Advertisement

Educational Studies in Mathematics

, Volume 100, Issue 1, pp 25–41 | Cite as

Inclusion in mathematics education: an ideology, a way of teaching, or both?

  • Helena Roos
Open Access
Article

Abstract

This literature review focuses on the definitions and roles of inclusion in the field of mathematics education to help promote the sustainable development of inclusion in the discipline. Discourse analysis was used to analyse 76 studies published between 2010 and 2016. The results show that the term inclusion is used both for an ideology and a way of teaching, and these two uses are most often treated separately and independently of each other. When inclusion is treated as an ideology, values are articulated; when treated as a way of teaching, interventions are brought to the fore. When the notion of inclusion is used as an ideology, the most extensive discourse concerns equity in mathematics education; when it is used as a way of teaching, the most extensive discourse relates to teaching interventions for mathematical engagement. Based on the literature review, if sustainable development of inclusion in mathematics education is to be promoted, scholars need to connect and interrelate the operationalisation and meanings of inclusion in both society and in mathematics classrooms, and take students’ voices into consideration in research.

Keywords

Inclusion in mathematics education Diversity Equity Participation Interventions Discourse analysis 

1 Introduction

This research investigates the notion of inclusion and its definition and role in the field of mathematics education in an effort to help promote the sustainable development of inclusion in this field. Although the notion of inclusion has received increasing attention in educational research in the last few decades, there is no agreed definition for it (Graham-Matheson, 2012), either for what it is or what it is needed for. According to Artiles, Kozleski, Dorn, and Christensen (2006), the absence of an agreed definition is based on differences of perspective and context in research on inclusion, which can be seen in the coverage of ethnic, social and special educational issues (Nilholm, 2007). In the educational context, which is the focus of this article, the notion of inclusive education (e.g., Armstrong, Armstrong & Spandagou, 2010) is sometimes used to promote support for diversity and equality, but it can also be used to describe a way of teaching children in special educational needs (SEN) (Ainscow, Booth, Dyson, & Farrell, 2006; Sheehy et al., 2009).

In mathematics education, the notion of inclusion is used in curriculum documents, in research and among teachers (e.g., Askew, 2015; Solomon, 2009). Three recent research overviews on SEN in mathematics (SEM) and inclusion in mathematics (Lewis & Fisher, 2016; Secher Schmidt, 2015, 2016) indicate a research interest in inclusion connected to mathematics education. However, these overviews deal with the manifestation of inclusion more or less implicitly, and none of them explicitly focuses on its definition or role in mathematics education research. The question of inclusion has also received attention in various ESM papers. Even here, the manifestation of inclusion in mathematics education is dealt with implicitly, foregrounding related notions such as equity (Hand, 2012; Lambert, 2015; Straehler-Pohl, Fernández, Gellert, & Figueiras, 2014) and participation (Foyn, Solomon, & Braathe, 2018; Ing et al., 2015). The reason for this gap might be the lack of a conceptual platform for inclusive education (Figureiras, Healy, & Skovsmose, 2016). Because of this, it becomes important to investigate definitions and ways of using inclusion in research.

One way to use the term inclusion is to describe what it means to be included in a society, as well as why it is crucial (UNESCO, 2009). The term can also describe a way of teaching, in which all students are taught in a regular classroom (e.g., Cornwall & Graham-Matheson, 2012). This dual use of the notion raises questions about what happens when the same term is used to describe both a way of taking part in society and a way of teaching in mathematics classrooms. And do these uses relate to each other? This article seeks to provide answers to these queries. Much research focuses on inclusion in general education, and this article strives to add to this knowledge through a literature review on inclusion in mathematics education. Hence, the aim is to investigate discourses of inclusion in mathematics education research to illustrate its meanings and operationalisation. The following research questions will be addressed:
  • What different meanings are ascribed to the notion of inclusion in mathematics education research?

  • How is the notion of inclusion operationalised and used in mathematics education research?

2 The study and its theoretical and methodological lenses

2.1 Data collection

In this literature review, various criteria were used for selecting studies to review. One criterion was that the studies connected inclusion to mathematics education and school. Only studies in English or the Scandinavian languages were selected, as I am fluent in those languages. Date of publication was a third criterion; to find research on the recent state of inclusion in mathematics education, the time span was set to 2010–2016. Finally, a quality criterion was used so only peer-reviewed research was included.

Five databases were searched: ERIC, Web of Science, PsycINFO, SwePub and Mathematics Education Database. ERIC and Web of Science were selected based on the results of Sheehy et al. (2009); the other databases were selected because they covered pedagogical and educational research both nationally and internationally. The search string contained the words (inclus* or inklu*) (education* or school or undervis* or skol* or utbildn*). Then, (math* or matemat*) was added. Then, the criteria for time span and peer-reviewed research were applied. To limit the search in PsycINFO, another criterion was added to search for research concerning 6–17-year-olds (school age). In Web of Science, the criterion research within education and special education was added in order to limit the result. In SwePub, the search string (inclus*) (education) (year) and (math*) was used because of the difference in structure of the database. The search resulted in 1296 research studies. Of these, 76 studies were retained after the criteria mentioned above were applied and 19 duplicates had been removed. These studies comprised 52 journal articles, 18 book chapters, 4 conference papers and 2 theses. Table 1 displays the distribution of the research selected by year.
Table 1

Distribution of the research material by year

Studies 2010

Studies 2011

Studies 2012

Studies 2013

Studies 2014

Studies 2015

Studies 2016

Sum

4

12

9

12

9

23

7

76

2.2 Theoretical lenses

In this study, the focus was on written language and ways of making meaning in terms of communication of research, ideas, values, concepts and presumptions. Hence, language both gets its meaning from social practice (Gee, 2014a) and makes meaning in a social practice. In the investigation of texts in the studies reviewed, discourse analysis (DA) was used both as a methodological device and as a theory, meaning it was used both as an analytical tool and in the explanation of the results.

DA was used from Gee’s perspective (2014a, b) because of its explanatory power regarding meaning making in text. This afforded an opportunity to grasp meanings ascribed to inclusion, and how the research operationalises inclusion in mathematics education. Here, meanings ascribed explain what inclusion is in the specific research, while operationalisation explains actions that need to be taken to promote inclusion. The theoretical notions big and small discourses provided by Gee (2014a, b) are used (henceforth referred to as Discourse with capital D and discourse with lowercase d respectively). (d)iscourse is focused on language in use, so-called stretches of languages seen in text (Gee, 2014a). Stretches of languages imply the relations between words and sentences. (D)iscourses are understood as ways of saying, doing and being, and the key is recognition. (D)iscourses are language plus actions, interactions, values, beliefs, symbols, objects, tools and places (Gee, 2014a). Hence, discourse and Discourse are interrelated since use of language is always affected by the context in which it is used, and the context is always affected by the use of language. This study accounts for this by looking at the relations and words used, and how they signal meanings and Discourses. Since the focus is on written language, Discourses are seen in the actions, values, beliefs, symbols, tools and objects visible in written text.

2.3 DA as an analytical tool

The discourse analytic procedure was begun by posing questions to the texts. The questions were chosen from those developed by Gee (2014b) and adapted to suit this study. The questions were chosen to illuminate the meanings, operationalisations and Discourses of inclusion in mathematics education research. The adaptations were made to highlight the context of this study—mathematics education and research on inclusion—using words like ‘inclusion’ and ‘scholar’. This resulted in the following questions: ‘How are the words and grammatical devices used to build a viewpoint on inclusion?’, ‘What is the theme for the text and why were these choices made?’, ‘Which subjects/topics are chosen and how do they relate to the theme?’, ‘What are the scholars saying about the subjects?’ (In this sense, according to Gee, the subject is to be understood as the particular topic the scholar has chosen), ‘How is what the scholar is saying and how she/he is saying it helping to create or shape what readers will take as the relevant context regarding inclusion?’, ‘Is what the scholar is saying about inclusion and how she/he is saying it just, more or less, replicating contexts of inclusion in mathematics education or transforming or changing them?’, ‘What is taken for granted by the scholars regarding inclusion?’, ‘What social groups, institutions, or cultures support and set norms for inclusion in mathematics education?’, ‘How are words being used to build up or lessen significance for inclusion?’ and ‘What Discourse is the language a part of?’

With the help of these questions, discourses (small d) could be construed based on the meanings ascribed to the notion of inclusion and/or operationalisation of inclusion. If a stretch of language defined inclusion or described access to mathematics overall, it was categorised as meanings ascribed. One such stretch of language was ‘whenever possible, all children should be in the same classroom, forming meaningful peer group relationships, and finding success and challenge in the curriculum’ (Tennant & Foley, 2014, p. 77).

If the research discussed actions taken to promote inclusion—for example, ‘effective teaching practices and intervention strategies’ (Scherer, Beswick, DeBlois, Healy, & Moser Opotiz, 2016, p. 634)—it was categorised as operationalisation. Some research discussed both meanings ascribed and operationalisation and were categorised as both (e.g., Healy & Powell, 2013). From this categorisation, the stretches of language (d) were organised into meanings ascribed to the notion of inclusion, and/or operationalisation of inclusion. After this categorisation, a meta-analysis was done in which the similarities and differences in answers to the questions asked of the different texts were identified. By doing this, similar stretches of language could be put together, and demarcated discourses could be construed. These discourses were analysed by asking the same questions asked of the studies. Then, two Discourses were construed from them, with the help from the answers to the question ‘What Discourse is the language a part of?’

3 Results

The results are presented with the two construed Discourses as main headings. Under each, operationalisation and meanings ascribed to the notion of inclusion in mathematics education research are displayed as discourses in subheadings.

3.1 Discourse of inclusion in mathematics in society

Of the 76 studies, 23 use words such as ‘society’, ‘ideology’, ‘political’, ‘(in)equity’ and ‘equality’ in relation to inclusion. They also talked about inclusion in mathematics outside of the classroom. Thus, the meanings ascribed and operationalisation of inclusion in mathematics education that were recognised have two themes in common: general educational approaches to inclusion in mathematics education and inclusion in mathematics education from an overall societal perspective. Hence, a Discourse of inclusion in mathematics in society (DIMS) is construed. The discourses construed within DIMS are presented below.

3.1.1 Meanings ascribed to the notion of inclusion in mathematics education research in the DIMS

Sixteen of the 23 studies in the DIMS discuss issues and meanings of inclusion on a societal level.

The discourse of equity in mathematics education

This discourse construes and defines inclusion in terms of justice in mathematics education. The word (in)equity is frequently used, and most often not defined but taken for granted. The term is used in relation to different issues. For example, Feza (2014) uses it when identifying ‘inequity factors [that] continue to exclude the majority of black children’ (p. 888). Basile and Lopez (2015) investigate ‘issues of equity with regard to students of colour’ (p. 519). Thus, both studies chose the words equity and inequity as related to race. Neumann (2014) refers to inclusion in terms of equity but relate to the subject of gender. In her study, she challenged the norms of teacher education by investigating ‘hidden beliefs and inequitable teaching practices’ (p. 90) in mathematics education. Pais and Valero (2011) and Valero (2012) discuss equity in relation to inclusion and exclusion in ‘society at large’. Valero (2012) discusses being ‘school mathematics incapable’ (p. 370), saying

Not being able to cope, participate, or succeed in the demands of school mathematics is in no way a characteristic of the individual learner, but it is a result of how the whole set of participants in the practices and discourses of school mathematics subjectify certain students.

The theme is processes of inclusion and exclusion. The inability to participate in school mathematics is seen not as a characteristic of the individual but a result of subjectifying students. Similarly, Pais (2014) discusses inclusion from a socio-political viewpoint through social justice and equity—in contrast to exclusion. Pais stresses the significance of inclusion by saying, ‘achieving equity means to fight different battles (for groups of people considered to be in disadvantage, inequity of resources, teacher formation, mathematical content for social justice etc.)’ (p. 1088).

A different perspective on equity is seen in a study where the subject is gifted students and their right to have opportunities to learn mathematics and the ‘relationship between the equity principle in mathematics education and the views on the education of gifted’ (Leikin, 2011, p. 167). In regard to social level, Leikin (2011) poses the question, ‘What type of ability grouping is the most effective for mathematically gifted students?’ (p. 180). Hence, equity and inclusion are being used with words focusing on ability. Healy and Powell (2013) focus on equity where the subject is disadvantaged students, stating, ‘by understanding the learning processes of such students we may better understand mathematics learning in general’ (p. 69). Inclusive education is discussed using words such as ‘empowerment’ and ‘equity’, and the authors highlight the significance of understanding the learning processes of disadvantaged students and thereby being able to address differences and create a more equitable mathematics education. Thus, the starting point is the individual student, but Healy and Powell (2013) also use statements such as ‘what macro social conditions are necessary for their [the disadvantaged students] inclusion’ (p. 87), implying inclusion from a societal perspective. Accordingly, they highlight why we should work with inclusion in terms of equity, and in terms of how to understand connections between students and societal levels. Hence, there is an attempt to provide an understanding of connections between meanings ascribed and operationalisation of inclusion. Panizzon (2015) chooses the theme of geographical location in relation to diversity and inclusion. The words ‘overcome inequity’ (p. 41) are used as well as ‘enhancing greater inclusivity’ in relation to ‘political imperative’ (p. 56), indicating the significance of inclusion in society.

The discourse of mathematics (not) for all

This discourse construes inclusion in terms of making mathematics education accessible for (not) all students. Pais (2014), who chose the subject not for all, stated, ‘perhaps we should acknowledge the crude reality that mathematics is not for all. Schools, however uncomfortable such awareness may be, are places of selection and teachers are agents of exclusion’ (p. 1091). Similarly, Diaz (2013) defines inclusion as equal mathematics for all, but also questions this by stating that ‘embedded in the relationship between math education and questions of inclusion a particular logic of equality paradoxically reinserts notions of inequality as differences between children’ (p. 36). That is, to be able to include all, children become objects that can be measured, compared and calculated. The subject of both studies (Pais, 2014; Diaz, 2013) is what ‘all’ children actually means, and is mathematics for all? Even Borges and César (2013) use the phrase ‘education for all students’, but in relation to the phrase ‘to achieve this we need to pay close attention to all vulnerable groups and promote equity’ (p. 1). Accordingly, ‘for all’ implies comparing groups. Similarly—yet differently—Sullivan chooses to discuss the subject of mathematics for all by saying, ‘On one hand, the goal might be to reduce differences between groups of students. On the other hand, the goal might be to improve the outcomes of all students’ (2015a, p. 13). These words increase the significance of problematising education for all students. It could mean focusing on all students, but it could also mean focusing on specific groups of students to reduce differences. Scherer et al. (2016) favour using ‘learning situations’ instead of ‘normality’ of students when discussing inclusive education. By using ‘new forms of providing meetings among differences’ and ‘constructing learning situations that permit such meetings’ (p. 640), they are bringing focus to the meetings, understanding differences and meeting needs of every student.

The discourse of including (or excluding) SEM students

This discourse construes inclusion in terms of students in difficulty in mathematics having (or not having) access to mathematics education. The stretches of language stress the theme of a relationship between inclusion and students in some kind of difficulty, either disabilities or poor performance. Barnard-Brak, Wei, Schmidt, & Sheffield (2014) chose the subject of national rankings in mathematics in relation to inclusion. By using the words ‘referring to the education of individuals with disabilities within general education setting’ (p. 118) and ‘how the inclusivity of students with disabilities at the classroom level across countries may be associated with achievement scores’ (p. 120), they take the definition of disabilities and education for granted, setting the norm for inclusion from a disability perspective. Schuelka (2013) uses the words ‘students with disabilities’ when discussing international tests of achievement (TIMSS, PISA and PIRLS) and how these tests ‘exclude students with disabilities from the culture of achievement’ (p. 218). Even Secher Schmidt (2016) discusses inclusion in relation to disadvantaged students. However, Secher Schmidt uses the words ‘in maths difficulties’ with ‘pupils’ (p. 7) instead of ‘with disabilities’. The subject of inclusive practices is described as practices the students have (or do not have) access to in general mathematics education. Thus, there is a difference among the studies described above, as well as in their point of departure. In some, the focus is on the students with disabilities who are included in the education, and in others on how the education is including the students.

3.1.2 Operationalisation of the notion of inclusion in mathematics education research in the DIMS

Seven of the 23 studies in the DIMS talk about how to work with inclusion on a societal level, meaning these studies operationalise inclusion in relation to issues such as curriculum in society, rather than in the classroom or at school.

The discourse of inclusion in relation to exclusion

The discourse of inclusion in relation to exclusion within operationalisation in DIMS identifies ideological actions for inclusion based on exclusion. Straehler-Pohl and Pais (2013) chose the subject of exclusion in relation to inclusion and used the words ‘pinpoint ideological injunctions’ to stress their interest and the contrast with ‘providing solutions’ (p. 1795). They challenge the norms of school by stating ‘schools need to be presented as inclusionary and emancipatory places, places where phenomena such as exclusion and failure are seen not as necessary parts of the same system which purports to be trying to abolish them, but as contingent problems, malfunctions of an otherwise good system’ (p. 1802). Hence, they describe the development of inclusion implicitly, in that a school as an institution needs to make issues of exclusion visible to be able to address them. Lindstrom (2010) chose the subject of educational approaches and accommodations to include students with learning disabilities (LD) in doing mathematics tests. The words ‘fairly, and validly assess students with LD’ in relation to ‘testing accommodations’ suggest that the students with LD can be seen as excluded if not given accommodations.

The discourse of valuing diversity

This discourse encompasses striving for inclusion in mathematics education by ideologically valuing diversity. Askew (2015) chose the subject of diversity when discussing inclusion, stating that inclusiveness is supported in mathematics classrooms by ‘welcoming diversity’ (p. 143). The use of words like ‘reconsideration of how we think about curriculum’ and ‘starting from the position of building learning communities’ (p. 130) suggests that an ideological change of perspective, valuing diversity, is being sought in order to embrace inclusion in mathematics education. Aragón, Dovidio, and Graham (2016) chose the subject of implementing inclusive ideologies in relation to differences. Here, diversity is brought to the fore by using an ideology that ‘takes into account that all people are not the same, and equal treatment may not be beneficial for all’ (p. 2). Inclusion is then operationalised in terms of advocating for an ideological stance of valuing diversity in mathematics classrooms.

The discourse of equity in mathematics education

The discourse of equity in mathematics education within operationalisation in the DIMS construes inclusion in terms of equity in relation to gender, tests and ethics. Tan (2015) chose the subject of gender in relation to equity and inclusion, asking, ‘What kinds of questions should we ask about gender and technology that help us to be more inclusive?’ (p. 98). This shows how inclusion is operationalised by asking questions about the teaching overall. Leder and Lubienski (2015) also use the theme of equity, but connect it to the subject of large-scale tests. They use the words ‘detailed analysis of gaps can help mathematics education scholars more effectively target their efforts to promote equity’ (p. 37) to stress this viewpoint on inclusion. One study uses equity with the theme of ethical issues in relation to mathematics teaching and inclusion (Forgaz, Bleazby, & Sawatzki, 2015). Here, ‘an inclusive approach means that every facet of human experience and all knowledge domains have ethical dimensions’ (p. 155), and ‘teachers are responsible for deciding how to implement and enact an inclusive mathematics curriculum’ (p. 162). Hence, inclusion is operationalised by focusing on the choice of examples.

Summing up, the most common way of using inclusion in DIMS is with equity and mathematics for all. Also, the ascribed meanings dominate in DIMS.

3.2 Discourse of inclusion in mathematics in the classroom

Of the 76 studies, 54 dealt with inclusion using words like ‘instruction’, ‘interventions’, ‘implementations’, ‘strategies’, ‘effectiveness of instruction’ and ‘impact of instruction’ in relation to mathematics taught in the classroom. Accordingly, the studies have inclusion in mathematics in the classroom in common. Hence, a Discourse of inclusion in mathematics in the classroom (DIMC) is recognised. The discourses identified within DIMC are presented below.

3.2.1 Meanings ascribed to the notion of inclusion in mathematics education research in the DIMC

Nine of the 54 studies in the DIMC discuss issues and meanings of inclusion in the mathematics classroom.

The discourse of participation

This discourse construes inclusion in terms of every student having opportunities to participate in mathematics activities in the classroom. The theme of the studies was what form inclusion in mathematics might take in the classroom. Two were my own (Roos 2013, 2015), where the emphasis on participation is clear in these statements: ‘Inclusion is seen as a social process of participation in the mathematical practice’ (2013, p. 2861) and ‘To be included can be seen as a process of participation’ (2015, p. 27). Secher Schmidt (2015) highlights participation by asking about the ‘pupil’s possibilities to participate in mathematics’ (p. 7). Tennant and Foley (2014) chose the theme of inclusive approaches to learning and teaching mathematics, and they described inclusion as follows: ‘Whenever possible, all children should be in the same classroom, forming meaningful peer group relationships, and finding success and challenge in the curriculum’ (p. 77). This signals participation in relations both between peers and with the content. In addition, success is a part of inclusion. Kleve and Penne (2016) talk about inclusion in terms of ‘stories about participation’ (p. 42) (or lack of it) in (mathematical) discourses, using the terms ‘insiders’ and ‘outsiders’ to describe students’ participation.

The discourse of inclusion in relation to exclusion

This discourse in DIMC focuses on the contrast between inclusion and exclusion. Four of the studies used the theme of the effects of being excluded from the general mathematics classroom versus being included in the classroom. Inclusion in relation to exclusion is seen in words such as ‘inclusion and non-inclusion settings’ (Kurth & Mastergeorge, 2010, p. 146), ‘inclusion versus specialised interventions’ (Fuchs et al., 2015, p. 134), ‘Were the interventions in the inclusive classroom as effective as in special education?’ (Zhang & Xin, 2012, p. 305) and ‘More access to general education context would be positively related to achievement in mathematics’ (Cosier, Causton-Theoharis, & Theoharis, 2013, p. 325).

3.2.2 Operationalisation of the notion of inclusion in mathematics education research in the DIMC

Forty-five studies discussed operationalisation of inclusion in mathematics in terms of how to work in school and in classrooms, using words like ‘teaching’, ‘classrooms’, ‘lessons’ and ‘instructions’. However, 21 of the 45 studies did not discuss inclusion per se but took its meaning for granted. These studies used wording like ‘inclusive classrooms’ (e.g., Moorehead & Grillo, 2014), ‘inclusive settings’ (e.g., Powell, 2015), ‘inclusive schools’ (e.g., Eisenhart et al., 2015) and ‘inclusive teaching’ (e.g., Watson & De Geest, 2012), without defining or discussing their meaning.

The discourse of teaching interventions for mathematical engagement

This discourse construes inclusion in terms of strategies for including students in mathematics education. Words and phrases signalling interventions are ‘schema-based instruction’ (Jitendra & Star, 2011); ‘interactive groups’ (Garcia-Carrión & Diez-Palomar, 2015); ‘cognitive guided instruction’ (Guðjónsdóttir & Kristinsdóttir, 2011; Hankes, Skoning, Fast, & Mason-Williams, 2013; Moscardini, 2014); ‘cluster-based instruction’ (Sunardi, Anwar, & Andayani, 2016); ‘techno-kinaesthetic visually based activities’ (Tabur, 2014); ‘cognitive strategy instruction on math problem-solving’ (Montague, Enders, & Dietz, 2011); ‘problem-solving procedures’ (Fletcher, 2014); ‘explicit instruction’ (Hinton, Flores, Schweck, & Burton, 2016); ‘simultaneous prompting procedure’ (Heinrich, Knight, Collins, & Spriggs, 2016); ‘universal design for learning’ (Hunt & Andreasen, 2011; Lambert & Stylianou, 2013); ‘anchored instruction’ (Bottage et al., 2015; Mannheimer Zydney, Bathke, & Hasselbring, 2014); ‘prompting’ (Davenport & Johnston, 2015); ‘regulated learning strategies’ (Ness & Middleton, 2012); ‘teacher coaching’ (Duchaine, Jolivette, & Fredrick, 2011); and ‘use of math apps’ (Zhang, Trussell, Gallegos, & Asam, 2015).

In a review, Hart Barnett and Cleary (2015) found two types of interventions in studies of ‘inclusive classrooms’ (p. 172). One type involves classroom instruction (in this review, these are cognitive-guided instruction, schema-based instruction, cluster-based instruction, cognitive strategy instruction on math problem-solving, anchored instruction, simultaneous prompting procedure, explicit instruction, teacher coaching). The other type involves designed tasks (in this review, these are universal design for learning, techno-kinaesthetic visually based activities, math apps, problem-solving procedures). Thus, the subject of these studies, which highlight a variety of interventions in relation to inclusion, is on how these interventions can achieve meaningful engagement in mathematics classrooms.

The discourse of teaching for maximising opportunities in mathematics for all

This discourse construes inclusion by focusing on teaching to enable all students to participate. Even though their points of departure are different and the studies discuss different subjects, the common theme is teaching to maximise opportunities to learn. This is visible in the words used, such as ‘what constitutes successful mathematics pedagogy for all students’ (Gervasoni, Hunter, Bicknell, & Sexton, 2012, p. 193); ‘effective teaching practices and intervention strategies’ (Scherer et al., 2016, p. 634); ‘to develop the potentials of all children to the fullest possible extent’ (Nolte, 2013, p. 1225); ‘to reach all students in mathematics classrooms’ (Freiman, 2011, p. 161); ‘teaching mathematics to all children’ (Bengtsson, 2012, p. 17); ‘to achieve a quality education for all’ (Borges & César, 2013, p. 1666); ‘effective teaching practices in elementary mathematics classrooms’ (Martinez & Benedetti, 2011, p. 19); ‘a positive and an inclusive approach to the (dis)engagement situation’ (Bishop & Kalogeropoulos, 2015); ‘indicators of effective mathematics teaching’ (Griffin, League, Griffin & Bae, 2013, p. 9); and ‘implication of […] strategies learning and participation in mathematics lessons’ (Radford, Blatchford, & Webster, 2011, p. 627).

Six of the studies have students with disabilities as their subject when discussing effective teaching practices to maximise opportunities in mathematics education. This subject is visible in words such as ‘low-attaining students’ (Watson & De Geest, 2012, p. 213), ‘children with SEN’ (Radford, Bosanquet, Webster & Blatchford, 2015, p. 1), ‘LD’ (Mundia, 2010, p. 151), ‘emotional disturbance’ (Davis Skerbetz & Kostewicz, 2015, p. 14), ‘autism’ (Kurth & Mastergeorge, 2012, p. 45) and ‘deafness’ (Vosganoff, Paatsch & Toe, 2011, p. 70). Two of the studies focus more on teachers’ roles (Radford et al., 2015) and teachers’ attitudes (Whitty & Clarke, 2012). Another subject is collaboration between teachers and between teachers and parents. This is visible in the words ‘can show a general education and a special education teacher how to team teach’ in relation to ‘a merger between general education and special education’ (Dieker, Stephan & Smith, 2012). Nelson (2011) also highlights collaboration, saying, ‘Parents and teachers collaborate to achieve equity and quality in mathematics’ (p. 533).

The discourse valuing diversity

This discourse encompasses striving for inclusion in mathematics education by taking diversity as a point of departure in teaching. This is evident in these words: ‘the teacher is expected to be aware of the needs of each of their students and adapt the classroom environment and curriculum so that each child makes progress’ (Brown, 2015, p. 256). Hence, Brown highlights the importance of taking diversity as a point of departure in teaching. Krainer (2015, p. 185) also uses words valuing diversity in classrooms: ‘Diversity is more regarded as a strength and opportunity than a weakness’. Sullivan (2015b, p. 251) uses the words ‘it is not so much the method of grouping but the approach that teachers take to addressing diversity that ensures that the needs of all students are addressed’.

Summing up, we notice that interventions are common in DIMC. The interventions often have a specific type of SEN student in mind, such as students with LD. It is notable that only one of the studies in DIMC has a student perspective on inclusion (Kleve & Penne, 2016).

To conclude, the discourses within DIMS present an overall picture in which (in)equity and access to society are central in the meanings ascribed to inclusion. In operationalisation, identification of exclusion processes, valuing diversity and being vigilant to issues of equity from an ideological stance are central. The discourses within DIMC present an overall picture in which participation and inclusion in relation to exclusion in education are central in the meanings ascribed to inclusion. In the operationalisation of inclusion, mathematics teaching is in focus in the form of interventions, teaching to maximise opportunities for all and taking diversity as a point of departure.

4 Discussion

In this research, DA contributed on both a theoretical and methodological level to construe discourses and Discourses. This has provided insights into different foci present in research regarding inclusion in mathematics education today.

The aim of this research was to investigate discourses of inclusion in mathematics education research. Two Discourses were construed—the Discourse of inclusion in mathematics in society (DIMS) and the Discourse of mathematics in the classroom (DIMC). The focus in the DIMS is on the ideological meaning of inclusion, which was seen in the themes and subjects in the discourses (e.g., equity, valuing diversity, gender). In contrast, research studies in the DIMC focus on operationalisation, with little or no reflection on the meanings ascribed to the notion of inclusion in mathematics education. This was seen in the themes and subjects, and the use of words like ‘classroom’, ‘interventions’ and ‘effective teaching’. Accordingly, there is a focus on teaching for inclusion in the DIMC. Here a discrepancy within and between the DIMS and the DIMC is visible regarding the ascribed meanings and operationalisation of inclusion. In the DIMS, a political and core value stance is present, and many scholars commonly use words that mediate values connected to human rights and equity. In DIMC, the focus is on actions for inclusion, which is not strange since there is a focus on the operationalisation of inclusion in mathematics education. It is worth mentioning that very few studies address both equity and actions for inclusion. A possible explanation could be that researchers prefer to work within one Discourse, using familiar theoretical and methodological approaches, rather than developing new theoretical and methodological lenses that could bridge the two Discourses. Moreover, most studies in DIMC and some in DIMS refer to inclusion as something assumed to be already known and do not define it. This could also be an explanation for the research focus in either DIMS or DIMC; since inclusion is not explicitly discussed and defined, other issues might be foregrounded.

Returning to the first research question—What different meanings are ascribed to the notion of inclusion in mathematics education research?—the results show that in the DIMS, equity in mathematics education is the main discourse. Other discourses that make ascribed meanings of inclusion in DIMS visible are mathematics (not) for all and including (or excluding) SEM students. In the DIMC, two discourses describe meanings of inclusion—participation and inclusion in relation to exclusion. When comparing the discourses in DIMS and DIMC regarding ascribed meanings, equity dominates in DIMS but is not visible in DIMC. Instead, in DIMC, the word ‘participation’ seems to be essential, highlighting the importance of the students’ active involvement.

Returning to the second research question—How is the notion of inclusion operationalised and used in mathematics education research?—the results show that few studies in DIMS operationalise inclusion, and when they do, it is connected to doing and thinking of inclusion ideologically. Conversely, in DIMC, the results show prevailing discourses of operationalisation of inclusion, dominated by discourses of teaching interventions for mathematical engagement and teaching for maximising opportunities in mathematics for all. In both DIMS and DIMC, discourses of valuing diversity are construed within operationalisation. In addition, even though there are similarities in operationalisation, there is a difference in what valuing diversity is connected to. In DIMS, diversity is connected to societal issues, and in DIMC diversity is connected to students, schools and classrooms. Diversity and inclusion in relation to exclusion were visible in both the DIMS and in DIMC. However, even though the same wording is used, the underlying message is different since the discourses connect either to contexts in society or within the classroom. Similarly, mathematics for all is found in both DIMS and DIMC, but a closer look at the phrasing reveals differences. For instance, in DIMS, for all is used with the words ‘what all children actually means’ and ‘vulnerable groups and promote equity’. In DIMC, for all is used with ‘maximising opportunities to learn’ and ‘teaching’.

From the results, the question arises of whether consensus on the meaning of inclusion is possible, or even desirable, since it is used for different purposes? This is in line with what Skovsmose concludes in Figureiras, Healy, and Skovsmose (2016)—that we should not expect well-defined meanings of inclusion and should be ready to assume that inclusion can comprise a variety of meanings (p. 23). However, based on this assumption that inclusion has a variety of meanings in mathematics education, there is a need for scholars to define inclusion in each particular context. This is also important to consider since many different research fields, such as mathematics education and special education, use inclusion and mathematics within their paradigms.

What happens when inclusion is used to describe both a way of taking part in society and a way of teaching in mathematics classrooms? We can conclude from the results of this review that several different meanings are ascribed to the concept and that most often inclusion was used either ideologically or as a way of teaching, but rarely as both. Consequently, we can say that even though it is rare in research today, the notion of inclusion can be used in both DIMS and DIMC within the same study, where issues connected to inclusion in mathematics education are visible both on a societal level and within the classroom (e.g., Borges & César, 2013; Scherer et al., 2016). This is important, because it is obvious that DIMS and DIMC interconnect even though scholars seem to separate them. Valero (2010) refers to this type of gap when discussing the importance of doing interconnected research so as to be able to cover the breadth of social practices. The reason for the gap between DIMS and DIMC might be that the research paradigms regarding equality issues and interventions, respectively, are moving in different directions and the ideologues have set their imprint in practice aside, and the interventionists have set politics at play aside. In addition, there are differences in theoretical and methodological approaches. If the research on inclusion within mathematics education could build theoretical and methodological interconnections as Valero (2010) suggests, the field would gain insights and a greater understanding of inclusion in mathematics education in both DIMS and DIMC. That said, both Discourses are needed to promote a solid development of inclusion in mathematics education in society and in mathematics classrooms. At the societal level, a vision and a direction are needed, while in the classroom, the vision and direction need to be made visible and made to happen. Hence, inclusion in mathematics education needs to be discussed and solid connections between research developed on both levels. Otherwise, there is a risk of inclusion becoming a purely decorative slogan, and not really changing perspectives or values in the school.

In addition, the results revealed that only one of the studies had a student perspective of inclusion in mathematics education. This seems strange since the results show discourses of equity that imply the participation of students and consideration of their needs. This is a research gap and we need to bring students’ voices to the fore in future research.

A comparison of this literature review with others dealing with SEN and inclusion implicitly (Lewis & Fisher, 2016; Secher Schmidt 2015, 2016) shows this one has brought the notion of inclusion to the fore and contributes with insights on the use of inclusion in mathematics education research. It also illuminates issues that researchers need to address. Hence, this review builds on the prior reviews, putting SEN in the background and focusing on discourses of inclusion in mathematics education overall. It is important to point out, however, that this review does not claim to cover all inclusive research. I am aware that research has been conducted in the spirit of inclusion, though using other notions. This because of the vocabulary used in the specific research paradigm. For instance, research has been conducted within the field of bilingualism and mathematics (e.g., Domínguez, 2011; Planas, 2014; Takeuchi, 2018) and even though the notion of inclusion is not used, the studies aim to create opportunities to include bilingual students. Another example is research with low-achieving students (Ben-David Kolikant & Broza, 2011) with the aim of promoting learning. Even though the notion of inclusion is not used, the research and its aim would certainly fit into DIMC.

In summary, when inclusion is used as an ideology, its meanings and values are articulated. These values are a vision of inclusion. However, if not connected to operationalising inclusion, the vision may not have any real impact in classrooms. On the other hand, if inclusion is only used to refer to a way of teaching, it is hard to justify why we need to work with inclusion in mathematics education. Instead, to promote a sustainable development of inclusion, the two uses need to be connected; a hope is that inclusion can be used more in terms of nuances of a colour, originating from the same core, but with variations expressing its various aspects and connecting and interrelating the ideological and operational aspects of inclusion.

References

  1. Ainscow, M., Booth, T., Dyson, A., & Farrell, P. (2006). Improving schools, developing inclusion. London: Routledge.Google Scholar
  2. Aragón, O. R., Dovidio, J. F., & Graham, M. J. (2016). Colorblind and multicultural ideologies are associated with faculty adoption inclusive teaching practices. Journal of Diversity in Higher Education, 3(10), 1–15.Google Scholar
  3. Armstrong, A., Armstrong, D., & Spandagou, I. (2010). Inclusive education: International policy and practice. Los Angeles: Sage Publications.Google Scholar
  4. Artiles, A. J., Kozleski, E. B., Dorn, S., & Christensen, C. (2006). Learning in inclusive education research: Re-mediating theory and methods with a transformative agenda. Review of Research in Education, 30, 65–108.Google Scholar
  5. Askew, M. (2015). Diversity, inclusion and equity in mathematics classrooms: From individual problems to collective possibility. In A. Bishop, H. Tan, & T. N. Barkatsas (Eds.), Diversity in mathematics education: Towards inclusive practices (pp. 129–145). Cham: Springer International Publishing.Google Scholar
  6. Barnard-Brak, L., Wei, T., Schmidt, M., & Sheffield, R. (2014). Inclusivity in the classroom and international achievement in mathematics and science: An exploratory study. International Journal of Educational Reform, 23(2), 116–132.Google Scholar
  7. Basile, V., & Lopez, E. (2015). And still I see no changes: Enduring views of students of color in science and mathematics education policy reports. Science Education, 99(3), 519–548.Google Scholar
  8. Ben-David Kolikant, Y., & Broza, O. (2011). The effect of using a video clip presenting a contextual story on LAS’ mathematical discourse. Educational Studies in Mathematics, 76(1), 23–47.Google Scholar
  9. Bengtsson, M. (2012). Mathematics and multilingualism: Where immigrant pupils succeed. Acta Didacta Napocensia, 5(4), 17–24.Google Scholar
  10. Bishop, A. J., & Kalogeropoulos, P. (2015). (Dis)engagement and exclusion in mathematics classrooms: Values, labelling and stereotyping. In A. Bishop, H. Tan, & T. N. Barkatsas (Eds.), Diversity in mathematics education: Towards inclusive practices (pp. 193–217). Cham: Springer International Publishing.Google Scholar
  11. Borges, I., & César, M. (2013). Deaf students and mathematics learning: Promoting inclusion and participation. In B. Ubuz, Ç. Haser, & M. A. Mariotti (Eds.), CERME 8: Congress of the European Society for Research in Mathematics Education (pp. 1666–1675). Turkey: Congress of the European Society for Research in Mathematics Education.Google Scholar
  12. Bottage, B., Toland, M. D., Gassaway, L., Butler, M., Choo, S., Griffen, A. K., & Ma, X. (2015). Abstract impact of enhanced anchored instruction in inclusive math classrooms. Exceptional Children, 81(2), 158–175.Google Scholar
  13. Brown, L. (2015). Commentary for section 3: From diversity to practices: Addressing, redressing and taking action. In A. Bishop, H. Tan, & T. N. Barkatsas (Eds.), Diversity in mathematics education: Towards inclusive practices (pp. 255–259). Cham: Springer International Publishing.Google Scholar
  14. Cornwall, J., & Graham-Matheson, L. (2012). Leading on inclusion: Dilemmas, debates and new perspectives (1st ed.). London: Routledge.Google Scholar
  15. Cosier, M., Causton-Theoharis, J., & Theoharis, G. (2013). Does access matter? Time in general education and achievement for students with disabilities. Remedial and Special Education, 34(6), 323–332.Google Scholar
  16. Davenport, L. A., & Johnston, S. S. (2015). Using most-to-least prompting and contingent consequences to teach numeracy in inclusive early childhood classrooms. Topics in Early Childhood Special Education, 34(4), 250–261.Google Scholar
  17. Davis Skerbetz, M., & Kostewicz, D. E. (2015). Consequence choice and students with emotional and behavioural disabilities: Effects on academic engagement. Exceptionality, 23(1), 14–33.Google Scholar
  18. Diaz, J. D. (2013). Governing equality mathematics for all? European Education, 45(3), 35–50.Google Scholar
  19. Dieker, L., Stephan, M., & Smith, J. (2012). Secondary mathematics inclusion: Merging with special education. Mathematics Teaching in the Middle School, 18(5), 292–299.Google Scholar
  20. Domínguez, H. (2011). Using what matters to students in bilingual mathematics problems. Educational Studies in Mathematics, 76(3), 305–328.Google Scholar
  21. Duchaine, E. L., Jolivette, K., & Fredrick, L. D. (2011). The effect of teacher coaching with performance feedback on behaviour-specific praise in inclusion classrooms. Education and Treatment of Children, 34(2), 209–227.Google Scholar
  22. Eisenhart, M., Weis, L., Allen, C. D., Cipollone, K., Stich, A., & Dominguez, R. (2015). High school opportunities for STEM: Comparing inclusive STEM-focused and comprehensive high schools in two US cities. Journal of Research in Science Teaching, 52(6), 763–789.Google Scholar
  23. Feza, N. (2014). Inequities and lack of professionalisation of early childhood development practice hinder opportunities for mathematics stimulation and realisation of South African policy on quality education for all. International Journal of Inclusive Education, 18(9), 888–902.Google Scholar
  24. Figureiras, L., Healy, L., & Skovsmose, O. (2016). Difference, inclusion, and mathematics education: Launching a research agenda. International Journal of Studies in Mathematics Education, 9(3), 15–35.Google Scholar
  25. Fletcher, N. (2014). Incorporating the common core’s problem solving standard for mathematical practice into an early elementary inclusive classroom. Journal of Mathematics Education at Teachers College, 5(1), 41–46.Google Scholar
  26. Forgaz, H., Bleazby, J., & Sawatzki, C. (2015). Ethics and the challenges for inclusive mathematics teaching. In A. Bishop, H. Tan, & T. N. Barkatsas (Eds.), Diversity in mathematics education: Towards inclusive practices (pp. 147–165). Cham: Springer International Publishing.Google Scholar
  27. Foyn, T., Solomon, Y., & Braathe, H. (2018). Clever girls’ stories: The girl they call a nerd. Educational Studies in Mathematics, 98, 77–93.Google Scholar
  28. Freiman, V. (2011). Mathematically gifted students in inclusive settings: The example of New Brunswick, Canada. In B. Sriraman & K. Hwa Lee (Eds.), The elements of creativity and giftedness in mathematics (pp. 161–171). Rotterdam: Sense Publishers.Google Scholar
  29. Fuchs, L. S., Fuchs, D., Compton, D. L., Wehby, J., Schumacher, R. F., Gersten, R., & Jordan, N. C. (2015). Inclusion versus specialized intervention for very-low-performing students: What does access mean in an era of academic challenge? Exceptional Children, 81(2), 134–157.Google Scholar
  30. Garcia-Carrión, R., & Diez-Palomar, J. (2015). Learning communities: Pathway for educational success and social transformation through interactive groups in mathematics. European Educational Research Journal, 14(2), 151–166.Google Scholar
  31. Gee, J. P. (2014a). An introduction to discourse analysis: Theory and method. New York: Routledge.Google Scholar
  32. Gee, J. P. (2014b). How to do Discourse Analysis: A toolkit (2nd ed.). London: Routledge.Google Scholar
  33. Gervasoni, A., Hunter, R., Bicknell, B., & Sexton, M. (2012). Powerful pedagogical actions in mathematics education. In Perry et al. (Eds.), Research in mathematics education in Australasia 2008–2011 (pp. 193–218). Rotterdam: Sense Publishers.Google Scholar
  34. Graham-Matheson, L. (2012). How did we get here? A brief history of inclusion and special educational needs. In J. Cornwall & L. Graham-Matheson (Eds.), Leading on inclusion: Dilemmas, debates and new perspectives (1st ed., pp. 7–21). London: Routledge.Google Scholar
  35. Griffin, C. C., League, M. B., Griffin, V. L., & Bae, J. (2013). Discourse practices in inclusive elementary mathematics classrooms. Learning Disability Quarterly, 36(1), 9–20.Google Scholar
  36. Guðjónsdóttir, H., & Kristinsdóttir, J. V. (2011). Team teaching about mathematics for all: Collaborative self-study. In S. Schuck & P. Pereira (Eds.), What counts in teaching mathematics (pp. 29–44). Dordrecht: Springer.Google Scholar
  37. Hand, V. (2012). Seeing culture and power in mathematical learning: Toward a model of equitable instruction. Educational Studies in Mathematics, 80(1–2), 233–247.Google Scholar
  38. Hankes, J., Skoning, J., Fast, G., & Mason-Williams, L. (2013). Closing the math gap of native American students identified as learning disabled: Investigations in mathematics learning. The Research Council on Mathematics Learning, 5(3), 44–60.Google Scholar
  39. Hart Barnett, J. E., & Cleary, S. (2015). Review of evidence-based mathematics interventions for students with autism spectrum disorder. Education and Training in Autism and Developmental Disabilities, 50(2), 172–185.Google Scholar
  40. Healy, L., & Powell, A. B. (2013). Understanding and overcoming ‘disadvantage’ in learning mathematics. In M. A. K. Clements, A. Bishop, C. Keitel-Kreidt, J. Kilpatrick, & F. K. S. Leung (Eds.), Third international handbook of mathematics education (pp. 69–100). Dordrecht: Springer International Handbooks of Education 27.Google Scholar
  41. Heinrich, S., Knight, V., Collins, B. C., & Spriggs, A. D. (2016). Embedded simultaneous prompting procedure to teach STEM content to high school students with moderate disabilities in an inclusive setting. Education and Training and Developmental Disabilities, 51(1), 41–54.Google Scholar
  42. Hinton, V. M., Flores, M. M., Schweck, K., & Burton, M. E. (2016). The effects of a supplemental explicit counting intervention of preschool children. Preventing School Failure, 60(3), 183–193.Google Scholar
  43. Hunt, J. H., & Andreasen, J. B. (2011). Universal design for learning. Mathematics Teaching in the Middle School, 3(17), 166–172.Google Scholar
  44. Ing, M., Webb, N. M., Franke, M. L., Turrou, A. C., Wong, J., Shin, N., & Fernandez, C. (2015). Student participation in elementary mathematics classrooms: The missing link between teacher practices and student achievement? Educational Studies in Mathematics, 90(3), 341–356.Google Scholar
  45. Jitendra, A. K., & Star, J. R. (2011). Meeting the needs of students with learning disabilities in inclusive mathematics classrooms: The role of schema-based instruction on mathematical problem-solving. Theory Into Practice, 50(1), 12–19.Google Scholar
  46. Kleve, B., & Penne, S. (2016). Learning subjects in school: Being outsiders or insiders in the disciplinary discourses of mathematics and Language 1. International Journal of Educational Research, 78, 41–49.Google Scholar
  47. Krainer, K. (2015). Commentary for section 2: Inclusive practices in mathematics teaching – the need for noticing and producing relevant differences. In A. Bishop, H. Tan, & T. N. Barkatsas (Eds.), Diversity in mathematics education: Towards inclusive practices (pp. 185–189). Cham: Springer International Publishing.Google Scholar
  48. Kurth, J., & Mastergeorge, A. M. (2010). Individual education plan goals and services for adolescents with autism: Impact of age and educational setting. Journal of Special Education, 44(3), 146–160.Google Scholar
  49. Kurth, J., & Mastergeorge, A. M. (2012). Impact of setting and instructional context for adolescents with autism. The Journal of Special Education, 46(1), 36–48.Google Scholar
  50. Lambert, R. (2015). Constructing and resisting disability in mathematics classrooms: A case study exploring the impact of different pedagogies. Educational Studies in Mathematics, 89(1), 1–18.Google Scholar
  51. Lambert, R., & Stylianou, D. A. (2013). Posing cognitively demanding tasks to all students: Mathematics teaching in the middle school. National Council of Teachers of Mathematics, 18(8), 500–506.Google Scholar
  52. Leder, G., & Lubienski, S. (2015). Large-scale test data: Making the invisible visible. In A. Bishop, H. Tan, & T. N. Barkatsas (Eds.), Diversity in mathematics education: Towards inclusive practices (pp. 17–40). Cham: Springer International Publishing.Google Scholar
  53. Leikin, R. (2011). The education of mathematically gifted students: Some complexities and questions. The Mathematics Enthusiast, 8(1), 167–188.Google Scholar
  54. Lewis, K. E., & Fisher, M. B. (2016). Taking stock of 40 years of research on mathematical learning disability: Methodological issues and future directions. Journal for Research in Mathematics Education, 47(4), 338–371.Google Scholar
  55. Lindstrom, J. H. (2010). Mathematics assessment accommodations: Implications of differential boost for students with learning disabilities. Intervention in School and Clinic, 46(1), 5–12.Google Scholar
  56. Mannheimer Zydney, J., Bathke, A., & Hasselbring, T. S. (2014). Finding the optimal guidance for enhancing anchored instruction. Interactive Learning Environments, 22(5), 668–683.Google Scholar
  57. Martinez, E. M., & Benedetti, N. (2011). Learning mathematics in mainstream secondary schools: Experiences of students with Down’s syndrome. European Journal of Special Needs Education, 26(4), 531–540.Google Scholar
  58. Montague, M., Enders, C., & Dietz, S. (2011). Effects of cognitive strategy instruction on math problem solving of middle school students with learning disabilities. Learning Disability Quarterly, 34(4), 262–272.Google Scholar
  59. Moorehead, T., & Grillo, K. (2014). Celebrating the reality of inclusive STEM Education co-teaching in science and mathematics. Teaching Exceptional Children, 45(4), 50–57.Google Scholar
  60. Moscardini, L. (2014). Developing equitable elementary mathematics classrooms through teachers learning about children’s mathematical thinking: Cognitively guided instruction as an inclusive pedagogy. Teaching and Teacher Education, 43, 69–79.Google Scholar
  61. Mundia, L. (2010). Problems in learning mathematics: Comparison of Brunei junior high school students in classes with and without repeaters. Journal of Mathematics Research, 2(3), 150–160.Google Scholar
  62. Nelson, V. R. (2011). Parents and teachers collaborate to achieve equity and quality in mathematics: A case study. In B. Atweh, M. Graven, W. Secada, & P. Valero (Eds.), Mapping equity and quality in mathematics education (pp. 35–48). New York: Springer.Google Scholar
  63. Ness, B. M., & Middleton, M. J. (2012). A framework for implementing individualized self-regulated learning strategies in the classroom. Intervention in School and Clinic, 47(5), 267–275.Google Scholar
  64. Neumann, M. D. (2014). Preservice teachers’ understanding of gender equity in k–6 mathematics teaching. Teacher Education and Practice, 27(1), 90–117.Google Scholar
  65. Nilholm, C. (2007). Perspektiv på specialpedagogik (2nd ed.). Lund: Studentlitteratur.Google Scholar
  66. Nolte, M. (2013). Twice-exceptional children: Mathematically gifted children in primary schools with special needs. In B. Ubuz, Ç. Haser, & M. A. Mariotti (Eds.), CERME 8: Congress of the European Society for Research in Mathematics Education (pp. 1225–1234). Turkey: Congress of the European Society for Research in Mathematics Education.Google Scholar
  67. Pais, A. (2014). Economy: The absent centre of mathematics education. ZDM Mathematics Education, 46, 1085–1093.Google Scholar
  68. Pais, A., & Valero, P. (2011). Beyond disavowing the politics of equity and quality in mathematics education. In B. Atweh, M. Graven, W. Secada, & P. Valero (Eds.), Mapping equity and quality in mathematics education (pp. 35–48). New York: Springer.Google Scholar
  69. Panizzon, D. (2015). Impact of geographical location on student achievement: Unpacking the complexity of diversity. In A. Bishop, H. Tan, & T. N. Barkatsas (Eds.), Diversity in mathematics education: Towards inclusive practices (pp. 41–61). Cham: Springer International Publishing.Google Scholar
  70. Planas, N. (2014). One speaker, two languages: Learning opportunities in the mathematics classroom. Educational Studies in Mathematics, 87, 51–66.Google Scholar
  71. Powell, S. R. (2015). Connecting evidence-based practice with implementation opportunities in special education mathematics preparation. Intervention in School and Clinic 2015, 51(2), 90–96.Google Scholar
  72. Radford, J., Blatchford, P., & Webster, R. (2011). Opening up and closing down: How teachers and TAs manage turn-taking, topic and repair in mathematics lessons. Learning and Instruction, 21, 625–635.Google Scholar
  73. Radford, J., Bosanquet, P., Webster, R., & Blatchford, P. (2015). Scaffolding learning for independence: Clarifying teacher and teaching assistant roles for children with special educational needs. Learning and Instruction, 36, 1–10.Google Scholar
  74. Roos, H. (2013). Inclusive mathematics from a special education perspective: How can it be interpreted? In B. Ubuz, Ç. Haser, & M. A. Mariotti (Eds.), CERME 8: Congress of the European Society for Research in Mathematics Education (pp. 2860–2869). Turkey: Congress of the European Society for Research in Mathematics Education.Google Scholar
  75. Roos, H. (2015). Inclusion in mathematics in primary school: What can it be? Licentiate thesis. Växjö: Linnaeus University.Google Scholar
  76. Scherer, P., Beswick, K., DeBlois, L., Healy, L., & Moser Opotiz, E. (2016). Assistance of students with mathematical learning difficulties, how can research support practice? ZDM Mathematics Education, 48, 633–649.Google Scholar
  77. Schuelka, M. J. (2013). Excluding students with disabilities from the culture of achievement: The case of the TIMSS, PIRLS, and PISA. Journal of Education Policy, 28(2), 216–230.Google Scholar
  78. Secher Schmidt, M. C. (2015). Inklusionsbestræbelser i matematikundervisningen. En empirisk undersøkelse af matematiklærares klassledelse og elevers deltagelsesstrategier I folkeskolen. Diss. Copenhagen: Danish School of Education. Aarhus University.Google Scholar
  79. Secher Schmidt, M. C. (2016). Dyscalculia ≠ maths difficulties: An analysis of conflicting positions at a time that calls for inclusive practices. European Journal of Special Needs Education, 31(3), 407–421.Google Scholar
  80. Sheehy, K., Rix, J., Collins, J., Hall, K., Nind, M., & Wearmouth, J. (2009). A systematic review of whole class subject-based pedagogies with reported outcomes for the academic and social inclusion of pupils with special educational needs. In Research Evidence in Education Library. London: EPPI-Centre, Social Science Research Unit, Institute of Education.Google Scholar
  81. Solomon, Y. (2009). Mathematical literacy: Developing identities of inclusion. New York: Routledge.Google Scholar
  82. Straehler-Pohl, H., Fernández, S., Gellert, U., & Figueiras, L. (2014). School mathematics registers in a context of low academic expectations. Educational Studies in Mathematics, 85(2), 175–199.Google Scholar
  83. Straehler-Pohl, H., & Pais, A. (2013). To participate or not to participate? That is not the question! In B. Ubuz, Ç. Haser, & M. A. Mariotti (Eds.), CERME 8: Congress of the European Society for Research in Mathematics Education (pp. 1794–1803). Turkey: Congress of the European Society for Research in Mathematics Education.Google Scholar
  84. Sullivan, P. (2015a). The challenge of reporting research to inform the creation of inclusive mathematics learning. In A. Bishop, H. Tan, & T. N. Barkatsas (Eds.), Diversity in mathematics education—towards inclusive practices (pp. 3–15). Cham: Springer Publishing.Google Scholar
  85. Sullivan, P. (2015b). Maximising opportunities in mathematics for all students: Addressing within-school and within-class differences. In A. Bishop, H. Tan, & T. N. Barkatsas (Eds.), Diversity in mathematics education—towards inclusive practices (pp. 239–253). Cham: Springer publishing.Google Scholar
  86. Sunardi, G., Anwar, M., & Andayani, T. R. (2016). The effect of cluster-based instruction on mathematic achievement in inclusive schools. International Journal of Special Education, 31(1), 78–87.Google Scholar
  87. Tabur, C. (2014). Calculator programming engages visual and kinesthetic learners. The Mathematics Teacher: An Official Journal of the National Council of Teachers of Mathematics, 107(8), 624–629.Google Scholar
  88. Takeuchi, M. A. (2018). Power and identity in immigrant parents’ involvement in early years mathematics learning. Educational Studies in Mathematics, 97(1), 39–53.Google Scholar
  89. Tan, H. (2015). Gender and technology: A case of graphics calculators in the Singaporean mathematics curriculum context. In A. Bishop, H. Tan, & T. N. Barkatsas (Eds.), Diversity in mathematics education—Towards inclusive practices (pp. 81–102). Charm: Springer Publishing.Google Scholar
  90. Tennant, G., & Foley, C. (2014). Inclusive approaches to learning and teaching mathematics. In R. Hyde & J.-A. Edwards (Eds.), Mentoring mathematics teachers. Supporting and inspiring pre-service and newly qualified teachers (pp. 77–92). London: Routledge.Google Scholar
  91. UNESCO. (2009). Policy guidelines on inclusion in education. Paris: UNESCO.Google Scholar
  92. Valero, P. (2010). Mathematics education as a network of social practices. In V. Durand-Gueier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education (pp. LIV–LXXX). Lyon: Institut National de Recherche Pedagogique.Google Scholar
  93. Valero, P. (2012). Preface to a socio-political look at equity in the school organization of mathematics. In H. Forgasz & F. Rivera (Eds.), Towards equity in mathematics education, advances in mathematics education (pp. 369–371). Berlin, Heidelberg: Springer.Google Scholar
  94. Vosganoff, D., Paatsch, L. E., & Toe, D. M. (2011). The mathematical and science skills of students who are deaf or hard of hearing educated in inclusive settings. Deafness & Education International, 13(2), 70–88.Google Scholar
  95. Watson, A., & De Geest, E. (2012). Learning coherent mathematics through sequences of micro tasks: Making a difference for secondary learners. International Journal of Science and Mathematics Education, 10, 213–235.Google Scholar
  96. Whitty, E., & Clarke, M. (2012). Irish mathematics teachers’ attitudes towards inclusion. European Journal of Special Needs Education, 27(2), 237–256.Google Scholar
  97. Zhang, D., & Xin, Y. P. (2012). A follow-up meta-analysis for word-problem-solving interventions for students with mathematics difficulties. Journal of Educational Research, 105(5), 303–318.Google Scholar
  98. Zhang, M., Trussell, R. P., Gallegos, B., & Asam, R. R. (2015). Using math apps for improving student learning: An exploratory study in an inclusive fourth grade classroom. Tech Trends, 59(2), 32–39.Google Scholar

Copyright information

© The Author(s) 2018
corrected publication November/2018

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Faculty of Technology, Department of MathematicsLinnaeus UniversityVäxjöSweden

Personalised recommendations