The impact of inclusive education on the mathematical progress of pupils with intellectual disabilities

ABSTRACT

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.

KEYWORDS:

• Inclusive education
• special education
• mathematical achievement
• intellectual disability

Introduction

Inclusive instruction is a common practice in many countries and an increasing number of pupils with special educational needs (SEN) attend inclusive classrooms alongside pupils without SEN (Wehmeyer and Shogren 2017). However, the inclusion of pupils with intellectual disabilities (ID) is still not as common as the inclusion of pupils with learning disabilities, language disorders or behavioural problems (Göransson et al. 2020; Wehmeyer, Shogren, and Kurth 2021). According to DSM-5 and ICD-11, pupils with ID display deficits in intellectual function (e.g. reasoning, abstract thinking, and academic learning) confirmed by clinical evaluation and individualized standard IQ testing. They also display deficits in adaptive function that result in failure to meet developmental and sociocultural standards for personal independence and social responsibility which means pupils with ID can have a very wide range of learning behaviours and social and self-care skills (American Psychiatric Association 2013; World Health Organization 2019). The ICD-11 distinguishes between mild, moderate, and severe ID and pupils with mild or moderate ID are expected to be able to learn mathematics and reading skills. In ICD-10, which was the guideline in place when this study was conducted, there was less emphasis on adaptive function.

In many countries pupils with ID are taught either in special schools or inclusive classrooms in mainstream schools alongside pupils without SEN (Kauffman et al. 2017). Special education support is important in both settings (Florian 2019; Zigmond and Kloo 2017), but there are substantial differences between the settings.

Special schools are attended by a heterogeneous group of pupils with SEN who may have severe disabilities and consequently, very low achievement levels. In these schools special education teachers undertake almost all of the instruction, with occasional support from a second teacher or paraprofessional. Usually, therapies (e.g. speech therapy, physiotherapy) are also embedded in the daily schedule in special schools. They are provided by specialists, usually in a one-to-one setting. The instruction is generally tailored to the needs of the individual (Hienonen, Hotulainen, and Jahnukainen 2020; Zweers et al. 2020). Often the curriculum prioritizes skills for daily life in order to give pupils the possibility of greater independence (Shurr and Bouck 2013). It is generally assumed that these aspects of special schools foster the development of the pupils with SEN (Hienonen, Hotulainen, and Jahnukainen 2020).

Inclusive classrooms, because of their composition, include pupils with heterogeneous academic achievement profiles. Extra resources, in the form of hours of special education teacher support, are allocated on the basis of either the needs of specific pupils or of school population indicators (e.g. schools receiving a lump sum to pay for resource that reflects the number of pupils with SEN enrolled). Differing local funding models mean that the number of hours per week of special education teacher support for inclusive classrooms can vary a great deal from region to region (Meijer 1999). The emphasis in inclusive classrooms is on academic learning rather than on skills for daily life. According to Klang et al. (2020) teachers of inclusive classes have higher expectations of all of their pupils than teachers at special schools have of theirs.

The optimal learning environment for pupils with ID remains a matter of debate and policy decisions are not necessarily made on the basis of empirical evidence (Hienonen, Hotulainen, and Jahnukainen 2020; Kauffman et al. 2017). Proponents of special education schools argue that pupils with ID benefit from the protective learning environment, tailored support in small classrooms, individualized feedback, specialized instructional methods, and not least, a classroom climate largely devoid of competition (Peetsma et al. 2001; Zigmond and Kloo 2017). Proponents of inclusive education claim that inclusive settings can stimulate greater achievement (Barth et al. 2004).

There is not a much research on how a specific educational setting can affect the academic achievement of a pupil with ID (Cole et al. 2021). According to a review by Freeman and Alkin (2000), inclusive education in mainstream schools had mostly neutral and occasional positive effects on the academic achievement of pupils with ID.

Other, more recent, studies have also found that inclusive instruction has a neutral to somewhat positive effect. Cole, Waldron, and Maijd (2004) compared the achievement gain of pupils with learning difficulties and mild ID in inclusive settings with the progress of pupils in pull-out resource programmes. The authors found no significant differences between the groups in their achievement gain, over one year, in reading and mathematics. In a 12-year longitudinal study, Turner, Alborz, and Gayle (2008) found that an inclusive setting had a small positive effect on achievement in reading, writing and mathematics for pupils with Down syndrome. However, differences in academic achievement at the beginning of the school career were not considered in the analysis. This is significant because only a small number of the pupils in the study attended an inclusive classroom and pupils with different cognitive profiles might have been selected for placement in special schools or inclusive settings; like was not being compared with like.

According to Cole et al. (2021), pupils with a greater academic ability or fewer behavioural issues are more likely to be enrolled in inclusive education. Three studies tackled this problem by selecting matched pairs. The only one of them focusing on pupils with ID found that primary school pupils with ID in inclusive classrooms made slightly more progress in literacy than their peers in special schools over the course of two academic years (Sermier Dessemontet, Bless, and Morin 2012). There was, however, no difference in progress in mathematics. A longer term study by Peetsma et al. (2001) of pupils with mild ID and pupils with learning and behavioural difficulties found that the setting had no significant impact on achievement when pupils were examined after two years of attendance, but a positive effect of inclusive education on mathematical and language skills emerged after four years. Cole et al. (2021) found that pupils from a sample with different types of SEN, including 10% pupils with mild ID, who spent at least 80% of their school hours per week in inclusive classrooms did significantly better in reading and mathematics than their peers who spent more time in separate special education classrooms.

So we can conclude that inclusive education can have a positive impact on the literacy and language skills of pupils with ID but the specific impact of an inclusive setting on mathematical achievement remains unclear. The academic effect of placing students with ID in different settings, inclusive or special, needs to be further examined to tease out which factors in which setting are most beneficial for the development of the pupils. Such knowledge could make inclusion more thoughtful, objective, and utilitarian (Kauffman et al. 2017).

This study aims to contribute to the better understanding of the impact of educational settings (inclusive education, special school) on the mathematical achievement gain of primary school pupils with ID. Therefore, it is important to take into account specific knowledge on the mathematical skills and development of pupils with ID.

The mathematical development of pupils with ID

Previous research has shown that pupils with various levels of ID are able to acquire mathematical skills (Browder et al. 2008; Lemons et al. 2015; Spooner et al. 2019) and that their progress does not differ fundamentally from that of typically developing pupils (Baroody 1999; Brankaer, Ghesquière, and De Smedt 2011). However, most of the studies were conducted with pupils with mild and moderate ID. Pupils with ID need more time and repetition to learn mathematical concepts (Faragher and Clarke 2014), and some pupils make little progress over the course of several school years. The empirical evidence suggests that progress seems to depend on the acquisition of specific numerical skills. According to a number of scholars (e.g. Aunio and Räsänen 2016; Jordan et al. 2007) early numerical competencies such as counting skills and principles, comparing quantities and numbers, and composing and decomposing numbers, are predictors of later mathematics performance.

A model by Krajewski and Schneider (2009) describes the early mathematical development of children with and without ID. It structures the development in three levels. At the first level, children are able to differentiate between discrete quantities and they use number words or Arabic numbers isolated from quantities. They recite the number sequence as a string (Fuson 1988). Gradually they acquire second level skills, including a milestone in mathematical development, the ability to link number words and Arabic numbers with a precise representation of quantity. This linkage is crucial for understanding the decomposition of numbers and learning that the relationships between numbers, such as difference, can be named with a number word (Krajewski and Schneider 2009). These skills are assigned to the third level of the model. The process of sequentially understanding the linkage between numbers and quantities starts with small numbers and progresses to larger ones. It can be that although children link small numbers with quantities, they may not yet link larger ones (level 2).

Researchers have shown that pupils with ID show different mathematical profiles. Some pupils struggle with the linkage of numbers and quantities (level 2) whilst others can solve addition and subtraction problems (Baroody 1999; Garrote, Moser Opitz, and Ratz 2015). Pupils with ID with different mathematical profiles might be placed in different settings, and it is important to consider these profiles when examining the achievement gain of pupils in different settings. Not much is known about the mathematical development of pupils with ID in inclusive classrooms because the pupils are taught in one-to-one settings in most intervention studies (e.g. Tzanakaki et al. 2014).

The study

The research review demonstrates that little is known about the effect of the setting (inclusive education, special school) on the development of pupils with ID, and specifically, it is not clear what effect the setting has on their mathematical development. This study aims to help close this research gap by using a longitudinal design to investigate the effect of the setting on the mathematical achievement of primary school pupils with ID. The research questions are:

• What are the differences between the mathematical profiles of pupils with ID in inclusive classrooms and special schools?

It is hypothesized that pupils with ID in special schools have a lower achievement level than pupils with ID in inclusive classes.

• What effect does the instructional setting have on the mathematical achievement gain of primary school pupils with ID?

It can be hypothesized, from evidence gathered by previous studies, that the inclusive setting has a neutral or slightly positive effect on the mathematical achievement of pupils with ID.

Method

Context of the study: schooling of pupils with ID in Switzerland

Pupils with ID in Switzerland either attend special schools or inclusive classrooms. While in some cantons, such as Lucerne, around 40% of the population of pupils with ID are enrolled in inclusive classrooms (Dienststelle Volksschulbildung Luzern 2021), in others, such as Thurgau, most of these pupils attend special schools and the stated aim of the authorities to achieve a ‘moderate’ increase in the numbers who move to inclusive education (Departement für Erziehung und Kultur Thurgau 2021). In the inclusive setting, resources for special education support are allocated on the basis of the input model (Meijer 1999); individual assistance is provided by a special education teacher for 6–10 h per week, depending on a pupil's individual needs. Sometimes teaching assistants support pupils with ID. In special schools, four to eight pupils with ID are taught in a class by a full-time special education teacher, or sometimes a special education teacher and a teaching assistant. In both settings, the pupils have individual learning objectives. Although there is no data showing which pupils with ID attend which school, it can be assumed that pupils with severe and profound ID attend special schools. In addition, the infrastructure for pupils with severe ID is not yet in place in inclusive schools (e.g. no nurse's stations).

Participants and settings

Participants were drawn from pupils already involved in two larger longitudinal studies in the French- and German-speaking parts of Switzerland (Schnepel et al. 2020; Sermier Dessemontet, Moser Opitz, and and Schnepel 2020). The studies were independently reviewed and approved by the ethics committee of the faculty of Arts and Social Sciences of the University of Zurich. In the inclusive setting, a notice inviting participation was published in a cantonal newsletter sent to principals and teachers. Invitations to participate were also sent to the principals of special schools for pupils with ID in five cantons. The teachers were free to decide if they wished for their school and pupils to participate. Parents had to provide written consent for pupils to be included in the study. Teachers contacted the parents and collected the written consent. The sample was 100 pupils with ID (sample^TOTAL).

A school psychologist or child psychiatrist had diagnosed the participants as having an ID prior to the study using the ICD-10 or DSM-5 guidelines. Some pupils had a more specific diagnosis or two diagnoses. In addition, some teachers reported that some pupils had behavioural issues (e.g. ID combined with aggressive behaviour, but without a diagnosis) (Table 1). The pupils were aged between 6 and 11 years (in months: M = 105.35, SD = 12.33). Forty-four pupils attended inclusive classes (group^INCLUSIVE) and 56 were enrolled in special schools (group^SPECIAL).

Table 1. Number of pupils with syndromes and diagnoses in each setting.

	Group^INCLUSIVE	Group^SPECIAL
	(n = 44)	(n = 56)
Down syndrome	6	8
Fragile X syndrome	0	3
Other syndromes	2	8
Autism spectrum disorder	5	13
Behavioural issues	15	9
Non-specific aetiology	25	31

Note: Double answers were possible.

Participants enrolled in an inclusive setting

The group^INCLUSIVE (n = 44) consisted of 18 girls and 26 boys with ID enrolled in 35 inclusive Grade 2 and 3 classes. Thirty pupils were in the German-speaking and 14 were in the French-speaking part of Switzerland. Twenty-four of the pupils had German or French as first language. Most participants had an ID with a non-specific aetiology (Table 1).

Like their peers without ID, the pupils with ID had four to five mathematics lessons per week (M = 4.9, SD = 0.29). Mathematics was taught by the general education teacher and a special education teacher was present in class for some of the lessons (M = 3.43, SD = 1.03; min = 1.5, max = 5). The general education teacher was therefore responsible for some of the mathematical education of the pupils with ID in 24 of the 35 inclusive classes.

Participants enrolled in special education schools

The group^SPECIAL included 56 pupils (22 girls, 29 boys) aged 6–10 years old enrolled in 15 different classes at special schools. Eight pupils were in schools in the German-speaking part of Switzerland, and 48 in the French-speaking part. Most of the participants had an ID with a non-specific aetiology and 13 of the pupils had also been diagnosed as having an autism spectrum disorder (Table 1). Pupils in this sample were taught in self-contained classes of four to eight pupils with ID. Thirteen of the classes were taught by a team consisting of a special education teacher and a teaching assistant. Two classes were taught by two special education teachers working in tandem full time (no teaching assistant). There were two to four lessons per week of mathematics (M = 2.29; SD = 0.60).

Measures

Mathematical achievement

Mathematical achievement was tested at the beginning of the school year in September (t1) and at the end of the same school year in June (t2). A trained research assistant tested each child individually in a quiet room at school, using selected subtests of the standardized TEDI-MATH test, which is available in both a French and a German version (Kaufmann et al. 2009; Van Nieuwenhoven and Grégoire 2015). The test took approximately 45 min, with a break at the halfway point. TEDI-MATH was developed specifically for kindergarten and primary school children and assesses basic numerical skills. The language requirements of the test are minimal. A study by Garrote, Moser Opitz, and Ratz (2015) has shown that the test is suitable for pupils with ID. The following subtests of TEDI-MATH were used: procedural and conceptual counting, writing and reading numbers, seriation of quantities and numbers, number conservation, decomposition of numbers, computation (addition/subtraction) supported by pictures, base-ten system, and computation with equations (addition/subtraction). Cronbach's alpha for the total test score (95 items) was 0.98 for both measurement points. The test scores for mathematical achievement at t1 (Math t1) ranged from 0 to 93 and had a normal distribution. The test scores for the post-test (Math t2) ranged from 0 to 98 and narrowly missed qualifying as a normal distribution (kurtosis: −1.33, SE = 0.62; skewness: 0.10, SE = 0.24).

Intelligence

Pupil intelligence scores were retrieved from school records. If a score was unavailable, a pupil's IQ was assessed using CFT 1-R (Weiß and Osterland 2013) or SON-R (Tellegen, Laros, and Petermann 2007). The average IQ score for the participants was 60.24 (SD = 11.89).

Background variables

Background information for the pupils with ID (e.g. age, aetiology, syndromes, and diagnoses) and the educational setting (e.g. hours of mathematics instruction, amount of support by a special education teacher) was gathered using a teacher questionnaire at t1.

Analyses

All statistical analyses were run using SPSS 25. The means of the variables Math t1, Math t2, IQ, age, and number of mathematics lessons in both settings were compared with t-tests for independent samples.

Previous research has shown that selecting matched pairs of students in different conditions (in this case, the inclusive classroom and special school settings) results in comparable groups of pupils (e.g. Sermier Dessemontet, Bless, and Morin 2012). A propensity score matching procedure was used to create statistically equivalent samples based on observed covariates. A balance of covariates is desirable in order to avoid biasing the estimate of treatment effects or effects of the setting (Fan and Nowell 2011). When every pupil in a condition is matched with another pupil with similar properties in the other condition, any differences between the groups should be due to the setting. To carry out the matching, a logistic regression model with the setting as dependent variable and Math t1, IQ, and age as independent variables was run. The propensity of each pupil to be in any one of the two settings, the propensity score, was calculated. Using these scores, each pupil from an inclusive setting was matched with a pupil from a special school; the difference between their propensity scores had to be below 0.1. Twenty-two matched pairs with 44 pupils (pairs^TOTAL) were found and used for the subsequent analyses.

Hierarchical regression analysis was used to examine the impact of the setting on the mathematical achievement of the sample pairs^TOTAL at t2. In this way, we controlled for other variables and determined if a newly added variable showed a significant improvement in R². The variable IQ was inserted as the first step, followed by the Math t1, and then the age variable in the subsequent steps. In step 4, the variable setting (inclusion, special school) was inserted into the model.

Results

Group descriptives

Table 2 shows the descriptives for the group^INCLUSIVE and the group^SPECIAL and the results of the t-tests. The groups differed significantly in age, IQ, Math t1 and Math t2, and the number of mathematics lessons per week. Pupils in special schools were older, had a lower IQ, and a lower level of mathematical achievement at t1 and t2. Pupils in group^INCLUSIVE had significantly more mathematics lessons per week than pupils in group^SPECIAL. The paired t-test revealed that both pupils in group^INCLUSIVE (t(44) = 8.16, p < 0.001) and pupils in group^SPECIAL (t(56) = 4.56, p < 0.001) had shown significant improvement in their mathematical skills between t1 and t2. The differences in the number of mathematics lessons between the settings indicate a collinearity which was confirmed by the high correlation of the setting and mathematics lessons variables (Eta² = 0.861, p < 0.001).

Table 2. Descriptives of sample^TOTAL, group^INCLUSIVE (n = 44) and group^SPECIAL (n = 56) and results of the group comparison (unpaired t-test).

	Sample^TOTAL	Group^INCLUSIVE	Group^SPECIAL	t(98)	p
	M (SD)	M (SD)	M (SD)
Age	105.96 (12.96)	99.95 (8.86)	110.68 (13.76)	−4.72	<0.001
IQ	60.24 (11.89)	65.34 (11.78)	56.23 (10.42)	4.10	<0.001
Math t1	34.35 (25.69)	45.11 (25.89)	25.89 (22.32)	3.98	<0.001
Math t2	43.71 (29.94)	58.70 (27.85)	31.93 (26.20)	4.92	<0.001
Math lessons	3.42 (1.43)	3.55 (1.15)	2.25 (0.67)	26.76	<0.001

Note: Age in months.

Mathematical profiles

The large range (t1: min. 0, max. 93, t2: min. 0, max. 98) and high standard deviation of the mathematical achievement variables (Table 2) indicate that there were big differences in mathematical skills between pupils. In sample^TOTAL, a large number of pupils (n = 40) could read some numbers and count up to 10 at t1. These pupils made little progress in assessed skills during one school year. Their skills were mainly on the first level of the model suggested by Krajewski and Schneider (2009). Of these 40 pupils with low mathematical achievement, 31 attended special schools. A second cluster, which included almost one third of the pupils (n = 31), could read and write numbers up to 10, count up to 20 and link numbers and quantities. They consolidated their skills over the nine month duration of the study and made achievement gains in reading numbers up to 100 and understanding number relationships. In this cluster, the number of pupils in special schools (n = 16) was almost identical to the number in inclusive classrooms (n = 15). A third cluster of pupils (n = 29) started with a basic knowledge of numbers up to 100 and first computation skills at t1. This group showed improvements in their ability to decompose numbers and understand the base-ten system by t2. Twenty of these pupils attended inclusive classrooms and nine attended special schools. So most of the pupils in group^SPECIAL had a very low level of mathematical achievement, with only a few having numerical knowledge of numbers up to 100 at t1. The hypothesis that pupils with ID in special schools have a lower achievement level than pupils with ID in inclusive classes is confirmed.

Descriptives of the sample after propensity score matching

Table 3 shows the means and standard deviations of the study variables of the groups in the sample pairs^TOTAL: 22 pupils in inclusive education (pairs^INCLUSIVE) and 22 pupils in special schools (pairs^SPECIAL). The results of the unpaired t-test show that the matching was successful. The pairs^INCLUSIVE and pairs^SPECIAL groups did not differ in the matching variables of age, IQ, and Math t1. They also did not differ in Math t2. The only significant difference was in the number of mathematics lessons (t(42) = −13.00, p < 0.001).

Table 3. Descriptives of subsamples pairs^INCLUSIVE (n = 22) and pairs^SPECIAL (n = 22) and results of the group comparison (unpaired t-test).

	Pairs^INCLUSIVE	Pairs^SPECIAL	t(42)	p
	M (SD)	M (SD)
Age	98.68 (8.27)	101.32 (13.40)	0.78	0.438
IQ	60.00 (11.02)	60.45 (12.58)	0.13	0.899
Math t1	29.23 (20.47)	34.41 (28.95)	0.69	0.497
Math t2	44.59 (27.13)	40.41 (31.73)	−0.47	0.641
Math lessons	4.95 (0.21)	2.50 (0.86)	−13.00	<0.001

Note: Age in months.

The two groups, pairs^INCLUSIVE and pairs^SPECIAL, were also shown to be quite similar in terms of special diagnoses and syndromes after the matching procedure. In each sample, six pupils had a diagnosed syndrome. However, in the group pairs^SPECIAL, more pupils had autism spectrum disorders and fewer pupils showed behavioural concerns than in group pairs^INCLUSIVE.

Mathematical profiles of the sample after propensity score matching

The mathematical profiles of the pupils in the two setting were comparable after the matching process. Fifteen pupils could only read some numbers and count to 10 at t1, 8 of them were in the group pairs^SPECIAL. Six of the 16 pupils who could already link numbers and quantities at t1 were in the group pairs^SPECIAL. Eight of the 13 pupils who already had a basic knowledge of numbers up to 100 and first computation skills at t1 were in the group pairs^SPECIAL. These results show that the pairs^SPECIAL and pairs^INCLUSIVE samples were comparable in terms of their mathematical profiles at t1. Most of the participants excluded from further analysis after the matching procedure were either pupils with low mathematical achievement enrolled in special schools (n = 23) or pupils with relatively high achievement in inclusive classes (n = 15).

Regression analyses

Hierarchical regression analyses were conducted to investigate the impact of the setting on Math t2 while controlling for IQ, Math t1, and age. The number of mathematics lessons was not inserted as a variable because of its collinearity with the setting variable (Eta² = 0.801, p < 0.001). Table 4 gives an overview of the results for the sample pairs^TOTAL. Including IQ in a first step in the model led to R²= 0.21 (p < 0.01). When Math t1 was put into the model, the proportion of explained variance increased significantly, R²= 0.84 (Δ F = 170.92, p < 0.001). R² did not increase when the age variable was put into the model. However, R² increased significantly when the setting was included in the model (Δ R² = 0.03, Δ F = 9.26, p < 0.01) with a small effect size (f = 0.03; Cohen 1969). The hypothesis that the inclusive setting has a neutral or slightly positive effect on the mathematical achievement of pupils with ID is confirmed. The model that included all of the variables explained 87.8% of variance (R²= 0.88, F(4, 39) = 78.53, p < 0.001).

Table 4. Hierarchical regressions analysis with Math t2 as dependent and IQ, Math t1, age, and setting as independent variables.

Step	Predictor variable	R^2	Δ R^2	Δ F	p
1	IQ	0.21	0.23	12.19	0.001
2	Math t1	0.84	0.63	170.92	<0.001
3	Age	0.85	0.01	3.88	0.056
4	Setting	0.88	0.03	9.26	0.004

Note: R² = 0.878 (adjusted), (n = 44, p < 0.001), Age in months, setting is coded 0 = special schools, 1 = inclusive education.

Discussion

The results of this longitudinal study confirmed existing research that there is a difference between the mathematical profiles of pupils with ID placed in inclusive classes and those who are placed in special schools (Cole et al. 2021). Pupils in inclusive classes had higher IQ scores and higher levels of mathematical achievement at t1 than their peers in special schools. However, all pupils with ID made significant learning gains in both settings. In order to investigate the effect of the setting – inclusive education versus special schools – a sample of matched pairs was selected. The analysis of the matched pairs showed that the inclusive setting had a small positive significant impact on pupils’ mathematical achievement over the course of a school year.

The differences between the mathematical profiles of pupils with ID in special schools and in inclusive classrooms

Comparing the two samples revealed that many more pupils with very low mathematical achievement were enrolled in special schools while pupils with higher mathematical achievement (basic knowledge of numbers up to 100 and computation skills) attended inclusive classrooms. More of the pupils with identified syndromes and autism spectrum disorders were enrolled in special schools. These diagnoses can affect the acquisition of mathematical and language competencies as well as learning behaviour and social skills. Difficulties in these areas can in turn have an impact on mathematical achievement gain (Jordan, Glutting, and Ramineni 2010). This study found that the effect of setting was relatively small. The different diagnoses, and the possibility that the setting did not have a very high impact in the first two or three years of schooling, makes it likely that the existence of the mathematical profiles may pre-date the study. This means that pupils who are enrolled in special schools have different academic profiles from those enrolled in inclusive education. This mechanism is confirmed by previous studies (Sermier Dessemontet, Bless, and Morin 2012; Peetsma et al. 2001). The assumption is that those pupils with ID who have a relatively high level of cognitive and mathematical skills and fewer behavioural issues are placed in inclusive classes (Zigmond and Kloo 2017; Cole et al. 2021; Gilmour 2018).

In this study, more teachers of inclusive classrooms mentioned that their pupils with ID had behavioural concerns. However, their judgement of pupil behaviour may have been harsher than that of their colleagues working in special schools where pupils often display challenging behaviours (Savoie and Gascon 2008). General education teachers might have also been likely to unfavourably compare the behaviour of pupils with ID to that of their students without ID.

Our results indicate that the assignment of pupils with ID to special schools or inclusive classrooms is not random and therefore, effects of the setting on academic achievement cannot be investigated by using a random treatment design (Cole et al. 2021). The propensity score matching procedure enables the selection of pupils with similar characteristics from different settings for further analyses and offers a methodological process that approximates randomized control trials (Cole et al. 2021). In this study, the matching ensured that the samples in inclusive and special education were comparable in IQ, mathematical achievement, and age. The matching also resulted in pupils having similar mathematical profiles in both settings.

Impact of the instructional setting on the mathematical achievement of pupils with ID

When the matched samples were compared, the pupils in inclusive classrooms made more progress in mathematics than pupils in special schools, controlling for IQ, age, and prior mathematical achievement. To the best of our knowledge, this is the first study to show the impact of educational setting on the mathematics achievement over the course of a school year. The positive effect of inclusive education on the academic achievement gain of pupils with ID is in line with the findings of other studies that examined progress in other subjects (Sermier Dessemontet, Bless, and Morin 2012; Peetsma et al. 2001; Cole et al. 2021). However, it is unclear which features of the setting have led to this result. Pupils in inclusive classrooms had more hours of mathematics instruction per week than pupils in special schools. According to Schnepel and Aunio (2021), the intensity (frequency) of instruction is an important factor in successful mathematical education programmes for pupils with ID. Teachers having higher expectations of pupils in inclusive classrooms can also have a positive impact on progress (Klang et al. 2020). There is also the positive effect of inclusive education on the achievement of pupils with ID resulting from their stimulation by peers without disabilities through social learning mechanisms (Barth et al. 2004; Justice et al. 2014). This argument and the results of this study together suggest that the assignment of pupils with ID to special schools can be interpreted as an ability grouping that can have a negative impact on the achievement of pupils in low-ability groups (Faber, Glas, and Visscher 2018).

Limitations and implications for further research

This study has some limitations. The diagnosis of ID relied on IQ only, and adaptive behaviour was not considered. It may be that the two groups have differences in adaptive behaviour that could have affected the results. However, research does show that mathematical progress is largely dependent on IQ and previous mathematical knowledge. Therefore, the important variables were included in the study. Independent of setting, many of the pupils progressed very little in mathematics over one school year. This might be because the instrument selected to assess mathematical achievement was one designed to assess early numerical and first computational skills and may not have been sensitive enough for assessing the achievement gain of pupils with very low mathematical achievement. In addition, the larger number of pupils diagnosed with an autism spectrum disorder in special schools might have affected the results.

Due to the differences between inclusive classes and special schools, the setting variable strongly correlates with other variables, such as the number of mathematics lessons, pupil-teacher-ratio, or number of pupils with and without SEN per class. These and other variables which were not considered by the study (e.g. teaching concepts, methods, and materials, learning objectives, teachers’ expectations) could also have had an effect on pupils mathematical learning. It should also be noted that having more hours of mathematics lessons with a special education teacher does not necessarily equate to a better quality of mathematics instruction.

Future studies which analyse the effect of the setting on pupil achievement gain should collect more information about the pupils (e.g. language skills, cognitive resources), instruction (e.g. methods, materials and how often pupils learn inside or outside the classroom) and teachers’ attitudes and teaching concepts.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Swiss National Science Foundation [grant number: 146086].

Notes on contributors

Susanne Schnepel

Susanne Schnepel is a senior researcher at the Institute of Education at the University of Zurich.

Rachel Sermier Dessemontet

Rachel Sermier Dessemontet is a professor at the Department of Special Educational Needs at the University of Teacher Education in the State of Vaud, Lausanne.

Elisabeth Moser Opitz

Elisabeth Moser Opitz is a professor for Special and Inclusive Education at the Institute of Education at the University of Zurich.