How IncluMath works
Built with and for students who learn differently
IncluMath is research-informed adaptive math practice. Every design choice below traces to peer-reviewed research in special education and the learning sciences. We keep the academic detail on this page on purpose, so the practice screens stay calm and uncluttered for students.
Adaptive
It meets each student where they are
Difficulty is not fixed. IncluMath estimates what a learner has mastered from how they answer, then chooses the next problem to keep them in the zone where learning is most efficient (challenged, but rarely overwhelmed).
- Aims for roughly an 85% success rate, the band where practice produces the most learning (a little higher for focus-support profiles, to reduce frustration).
- Spaces review of earlier skills over time instead of cramming, so they stick.
- Help is on-demand only. Hints and worked examples appear when a student asks or after a wrong answer, never before a first attempt, and they fade as mastery grows.
Research behind this
- Wilson, Shenhav, Straccia & Cohen (2019). Eighty-five percent rule for optimal learning. Nature Communications, 10:4646.
- Settles & Meeder (2016). A trainable spaced-repetition model. Proceedings of ACL 2016.
- Razzaq & Heffernan (2010). Hints: is it better to give or to wait to be asked? Proc. ITS 2010.
- Kalyuga (2007). Expertise reversal effect. Educational Psychology Review, 19, 509-539.
Teaching, not just testing
It teaches the idea before it asks for the answer
Every concept starts with explicit, step-by-step instruction: shown, then practiced together, then tried independently. Ideas are built from objects you can move, to pictures, to symbols, so the math means something before it becomes abstract.
- Concrete → representational → abstract (CRA): students count and move manipulatives, then a number line, then work with symbols.
- Worked examples and guided practice carry students from “I do” to “we do” to “you do.”
- Word problems are taught by structure (combine, compare, change), using bar models, not keyword tricks.
- Targeted fact-fluency practice spans both addition/subtraction and multiplication/division.
Research behind this
- Bruner (1966). Toward a Theory of Instruction. Harvard University Press.
- Peltier, Morin, Bouck et al. (2020). Manipulatives meta-analysis. The Journal of Special Education, 54(1):3-15 (Tau-U = 0.91).
- Gersten, Chard, Jayanthi et al. (2009). Mathematics instruction for students with LD: a meta-analysis. Review of Educational Research, 79(3):1202-1242.
- Jitendra, Harwell, Dupuis & Karl (2017). Schema-based instruction cluster RCT. Journal of Learning Disabilities, 50(3):322-336.
- Douglas, Myers, Mason, Powell & Lariviere (2026). Fact-fluency meta-analysis. Journal of Learning Disabilities, 59(3):135-160 (g = 0.76).
Calm by design
No points, no streaks, no pressure
IncluMath deliberately leaves out the reward loops that other apps use. There are no points, coins, streaks, leaderboards, or countdown timers a student can see. Feedback is specific and private, and the colors and pacing are chosen to lower anxiety, not raise it.
- Errors are shown in a warm amber, never alarming red.
- Feedback names what the student did (“you regrouped the tens correctly”) instead of generic praise.
- After a few errors in a row, a short optional breathing break is offered, always free.
Research behind this
- Deci, Koestner & Ryan (1999). A meta-analysis of extrinsic rewards and intrinsic motivation. Psychological Bulletin, 125(6):627-668.
- Xia, Song, Wang, Tan & Mo (2016). Color and approach-avoidance motivation. Frontiers in Psychology, 7:784.
- Balban, Neri, Kogon et al. (2023). Brief structured respiration practices. Cell Reports Medicine, 4(1):100895.
- Wisniewski, Zierer & Hattie (2020). The power of feedback revisited. Frontiers in Psychology, 10:3087.
Built for every learner
Support without labels
Students are never asked to name a disability. Instead, a teacher or parent chooses a functional support profile (extra math support, focus support, sensory-friendly, and others) that quietly adjusts pacing, scaffolding, and sensory load. This avoids the well-documented effects of putting a label in front of a learner before a task.
- Functional profiles cover the range of IDEA categories, common 504 conditions, and gifted/2e. These profiles are configured by adults, never disclosed by students.
- Designed toward WCAG 2.2 AAA, with full keyboard use, screen-reader labels, reduced-motion support, and large touch targets.
Research behind this
- Steele & Aronson (1995). Stereotype threat. Journal of Personality and Social Psychology, 69(5):797-811.
- Shifrer (2013). The disability label and educational expectations. American Sociological Review, 78(3):407-428.
- World Health Organization (2001). International Classification of Functioning, Disability and Health (ICF).
IncluMath is an adaptive math practice tool, not a medical device, therapeutic intervention, or substitute for professional educational assessment. Its instructional methods are informed by peer-reviewed research; the app itself has not been evaluated in a controlled study.