Research

Why Medräknad works.

Pupils who struggle with maths do not need more tests — they need teaching that explains. Medräknad's intensive teaching programmes are ready-made, teacher-led interventions built on what the research agrees on most. Here are the principles behind the programmes and what they mean in practice — for teachers, SENCOs and school leaders.

Last review: 2026-07 — We review the sources annually. Get in touch if a reference needs updating.

Forskningsstommar

Teaching

Explicit instruction — the teacher shows, the pupil succeeds

Explicit instruction means presenting new material in small, clear steps with clear expectations, structured practice and immediate feedback. The teacher models the thinking and keeps the level just above what the pupil can manage alone. Meta-analyses consistently show explicit, systematic instruction outperforms less structured approaches for pupils with maths difficulties. It is not the opposite of understanding — it is what makes understanding possible.

↳ What it means for you: every intensive teaching programme is a complete sequence — pre-test, short teacher-led small-group lessons with modelling and guided practice, and a post-test that shows progress. Teachers get a full script with concrete delivery suggestions and no planning burden. The lessons teach — they do not just test.

4 sources
  • Kroesbergen, E. H., & Van Luit, J. E. H. (2003). Mathematics Interventions for Children with Special Educational Needs. Remedial and Special Education, 24(2).
  • Miller, S. P. (2002). Validated Practices for Teaching Students with Diverse Needs and Abilities. Allyn & Bacon.
  • 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).
Pedagogy

C-R-A — concrete, representational, abstract

Pupils who struggle with maths benefit from meeting an idea three times in three ways: first with physical materials (concrete), then with pictures or models (representational), finally with numbers and symbols (abstract). The sequence is not a staircase climbed once, but an overlap pupils move back and forth in.

↳ What it means for you: lessons start concrete — base-ten materials, coins, familiar objects — move through pictures and models, and land in numbers. Every task builds the bridge between representations, so a base-ten rod, a ten-pence coin and the digit in the tens place belong together in the pupil's mind.

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).
Knowledge building

Four knowledge domains in balance

Mathematical knowledge is built across four domains, all of which matter: conceptual understanding (knowing why), declarative knowledge (rapid recall of facts such as times tables), procedural knowledge (following methods) and problem solving (using knowledge in new situations). Pupils drilled only on procedures get stuck when problems change; pupils with good understanding but weak recall are overloaded by every calculation. The balance is decisive.

↳ What it means for you: the programmes train more than methods. Each unit builds understanding first and connects it to facts, procedures and problem solving — so pupils cope even when a task looks new. The assessment shows which of the domains the pupil needs to develop most — not just whether the answer was right.

3 sources
  • Hudson, P., & Miller, S. P. (2006). Designing and Implementing Mathematics Instruction for Students with Diverse Learning Needs. Pearson.
  • Skolverket. (2022). Läroplan för grundskolan, förskoleklassen och fritidshemmet — Lgr22. Skolverkets förlag.
  • Goldman, S. R., & Hasselbring, T. S. (1997). Achieving meaningful mathematics literacy for students with learning disabilities. Journal of Learning Disabilities, 30(2).
Diagnostics

Wrong answers that reveal how the pupil thinks

A wrong answer is rarely random — it shows how the pupil is thinking. By designing tasks so that known misconceptions show up in the answers, we can move from “the pupil got it wrong” to “the pupil seems to believe zero means nothing”. That is the difference between measuring and understanding.

↳ What it means for you: teachers see where understanding breaks down, and the programmes contain the exact units that repair that misconception. Parents get an understandable picture of what their child needs — not just a score.

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).
Curriculum

Anchored in the national curriculum

All content is anchored in the curriculum. Diagnostics and programmes are structured around the core mathematical competencies — concepts, procedures, problem solving, reasoning and communication — the same ways of showing knowledge that schools and national assessments evaluate.

↳ What it means for you: what pupils practise in Medräknad is traceable to the curriculum. Teachers and school leaders can show exactly which competencies an intervention targets, and reports speak the school's language.

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.
Practice

Practice at the right pace consolidates knowledge

When a pupil practises everything in one go, the knowledge often holds through the lesson — and is gone the following week. When the same practice is split into short sessions a few days apart, and earlier content returns in the next session, the knowledge is truly consolidated. This is one of the best-replicated findings in learning research.

↳ What it means for you: the intensive teaching runs as short lessons several times a week over five weeks — not one long block. Every lesson opens with a brief recap of the previous lesson, so pupils revisit what matters at the right pace.

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.
School support

Where Medräknad fits in the school's support work

Many schools work in three tiers: ordinary classroom teaching for all, targeted small-group support for those who need more, and individual intensive support for a few. Which pupils need the support shows up in the screenings and assessments the school runs during the year — the results point out who is not keeping up in ordinary teaching, and in which area. Medräknad supports the whole chain: the intensive teaching works both in small groups and one-to-one, and the classroom resources — posters, practice programmes and visual supports — support ordinary teaching.

Tier 3Tier 2Tier 1Ordinary teaching — all pupils
▲ Tier 3 — individual intensive support — ~5 % of pupils■ Tier 2 — support teaching in small groups — ~15 % of pupils■ Tier 1 — ordinary teaching — All pupils (~80 % succeed here)Which pupils need support shows in the screenings and assessments the school runs during the year. Medräknad supports the whole chain — the intensive teaching in small groups or one-to-one, the classroom resources in ordinary teaching.

↳ What it means for you: the school's own screenings and tests show which pupils need support teaching and in which area. Once the intervention starts, Medräknad's pre-test belongs to the intensive teaching — it shows the pupil's starting point in the chosen area. The intensive teaching is a ready-made, bounded intervention (typically 4–7 weeks of short lessons several times a week) that works equally well in a small group or one-to-one, and the post-test shows whether it worked. The decision about which pupil receives support always belongs to the teacher.

3 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).
  • Björn, P. M., Aro, M., Koponen, T., Fuchs, L. S., & Fuchs, D. (2018). Response-to-Intervention in Finland and the United States: Mathematics Learning Support as an Example. Frontiers in Psychology, 9.

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