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Malcolm Swan

Emeritus Professor of Mathematics Education,

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Biography

Malcolm is currently Director of the Centre for Research in Mathematics Education. His research is mainly into the theory, development and evaluation of teaching situations and professional development in mathematics education. This includes: the design of situations which foster reflection, discussion and metacognitive activity; the design of situations in which children construct mathematical concepts and develop problem solving strategies; and the design of formative and evaluative assessment.

In the UK, Malcolm is perhaps best known for leading the design of "Improving Learning in Mathematics" published in 2005 and funded by the UK government. These curriculum and professional development resources were sent to all mathematics teachers in secondary and further education in England. This was followed in 2007 by "Thinking through Mathematics" which was distributed to all adult education institutions. In 2009, Malcolm was awarded the International Society for Design and Development in Education Prize for his teaching materials: "the Language of Functions and Graphs".

More recently, Malcolm lead the development of 'Classroom Challenges', a series of 100 formative assessment lessons supporting the Common Core State Standards for Mathematics in the US, funded by the Bill and Melinda Gates foundation. These lessons have proved extremely popular and effective across the US. In recognition of the international impact that the design work at Nottingham has had, Malcolm (with Hugh Burkhardt) has been awarded the Emma Castenuovo 2016 award for "excellence in the practice of mathematical education" by the International Commission on Mathematical Instruction.

Research Summary

Malcolm's research interests lie in the design of teaching and assessment for mathematics education. This involves designing and analysing processes and products with and for mathematics teachers and… read more

Selected Publications

Malcolm is a member of the Centre for Research in Mathematics Education. His research supervision areas include:

  • "design research" into the theory, development and evaluation of teaching situations and innovative tools and processes for mathematics education
  • professional development of teachers, with regard to the evolution of values, beliefs and practices
  • collaborative, dialogic approaches to mathematics teaching
  • metacognition and problem solving
  • formative and summative assessment

Research proposals: please email Malcolm if you would like to discuss the appropriateness of your research topic. See also: School of Education research supervision areas.

Current Research

Malcolm's research interests lie in the design of teaching and assessment for mathematics education. This involves designing and analysing processes and products with and for mathematics teachers and learners. Current and recent research projects include:

Mathematics Assessment Project (funded by the University of California) This project aims to develop formative assessment lessons and summative tests, with associated professional development materials, for US students aged 12 -18. This involves detailed study of teachers facing new pedagogical and mathematics challenges. It contributes to the new Common Core Standards, being developed by US states. http://map.mathshell.org.uk

Promoting Inquiry-based learning in Mathematics and Science (funded by the EU) This collaborative project, involving 12 countries, seeks to promote a greater uptake of inquiry-based learning in mathematics and science at both primary and secondary levels across Europe. Central to this is the development of professional development resources for teachers. http://www.primas-project.eu

Bowland Maths (funded by the Bowland Charitable Trust) This project seeks to develop multimedia teaching resources that make mathematics more engaging and relevant to pupils, and foster learning of the key concepts and processes introduced in the 2007 Key Stage 3 curriculum. Currently, we are designing video-led CPD materials to help teachers develop the pedagogical skills required to effectively use these resources and formative assessments which foster key concepts and processes. http://www.bowlandmaths.org.uk

Problem Solving in Mathematics and Science (funded by Shell Centre Publications Ltd) The strategic processes involved in mathematical and scientific think have much in common - both involving inquiry, including classifying, representing, controlling variables, and so on. This project aims to explore this area and the curriculum opportunities it presents.

Lessons for Mathematical Problem Solving (funded by the Nuffield Foundation). This project seeks proof-of-concept of new and sustainable models of partnerships that support professional learning in secondary school mathematics with the involvement of Higher Education. The focus is on improving students' problem-solving capabilities in mathematics.

Formative Assessment in Science and Mathematics Education (Funded by the EU). This EU project aims to research the use of technology in formative assessment classroom practices in ways that allow teachers to respond to the emerging needs of low achieving learners in mathematics and science so that they are better motivated in their learning of these important subjects.

Past Research

Malcolm has worked at the University of Nottingham since 1979 and during that time has taken a central role in numerous research and development projects. Notable examples include:

Improving Learning in Mathematics (2004-5; funded by the DfES) - national professional development project for 16-19 mathematics education; This was subsequently extended to working with adults in the Maths4Life project Thinking through Mathematics (2006) funded at the NRDC (National Research and Development Centre at the London Institute). http://www.nationalstemcentre.org.uk/elibrary/collection/282/improving-learning-in-mathematics

World Class Arena (2003-5; funded by QCA) - curriculum and assessment for problem solving in mathematics, science and technology (http://www.worldclassarena.org)

Mathematics Assessment Resource Service (MARS) (1997 onwards; Funded by the National Science Foundation) - international project into assessment design with Michigan State University

Malcolm is on the executive committee for the International Society for Design and Development in Education. (http://www.isdde.org)

  • JONES, I, SWAN, M and POLLITT, A, 2015. Assessing mathematical problem solving using Comparative Judgement International Journal of Science and Mathematics Education. 13(1), 151-177
  • EVANS, S and SWAN, M, 2015. Developing Student Questioning when problem solving: The role of sample student responses. In: 9th Congress of European Research in Mathematics Education. (In Press.)
  • WAKE, G., SWAN, M. and FOSTER, C., 2015. Professional learning through the collaborative design of problem-solving lessons Journal of Mathematics Teacher Education. 19(2), 243-260
  • SWAN, M, 2015. Designing formative assessment lessons for concept development and problem solving In: PME-NA_37 (North American chapter of the International Group for the Psychology of Mathematics Education). 33-51
  • SWAN, M, 2014. Improving the alignment between values, principles and classroom realities. In: LI, Y and LAPPAN, G, eds., Mathematics Curriculum in School Education Springer.
  • SWAN, M, 2014. Design Research in Mathematics Education. In: LERMAN, S, ed., Encyclopedia of Mathematics Education Springer.
  • FOSTER, C., WAKE, G. and SWAN, M., 2014. Mathematical knowledge for teaching problem solving: Lessons from lesson study In: Proceedings of the Joint Meeting of PME 38 and PME-NA 36. 3. 97-104
  • WAKE, G, FOSTER, C and SWAN, M, 2014. Teacher knowledge for modelling and problem solving In: Proceedings of the 8th British Congress of Mathematics Education.. 34. 335–342
  • SWAN, M, 2014. Designing tasks and lessons that develop conceptual understanding, strategic competence and critical awareness In: Encontro de Investigação em Educação Matemática 2014.
  • SWAN M and BURKHARDT, H, 2014. Lesson Design for Formative Assessment Educational Designer. 2(7), 24
  • SWAN, M., PEAD, D., DOORMAN, M. and MOOLDIJK, A., 2013. Designing and using professional development resources for inquiry-based learning ZDM: the International Journal on Mathematics Education. n/a(n/a), n/a
  • BURKHARDT, H and SWAN, M, 2013. Task design for systemic improvement: principles and frameworks In: Proceedings of ICMI Study 22: Task Design in Mathematics Education. 433-442
  • WAKE, G, FOSTER, C and SWAN, M, 2013. A theoretical lens on lesson study: Professional learning across boundaries In: International Group for the Psychology of Mathematics Education, Kiell. 4. 369-376
  • SWAN, M, 2013. Values, Principles and Design in Mathematics Education. In: Proceedings of the Hong Kong Mathematics Education Conference 2013 2-14
  • SWAN, M, 2012. Some reactions of a Design Researcher. In: GUEUDET,G, PEPIN, B and TROUCHE, eds., From Text to 'Lived' Resources: Mathematics Curriculum Materials and Teacher Development Springer. 181-189
  • SWAN, M. and BURKHARDT, H., 2012. A designer speaks: designing assessment of performance in mathematics Educational Designer: Journal of the International Society for Design and Development in Education. 2(5), 19
  • SWAN, M., 2011. Towards the creative teaching of mathematics. In: THOMSON, P. SEFTON-GREEN, J, ed., Researching Creative Learning: Methods and Issues Routledge. 54-67
  • SWAN, M, 2011. Designing tasks that challenge values, beliefs and practices: A model for the professional development of practicing teachers. In: SULLIVAN, P. and ZASLAVSKI, O., eds., Constructing knowledge for teaching secondary Mathematics: Tasks to enhance prospective and practicing teacher learning Springer.
  • SWAN, M, 2011. Designing tasks for teacher education In: Proceedings of the 35th Conference if the International Group for the Psychology of Mathematics Education. 1.131-1.134
  • SWAN, M. and SWAIN, J., 2010. The impact of a professional development programme on the practices and beliefs of numeracy teachers Journal of Further and Higher Education. 34(2), 165-177
  • SWAN, M and SWAIN, J, 2010. The impact of a Professional Development Programme on the Practices and Beliefs of Numeracy Teachers Journal of Further and Higher Education. 34(2), 165-177
  • SWAIN, J. and SWAN, M., 2009. Teachers’ attempts to integrate research-based principles into the teaching of numeracy with post-16 learners Research in Post-Compulsory Education. 14(1), 75-92
  • SWAN, M, 2008. The design of multiple representation tasks to foster conceptual development. International Congress for Mathematics Education 11. Available at: <http://tsg.icme11.org/tsg/show/35>
  • SWAN, M., 2008. A designer speaks: Malcolm Swan: designing a multiple representation learning experience in secondary algebra Educational Designer: Journal of the International Society for Design and Development in Education. 1(1), 3
  • SWAN, M and LACEY, P., 2008. Mathematics Matters National Centre for Excellence in Teaching Mathematics.
  • PEAD, D and SWAN, M, 2008. Professional development resources Bowland Trust/ Department for Children, Schools and Families. Available at: <http://www.bowlandmaths.org.uk/>
  • SWAN, M, 2007. The impact of task-based professional development on teachers' practices and beliefs: A design research study Journal of Mathematics Teacher Education. 10(4-6), 217-237 (In Press.)
  • SWAN, M., TURNER, R., YOON, C. and MULLER, E., 2007. The Roles of Modelling in Learning Mathematics. In: BLUM, W., GALBRAITH, P.L., HENN, HANS-WOLFGANG and NISS, M., eds., Modelling and Applications in Mathematics Education: The 14th ICMI Study Springer. 275-284
  • SWAIN, J. and SWAN, M., 2007. Thinking Through Mathematics: Research report National Research and Development Centre for Adult Literacy and Numeracy. (978-1-905188-42-0)
  • SWAN, M., 2006. Collaborative learning in mathematics: a challenge to our beliefs and practices Leicester: National Institute of Adult Continuing Education.
  • SWAN, M.B., 2006. Learning GCSE mathematics through discussion: what are the effects on students? Journal of Further and Higher Education. 30(3), 229-241
  • CRUST, R., PEAD, D.A., SWAN, M.B., BELL, A. and BURKHARDT, H., 2005. Making sense of evidence: finding relationships in data London: nferNelson.
  • SWAN, M.B., 2005. Improving learning in mathematics: challenges and strategies Department for Education and Skills.
  • SWAN, M.B., 2005. Improving Learning in Mathematics: Resources for Teaching, Multimedia Resource, Professional Development Guide
  • SWAN, M.B., PEAD, D.A., CRUST, R., BELL, A. and BURKHARDT, H., 2005. Developing Problem Solving (12-14) Optimising: Making the Best of Limited Resources nferNelson.
  • CRUST, R., PEAD, D.A., SWAN, M.B., BELL, A. and BURKHARDT, H., 2005. Developing Problem Solving (8-11) Generalising: Finding Patterns and Relationships nferNelson.
  • SWAN, M.B., PEAD, D.A., CRUST, R., BELL, A. and BURKHARDT, H., 2005. Developing Problem Solving (12-14) Making Sure: Reasoning and Proving
  • SWAN, M.B., PEAD, D.A., CRUST, R., BELL, A. and BURKHARDT, H., 2005. Developing Problem Solving (12-14) Modelling: Finding Relationships in Data nferNelson.
  • SWAN, M.B., 2005. Freedom and Constraint Mathematics Teaching. June 2005, 191
  • CRUST, R., PEAD, D., SWAN, M.B., BELL, A. and BURKHARDT, H., 2005. Developing Problem Solving (8-11) Representing: Using Diagrams, Tables and Graphs nferNelson.
  • BELL, A., BURKHARDT, H., CRUST, R., PEAD, D.A. and SWAN, M.B., 2004. Strategies for Problem Solving and Proof. In: International Perspectives on Learning and Teaching Mathematics Nationellt Centrum för Matematikutbildning, Göteborg University.
  • SWAN, M.B., 2003. Making Sense of Mathematics. In: Enhancing Primary Mathematics Teaching. Open University Press, Buckingham. 112-124pp
  • RICHARDSON, M., BAIRD, J. A., RIDGWAY, J., RIPLEY, M., SHORROCKS-TAYLOR, D. and SWAN, M., 2002. Challenging minds? Students` perceptions of computer-based World Class Tests of problem solving Computers in Human Behavior. VOL 18(NUMBER 6), 633-649
  • SWAN, M.B., 2002. The Shell Centre Approach to Research and Development In: PME 2002.
  • SWAN, M., 2002. Always, sometimes or never true? Mathematics Teaching. ISSU 181, 32-33
  • SWAN, M.B., 2002. World Class Arena Problem Solving in Mathematics, Science and Technology Cycle 2 (1-4)
  • SWAN, M.B., 2002. Learning from Mistakes, Misunderstandings and Misconceptions in Mathematics
  • SWAN, M.B. and GREEN, M., 2002. Learning Mathematics through Discussion and Reflection
  • SWAN, M.B., 2002. Classroom Assessment Techniques Mathematical Thinking, classroom Assessment Techniques Available at: <http://www.flaguide.org/cat/math/math/math1.php>
  • SWAN, M.B., 2002. World Class Tests in Problem Solving
  • SWAN, M.B., 2001. Dealing with Misconceptions in Mathematics. In: Issues in Mathematics Teaching 147-165
  • SWAN, M.B., RIDGWAY, J. and BURKHARDT, H., 2001. Assessing Mathematical Thinking via FLAG.. In: The Teachng and Leaning of Mathematics at Unvierstiy Level, An ICMI Study Kluwer Academic Publishers, Dordrecht, Boston. 423-430
  • SWAN, M.B., 2000. Learning through Discussion in GCSE Mathematics 3(3), 43-44
  • SWAN, M., 2000. GCSE mathematics in further education: challenging beliefs and practices Curriculum Journal. VOL 11(PART 2), 199-224
  • SWAN, M., BELL, A., PHILLIPS, R. and SHANNON, A., 2000. The purposes of mathematical activities and pupils' perceptions of them Research in Education. ISSU 63, 11-20
  • SWAN, M., 2000. Making sense of algebra Mathematics Teaching. ISSU 171, 16-19
  • SWAN, M., 1999. Discussion Activities, Teaching Beliefs, and the Learning of Mature, Low-Attaining Students Nordisk Matematikkdidaktikk. 6(3,4), 7-24
  • SWAN, M.B. and SHANNON, A., 1999. Balanced Assessment for the Maths Curriculum, High School Assessment
  • SCHWARTZ, J. and SWAN, M.B., 1999. Balanced Assessment for the Maths Curriculum, Advanced High School Assessment
  • BURKHARDT, H. and SWAN, M.B., 1998. Balanced Assessment for the Mathematics Curriculum: Advanced High School Assessment Package 1
  • SWAN, M., 1998. Learning through reflection with mature, low attaining students PME CONFERENCE. CONF 22(VOL 4), 4-113-4-120
  • BURKHARDT, H. and SWAN, M.B., 1998. Balanced Assessment for the Mathematics Curriculum: High School Assessment Package 2
  • SWAN, M. and PHILLIPS, R., 1998. Graph interpretation skills among lower-achieving school leavers Research in Education. ISSUE 60, 10-20
  • SWAN, M.B., 1998. Learning How to Learn. In: Teaching, Learning and Mathematics: Challenging Beliefs 53-56
  • BURKHARDT, H. and SWAN, M.B., 1998. Balanced Assessment for the Mathematics Curriculum: High School Assessment Package 1
  • BELL, A., PHILLIPS, R.J., SHANNON, A. and SWAN, M.B., 1997. Students' perception of the purposes of mathematical activities Psychology of Mathematics Education: 21st International Conference.

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