Concretisations: a Support for Teachers to Carry Out Instructional Innovations in the Mathematics Classroom


We recognise that though teachers may participate in various forms of professional development (PD) programmes, learning that they may have gained in the PD may not always lead to corresponding perceivable changes in their classroom teaching. We offer a theoretical re-orientation towards this issue by introducing a construct we term “concretisation”. Concretisations are resources developed in PD settings which can be converted into tangible tools for classroom use. In theorising such resources, we contribute in informing the design process of teacher professional development for better impact into actual classroom practice. We purport principles of design which render concretisations effective. Subsequently, we test these principles by presenting a specific case of teaching mathematical problem solving.

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    Names of schools, teachers, and students that appear in this paper are pseudonyms.


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Leong, Y.H., Tay, E.G., Toh, T.L. et al. Concretisations: a Support for Teachers to Carry Out Instructional Innovations in the Mathematics Classroom. Int J of Sci and Math Educ 17, 365–384 (2019).

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  • Concretisations
  • Instructional practices
  • Mathematics teacher development
  • Problem solving