Research

What Medräknad is built on.

Medräknad is product work — it isn't a research contribution in itself. The value lies in consistently following what is already well-established. These are the strands we lean on, why, and how each shows up in the product.

Last review: 2026-04 — We review the sources annually. Get in touch if a reference needs updating.

Forskningsstommar

Framework

RTI / MTSS — three tiers of support

RTI (Response to Intervention) and MTSS (Multi-Tiered Systems of Support) is the framework that structures the entire product. Tier 1 is good universal teaching; Tier 2 is targeted small-group support; Tier 3 is intensive individual intervention. Each layer needs different data and different actions.

↳ How Medräknad uses it: the whole service is organised in three layers. Tier 1 is free for primary schools. Tier 2 and 3 is where the diagnostics — the misconception map and the adaptive sessions — live. The decision to move a pupil between tiers is a teacher decision, never a system decision.

2 sources
  • Gersten, R., Beckmann, S., Clarke, B., et al. (2009). Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools. IES Practice Guide.
  • Fuchs, L. S., Fuchs, D., & Compton, D. L. (2012). Smart RTI: A Next-Generation Approach to Multilevel Prevention. Exceptional Children, 78(3).
Pedagogy

CRA — concrete, representational, abstract

Pupils who struggle with maths benefit from an idea being presented three times in three forms: first with physical objects (concrete), then with diagrams (representational), then with numbers and symbols (abstract). The sequence is not a staircase the pupil "completes" — it's an overlap pupils move back and forth in.

↳ How Medräknad uses it: every item is tagged with its CRA level. The adaptive engine can drop a pupil back to representational when abstract is wobbly. The premium tier delivers virtual manipulatives (egg cartons, base-10 blocks, fraction bars, number lines) — the same idea in digital form.

2 sources
  • Hudson, P., & Miller, S. P. (2006). Designing and Implementing Mathematics Instruction for Students with Diverse Learning Needs. Pearson.
  • Strickland, T. K., & Maccini, P. (2010). Strategies for Teaching Algebra to Students with Learning Disabilities: Making Research to Practice Connections. Intervention in School and Clinic, 46(1).
Diagnostics

Misconception-tagged distractors

A good wrong answer is not a random error — it's a window into the pupil's thinking. By designing every wrong option to match a known misconception we move from "the pupil got it wrong" to "the pupil seems to think 0 is absence rather than a placeholder". That's the difference between diagnostic and summative assessment.

↳ How Medräknad uses it: every multiple-choice item has 4 options, all wrong ones tagged with a specific misconception from a controlled vocabulary. When a pupil hits the same tag twice, the system drills — more items targeting the same misconception, to separate a transient slip from a robust misunderstanding.

3 sources
  • Ryan, J., & Williams, J. (2007). Children's Mathematics 4–15: Learning from Errors and Misconceptions. Open University Press.
  • Eedi (Diagnostic Questions). (2020). Diagnostic Questions: Why misconception-tagged distractors work. Whitepaper.
  • Bell, A. (1993). Some experiments in diagnostic teaching. Educational Studies in Mathematics, 24(1).
Practice

Distributed practice

Massed practice (everything in one go) gives fast feedback and poor long-term retention. Distributed practice (the same volume spread over multiple days) is harder in the moment but yields significantly better learning over time. This is one of the most replicated findings in cognitive science.

↳ How Medräknad uses it: adaptive sessions are short (5–15 min) and designed to run several times a week, not as hour-long sittings. Skill mastery scores decay if a pupil doesn't return to a skill — this drives re-exposure at the right interval.

2 sources
  • Cepeda, N. J., Pashler, H., Vul, E., Wixted, J. T., & Rohrer, D. (2006). Distributed practice in verbal recall tasks: A review and quantitative synthesis. Psychological Bulletin, 132(3).
  • Rohrer, D., & Taylor, K. (2007). The shuffling of mathematics problems improves learning. Instructional Science, 35.
Tier 2 / 3

Explicit / direct instruction

Pupils with mathematical difficulties benefit more from clearly structured, sequenced instruction than from purely exploratory pedagogy. That doesn't mean the pupil shouldn't think — it means the teacher should model the thinking, take out the noise, and keep the level just above what the pupil can do alone.

↳ How Medräknad uses it: Tier 2 and Tier 3 reports always suggest concrete next steps along the CRA axis, with example phrases for the teacher to use. The AI drafts are linguistically thin — they are designed to be reviewable in seconds.

2 sources
  • Doabler, C. T., & Fien, H. (2013). Explicit Mathematics Instruction: What Teachers Can Do for Teaching Students with Mathematics Difficulties. Intervention in School and Clinic, 48(5).
  • Gersten, R., Chard, D. J., Jayanthi, M., et al. (2009). Mathematics Instruction for Students with Learning Disabilities: A Meta-Analysis of Instructional Components. Review of Educational Research, 79(3).
Curriculum

Lgr22 — Swedish national curriculum

Content is anchored in Lgr22's central knowledge structure and assessment criteria for mathematics. We follow Skolverket's structures for years F–6 (initially) and years 7–9 (next). Each item is tagged against a strand: number sense, algebra, geometry, probability/statistics, or mathematical contexts and problem-solving. The UK product mirrors this against the National Curriculum.

↳ How Medräknad uses it: the adaptive engine filters items by year-group ± 1 so a Y3 pupil can encounter Y2 or Y4 material when pedagogically right. The teacher reports cite Lgr22 / NC strands so reports are traceable to the curriculum.

3 sources
  • Skolverket. (2022). Läroplan för grundskolan, förskoleklassen och fritidshemmet — Lgr22.
  • Department for Education. (2014). National Curriculum in England: Mathematics programmes of study, key stages 1 and 2.
  • PRIM-gruppen, Stockholm University. National test materials and diagnostic instruments, Y3, Y6, Y9.

Missing a reference?

We appreciate being challenged. Send corrections — we update the list at the next review.

Get in touch