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, with 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.