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Reality, Abstraction, Mathematics, Reality (RAMR) cycle

See also: teaching-mathematics, cser-practices-and-pedagogies, what-do-mathematicians-do, what-is-mathematics, goompi-model

A pedagogical framework for design for learning arising from a view of teaching being more powerful if it reveals the underlying structure of mathematics and relates it to the (mathematics) knowledge within local cultures/communities. A view based on the goompi-model

Four phases (RAMR)

  1. Reality (How it relates to real life).

    • Identify local cultural and environmental knowledge that can be used to introduce the idea.
    • Ensure existing knowledge prerequisite to the idea is known
    • Construct kinaesthetic activities that introduce the idea (and are relevant in terms of local experience)

  2. Abstraction (Whole body and hands on activities).

    • Develop a sequence of representational activities (physical to virtual to pictorial materials to language to symbols)
    • Develop two-way connections between reality, representational activities, and mental models through body > hand > mind activities
    • Allow opportunities to create own representations, including language and symbols

  3. Mathematics (Mathematics needed to do the task).

    • Enable students to appropriate and understand the formal language and symbols for the mathematical idea
    • Facilitate students' practice to become familiar with all aspects of the idea.
    • Construct activities to connect the idea to other mathematical ideas.

  4. Reflection (How the students are going - but also more).

    • Lead discussion of the idea in terms of reality to enable students to validate and justify their own knowledge
    • Set problems that apply the idea back to reality.
    • Organise activities so that students can extend the idea (use reflective strategies - being flexible, generalising, reversing, and changing parameters)

Comments#

Strong echoes of other practices, including (but certainly not limited to) enactive-mathematics-pedagogy and cra; effective-pedagogy-in-mathematics

References#

Carter, M., Cooper, T., & Anderson, R. (2016). Teachers' Use of a Pedagogical Framework for Improvement in Mathematics Teaching: Case Studies from YuMi Deadly Maths. Opening Up Mathematics Education Research, 166--173.

Nutchey, D., Grant, E., & English, L. (2016). Experiencing mathematics for connected understanding: Using the RAMR framework for accelerating students' learning. Opening Up Mathematics Education Research, 495--502.