Mathematics Interventions for Children with Special Needs

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NICHCY’s Structured Abstract 25 describes the following:

Title | Mathematics Interventions for Children with Special Needs

Author | Kroesbergen, E.H., & Van Luit, J.E.H.

Source Remedial and Special Education, 24(2), 97-114.

Year Published | 2003

This article presents results of a meta-analysis of 58 studies of mathematics intervention for elementary students with special needs. Studies in preparatory mathematics, basic skills, and problem solving were reviewed. Duration and method of instruction proved important. Direct instruction and self-instruction were more effective than mediated instruction. Computer assisted instruction and peer tutoring showed smaller effects than other approaches.

Many students have difficulty learning math. Learning challenges can range from mild to severe and may be temporary or long term. In general, these students have: memory deficits, problems with learning and applying helpful strategies, and difficulty applying what they already know to new tasks.

Depending on a child’s age and specific challenges, interventions can be tailored to focus on various steps in the learning process: preparatory arithmetic (number sense, counting skills); automatization of basic math facts (addition, subtraction, multiplication, division); and/or mathematical problem-solving strategies.

In this meta-analysis, interventions are explored that address the knowledge and skills associated with each step mentioned above.

Research Questions

  1. What makes a particular mathematics intervention effective?
  2. Which domain (preparatory skills, basic skills, problem solving) is most investigated, and which domain produces the highest effect sizes?

Research Design

  • Number of Studies Included | 58
  • Number of Subjects | 2,509. The average number of subjects per study was 41.1, with a range of 3-136.
  • Years Spanned | 1985-2000

Research Subjects
General and special education students in kindergarten and elementary school. Participants had special education needs, needed extra help, and/or typically required some type of specific mathematics intervention.

Age/Grade of Subjects
Kindergarten and elementary school-age children. Studies with an average participant age greater than 12 were excluded.

Specified Disability
Mathematics Disabilities

Students participated in mathematical interventions that used 1 of 3 methods:

  1. Direct instruction, an approach used to teach task-specific strategies,  is usually written ahead of time, and structured step by step to ensure mastery before the student proceeds. Teacher instruction is slowly removed, and practice and review are used to avoid loss once the instructional unit has been completed. (Goldman, 1989)
  2. Self-instruction, an approach that provides students with a set of verbal prompts so they can remember what they are doing, often utilizes modeling-in-context to help learners acquire the verbal-prompt sequences. Verbal cues have been used as mediators for cognitive and metacognitive operations. (Goldman, 1989)
  3. Mediated/assisted instruction, an approach focused on learning through guided experience. In contrast with self-instruction and direct instruction models in which learners are provided with an “expert” task model and then trained to use it accurately, the mediated/assisted model begins with a student’s demonstration of a given task that is altered in the direction of task demonstration that is more “expert.” Specific methods are used to make the task more explicit such as modeling, coaching, fading, questioning, and explanation. (Goldman, 1989)

Most of the studies used direct instruction in their intervention. They also included other variables such as the use of computer-assisted instruction (CAI), peer tutoring; and characteristics of Realistic Mathematics Education (RME) such as guided reinvention, phenomenological exploration, the use of self-developed models and meaningful contexts, student contribution, and interactivity.

Duration of Intervention

  1. Duration varied from 2 to 140 sessions.
  2. Duration of the sessions ranged from 10-60 minutes, with a mean of 35 minutes.
  3. Total instruction time varied from 1 week to 1 year.


  1. Most interventions studied in the meta-analysis addressed basic skills.
  2. Interventions focused on basic skills were the most effective (that is, they showed the highest effect sizes).
  3. In studies concerned with problem solving, interventions for students with mild intellectual disability were more effective than those for students with learning disabilities, because students with mild intellectual disability often received intensive training focused on basic skills across an extended period of time.
  4. Perhaps surprisingly, interventions implemented over a longer time period were not as effective as those of shorter duration, especially for interventions focused on preparatory tasks (e.g., number sense, counting skills). Overall, self-instruction was most effective. However, direct instruction was most effective for learning basic skills.
  5. Computer-assisted instruction (CAI) produced lower effect sizes than other interventions. Results showed that, in general, traditional interventions with teachers delivering the instruction (as opposed to computers) were most effective.
  6. Mediated/assisted instruction was found to be less effective than either direct instruction or self-instruction.
  7. Interventions making use of peer tutoring were found to be less effective than other interventions.

Combined Effects Size
One effect size was calculated for each study, unless the study made use of more than one experimental condition. Sixty-one effect sizes were reported for the 58 studies.

  • Special needs: Learning Disabilities (LD) 1.36; mild intellectual disability 0.80; low performing 0.74; mixed groups 0.73
  • Content: basic facts 1.14; preparatory 0.91; problem solving 0.63
  • Method: self-instruction 1.45; direct instruction 0.91; mediated/assisted 0.34 (however, direct instruction was most effective for learning basic skills)
  • Medium: teacher 1.05; computer 0.51
  • Peer tutoring: No 0.96; Yes 0.87

When choosing and organizing a math intervention, keep in mind the following findings:

  1. Self-instruction and direct instruction seem to be adequate methods for students with special needs.
  2. Direct instruction appears to be most effective for learning basic math facts.
  3. Self-instruction methods are an effective way of learning problem-solving skills.
  4. The use of computer assisted-instruction is beneficial when students need to be motivated to practice certain kinds of problems. However, the computer cannot remediate the basic difficulties that the children encounter.
  5. Children with special needs do not always benefit from working in groups or working with a peer tutor.
  6. Interventions of shorter duration tended to be more effective than those implemented over a longer period of time. A possible explanation is that shorter interventions tended to focus on a very small and specific domain of knowledge, while longer interventions focused on a broader domain of knowledge and required more time.


* Meta-Analysis | A widely-used research method in which (1) a systematic and reproducible search strategy is used to find as many studies as possible that address a given topic; (2) clear criterion are presented for inclusion/exclusion of individual studies into a larger analysis; and (3) results of included studies are statistically combined to determine an overall effect (effect size) of one variable on another.

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