Reviews and meta-analyses have been conducted, providing information about the instructional features that have been found to be effective in teaching mathematics to children who perform poorly or who have learning disabilities.
Five instructional features, in particular, exhibited a moderate to high degree of effectiveness in several reviews:
(1) explicit instruction,
(2) peer-assisted instruction,
(3) computer-assisted instruction,
(4) self-instruction and
(5) applying a concrete-representational-abstract sequence (CRA).
These instructional features can thus be considered as essential in mathematics interventions, at least for school-aged children performing poorly in mathematics or those with mathematical learning difficulties.
Explicit instruction (also referred to as direct instruction) includes elements of modelling mathematics concepts and strategies for students in the form of step-by-step, guided and independent practice opportunities and continuous feedback (Forbringer & Fuchs, 2014). It was found to be an effective instructional feature for students performing poorly in mathematics (e.g. Baker et al., 2002) or for those with learning difficulties (e.g. Gersten et al., 2009; Kroesbergen & Van Luit, 2003; Miller et al., 1998). More specifically, explicit instruction was found to be the most effective instructional feature in teaching computation skills to primary school-aged children with special educational needs (Kroesbergen & Van Luit, 2003).
Peer-assisted instruction (also referred to as peer-mediated instruction or peer tutoring) involves pairs of students working collaboratively on structured, individualised activities. It enables peers to provide an answer or suggestions that might help them solve the problem (Baker et al., 2002; Kunsch et al., 2007). Peer-assisted instruction was an effective instructional feature, especially with primary school-aged children performing poorly in mathematics (Baker et al., 2002; Kunsch et al., 2007). The effect was least noticeable when the instruction was used with secondary school-aged students or children with learning difficulties (Kunsch et al., 2007). Kroesbergen and Van Luit (2003) did not find a statistically significant effect for peer-assisted instruction of children with special educational needs. Kunsch et al. (2007) explains that the finding that peer-assisted instruction was not a very effective feature among children with learning difficulties may have resulted from the fact that there was a likelihood that both tutors and tutees were cognitively disadvantaged regarding the required actions in peer-assisted instruction.
In computer-assisted instruction (CAI), technology is utilised, such as in using a mathematics computer software. CAI was an effective way to improve performance in word-problem-solving skills with children with low performance in mathematics or those with learning difficulties in both primary and secondary school (Xin & Jitendra, 1999). Reviews by Miller et al. (1998), Kroesbergen and Van Luit (2003) and Li and Ma (2010) also support the use of CAI with children with learning difficulties or with special educational needs, although Kroesbergen and Van Luit (2003) report that interventions using CAI had a smaller effect than interventions in which a teacher instructed the students.
Self-instruction (also referred to self-management and self-monitoring) has to do with providing students with a set of verbal cues (e.g. checklists) as mediators for cognitive and metacognitive operations so that they can remember what they are doing (Goldman, 1989). Overall, self-instruction was regarded as an effective instructional feature for primary school children with special educational needs in mathematics (Kroesbergen & Van Luit, 2003) and a beneficial instructional feature in teaching arithmetic skills (e.g. Codding et al., 2009, 2011; Miller et al., 1998) to students performing poorly in mathematics and those with learning difficulties.
Concrete-representational-abstract sequence (CRA) is a three-phase process that first involves instruction using concrete objects (e.g. mathematics manipulatives), gradually advancing to pictures representing objects and finally to an abstract level using numbers and symbols (Maccini et al., 2007). CRA was reported to be an effective instructional feature, especially in teaching computation skills (Maccini et al., 2007; Methe et al., 2012). Furthermore, the use of manipulatives and drawings in teaching a range of mathematics topics (Miller et al., 1998) and more specifically in teaching word-problem solving (Xin & Jitendra, 1998) proved to be an effective instructional feature for students performing poorly in mathematics or those with learning difficulties.
- Baker, S., Gersten, R., & Lee, D.-S. (2002). A synthesis of empirical research on teaching mathematics to low-performing students. The Elementary School Journal, 103(1), 51–73. http://www.jstor.org/stable/1002308.
- Forbringer, L. L. & Fuchs, W. W. (2014). RtI in math. Evidence-based interventions for struggling students. New York: Routledge.
- Goldman, S. R. (1989). Strategy instruction in mathematics. Learning Disability Quarterly, 12(1), 43–55. doi:10.2307/1510251.
- Kroesbergen, E. H., & Van Luit, J. E. H. (2003). Mathematics interventions for children with special educational needs. A meta-analysis. Remedial and Special Education, 24(2), 97–114. doi:10.1177/07419325030240020501.
- Kunsch, C. A., Jitendra, A. K., & Sood, S. (2007). The effects of peer-mediated instruction in mathematics for students with learning problems: A research synthesis. Learning Disabilities Research & Practice, 22(1), 1–12. doi:10.1111/j.1540-5826.2007.00226.x.
- Miller, S. P., Butler, F. M., & Lee, K. (1998). Validated practices for teaching mathematics to students with learning disabilities: A review of literature. Focus on Exceptional Children, 31(1), 1–24.
- Xin, Y. P., & Jitendra, A. K. (1999). The effects of instruction in solving mathematical word problems for students with learning problems: A meta-analysis. The Journal of Special Education, 32(4), 207–225. doi:10.1177/002246699903200402.