# RME literature

### On this page we list a variety of books and articles which will be of interest to teachers, researchers and student teachers.

**RME theory, design and ‘classics’ **

Freudenthal, H. (1973) *Mathematics as an Educational Task*. Reidel Publishing, Dordrecht

Gravemeijer, K. & Stephan, M. (2002) Emergent models as an instructional design heuristic, in K. Gravemeijer, R Lehrer, B. Van Oers & L. Verschaffel (eds) *Symbolizing, Modeling and Tool Use in Mathematics Education* Dordrecht: Springer.

Gravemeijer, K., McClain, K., & Stephan, M. (1998). Supporting students’ construction of increasingly sophisticated ways of reasoning through problem solving. In: A. Olivier & K. Newstead. *Proceedings of the 22nd conference of the International Group for the Psychology of Mathematics Education, Volume 1*, 194 -209.

Gravemeijer, K. (2020) Emergent modelling: an RME Design Heuristic Elaborated in a Series of Examples *Educational Designer, *13^{th} July

Streefland, L. (1985). Wiskunde als activiteit en de realiteit als bron [Mathematics as an activity and reality as a source]. *Nieuwe Wiskrant*, 5(1), 60-67.

Streefland, L. (1991). *Fractions in Realistic Mathematics Education*. Kluwer Academic Publishers.

Treffers, A. (1987) *Three Dimensions. A Model of Goal and Theory Description in Mathematics Instruction – The Wiskobas Project*. D. Reidel Publishing, Dordrecht

Van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: an example from a longitudinal trajectory on percentage. *Educational Studies in Mathematics*, 54 (1), 9-35.

Van den Heuvel-Panhuizen, M. (ed) (2008) *Children Learn Mathematics. A learning-teaching trajectory with intermediate attainment targets for calculation with whole numbers in primary school*. Sense Publishers, Rotterdam/Tapei

Van den Heuvel*–*Panhuizen*, *M. (2002). Realistic Mathematics education as work in progress. In. F. L. Lin (Ed) *Common Sense in Mathematics Education.** Proceedings of 2001 The Netherlands and Taiwan Conference on Mathematics Education*, Taipei, Taiwan, November, pp. 1 – 42.

Van den Heuvel-Panhuizen, M. (ed.) (2020) *National Reflections on the Netherlands Didactics of Mathematics: Teaching and Learning in the Context of Realistic Mathematics Education. * Springer, Cham

Van den Heuvel-Panhuizen, M. (ed.) (2020) *International Reflections on the Netherlands Didactics of Mathematics: Visions on and Experiences with Realistic Mathematics Education.* Springer, Cham

__Van____ den Heuvel-Panhuizen, M. & Buys, K. __(eds) (2008) Young Children Learn Measurement and Geometry. Sense Publishers, Rotterdam/Taipei

Van den Heuvel-Panhuizen M. & Drijvers, P. (2020) Realistic Mathematics Education. In: Lerman S. (eds) *Encyclopedia of Mathematics Education*. Springer, Cham. [This is a log-in only article, but an extensive reference list is available with links to articles on Google Scholar]

Van Reeuwijk, M. (2001). *From Informal to Formal, Progressive Formalization: An Example on Solving Systems of Equations*. Utrecht, Freudenthal Institute.

### Guided reinvention and classroom cultures – RME and teachers

Cobb, P., Qing Zhao, Q. & Visnovska, J. (2008). Learning from and adapting the theory of Realistic Mathematics Education, *Éducation et didactique*, 2(1)

Solomon, Y., Hough, S., & Gough, S. (2021) The role of appropriation in guided reinvention: establishing and preserving devolved authority with low-attaining students, *Educational Studies in Mathematics* 106, pp. 171–188*.*

Stephan, M., Underwood-Gregg, D. & Yackel, E. (2014) Guided reinvention: what is it and how do teachers learn this teaching approach?, in Y. Li, E. A. Silver & S. Li (eds) *Transforming Mathematics Instruction* (pp 37-57). Dordrecht: Springer.

Yackel, E. & Cobb, P. (1996) Sociomathematical norms, argumentation, and autonomy in mathematics. *Journal for Research in Mathematics Education*, 27 (4). 458-477.

**Applications and textbooks**

Beishuizen, M. (1999) The empty number line as a new model, In Thompson, I. (Ed) *Issues in Teaching Numeracy in Primary Schools*. Suffolk. Open University Press. pp. 174-187

Dickinson, P., Eade, F., Gough, S. Hough, S. & Dudzik, S. (2012) *Making Sense of Maths* Textbook Series. London: Hodder Education – these are out of print but still available on Amazon etc

Fosnot, C.T., & Dolk, M. (2001). *Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction*. Portsmouth: Heinemann.

Fosnot, C.T., & Dolk, M. (2001). *Young Mathematicians at Work: Constructing Multiplication and Division*. Portsmouth: Heinemann.

Fosnot, C.T., & Dolk, M. (2002). *Young Mathematicians at Work: Constructing Fractions, Decimals, and Percents*. Portsmouth: Heinemann.

Frykhom, J. (2013) *Learning to Think Mathematically with the Ratio Table. *The Math Learning Centre, Oregon

__Gutstein, E. __(2006). *Reading and writing the world with mathematics: Toward a pedagogy for social justice.* New York: Routledge.

Mathematics in Context Series. Encyclopaedia Britannica

Mathematics in Context Study Working Papers and Technical Reports

**Work by the Manchester Met RME team**

Dickinson, P. & Eade, F. (2004) Using the number line to investigate the solving of linear equations. *For the Learning of Mathematics* 24 (2) pp 41- 47

Dickinson, P. & Eade, F. (2005) Trialling realistic mathematics education (RME) in English secondary schools, in Hewitt, D. (Ed) *Proceedings of the British Society for Research into Learning Mathematics* 25(3), pp 1-14.

Dickinson, P., Eade, F., Gough, S., & Hough, S. (2010) Using Realistic Mathematics Education with low to middle attaining pupils in secondary schools, in Joubert, M. and Andrews, P. (Eds.) *Proceedings of the 7th British Congress for Mathematics Education*, pp 73-80.

Dickinson, P., Eade, F., Gough, S., Hough, S., & Solomon, Y. (2019) Implementing RME in England and the Cayman Islands – dealing with clashing educational ideologies, in Marja Van den Heuvel-Panhuizen (ed) *International reflections on the Netherlands Didactics of Mathematics*, Springer.

Dickinson, P., Gough, S., & Hough, S. (2014) Using context and models at Higher Level GCSE: adapting Realistic Mathematics Education (RME) for the UK curriculum, in Pope, S. (Ed.) *Proceedings of the 8th British Congress for Mathematics Education*, pp 105-112.

Dickinson, P., Hough, S., Searle, J., & Barmby, P. (2011). Evaluating the impact of a Realistic Mathematics Education project in secondary schools, in C. Smith (Ed.) *Proceedings of the British Society for Research into Learning Mathematics (BSRLM*), 31(3), 47–52.

Hough, S., Solomon, Y., Dickinson, P., & Gough, S. (2017) Investigating the Impact of a Realistic Mathematics Education approach on achievements and attitudes in Post 16 GCSE classrooms. The Nuffield Foundation

Hough, S., Solomon, Y, & Gough, S. (2019) Connecting the everyday with the formal: the role of bar models in developing low attainers’ mathematical understanding, in Van den Heuvel-Panhuizen (ed) *CERME 11 – Eleventh Congress of the European Society for Research in Mathematics* *Education*, Feb 2019, Utrecht, Netherlands, 4523-4530.

Kathotia, V., O’Brien, K. & Solomon, Y. (2021) Just mathematics? Fostering empowering and inclusive mathematics classrooms with Realistic Mathematics Education, *Mathematics Education and Society Conference 11.*

Solomon, Y., Hough, S., & Gough, S. (2021) The role of appropriation in guided reinvention: establishing and preserving devolved authority with low-attaining students, *Educational Studies in Mathematics* 106, pp. 171–188.