What math instruction helps students who struggle with math? The CRA framework
The Concrete-Representational-Abstract (CRA) sequence — moving from physical manipulatives, to drawn representations, to abstract symbols — is a research-informed approach for students who experience persistent difficulty with mathematics (sometimes identified as dyscalculia). IncluMath builds practice on CRA with adaptive scaffolding that targets roughly an 85% success rate, with no timers, points, or leaderboards.
What the CRA sequence is
CRA moves a concept through three stages: concrete (manipulating physical or virtual objects), representational (drawing the quantities), and abstract (working with numerals and symbols). A meta-analytic review of the framework reported strong effects across single-case studies (Ebner et al., 2025, Learning Disabilities Research & Practice), and CRA meets What Works Clearinghouse criteria as an evidence-based practice for mathematics instruction for students with learning disabilities (Bouck, Satsangi & Park, 2018, Remedial and Special Education).
Adaptive difficulty at the "85% sweet spot"
Difficulty is tuned so the learner succeeds about 85% of the time — the success rate associated with the fastest learning in adaptive tasks (Wilson, Shenhav, Straccia & Cohen, 2019, Nature Communications). IncluMath estimates skill mastery with Performance Factor Analysis (Pavlik, Cen & Koedinger, 2009, Proc. AIED) and silently presents easier items when a learner is struggling — no visible "level down."
No timers, warm feedback, scaffolds only on demand
Math anxiety depresses performance, and visible time pressure and red error states make it worse (Ashcraft & Krause, 2007). IncluMath uses no countdown timers, no points or leaderboards (see the anti-gamification stance), warm amber rather than red for errors, and scaffolds that appear only on request or after an incorrect attempt — never as unsolicited hints for students who are already succeeding (Razzaq & Heffernan, 2010).
Frequently asked
- What math instruction helps students who struggle with math?
- The Concrete-Representational-Abstract (CRA) sequence is a research-informed approach: students move from physical manipulatives, to drawings, to abstract symbols. IncluMath delivers CRA practice with adaptive scaffolding targeting an ~85% success rate.
- Is IncluMath a "dyscalculia app"?
- IncluShift does not use diagnostic terms as product identifiers. IncluMath supports any student who experiences difficulty with mathematical concepts, whatever the underlying cause.
- Does IncluMath use timers, points, or leaderboards?
- No. There are no countdown timers shown to students, no points or coins, and no leaderboards. Progress tracking is private and mastery-based.
- What grade levels does it cover?
- IncluMath supports K-12 mathematics, adapting item difficulty to the individual learner.
Related on IncluShift
References
- ·Ebner, A. et al. (2025). A meta-analytic review of the Concrete-Representational-Abstract framework. Learning Disabilities Research & Practice.
- ·Bouck, E.C., Satsangi, R., & Park, J. (2018). Evidence-based practice for mathematics instruction for students with learning disabilities. Remedial and Special Education, 39(4), 211-228.
- ·Wilson, R.C., Shenhav, A., Straccia, M., & Cohen, J.D. (2019). The eighty-five percent rule for optimal learning. Nature Communications, 10, 4646.
- ·Pavlik, P.I., Cen, H., & Koedinger, K.R. (2009). Performance Factor Analysis — a new alternative to knowledge tracing. Proc. AIED 2009.
- ·Ashcraft, M.H., & Krause, J.A. (2007). Working memory, math performance, and math anxiety. Psychonomic Bulletin & Review, 14(2), 243-248.
- ·Razzaq, L., & Heffernan, N.T. (2010). Hints: Is it better to give or to wait to be asked? Proc. ITS 2010.
Full bibliography on the Research page.
Disclaimer. This page is educational and research-informed. IncluShift products are adaptive practice and administrative tools, not medical devices, therapeutic interventions, or substitutes for professional educational assessment. Instructional methods are informed by peer-reviewed research; individual products have not been evaluated in controlled studies. This is not legal or clinical advice.