgemental Mathematics.
*The Actuary*. - Jones, I. (2013). Let students judge: Assessing nebulous knowledge.
*ALT Newsletter*. [official] - Jones, I., Inglis, M. and Gilmore, C. (Summer 2013). Equality in the primary maths classroom.
*Primary Maths*, 12-13.

#### Recent Other

- Jones, I., Inglis, M. and Gilmore, C. (2011). Imperative and punctuative operational conceptions of the equals sign.
*Informal Proceedings of the British Society for Research into Learning Mathematics, 31*(1), 79-84. - Jones, I. (2010). Why do GCSE examination papers look like they do?
*Informal Proceedings of the British Society for Research into Learning Mathematics, 30*(3), 61-66.

#### Recent Presentations

- Hunter, J. and Jones, I. (June 2018).
*Free-response tasks in primary mathematics: a window on students' thinking*. Mathematics Education Research Group of Austalasia, Massey University, Auckland. - Jones, I. (June 2018).
*Comparative judgement for research and improving education.*University of Auckland. - Jones, I. (June 2018).
*Using comparative judgement to assess deep understanding in mathematics*. Mathematics Education Research Group of Austalasia: Teachers’ Day, Massey University, Auckland. - Jones, I. (June 2018).
*Conceptual understanding and how to assess it.*New Zealand Council for Educational Research and Victoria University of Wellington. - Jones, I. (June 2018).
*Comparative judgement for moderating assessment.*Presentation to Community of Learning schools group in Christchurch. - Inglis, M., Foster, C. and Jones, I. (March 2018).
*Statistics Working Group: A hands-on introduction to Bayesian statistics*. British Society for Research into Learning Mathematics day conference, University of Nottingham. - Jones, I. and Barmby, P. (March 2018).
*Do students make progress during Year 7?*British Society for Research into Learning Mathematics day conference, University of Nottingham. - Jones, I. (February 2018).
*Procedural and conceptual understanding in mathematics*. CCEA, Belfast. - Davis, B., Alcock, L. and Jones, I. (March 2018).
*What do mathematicians mean by proof?*Poster presentation at the Conference on Research in Undergraduate Mathematics Education, San Diego. - Jones, I. and Inglis, M. (October 2017).
*Using comparative judgement in the mathematics classroom*. The Power of Six National Maths Conference, London. - Jones, I. and Sangwin, C. (March 2017).
*Should multiple choice items be used to assess mathematical knowledge?*The 10th Annual UK Rasch User Group Day, Coventry. - Jones, I. (March 2017).
*Comparative judgement: an overview*. Department of Health, Leeds. - Jones, I. (February 2017).
*What is mathematical understanding? You know it when you see it*. Talk for teachers, Auckland, New Zealand. - Jones, I. (February 2017).
*A conceptual approach to assessing mathematics*. Massey University, New Zealand. - Jones, I. (November 2016).
*Snapshots of deep learning over time: A novel approach to measuring student progress.*AEA-Europe Conference, Cyrpus. - Jones, I. (October 2016).
*Comparative judgement for robust assessment: The case of mathematics.*Royal Society: Assessing experimental science in 1118 education: New research directions. - Jones, I. (September 2016).
*Bin that rubric: A better way to assess conceptual understanding.*EAMS Conference, University of Newcastle-upon-Tyne. - Jones, I. (September 2016).
*Conceptual understanding: You know it when you see it.*CETL-MSOR Conference, Loughborough University. - Jones, I. (September 2016).
*Promoting and assessing conceptual understanding of mathematics.*MatRIC Confer- ence, Loughborough University. - Jones, I. and Karadeniz, I. (August 2016).
*An alternative approach to assessing achievement.*PME40, Hungary. - Jones, I. (June 2016).
*A conceptual approach to assessing mathematics.*University of Nottingham. - Jones, I. (March 2016).
*A conceptual approach to assessing achievement in mathematics.*University of Oxford. - Jones, I. (March 2016).
*A conceptual approach to assessing mathematics.*The 9th Annual UK Rasch User Group Day, Durham University. - Jones, I. (February 2016).
*A conceptual approach to assessing achievement and progress.*British Society for Research into Learning Mathematics day conference, Manchester Metropolitan University. - Jones, I. (November 2015).
*Assessing conceptual understanding of mathematics using comparative judgement.*University of Leicester. - Jones, I. (November 2015).
*Randomised controlled trials and comparative judgement.*AEA-Europe Conference, University of Glasgow. - Jones, I. (September 2015).
*Promoting and assessing conceptual understanding of mathematics.*MatRIC Conference, Loughborough University. - Brown, M. and Jones, I. (April 2015).
*Vision for science and mathematics education.*Heads of Departments of Mathematical Sciences conference, University of Birmingham. - Jones, I. (March 2015).
*Measuring conceptual understanding of STEM subjects using comparative judgement.*The 9th Annual UK Rasch User Group Day, Pearson, London. - Jones, I. (November 2014).
*Mathematics education and comparative judgement.*Association for Educational Assessment - Europe conference, Tallinn. - Jones, I., Inglis, M. and Sirl, D. (March 2014).
*Blatant violation of independence: Should statistical tests be conducted on comparative judgement data?*The 8th Annual UK Rasch User Group Day, University of York. - Jones, I., Inglis, M., Wheadon, C. and Humphries, S. (March 2014).
*Has Advanced-level Mathematics got easier over time?*British Society for Research into Learning Mathematics day conference, King’s College London. - Jones, I., Inglis, M., Wheadon, C. and Humphries, S. (November 2013).
*A comparative judgement study of national assessment standards.*Association for Educational Assessment - Europe conference, Paris. - Jones, I. (November 2013).
*Mathematical understanding: You know it when you see it.*MathSpeak2013 conference, London. - Jones, I. (October 2013).
*Measuring conceptual understanding in mathematics.*University of Durham. - Jones, I. (March 2013).
*The problem solving problem: Can comparative judgement help?*Cambridge Assessment. - Jones, I. and Whythe, H. (March 2013).
*Modelling comparative judgement data for educational assessment: Some issues arising.*7th UK Rasch Users Day meeting, Manchester.

- Member of the Mathematical Pedagogy Group.
- Member of the Mathematical Cognition Group.
- Member of the JMC's working group for GCSE mathematics.
- Member of the Editorial Board of Research in Mathematics Education.
- I recently sat on the Royal Vision Committee for Science and Mathematics Education 5-19.
- I recently sat on the Royal Society Vision Committee for science and mathematics education 4-19.
- I was secretary of the British Society for Research into Learning Mathematics.
- I currently sit on the Editorial Board of Research in Mathematics Education.
- I am the scientific advisor to No More Marking Ltd.
- Fellow of the Higher Education Academy.

### Links

- Departmental Enterprise Coordinator for the MEC.
- Lead developer on the STACK project to create online mathematics assessments for use across the university.
- UCU departmental representative for the MEC.
- Personal Casework Coordinator on Loughborough University UCU committee.
- PhD supervision: Ben Davies, Tom Francome and Emine Şimşek.
- Editor of the MEC's Research Update newsletter for schools.