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Concrete–representational–abstract instructional strategy (CRAIS): a three-stage sequence from concrete materials through drawings to symbols

Design · All designs
Evidence · 1 claim (1 for) · 1 study (1 causal), q2 · 0 of 1 report an effect size · 1 claim rests on one study

Description

CRAIS is an instructional strategy in which each mathematics concept is taught in three sequenced stages: modelling with concrete materials, then semi-concrete drawings representing concrete objects, then symbolic notation using "only numbers, notation, and mathematical symbols". Each part builds on the previous instruction to promote learning, retention, and conceptual knowledge (Access Center, 2004). The article applies CRAIS to circles, volume of solids, and angles of elevation and depression, involving students in cutting, modelling, and drawing before symbolic representation. Its root is traced to Dale's Cone of Experience, where learners retain more by what they do.

Design Implications

Context

Requirements

  • Teachers should make sure students understand what has been taught at each step before moving instruction to the next stage (NCTM recommendation cited from Berkas & Pattison, 2007)

Constraints

  • The article describes CRAIS as originally a strategy for teaching mathematics to students with learning difficulties (Butler et al., 2003)

Target Learners

  • senior secondary school mathematics students
  • students with mathematics learning difficulties

Learning Goals

  • conceptual understanding of mathematics topics
  • achievement in mathematics

Claims

Examples

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Key Sources

  • Sabainah Oyebola Akinoso. (2015). Teaching Mathematics in a Volatile, Uncertain, Complex and Ambiguous (VUCA) World: The Use of Concrete – Representational – Abstract Instructional Strategy. JISTE Vol. 19, No. 1, 2015. https://www.jiste.org/
Page metadata
Field Value
type design
id crais-three-stage-instructional-sequence
title Concrete–representational–abstract instructional strategy (CRAIS): a three-stage sequence from concrete materials through drawings to symbols
description CRAIS is an instructional strategy in which each mathematics concept is taught in three sequenced stages: modelling with concrete materials, then semi-concrete drawings representing concrete objects, then symbolic not...
status review
generated by process:settle-candidates on 2026-11-01
trust unverified — no one has confirmed this page's content
sources 1 — sabainah-oyebola-akinoso-2015

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