Qualitative Study: Mathematics Teachers' Strategies in Delivering Geometry Material in Inclusive Classes

Introduction. With the increasing number of students with special educational needs (SEN), the Ukrainian system of mathematics teacher education faces significant challenges, particularly the insufficient knowledge and practical skills required for effective teaching in inclusive classrooms. The study of international models and practices is of particular importance for the Ukrainian education system. It not only enables the identification of effective strategies and approaches for organizing inclusive mathematics education but also supports the modernization of professional training for future mathematics teachers in the context of inclusive education. Purpose. The purpose of the study is to analyze contemporary international models and practices of inclusive mathematics education in general secondary schools, with a focus on improving the professional preparation of future mathematics teachers in higher education institutions. Methods. To achieve this aim, general scientific methods (analysis, synthesis, concretization, comparison, classification, generalization) were applied, allowing for a comprehensive examination of international models and practices in inclusive mathematics education. Results. The findings indicate that mathematics teacher training should explicitly incorporate issues related to the implementation of inclusive practices. The role of mathematics and mathematics education in the formation and development of personality has been substantiated. It has been emphasized that new approaches, models, and effective practices should be introduced into mathematics teaching within inclusive education. Several models for implementing inclusive education, including mathematics instruction, have been presented and compared. Such international experience can be adapted and partially integrated into Ukrainian practice, as well as serve as a foundation for modernizing the professional preparation of future mathematics teachers. It is concluded that international experience reveals a wide spectrum of models and practices in inclusive mathematics education, which combine adapted teaching methods, differentiated approaches, extensive use of digital technologies and platforms, and strategies for collaboration with specialists in psychological and pedagogical support. Originality. The scientific novelty of the study lies in the analysis, comparison, systematization, and conceptual justification of international experience in inclusive mathematics education within the context of modernizing mathematics teacher preparation. It also lies in a transformational approach that translates international practices into specific, well-founded, and ready-to-implement recommendations for the Ukrainian education system. Conclusion. International practice demonstrates a systematic and multi-component approach to inclusive mathematics education, offering diverse models and effective strategies. Among them, the European multi-track model is particularly relevant for Ukraine, as its flexibility allows for the combination of different forms of learning while addressing individual student needs. The most effective framework for implementing inclusive education is Universal Design for Learning (UDL), which emphasizes flexibility and the adaptation of both content and teaching methods. The international models highlighted in this study can be adapted to Ukrainian realities. Some models, such as the “pull-out” and “cluster” approaches, are already partially implemented in Ukraine through the organization of resource rooms. Effective inclusive mathematics education is impossible without close collaboration between teachers and assistants, as well as the continuous professional development of educators. The process of professional training for future mathematics teachers is crucial, as it shapes their inclusive competencies and readiness for teaching in inclusive classrooms. In this context, modernizing teacher education programs requires the inclusion of specific components and specialized modules on inclusive education. These should address not only theoretical knowledge but also practical skills, such as task differentiation, the use of digital tools, and effective collaboration with representatives of psychological and pedagogical support for children with SEN. Future research should focus on developing methodological materials for university lecturers that integrate inclusion-related issues into courses on general methods of teaching mathematics in secondary schools.

In this study, we aim to assess the effectiveness of Project-Based Learning (PjBL) based on Multiple Intelligences (MI) theory on students' critical thinking and mathematical communication skills. This research is a quasi-experiment using non-equivalent (pre-test and post-test) control-group design. The population in this study were VIII grade students in a public junior high school in Yogyakarta and two sample classes were selected based on recommendations from teachers and had mathematical abilities that could be considered equal. The experimental class applied PjBL based on MI theory and the control class applied PjBL learning. Data collection was conducted using a test instrument in the form of description questions. This instrument is valid and reliable. Learning is said to be effective if: (1) the mean test score of critical thinking and communication skills is at least 70 (from a score range of 0-100); (2) the mean of post-test of critical thinking and communication skills is higher than the mean of pre-test; (3) the mean final score of students' critical thinking and mathematical communication skills in the experimental class is higher than the control class. Data analysis used one-sample t-test, paired-sample t-test, and T2 Hotteling test. The results of the study using the significance level α = 5% showed that (1) PjBL learning based on MI theory is effective in terms of students' critical thinking and mathematical communication skills; (2) PjBL based on MI theory learning is more effective than PjBL learning in terms of communication, but not more effective in terms of critical thinking skills. Although the data from the sample showed the acquisition of mean scores and the increase in the mean value of critical thinking learning in PjBL based on MI theory was better than PjBL learning in terms of critical thinking skill, but statistically both did not show a significant difference.

Integrating children with special educational needs in ordinary schools has been a central aspect of providing educational rights to every child. Sri Lanka is a country that values education, and the government schools provide free education facilities to every student concerning special educational opportunities for disabled students as well. Children with disabilities in Sri Lanka are educated through inclusion in mainstream or specialized schools. Teachers are the most important persons contributing to achieving the expected outcomes of inclusive education policy. They are the people who take action and implement educational reforms at the school level. A key element in the successful implementation of inclusive education is teachers’ ability to maintain and teach a classroom with an inclusive background. Therefore, the present research inquired about the strategies used by teachers in inclusive classrooms regarding students with special educational needs. The main objectives of the study are to find out the awareness about inclusive education among the teachers who are in inclusive classrooms, to identify the motivational strategies used by the teachers who are in inclusive classrooms, and to find out the teaching methods used by the teachers who are teaching in inclusive classrooms. Qualitative methods were used to collect data with classroom observations and semi structured interviews. A purposive sampling method was used to select the sample, and gathered data were analyzed thematically. Evidently, the teacher’s awareness of inclusive education was insufficient, and they were not provided with proper training regarding teaching in an inclusive classroom. Teachers used motivational strategies like reinforcement methods, assisting the issues of the SEN students, arranging the classroom environment according to the needs, and giving equal opportunities to the students. Most teachers used the lecture method in the classroom. Brainstorming and role-play were also visible. Less use of student-centred methods was visible. Proper awareness and training are needed to uplift the quality of teaching in inclusive classrooms in Sri Lanka.

This study aims to explore The mediating role of Resilience in the relationship between mindfulness and creative teaching self-efficacy among special needs teachers in inclusive classrooms. A correlational design was employed. The relationships between the research variables were analyzed in the form of examining the paths of a structural equation model. The study population included teachers of Special Education and Integration. 200 teachers were selected using the convenience sampling method. The results of structural equation modeling showed that mindfulness directly and positively predicts creative self-efficacy in teachers in inclusive classrooms. The results of structural equation modeling also showed that mindfulness directly and positively predicted resilience in teachers in inclusive classrooms. Another finding showed that resilience directly and positively predicted creative self-efficacy in special needs teachers in inclusive classrooms.

Understanding and handling diversity, as well as inclusion, are critical in ensuring effective teaching and learning, especially in the mathematics classroom, where students have varied abilities. Despite the growing research in inclusive education, little is known about how mathematics teachers in the Ghanaian context understand the theory of multiple intelligences (MIs), leaving a gap in how this theory can be applied in the classroom to improve practice and inclusion. In this study, the authors explored Ghanaian mathematics teachers’ conceptions of the theory of MIs using a basic qualitative method design. 12 senior high school mathematics teachers in one municipality of Ghana were engaged through questionnaires and semi-structured interviews, including field notes, to provide information on their conceptions of the theory of MIs. Thematic analysis revealed that mathematics teachers conceived the theory of MIs as a theory of different styles for learning, multiple teaching strategies, and a theory for catering to diverse student needs. The findings highlight the need for professional development and teacher training curriculum development to enhance teachers' understanding of the theory of MIs to improve their practice and handling of inclusiveness and diversity in the classroom.

Der Beitrag stellt ein videobasiertes Lehrkonzept vor, das in interdisziplinärer Kooperation entwickelt und durchgeführt worden ist. Mit der Lehrveranstaltung wird das Ziel verfolgt, die auf inklusiven Unterricht bezogene professionelle Wahrnehmung von Studierenden zu fördern. Um dies zu erreichen, arbeiten die Studierenden zunächst ihre Subjektiven Theorien über guten inklusiven Unterricht heraus, die potenziell im Widerspruch zu bildungswissenschaftlichem Wissen stehen. Da es nicht nur eine mögliche Perspektive auf guten inklusiven Unterricht gibt, werden im Seminar die Perspektiven der Pädagogischen Psychologie, der Schulpädagogik und der Sonderpädagogik integrativ vermittelt. Die Teilnehmer*innen operationalisieren die Befunde und überführen sie in ein Raster zur Beobachtung von inklusivem Unterricht. Das Raster kommt schließlich bei Videoanalysen und Unterrichtshospitationen zum Einsatz. Das Seminar wurde hinsichtlich verschiedener Variablen wie inklusionsbezogenen Einstellungen und bildungswissenschaftlichem Wissen positiv evaluiert.

This study aims to explore the challenges faced by teachers in pre-school inclusive classrooms in Albania. Through a qualitative methodology, the research investigates the specific difficulties encountered by educators and offers suggestions for adapting teaching practices to effectively meet the needs and abilities of all students, regardless of their conditions and circumstances. The study includes 23 teachers interviewed in 5 schools/kindergartens where they teach in the preschool program classes in the city of Durrës. While the focus group included 26 third-year bachelor students enrolled in Preschool education for the 2022-2023 academic year at the University of Durrës Aleksandër Moisiu. The findings of the study highlight several key factors that can alleviate the challenges faced by teachers in inclusive classrooms. Firstly, it emphasizes the importance of providing assistant teachers, particularly specialized educators in the field of special education, to accompany students with disabilities. These professionals can offer dedicated support, expertise, and guidance, enabling a more inclusive learning environment. Additionally, the research emphasizes the significance of reducing the student-to-teacher ratio in these classrooms. By lowering the number of students, teachers can provide more individualized attention and support to each child, catering to their unique requirements. Furthermore, the study emphasizes the need for enhancing teachers' knowledge and skills in adapting teaching methods to accommodate the diverse needs and abilities of students with disabilities. Professional development programs, workshops, and training sessions can empower educators with effective strategies, specialized techniques, and resources necessary for inclusive classroom practices. In conclusion, by addressing these key factors, pre-school inclusive classrooms can meet the requirements of inclusive education. It is anticipated that these efforts will contribute to the alleviation of challenges and promote an inclusive educational environment where all students can thrive.
 
 Received: 29 July 2023 / Accepted: 30 September 2023 / Published: 5 November 2023

En el proceso de inclusión educativa, se ha intentado diversas formas para aprovechar las condiciones en las que se desarrolla la educación básica, que permita que el estudiante con discapacidad pueda aprender con calidad. Por ello, el propósito es describir el diseño de estrategias en la educación inclusiva para mejorar el proceso de aprendizaje en aulas normales en la amazonia peruana. Es producto de un estudio no experimental descriptivo propositiva, siendo la muestra de 183 docentes. Se encontró que los educadores de las instituciones regulares consideran deficiente el uso de técnicas básicas para el desarrollo social del niño incluido, escaso uso de las inteligencias múltiples y la participación activa. Por su parte, los maestros de las aulas inclusivas indican que no se han incorporado técnicas para resolver conflictos y técnicas de toma de decisiones. Los docentes del centro especial, consideran que no se ha puesto importancia en la gestión y los valores de los profesores inclusivos ante el proceso educativo, como la planificación, la identificación de nuevas oportunidades para conseguir agrupaciones heterogéneas, desarrollo social y la resolución de problemas y el uso de instrumentos como el plan de orientación individual y la evaluación psicopedagógica. Ante esto, se diseñó estrategias metodológicas fundamentado en la teoría de la complejidad y las inteligencias múltiples que demuestra su efectividad, tanto en su concepción teórica como en la práctica, demostrando eficacia en el logro de aprendizaje de estudiantes incluidos.

The overarching purpose of this research is to critically evaluate the evolving interaction between governmental policies and processes in the implementation of Assistive Technology (AT) for inclusive education. The authors primarily assess the teachers’ knowledge and skills to employ inclusive pedagogy, specifically through the use of AT in inclusive classrooms. This study employs quantitative analysis to investigate the knowledge and skills of teachers in inclusive classrooms. Data were collected from 200 teachers across India. Partial least squares (PLS)—Structural equation modeling (SEM) was used to test the proposed hypotheses. Specifically, it examined the parameters such as, teachers’ knowledge on foundation (TWF), strategies to teach AT to students (STR), student assessment using technology (SAT), professional and ethical practice of technology (PEP) as well as learning environment and social interaction (LSI).TWF, STR and LSI have a strong and direct impact on SAT. STR has a direct impact on PEP. However, TWF and LSI do not predict PEP. The results indicate a lack/inadequacy in knowledge and skills of Indian teachers to employ AT in inclusive classrooms. This study is the first attempt to quantitatively assess teacher’s knowledge and skills for the use of AT in an inclusive-Indian-classrooms.

The aim of this study is to investigate which supportive factors positively influence inclusive mathematics education so that it is accessible to all pupils in mainstream primary and secondary school settings from the mathematics teachers’ perspectives. The study is designed as a qualitative descriptive study. It was conducted by collecting 16 narratives about selected pupils/students provided by mathematics teachers. In them, they described their experiences with inclusive mathematics education. 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. The stories were structured by the researchers into units of meaning, numerically coded, content-analyzed, and categorized. Participants in the study were 16 mathematics teachers who were working in mainstream schools. From the stories, we identified 583 meaning units that were assigned a numerical code. Using continuous qualitative analysis procedures, we abstracted five main final categories that describe the support factors in inclusive mathematics education from the mathematics teachers’ perspective in terms of including every pupil without distinction, including those who require some level of additional support. The final categories include: 1. Identifying the pupil’s/student’s internal resources in mathematics education; 2. The mathematics teacher’s responsive approach toward the pupil/student; 3. Modifying conditions in mathematics instruction and implementing accommodations for pupils/students; 4. School-family collaboration; 5. Support mechanisms for the school as an institution in the context of inclusive mathematics education.

Mathematical thinking is absolutely essential for school learning at all levels, including the HOT and LOT. The purpose of this study is to characterize the mathematical critical thinking ability pattern using Ennis and Gardner's theory of multiple intelligences. The research conducted in this study is qualitative. Purposive sampling was used in this study, which was conducted at SMPN 29 Bandar Lampung. Five people were involved in this study. To collect data, the researcher used a mathematical critical thinking essay test, a multiple intelligence questionnaire administered by a psychology expert, and in-depth interviews. Techniques for data analysis include data reduction, data visualization, inference, and verification (conclusion drawing and verification). The triangulation technique is used to find the truth of the data. The findings indicated that students were able to articulate the steps involved in developing mathematical critical thinking abilities. Additionally, students are more critical when it comes to problem-solving and approach the problem appropriately. Students provide direct responses rather than generalizations. Mathematics-related critical thinking patterns are frequently inductive.

Curved-side spatial structures are one of the geometry materials taught at the junior high school/Islamic junior high school level, especially in class IX. Completing questions up to the room side arch can help students finish problems contextual to others. Training students' critical thinking skills in solving a mathematical problem is one of the tasks of a mathematics teacher. From the data from the researcher's interview with the mathematics teacher of grade IX students of Palu Christian Middle School, information was obtained that the teacher had carried out learning activities with various strategies to train students' critical thinking skills in solving mathematical problems. However, students' critical thinking skills did not change, and there was no increase. This study aims to obtain a clear description of the critical thinking skills of grade IX students in solving mathematical problems. This research is a qualitative study. The data collection methods used in this study were test and interview methods. The critical thinking indicators used were focus, reason, inference, situation, clarity, and overview. This study involved 28 Palu Christian Middle School students in the odd semester of the 2022/2023 Academic Year. Three students were selected as research subjects, where one student represented each level of mathematical ability, namely high mathematical ability (ST), medium mathematical ability (SS), and low mathematical ability (SR). The results of this study indicate that students with high mathematical ability meet all critical thinking indicators. Students with moderate mathematical abilities fulfill several indicators of critical thinking, namely focus, clarity, and overview. Students with low mathematical abilities fulfill several indicators of critical thinking, namely clarity and overview.

Teacher self-efficacy is a crucial factor for successful learning in inclusive classrooms. This study explores the self-efficacy of preservice mathematics teachers to teach in inclusive classes. The study used an exploratory sequential design through a survey and continued with interviews. The survey stage involved seventy-seven participants. The survey data were analyzed descriptively followed by semi-structured interviews with ten participants selected using purposive sampling. Qualitative data were analyzed using the Bogdan & Biklen technique. The results showed that aspects of self-efficacy in using mathematics-inclusive instruction and managing behavior were in the moderate category. Experience with inclusive education lectures, training, and interactions with students with disabilities (SWD) influence these aspects. However, self-efficacy in collaborations is in the low category. The majority of participants express worry about collaborating with external parties such as parents, doctors, and psychologists. This is due to limited experience in conducting collaboration. This finding is expected to be a recommendation for universities and related parties to organize education and training that facilitates preservice mathematics teachers to develop teaching skills in inclusive classroom.

Learners with Special Educational Needs (LSENs) experience unique educational journeys in inclusive English classrooms. The study aimed to understand response patterns and task completion dynamics of learners with special educational needs (LSENs), particularly focusing on the deaf and visually impaired, within inclusive English instructional environments to inform effective pedagogical approaches and support structures. The qualitative study employed a case study method at Abra High School in rural Abra Province, Philippines. Purposive sampling selected two Grade 7 learners with special educational needs (deaf and visually impaired) enrolled in English classes. Data collection involved semi-structured interviews, classroom observations using protocols, and document analysis using templates to explore learner experiences, classroom dynamics, and educational materials. Thematic analysis was applied to interview transcripts, observation notes, and document reviews. text. The study yielded significant insights into the English language learning experiences of learners with special educational needs (LSENs), focusing particularly on visually impaired and deaf students within inclusive classrooms. It found that assistive technologies such as screen readers and tactile aids were instrumental for visually impaired learners, enabling them to effectively access and engage with English materials. Similarly, deaf learners benefited greatly from visual communication tools like sign language interpreters and captioning, facilitating their comprehension and active participation in English tasks. Support systems emerged as crucial components in navigating English learning for LSENs. Personalized teacher guidance and peer collaboration were highlighted as essential factors that fostered inclusivity and mutual support among students. These support mechanisms enhanced engagement and contributed significantly to the student's comprehension and ability to navigate complex language structures. Despite these supportive measures, the study also identified challenges faced by LSENs, particularly in understanding abstract concepts and intricate language nuances. However, the study also highlighted the effectiveness of tailored instructional approaches that incorporated visual aids and provided clear explanations, instilling confidence in the potential of these methods to address these challenges effectively. Ultimately, the findings emphasize the transformative potential of inclusive practices in enhancing the educational experiences of learners with special educational needs in English language education. They advocate for continued efforts to integrate assistive technologies, personalized support systems, and tailored instructional strategies to ensure equitable access and optimal student learning outcomes.

The study assessed the teachers’ differentiated instruction (DI) practices in teaching mathematics in inclusive classes in secondary schools in Makambako Town Council. This study specifically focused on exploring the teachers’ understanding and resource limitations towards the practices of DI in teaching mathematics in inclusive classrooms in secondary schools. The phenomenology study design, informed by the qualitative approach, was employed. The data for the study were collected through interviews and classroom observations. Fifteen participants, including eight teachers, four heads of schools, and three ward educational officers, were used as a sample size for the study conducted in 4 public secondary schools. The collected data were analysed thematically. Ethical clearances were obtained from the respective organs to maintain ethical issues, whereby informants filled out informed consent forms. The study findings revealed multiple DI understandings and resource limitations as among the stumbling blocks towards teachers’ practices of DI in teaching mathematics in inclusive classes. Resources like the availability of mathematics teachers, materials, and time were found to be the major resource challenges towards the practices of DI in teaching mathematics. Based on the findings, the study concludes that for the successful practice of DI, efforts have to be made to address these resource challenges. Therefore, the study suggests hiring more mathematics teachers in secondary schools and providing them with guidance on implementing DI effectively. The government should provide sufficient materials for improving mathematics teaching in inclusive classes.