3. Research Results
Based on processed written stories from mathematics teachers, we identified their intuitive inclination toward the social model of perception of disability or other types of disability (for instance, medical). Teachers try to overcome barriers, find ways to get closer to the pupils, prepare an environment for learning mathematics, make mathematical content accessible, and individualize teaching based on the specific needs of individual pupils.
Within the research, we identified five categories related to supportive factors in inclusive mathematics education from mathematics teachers’ perspectives. We will look at them in more detail in the following text.
3.1. Identifying the Pupil’s/Student’s Internal Resources in Mathematics Education
This category presents the pupil’s positive personal reserves, the identification of which is essential for learning in general. Qualities such as goal-orientedness, ambition, willpower, activity, industriousness, diligence, speed, promptness, perseverance, creativity, showing interest, and courage to apply and ask questions have emerged as significant positive resources in pupils’ mastery of mathematics. It was important that teachers were able to recognize these as beneficial factors for the child themselves. If teachers identified positive skills in cognitive functions, such as good long-term, mechanical memory, the ability to concentrate, and the ability to apply learned procedures, they saw this as a mainstay for children with difficulties or for children with increased needs for support in learning mathematics. The pupil’s well-developed social-emotional characteristics also emerged as significantly helpful. For example, teachers noted pupils’ willingness to help, emotional sensitivity and social responsiveness, willingness to integrate into the classroom collective, ability to show leadership in a group, and ability to communicate their opinions and express their needs assertively.
Another interesting factor mentioned by the teachers was the specific talents of the pupils, for example, artistic, musical, and sporting talents, which contributed to a positive self-image of the pupil himself/herself. In the following, we provide examples from the stories of mathematics teachers falling under this category:
1.13. Marek is very ambitious and wants to achieve excellent results. 1.33. Marek is very active during lessons. 2.24. Since he likes to paint and paints very nicely, I asked him to paint three pictures for the mathematics classroom according to his imagination. 2.27. Many people have also commissioned him to paint the whole family according to the photograph. They were blown away by the result. The pupil was getting positive feedback on his artistic ability. 3.80. He was also struggling in other lessons, but we were able to work together as a team to support the pupil in his artistic talent; we created a space for him on more than one occasion by organizing a concert for the whole school where he played the drums himself. He was a star for a while then, and we were all proud of him. 8.14. He excelled in his subjects in that he was able to remember the material he had already learned permanently compared with his classmates. 8.16. In mathematics, based on his excellent mechanical memory, he was able to solve more complex mathematical problems. 8.17. In problems for which he knew the procedure, he was faster than his classmates. 9.6. The pupil was very diligent. 9.9. The pupil did not seek relief on his own and wanted to know everything like his peers in the class. 9.11. A very nice, polite, hardworking, and sensitive girl popular in the group. 9.12. She got along better with younger children, as she was a little behind in development. 9.13. She got a B or an A for the enormous effort she always put in and tried to manage everything like the other pupils. 9.23. Initiative, kindness, willingness, to help teachers or classmates. 11.15. Good at counting from memory, which he had apparently mastered before the accident. 11.30. However, he quickly established very good relationships with his classmates, mainly through sports. 12.10. The pupil’s strengths include purposefulness, perseverance, tenacity, and a willingness to fit in with the class. 14.26. Popular and involved in the boys’ group due to his sporting talents. 15.18. When unclear during class, has no problem speaking up and asking questions. If we work in groups, he shows himself as a leader. When tested on a lesson, if she does not master the material, she admits that she has not learned. 15.21. Annie is very hardworking. She is quiet during the lesson, but if there is a debate, she can express her opinion. 15.23. She likes to design her own clothes, which is interesting and sometimes overlooked. 16.26. All I know about art is that she is good at it and creative.
3.2. Perceptive Approach of the Mathematics Teacher toward the Pupil/Student
We identified the following supportive factors on the part of mathematics teachers as key in this category: responsiveness in their approach to pupils, use of a one-to-one approach, and building a secure teacher-pupil relationship. Teachers also built on pupils’ specific talents seemingly unrelated to mathematics teaching (for example, a pupil painting pictures for the mathematics classroom), recognized pupils’ strengths and positive reserves, and supported pupils’ intrinsic motivation. On the other hand, they were perceptive and sensitive to the specificities of some pupils, able to identify, understand, and respect their particular expressions. For children with disabilities, there were problems based primarily on their diagnosis, such as obsessive-compulsive behavior and pedantry in a child with Asperger’s syndrome. These manifestations were also evident in the mathematics teaching itself, where, for example, the pupil strictly demanded consistency in the teacher’s expression, the use of precise mathematical concepts, and rigid adherence to the conditions of problem solvability. It was important for the teacher to understand what was causing such behavior. It was not a manifestation of the teacher’s insolent behavior but compensation for his anxiety resulting from his primary diagnosis.
A human, responsive, sensitive, respectful, friendly, and creative approach on the part of the teacher helped to overcome the difficulties and barriers in teaching mathematics to individual pupils. Participatory observation of the pupil’s behavior and learning style proved crucial in order to get to know the pupil better, understand his/her specific expressions, recognize early signs of possible problems, and prevent the situation from getting worse. Teachers also responded to the current mood of the whole class, not only to the content of the curriculum. In order to facilitate the processes of inclusive mathematics teaching, it is crucial that the teacher, in addition to taking into account the content of the subject taught itself, also take into account the broader context relating to individual pupils and the dynamics of classroom relationships. In the following, we provide examples of stories from mathematics teachers falling into this category:
2.29. We encouraged pupil creativity through a buddy approach and gained pupil confidence and interest in coming to school. 2.37. When explaining, I naturally notice and observe his behavior, and I can already recognize signs that he does not understand. 2.42. I alternate methods depending on the current mood in the classroom and the content of the curriculum. 2.47. I organize many competitions in which clever pupils measure their mathematical and science skills, and pupils who are not fond of mathematics help me organize them. They often find it motivating and discover that math can be fun too and is not just about formulas in the way many people prefer. 5.7. Based on our observations, we recommended that parents go for a rediagnosis, where our assumptions that the child did not just have an attention deficit disorder were confirmed. 8.11. When the pupil was negative, it was often necessary to positively motivate and redirect them. 8.18. He was more comfortable with activities where he was not distracted and could work independently. 8.25. Over time, after frequent classroom sessions, there was a change, on the part of his classmates, towards understanding a classmate with a disability and on his part to improve his respect for the needs of others. 16.20. In the meantime, however, I have attended online webinars on the topic of integrated pupils, Asperger’s Syndrome, etc. It has helped me a lot to open my eyes, to possibly find my lost energy again, to put aside my anger at Martin and his parents, and to change my attitude towards Martin. Martin’s change was radical. During the last month of the school year, I gave him individual attention, explained the material over breaks, and had him write simple remedial papers, his grades improved a lot, and he was willing to go to the blackboard. It was good. 2.15. In his maths workbook I discovered drawings of people holding knives, a person’s heart is pierced, and various depressing pictures. 2.16. At the same time during the week I was contacted by the Slovak language teacher who had me read the pupil’s essay work. In it, he described a favorite book that described committing suicide with his best friend. 8.21. Individual problems that arose were dealt with as soon as possible so that there were no misunderstandings, and the pupil was not negative and enjoyed coming to school. 3.52. In mathematics, the goal was not so much to get a straight A as to take responsibility for one’s own growth. I am a facilitator of classroom processes. 3.40. Fortunately, there was no significant frustration in the sense of having a lot of stress and dislike of math. 4.13. The student has improved in logical thinking and in working in graphing software during the first year as he is studying computer graphics. I also notice an improvement in his independence in his work. 4.29. He definitely needs to be checked continuously as he loses concentration quickly, sometimes starts well, and suddenly stops counting after a few intermediate calculations. Therefore, he then needs to be kick-started again. 2.40. I could see the signs of stress in the examples that the pupils had to solve on the blackboard. He works best when he is confident that he will not go to the blackboard. 3.33. I very much avoided any exposure to stress or answering him in front of the blackboard. 3.20. Classroom work was therefore primarily focused on the collective and relationships, which later proved crucial because by Year 8 and 9 Alex was a full part of the class, regardless of the fact that he was falling behind in his learning.
3.3. Modifying Conditions in Inclusive Mathematics Education and Implementing Accomodations for the Pupil/Student
In the context of this category, we identified modifications of teachers’ approaches to inclusive mathematics teaching in the following areas: the spatial arrangement of the classroom; innovative and alternative ways of accessing the material; and reviewing knowledge. To promote inclusion in mathematics teaching, mathematics teachers applied various spatial modifications in the classroom, for example, placing school desks or making changes to the seating chart, etc. Teachers also allowed pupils to co-create the seating chart so that they themselves could learn well. The methods of testing and reviewing knowledge varied according to the needs of individual students. They often chose an individualized form of examination. For example, if a pupil had difficulty with an oral examination, they allowed them to respond in writing. More difficult mathematical tasks were analyzed and explained in more detail by teachers for selected pupils. Unnecessary failures and setbacks were prevented by allowing pupils to revise and correct written assignments and tests.
Some teachers also chose unconventional ways of marking; for example. they did not give a mark on a paper with many errors but only wrote explanatory comments. They reduced the number of assessments during the school year. Tests were allowed to be written not only in class directly with classmates but also outside the classroom with an assistant or with another professional staff member, often with more time or in a simplified version of the content. Mathematical examples, both in class and on the examinations, were differentiated according to pupils’ abilities. Often, additional in-depth explanations of some of the more difficult problems were chosen for some pupils. In mathematics lessons, teachers encouraged peer learning-mutual support between classmates. One teacher even attempted to introduce peer learning for younger pupils from pupils in the upper years.
Teachers also used a variety of approaches to externally motivate pupils—for example, facilitative-reflective learning. Technical modifications in the classroom were also approached; for example, pupils could use computers to take notes or copy notes from the internet to record explanations of the material for additional study at home. Teachers used interactive whiteboards, various computer programs, or computer applications. There was also a need to modify access to new knowledge through interactive internet platforms, for example, the use of EduPage, a school-based platform for school and family communication. Increased monitoring of some pupils’ progress during lessons was required by the teacher to capture their uncertainty with the curriculum. For some pupils, it was also necessary to modify the learning materials themselves, for example, to increase the font size, leave only one example on a page, leave more space for completing the assignment, etc. Some of the teaching texts had to be reworked into a less extensive form with specific sample examples and solution procedures. It was also advisable to color-code the teaching material for better orientation of the pupil. It was necessary to make the material more concrete—to link it to examples from everyday life (for example, working with money models). Teachers also considered the provision of one-to-one consultations outside the classroom to be an important support in the teaching of mathematics. Teachers also took the approach of creating their own support tools, such as help summary notes and guides, tables, mind maps, etc. Teachers were forced to reduce some very challenging topics for selected pupils—sometimes even omitting them altogether or not assessing them for a given pupil. In the following, we give examples of stories from mathematics teachers falling into this category:
1.24. In mathematics lessons, pupils do not sit at desks of two but may move their desks at will. 2.31. He did not want to answer orally, and the teachers accepted this and only tested him in writing. 2.36. There was a problem in geometry, especially in construction problems and in combinatorics, where the problems had to be analyzed verbally in more detail. We solved this problem by having him gradually do only the write-ups of the problem, then I would sit at the desk with him for a mathematical chat and assess the correct problem-solving procedures with a motivational mark. 2.45. In the case of a failure, the pupil could correct the write-ups. 3.37. He also sat alone for some of the lessons, but that was rather dysfunctional; it was very good when he sat next to someone who could support him and guide him. 3.61. I also developed a lot of intergenerational learning, so we did lessons here and there with other classes where they had the opportunity to teach the younger pupils as well. 10.7. He was helped by a classmate and a friend. 12.20. The pupil tries to fit in with the group. Her classmates also help her with her learning, either in moving around the school or at school events; the class really tries, but such pupils have their own world of topics and problems, and they get along better with young people with similar problems 3.62. I gradually individualized the assessment by taking the scale very loosely, marking by eye at first as needed, then later on, when there were more mistakes, I preferred not even to mark, just to write comments. 3.63. For Alex, it was enough to have 2–3 marks; he didn’t need to have everything marked. 3.64. I differentiated the examples if necessary or didn’t mark them if they were difficult. 4.7. In languages, he got easier tests, mostly in the form of make-ups; in math and vocational subjects, the teacher would come by more times and possibly explain or help him solve something. 4.10. He gets the grades he needs, but individual problems are usually taken into account. For example, if they are assessed in a subject by writing notes, pupils with dyslexia and dysgraphia may have them written on a computer or copied from the internet. 5.24. They always write notes outside of class with an assistant. 5.25. They are not reduced in content; the pupil has more time to work them out. 6.7. The pupil is graded with marks and has more time set aside for written work. 7.9. Due to this, he has had, for example, extended times for writing matriculation tests and so on. 7.23. However, I have tried to make more use of the dialogic form of explanation of the curriculum in his classroom. Sometimes he would even record the lessons so that he could come back to them at home—he would not be able to take notes effectively. 7.24. If I needed to test, I modified the assignments for Lukas so that they were concise; he had them printed on A3 and had more space in them. 7.25. He was given time compensation. 8.22. For the pupil, as a tutor, I would produce teaching texts so that the material was not extensive, with sample examples and solution procedures. The problems were color coded for better orientation in the text. The pupil was also given the opportunity to clarify the material by tutoring if necessary. 9.5. When testing and writing revision work, the pupil had more time to work it out and tended to be given oral feedback. 9.10. The real-life examples she was able to imagine were very helpful. 11.10. Since a reduction of the curriculum was not necessary, we adapted the way we made new knowledge available—for example, notes on EduPage, sample assignments, and opportunities for individual consultation. 11.11. Furthermore, when testing the pupil, we modified the wording of assignments, took into account the need for more time, did not take into account inaccurate drawings, etc. 11.16. When guided, he could work calmly on the blackboard and write in the notebook. 11.18. While sitting at the front, he tried to keep up with the pace of the work with the class. 11.24. He was given individual counseling many times. In tests, he had simply worded assignments, fewer problems, and more time to work them out. 14.16. Connecting mathematics with opinion and practice. 14.17. Counting with money. 14.18. Creating and using his own tools and pull-ups. 14.19. Using movement and experiential learning. 14.22. Using the interactive whiteboard—and tutorials. 1.23. According to the statement of the pedagogical-psychological counseling office, the pupil should not be evaluated in this subject unit. 2.30. As the problem was caught early, the pupil was assessed on the half-term report card like the other children except for the oral answers. 2.31. He did not want to answer orally, and the teachers accepted this and only tested him in writing. 12.8. We have had to significantly reduce thematic units, for example, functions, and omit some structural geometry altogether. 12.11. The pupil was assessed with a mark of 2 (in Slovakia, the grading system in primary and secondary schools is determined on a scale of 1 to 5, with 1 being the best rating and 5 being the worst (rated as insufficient)). Secondary school mathematics is difficult; there are many topics that are unmanageable for such children; certainly, geometry is included: both planimetry and stereometry—where there are many lines, the blind person gets lost, in secondary school these topics are unmanageable. 3.42. We worked a lot in the classroom on accepting and setting our own limits, the challenge ticket, where pupils set themselves a target, an assessment they wanted to achieve, and if they got close to it, they were happy. 4.25. The assignment always needs explaining in more detail and, most importantly, without disturbing fellow pupils. 6.19. He has the opportunity for individual consultations if necessary. 3.51. Later on, I also worked more often with group work. The essence of the method of work, which I increasingly refined, was facilitative-reflective learning built on freedom and responsibility. I often reflected with the pupils on their work together in a circle; we met every morning in the morning circle. We went on a dozen field trips, camps, and outdoor schools together. We also went somewhere together 2–3 times a year. Building relationships in the classroom was my priority. 2.38. Of course, I would explain the lesson to him again on the blackboard so that I would not draw the attention of all my classmates to the problem. 3.81. Teachers, following my guidance, were able to step back from the subject requirements and require less rather than requiring more so that the student would not fail the subject.
3.4. School-Family Cooperation
In the context of teaching mathematics, teachers highlighted the important aspects of communication and cooperation with the student’s family. It was important to share information with the pupil’s parents/guardians about how the pupil was performing in school. It proved helpful to come to some consensus with parents on how to support the pupil. In addition to face-to-face interviews, teachers also used telephone or online consultations when communicating with parents. Parents were contacted not only in cases of problems but also in cases of successes, which shows an effort for friendly contact from the teacher to the family. Contact with the family proved to be optimal to conduct on a regular basis, constantly inviting parents to communicate.
Teachers reported that it was important to remind parents of the need for regular attendance at school so that the pupil does not unnecessarily skip new material and to take measures to improve the pupil’s homework. Teachers also communicated as beneficial consultations for parents in the presence of not only the teacher but also other professionals from the school support team, such as a psychologist or a therapeutic educator, which were aimed at addressing the pupil’s overall situation. During the consultations, teachers were advised to map out the possibilities of supporting the pupil in his/her whole ecosystem. In some cases, only one parent communicated better with the teacher. In those cases, the teachers accepted him/her as a supportive communication partner between the school and the pupil’s family.
It was found to be ideal if parents could communicate with other members of the support team at the school in addition to the teacher. Openness and cooperation from the pupil’s parents with the teacher proved to be essential for improving the pupil’s behavior and overall functioning at school. Another effective way of teacher-parent consultation was when the pupil himself was invited to join in. Not all teachers used this method, but from our point of view, the voice and presence of the pupil when making decisions about their learning is significant. Not only supporting the pupil himself but also encouraging his parents and pointing out his progress, however small, proved to be important. The following are examples of stories from mathematics teachers falling into this category:
2.11. I was informed by the child’s mother about the pupil’s disinterest and refusal to come to school. 2.1. In the mathematics workbook I discovered drawings of people with a knife in their hand, a person’s heart pierced through, and various depressing pictures. 2.2. At the same time during the week, I was contacted by the Slovak language teacher, who gave me the pupil’s essay work to read. In it, he described a favorite book that described committing suicide with his best friend. 2.3. I contacted the pupil’s mother, and she confirmed that he also painted depressing pictures at home (I had not yet stated that the pupil had attended the Art Department of the Primary School for 7 years). 2.18. I had the mum read the essay work, drawing attention to the pictures in the exercise books. 2.19. We agreed to see a psychologist, and I informed colleagues at school again. 2.51. In case of any problems but also praise, I contact parents by phone or via Edupage. I prefer a personal conversation. Therefore, all parents have my telephone number. 3.21. The family was in regular contact with me as the class teacher. 3.23. It was necessary to call them to the school on an ongoing basis. 3.24. To draw attention to the pupil’s attendance at school, unnecessary absences, or very poor homework. 3.77. However, the father communicated more with me most of the time. 5.26. Parents cooperate with teachers and the assigned aide. 5.27. They are cooperative in problem-solving. 5.28. They are open to suggestions from the special education teacher on how to improve the student’s behavior and overall functioning in school. Family support—positive communication. 6.20. Parents are cooperative with the school. 7.29. Otherwise, what I like about our school is that we provide a teacher-parent-student triad consultation; this student also used it. 8.20. The student was not educated by parents but by relatives who cooperated with the school in an exemplary manner. 9.20–9.22. The parents did not expect great achievements; they knew their child and were grateful for any praise that was given to the pupil. 11.27. At the parent-teacher association, both the mother and pupil Z were present, and the teacher told the mother about the pupil.
3.5. Support Mechanisms of the School as an Institution in the Context of Inclusive Mathematics Education
Identifying the internal resources of the pupil himself, the approach of the mathematics teacher, the collaboration with parents, and the modifying conditions of the inclusive school climate have emerged as key supporting factors in inclusive mathematics education. However, teachers could not imagine successful inclusive mathematics education without creating an overall inclusive school climate. For example, they utilized the services of the school’s special educator for the individual student during and outside of school hours. Teachers also cited support from outside counseling services as important. Teachers found it helpful to be able to approach their colleagues and/or school management with confidence. A supporting aspect was the teachers’ communication with each other about specific pupils, which was friendly and reciprocal.
Teachers also identified respectful relationships with pupils as helpful, and if the school as a whole was set up in a supportive way towards meeting pupils’ individual needs. In addition, to support for learning itself, comprehensive support was not neglected in terms of improving classroom relationships, which teachers considered to be an important factor in the school success of individual pupils. They tried to convey a sense of equality to all pupils, not to define them in terms of difference, otherness, or specialness, but to see each of them as unique individuals with their own specific needs. Everyone needs some form of support, not just pupils with SEN status. Creating an atmosphere where every pupil is supported has proved important. An open door and participation policy were communicated by the school. Parents were invited to step in and get involved in the school in a variety of non-traditional ways, not just being invited into the school when something needed to be addressed.
The inclusive school consciously worked to build a school support team as a service for pupils, teachers, and parents. Emphasis was placed on the early detection of emerging problems, and this was completed through teamwork. The school’s overall setting towards pupils with SEN status, but also pupils with increased support needs in some specific areas, also proved important. Instead of pressure for exclusion from school, the available support mechanisms were activated. In the following, we provide examples from the narratives of mathematics teachers falling under this category:
9.26. She worked on her own or with the teacher’s help in class; if she could not keep up, she worked out the examples at home or with the special education teacher. 7.26. If she was still not successful in the tests, I tested her individually after class verbally and in the presence of the school psychologist. 8.87. The pupil was allowed to sit as close as possible to the teacher and as far away from the window as recommended by the Centre for Educational Psychological Counselling and Prevention for sufficient concentration in class. 1.8. In the event of problems in the educational process, he could refer to the class teacher, the educational counselor, and the school management. 1.16. Teachers discuss, consult with each other, and find the right strategies to teach Marek. 3.25. A lot of consultation has taken place. 1.36. There is a friendly, communicative atmosphere in the school. The relationships between teachers and pupils are equal. 2.53. I think we are a very open school for children, and there is a rather friendly atmosphere in the teacher-pupil relationship. 3.13. We are pupil-friendly. 3.14. He had sufficient support mechanisms set up, many of them directly supporting the family environment, better relationships, and reflection on the mother and son relationship. 3.67. I did not distinguish whether someone was integrated or not. 3.69. Alex had no outward specifics of support because all pupils had them. 3.76. I once managed to talk mum into coming to mentor the class in making a fish ray. She created a life-size Raja with the children, which was a magnificent piece of work. I was very happy that mom was involved and had the opportunity to show the kids her talent as well as support her son. 5.35. The school is inclusive—it has a special education teacher, a psychologist, and teaching assistants. 8.6. The pupil was supported by a teaching assistant, educational advisor, and the school’s special education teacher in the teaching process. 8.21. Individual issues that arose were dealt with as early as possible so that there were no misunderstandings and the pupil was not negatively adjusted and enjoyed coming to school. 12.9. The school did not put pressure on the pupil to drop out rather the opposite, it tried to help her to manage her studies. 14.30. Most of the staff had their hearts in the right place and tried to teach and support such children
4. Discussion
Stories from mathematics teachers in the form of texts provided us with a lot of material and were the subject of reflection on how mathematics teachers understand inclusive mathematics education. The research data collected was extensive, and through qualitative analysis, we abstracted 5 main categories—themes that described the supporting factors of inclusive mathematics education from mathematics teachers’ perspectives. Teachers provided information about their pupils with any form of disability (health, social, or other) or an increased need for support and about their situations in mathematics education and inclusion. Within some of the categories, we also found similar findings in related scholarly sources.
In the context of category 1, “Identifying the pupil’s/student’s internal resources in mathematics education”, teachers communicated the importance of identifying positive personal reserves in individual students that they could then build upon in inclusive mathematics education. They cited two key areas on which they could build, namely cognitive and social-emotional skills. Identifying these proved crucial throughout the process. Similar to Tan, Padilla, and Lambert [
1], we also focused on whether mathematics teachers draw on, for example, the pupils’ personalities, their courage, creativity, ingenuity, unique perspectives, and their different or specific ways of knowing in contexts of teaching and learning mathematics. DeVries, Voßb, and Gebhardt [
43] found that students with special needs have lower levels of academic self-esteem, social inclusion, and emotional inclusion than their typically developing peers. However, these differences narrow between grades 6 and 7 in inclusive schools.
In the context of category 2, “Perceptive approach of the mathematics teacher toward the pupil/student” in our research, teachers mainly emphasized responsiveness in approaching the pupil, building a secure relationship, and using an individual approach in terms of knowing the pupil. Hugo & Hedegaard [
25] state that, from a student perspective, receptive, affirming, and understanding teachers are key to promoting inclusion. The authors place emphasis on the relationships between teachers and students and call this ability relational competence. During the interviews, DeSimone and Parmar [
27] identified the importance of the mathematics teacher’s personal responsibility to the students in inclusive mathematics education. They described, for example, an interview with a New York teacher who believed she was the primary person responsible for her students and their grades. McDonough & Clarke [
32] consider that one of the characteristics of effective teachers practicing effective mathematics teaching is showing pride and joy in the achievements of individual students, which also strengthens their relationships with each other.
Our research shows that teacher sensitivity in the context of students’ expressions and their specificities in terms of not only their problems but also the way they learn is an important aspect of inclusive mathematics teaching. Rouse [
23] makes a similar point when he says that “knowing” means knowing not only the specifics of different disadvantages but also the ways in which individual children learn. Our research revealed the importance of teachers understanding the causes of problem behavior in pupils, as highlighted by Kováčová et al. [
24]. The author states that problem behavior can be exacerbated by unprepared teachers.
An interesting experience in our research was shared with us by one participant, a mathematics teacher, who only realized that she had to completely change her approach to her pupil after receiving specialist training on autism. She literally wrote: “I managed to find the lost energy and put my anger at Martin aside”. The teacher in question communicated to us how the knowledge she had gained about the specifics of autism had changed the way she viewed the pupil in question. The consequence was also a radical change on the part of the pupil. The teacher writes: “He improved a lot, he was willing to go to the blackboard, which he refused to do before, it was good”. Our research thus highlights the importance of considering a wider context than that contained in the subject of mathematics alone.
Similarly, Hugo & Hedegaard [
25] found a positive impact from teaching that also focused on the needs and abilities of the student, not just the content of the subject itself. They also see teaching as a form of participation and a focus on the individual learner, not just as a focus on the topic being covered alone. This is confirmed by the teachers’ statements in our research, where they abandoned their role as just a mathematics teacher and redirected their attention to more important matters concerning the learner himself. For example, the teacher drew attention to unusually depressing drawing content in the workbook, which indicated a deterioration in the pupil’s emotional state. This is in line with Tan and Kastberg [
4], who recommend moving from a medical model to a social model of understanding disability.
In the context of Category 3, “Modifying conditions in inclusive mathematics education and implementing accommodations for the pupil/student”, we collected a variety of data that included modifications and variations in how teachers make mathematics content accessible to all students without discrimination. Many of the practices they used, created, and innovated in their teaching overlapped with the characteristics of effective teachers articulated by McDonough and Clarke [
32]. We found agreement, for example, in the use of visual aids, different organizational styles and teaching approaches, assessment methods, and the setting of realistic goals. In our research, consistent with the authors, teachers used a reflective approach in their teaching—i.e., reflecting on the flow of the lesson, whether all students understood the content, whether it could be taught in other ways, etc. Our research has also highlighted the importance of preventing student failure and setbacks. Pupils were invited to co-create what was happening, for example, by designing the spatial layout of the classroom, monitoring their progress, etc. Kobelt, Neuhaus, and Refle [
28] emphasize the teacher’s ability to invite pupils to co-construct and participate in their learning. Teachers tried to lead pupils out of the passive role of information receivers and towards active participation.
In our research, we also observed teachers’ use of various modifications and concessions in their teaching based on students’ IEPs (for example, simplifying texts, not assessing certain topics, reducing the curriculum, extending the time for completing assignments, modifying tests, etc.). Pupils’ mathematical understanding, for example, with LD, can be supported by encouraging these pupils to “discuss, critique, explain and, if necessary, justify their interpretations and solutions” [
27]. According to Faragher, Clarke, and Hill [
16], the teaching strategies and techniques needed for selected students are applicable to all students. For example, the teacher re-explained the material once more and more explicitly for the sake of one student, but several other students benefited from this repetition, according to the teacher. The use of familiar and effective teaching strategies, such as differentiated instruction graded according to students’ abilities, peer teaching, facilitative-reflective learning, intergenerational learning, experiential learning, individual consultations, model tasks, and group learning, also emerged in the mathematics teachers’ narratives in our research.
Among technological devices, teachers used various applications, interactive whiteboards, and specialized teaching programs. Faragher, Clarke, and Hill [
16] talk about the positive role of using technology-enhanced learning in mathematics. The positive aspects of the meaningful use of technology in teaching in the preparation of future mathematics teachers are also discussed in several pieces of research, for example [
35,
36].
In the context of category 4, “School-family collaboration”, our research found that communication and collaboration with students’ legal guardians were strong supportive factor in inclusive mathematics education. Booth and Ainscow [
5] say that linking inclusive values to practice—the educational process and to communication (including communication with the pupil’s parents)—is important in an inclusive school philosophy. According to Money et al. [
16], inclusive communication is about eliminating communication barriers. It means sharing information in ways that everyone understands and in all forms of communication (face-to-face, written, online, and telephone). Caby and Caby [
44] say that the knowledge, experience, and cultural context of the family—which may be different from that of the teacher—must also be taken into account, and the way we communicate and collaborate must be adapted accordingly. Our research has shown that some schools or individual teachers already involve parents and pupils as members of the support team. In their work, Vlcek et al. [
36] and Booth and Ainscow [
5] also discuss this important aspect. They emphasize the important role of the parent/guardian in the support team. Vlcek et. al. [
36] stress the importance of achieving goals through the implementation of important, consistent support strategies in a variety of settings, including the home. Our research confirmed that mathematics teachers perceived the need to support students in their entire ecosystem, not just at school, and sought different ways to do so.
In the context of category 5 “Support mechanisms of the school as an institution in the context of inclusive mathematics education”, our research found that in order for teachers to translate an inclusive philosophy into mathematics education in the sense of making “mathematics for all” accessible, it is important to create an inclusive climate at all levels, including the school management, the principal, and the whole community of parents and students. Garcia-Melger et al. [
37] discuss the need for a consensus understanding of inclusion among all stakeholders. Roos [
6] stresses the consistency between an inclusive vision and its practical implementation in the classrooms themselves.
Our research has highlighted the need for teachers to collaborate with professionals and seek their support services. They also sought to create a multidisciplinary approach. DeSimone and Parmar [
27] pointed out that the most valuable support resources for mathematics teachers in inclusion programs were other people, primarily special education teachers, assistants, educational counselors, and/or school psychologists. In their research, research participants met 1–2 times a week with special education professionals at their school or sought advice from other colleagues who taught inclusively. Collaborative strategies and a true team mentality were the main reasons why general educators were able to meet the challenges of their mathematics classrooms and turn those challenges into some level of success” [
27].
All of the schools included in our research had some form of on-site professional support available, with the exception of one smaller school. However, we should note here that access to funding for these in-school support services is inadequate in Slovakia. In line with Garcia-Melger et al. [
37], access to funding has a non-negligible influence on decision-making processes about how to support individual pupils with difficulties. Our research, as mentioned above, has highlighted the great importance of creating friendly relationships within the school as well as open and collaborative communication between the school as an institution and all stakeholders. Teamwork and cooperation help teachers master their work. [
27] The need for an open-door policy was voiced. Teachers stressed solving problems right away or preventing them and not creating negative pressure on the school as an educational institution. We conclude with a statement from a teacher in our research that captured the philosophy of inclusive mathematics education very well, “I didn’t distinguish whether someone was integrated or not”.
Our results confirm what DeSimone and Parmar [
27] formulate: that the most valuable support source for general educators who taught mathematics in inclusion programs were other people—primarily special education teachers, assistants, educational counselors, and/or school psychologists.