This systematic review investigates the characteristics of effective mathematics interventions for students with intellectual disabilities (ID) age 5 to 12, focusing on early numeracy, arithmetic, and arithmetical problem solving skills. Twenty studies from 2008–2020 were reviewed: 17 had a single-subject design and three a group-comparison design. The studies included a total of 135 students with ID. Consistent with previous studies, the analysis showed that interventions with systematic and explicit instruction with feedback and the use of manipulatives are effective instructional approaches and strategies for students with ID. This study reveals that effective interventions are well-structured, high intensity learning sequences adapted to the students’ achievement level. The intensity of an intervention requires careful consideration of the number of intervention sessions per week and their duration. Further studies should investigate which instructional strategy is most effective for each type of skill and the optimum intensity of interventions.

Little is known about the mathematical development of students with intellectual disabilities (ID) in inclusive classrooms. It is important to have a research-based understanding of the subject since inclusive education is becoming the norm in many countries, and an increasing number of students with an ID now attend mainstream schools. We investigated the learning gains of 38 students with ID from 31 grades 2 and 3 inclusive classrooms. Data on mathematics achievement were collected at the beginning and at the end of one school year. A cluster analysis revealed four homogeneous groups that differed significantly in their mathematical progress. Students in the same cluster improved in the same subskills. Prior knowledge is a significant predictor for progress and explains more variance than IQ. In addition, the acquisition of the quantity-number concept, especially the linkage of quantities and numbers, seems to be an important factor for mathematical development. These results show that mathematics instruction needs to be tailored to the specific knowledge profiles of students.

The purpose of this study was to identify the different profiles and patterns of progress in numerical skills of 6- to 10-year-old elementary school students with mild or moderate intellectual disability (ID). A standardised test of numerical and arithmetic skills was administered to 57 students with ID at the beginning and at the end of a school year. A cluster analysis was conducted with the participants’ numerical skills at Time 1 and Time 2. Four groups of children which exhibited significantly distinct profiles at the beginning of the school year were identified: (1) children with inconsistent basic numerical skills with numbers up to 10, (2) children with basic numerical skills with numbers up to 10, (3) children with numerical skills with numbers up to 20, (4) children with numerical skills with numbers up to 100 and arithmetic skills. The group of children with inconsistent basic numerical skills with numbers up to 10 did not progress significantly during the school year. In contrast, most children with the second, third and fourth profile extended their numerical skills to larger number domains (respectively up to 20, 100 or 1000) during the school year. The implications of these findings are discussed.

This study investigated the differences between the mathematical profiles of primary school pupils with intellectual disabilities (ID) enrolled in inclusive classrooms and those enrolled in special schools. It also considered whether the instructional setting has an impact on mathematical achievement gain. The mathematical achievement of 100 pupils with ID in inclusive classrooms (group^INCLUSIVE, n = 44) and special schools (group^SPECIAL, n = 56) was assessed at the beginning and the end of one school year. The results show that pupils with ID have a different mathematical profile in each setting. More of the pupils with very low mathematical achievement were enrolled in special schools and they made little progress over the course of the year. More of the pupils with ID who had computational skills were in inclusive classrooms. Due to large differences in age, IQ, and prior mathematical achievement between the two groups, a sample of matched pairs with one pupil from each setting was selected (n = 44). Regression analysis showed that the inclusive setting had a small positive effect on mathematical achievement gain after nine months. The study provides evidence that inclusive education is beneficial for the mathematical achievement gain of pupils with ID.

Research in inclusive settings is complicated by the nested relationships between the general education teacher (GET), the special education teacher (SET) and pupils. In this study, the impact of SET resource and selected variables of teacher competence (professional mathematical knowledge SET, attitude towards inclusion GET, classroom management GET) on the mathematical achievement gain of typically developing pupils (TYP) and pupils with intellectual disability (ID) was examined. Mathematical achievement was tested at the beginning of the school year (t1) and the end (t2) in 34 inclusive classrooms (sample ID: n = 42; sample TYP n = 525). IQ and gender – and the average mathematical achievement at class level in the sample TYP – were included as control variables. For pupils with ID, hierarchical regression modelling revealed that the mathematical knowledge at t1 explained most of the variance in mathematical achievement gain. For the group TYP, the results of a multi-level analysis showed that mathematical knowledge at t1, IQ and the average mathematical achievement at class level all had a positive effect on mathematical achievement gain. The more hours a SET was present in the classroom, the more the mathematical achievement of the group TYP increased. The other teacher competence variables had no apparent impact.