A Review of the Implementation of Technology-Enhanced Heutagogy in Mathematics Teacher Education Angel Mukuka, Benjamin Tatira Education Sciences, 2025 Low achievement in mathematics across educational levels has long been a concern for researchers. Recent evidence points to equipping teachers with skills and competencies that align with the demands of the modern, technology-rich world. This systematic review explored how technology-facilitated heutagogical practices contribute to the professional development of preservice and in-service mathematics teachers. Drawing on 21 empirical studies published between 2017 and 2024, this review identified three major findings. First, technology-enhanced heutagogical practices promote teaching skills by fostering learner autonomy, self-reflection, and professional identity development. Second, tools such as mobile apps, Massive Open Online Courses (MOOCs), adaptive learning platforms, and collaborative digital environments support the integration of heutagogical principles. Third, implementation is challenged by limited digital access, institutional constraints, and the need for gradual adaptation to self-determined learning models. These findings prove the need for policy and institutional investment in digital infrastructure, blended learning models, and teacher support. Theoretically, this study affirms heutagogy as a relevant pedagogical approach for preparing mathematics teachers in dynamic learning contexts. There is also a need for more empirical studies to investigate scalable models for technology-driven heutagogy, especially in resource-constrained settings.
Exploring Grade 11 Learners’ Understanding of Trigonometric Equations: An Evaluation of a Remedial Teaching Intervention Mathematics Teaching Research Journal, 2025
Undergraduate students’ understanding of the application of integral calculus in kinematics Benjamin Tatira Eurasia Journal of Mathematics Science and Technology Education, 2025 In calculus, students can integrate functions that require procedures or algorithmic rules, but they grapple with contextual problems involving real-life motion of physical bodies. When undergraduate students learn the application of integration, they are expected to comprehend the concept of integration and apply it to optimization. This study used the action-process-object-schema (APOS) theory to determine undergraduate students’ construction of the application of integral calculus to kinematics. This study was qualitative and involved a case study of 150 secondary mathematics students registered for a Bachelor of Education degree at a university in South Africa. Data were collected through a written test by all the students and semi-structured interviews with eight students. The eight students were selected purposively, and the interview questions were meant to clarify some of the responses raised in the test. The content analysis of the written responses was done to reveal the stages of students’ concept development of kinematics. The findings revealed that students had significant challenges performing second- and third-level integration. These involve substituting the initial conditions at least once to find the constant integration for each level. Furthermore, students’ connection with displacement, velocity and acceleration concepts was weak, coupled with their failure to consider the point when the object was momentarily at rest.
Analysis of pre-service mathematics teachers' proof comprehension through Toulmin's argumentation model Angel Mukuka, Benjamin Tatira Journal on Mathematics Education, 2025 The comprehension of mathematical proofs by preservice mathematics teachers is vital for their ability to effectively teach mathematical reasoning. Despite its importance, existing research reveals a significant gap in preservice teachers’ understanding and application of formal proof methods, especially in the context of mathematical argumentation. This study examined how preservice teachers construct mathematical proofs, using Toulmin’s argumentation model as a framework. A qualitative exploratory case study design was adopted, involving written proofs from 72 third-year preservice teachers at a South African university, supplemented by task-based interviews with nine participants. The findings indicate that 62.5% of the participants were able to construct correct direct proofs, and 61.1% applied the contraposition proof method correctly. However, only 30.6% produced valid proofs using the contradiction method. Further analysis uncovered notable gaps in essential components of proof construction, such as warrants, backing, and rebuttals, particularly when dealing with tasks requiring contraposition and contradiction methods. While many participants (62.5%) demonstrated procedural fluency in direct proofs, 31.9% failed to provide explicit definitions or logical precision, suggesting a superficial engagement with proof construction. These results highlight the need for teacher education programs to emphasize a deeper conceptual understanding of proof structures, which is crucial for preparing preservice mathematics teachers to foster reasoning and argumentation skills in their future classrooms.
In-service mathematics teachers’ perceptions of GeoGebra integrative training materials: The case of geometry teaching Israel Yeukai Marange, Benjamin Tatira Eurasia Journal of Mathematics Science and Technology Education, 2025 The further education and training phase curriculum and assessment policy statement of South Africa expects mathematics teachers to integrate educational technologies into their teaching. However, the importance of technology integration and adoption has not been fully implemented in schools. In-service mathematics teachers’ perceptions of GeoGebra integrative training materials and their impact on the artefacts of teachers’ professional development were explored in this study. The study adopted two adult learning theories, namely andragogy and transformational learning. These theories were integrated into Ahmed et al.’s (2021) in-service training framework. A mixed-methods methodology was employed by purposively sampling 29 mathematics secondary teachers from twelve randomly selected schools in the OR Tambo Inland District of Eastern Cape Province in South Africa. Data were collected by using a questionnaire with four open-ended and seven closed-ended questions. The questionnaire was administered at the end of professional teacher development training for mathematics teachers. The researchers used descriptive, inferential statistics and thematic approaches to analyze and interpret the results. The findings revealed that in-service mathematics teachers highly rated the GeoGebra integrative training materials. The participants positively felt that the training materials ushered interest in teaching geometry with confidence. They felt highly motivated and showed interest in disseminating information to other colleagues. The study also revealed improved in-service teachers’ professional skills. These skills included improved technological, pedagogical, communication, collaboration and content skills.
Analysis of preservice teachers’ understanding of solving trigonometric equations: A perspective through actions, processes, objects, and schemas theory Angel Mukuka, Benjamin Tatira Pythagoras, 2025 This study analysed first-year preservice teachers’ understanding of trigonometric equations at a South African university in the Eastern Cape province. We employed the Action-Process-Object-Schema (APOS) framework to analyse the mental constructions made by preservice teachers in solving trigonometric equations. A qualitative case study design was employed to analyse test scripts from 223 preservice teachers, complemented by follow-up interviews with eight of these participants. Findings show that the success rate in the two analysed items was low. Students who had not developed specific mental structures could not solve the given problems. Only 15.5% of the participants reached the Object level, while 76% remained at the Action or Process stages. Conversely, 8.5% of the participants were at the pre-Action stage, having not shown evidence of action mental structures conjectured in the genetic decomposition. Challenges encountered include difficulties with algebraic manipulations, reference angles, angle relationships across quadrants, and conversions between degrees and radians. The analysis further revealed a lack of understanding of the periodic nature of trigonometric functions and the general solution derivation. Contribution: These findings reflect global trends in mathematical struggles across various educational levels, particularly in solving trigonometric equations. The study highlights the importance of assessing preservice teachers’ mathematical knowledge both at the entry and exit points of their training programmes. Such dual assessments could improve their content mastery and teaching effectiveness. This suggests that adjusting educational strategies to address these identified gaps could foster significant growth.
Exploring Grade 12 Learners’ Understanding of Geometric Transformations Through the STAD Cooperative Learning Model Angel Mukuka, Benjamin Tatira Education Sciences, 2024 Research has shown that both learners and teachers struggle to understand and teach geometric transformations meaningfully. This mixed-methods case study examined the efficacy of the Student Teams Achievement Division (STAD) cooperative learning model in fostering learners’ conceptual understanding of geometric transformations. This study involved 28 Grade 12 learners from one intact class. In addition to pre- and post-intervention tests, which measured learners’ conceptual understanding of geometric transformations, participants completed a feedback questionnaire at the end of the intervention. The results show that the STAD model significantly improved learners’ grasp of geometric transformations, as demonstrated by higher test scores in the post-test. Participants also highlighted the importance of well-crafted questions during group discussions and oral quizzes, teacher explanations during whole-class presentations, and the motivational impact of criteria for selecting and awarding top-performing groups. Based on Shapiro’s intervention evaluation criteria, the STAD model was found to be effective, with high levels of acceptability, integrity, and social validity. While this study confirms the STAD model’s effectiveness in enhancing conceptual understanding and social learning, it also emphasizes the importance of considering contextual factors, such as group dynamics and classroom resource availability, when implementing this cooperative learning model. Teachers are encouraged to tailor this learning strategy to their specific classroom environments and learners’ needs.
Mathematics teacher education in a globalized age: Heutagogy and virtual learning environments in context Angel Mukuka, Jogymol K. Alex, Benjamin Tatira Impacts of Globalization and Innovation in Mathematics Education, 2024 Globalization has a significant bearing on mathematics teacher education and there is need for a comprehensive restructuring to meet the demands of the interconnected world. This study advocates for a paradigm shift that encompasses cross-cultural competencies, linguistic diversity, and a nuanced understanding of global educational trends. It further highlights the significant influence of virtual learning environments (VLEs) in responding to the challenges posed by globalization and emphasizes the synergy between VLEs and heutagogical practices. Drawing from the cited case studies and other existing literature, this chapter underscores the departure from conventional pedagogical methods towards a learner-cantered, self-determined approach. The chapter concludes by discussing the far-reaching implications for policy, practice, and theory, urging stakeholders to recognize the benefits of heutagogy in preparing mathematics teachers for the complexities of the twenty-first century teaching and learning.
Schema development in solving systems of linear equations using the triad framework Mathematics Teaching Research Journal, 2024
EXPLORING GRADE 11 LEARNERS’CONCEPTUALISATION OF THE NATURE OF ROOTS OF QUADRATIC EQUATIONS S Ndluzonke, B Tatira Association for Mathematics Education of South Africa, 101 , 2025 2025
A Review of the Implementation of Technology-Enhanced Heutagogy in Mathematics Teacher Education A Mukuka, B Tatira Education Sciences 15 (7), 822 , 2025 2025 Citations: 5
Undergraduate students’ understanding of the application of integral calculus in kinematics B Tatira Eurasia Journal of Mathematics, Science and Technology Education 21 (3), 2601 , 2025 2025 Citations: 4
The effect of the COVID-19 pandemic on pre-service teachers’ mathematical perceptions and motivation at a selected higher education institution in South Africa T Simayi, B Tatira Edelweiss Applied Science and Technology 9 (8), 1671-1683 , 2025 2025
Exploring Grade 11 Learners' Understanding of Trigonometric Equations: An Evaluation of a Remedial Teaching Intervention. V Tunzana, A Mukuka, B Tatira Mathematics Teaching Research Journal 17 (2), 80-103 , 2025 2025 Citations: 5
Analysis of preservice teachers’ understanding of solving trigonometric equations: A perspective through actions, processes, objects, and schemas theory B Mukuka, A., & Tatira Pythagoras 45 (1), 1-15 , 2025 2025 Citations: 4
Union: Jurnal Ilmiah Pendidikan Matematika E Machisi, B Tatira 2025
Integrating PHET simulations and YouTube videos in teaching vertical projectile motion in Grade 12. BT Sizwe Deluboma Multidisciplinary Science Journal 7 (11), 1-9 , 2025 2025 Citations: 3
Analysis of pre-service mathematics teachers’ proof comprehension through Toulmin’s argumentation model A Mukuka, B Tatira Journal on Mathematics Education 16 (1), 111-130 , 2025 2025 Citations: 5
In-service mathematics teachers' perceptions of GeoGebra integrative training materials: The case of geometry teaching IY Marange, B Tatira EURASIA Journal of Mathematics, Science and Technology Education 21 (2), 1 , 2025 2025 Citations: 7
ANGEL MUKUKA & BENJAMIN TATIRA A Strand BOOK OF PROCEEDINGS–LONG PAPERS , 2025 2025
Exploring Grade 12 learners’ understanding of geometric transformations through the STAD cooperative learning model A Mukuka, B Tatira Education Sciences 14 (12), 1332 , 2024 2024 Citations: 9
Unpacking pre-service teachers’ conceptualization of logarithmic differentiation through the APOS theory B Tatira, A Mukuka Eurasia Journal of Mathematics, Science and Technology Education 20 (12), em2541 , 2024 2024 Citations: 5
Undergraduate students’ abstractions of kinematics in differential calculus B Tatira Eurasia Journal of Mathematics, Science and Technology Education 20 (9), em2497 , 2024 2024 Citations: 4
Gender dynamics in GeoGebra integration: In-service mathematics teachers’ development IY Marange, B Tatira Eurasia Journal of Mathematics, Science and Technology Education 20 (6), em2457 , 2024 2024 Citations: 11
First-Year Undergraduate Students’ Ways of Thinking in Combinatorics B Tatira Journal of Medives: Journal of Mathematics Education IKIP Veteran Semarang 8 … , 2024 2024
The impact of virtual laboratories on the academic performance of grade 12 learners in impulse and momentum B Tatira, T Mshanelo Edelweiss Applied Science and Technology 8 (6), 4150-4157 , 2024 2024 Citations: 1
Mathematics teacher education in a globalized age: Heutagogy and virtual learning environments in context A Mukuka, JK Alex, B Tatira Impacts of globalization and innovation in mathematics education, 41-66 , 2024 2024 Citations: 2
Schema Development in Solving Systems of Linear Equations Using the Triad Framework. B Tatira Mathematics Teaching Research Journal 16 (1), 167-189 , 2024 2024 Citations: 5
Teaching Euclidean geometry with GeoGebra: Perceptions for in-service mathematics teachers IY Marange, B Tatira Eurasia Journal of Mathematics, Science and Technology Education 19 (12), em2367 , 2023 2023 Citations: 18
MOST CITED SCHOLAR PUBLICATIONS
The Balobedu Cultural Activities and Plays Pertinent to Primary School Mathematics Learning. B Tatira, LHN Mutambara, CJ Chagwiza International education studies 5 (1), 78-85 , 2012 2012 Citations: 21
Teaching Euclidean geometry with GeoGebra: Perceptions for in-service mathematics teachers IY Marange, B Tatira Eurasia Journal of Mathematics, Science and Technology Education 19 (12), em2367 , 2023 2023 Citations: 18
Mathematics Education Students’ Understanding of Binomial Series Expansion Based on the APOS Theory B Tatira Eurasia Journal of Mathematics, Science and Technology Education 17 (12), 13 , 2021 2021 Citations: 16
Undergraduate students’ conceptualization of elementary row operations in solving systems of linear equations B Tatira Eurasia Journal of Mathematics, Science and Technology Education 19 (11), em2349 , 2023 2023 Citations: 12
Voices from the field: Pre-service teachers’ first time experiences of teaching Physical Sciences during school-based experience S Boateng, B Tatira International Journal of Learning, Teaching and Educational Research 22 (6 … , 2023 2023 Citations: 12
Gender dynamics in GeoGebra integration: In-service mathematics teachers’ development IY Marange, B Tatira Eurasia Journal of Mathematics, Science and Technology Education 20 (6), em2457 , 2024 2024 Citations: 11
Exploring Grade 12 learners’ understanding of geometric transformations through the STAD cooperative learning model A Mukuka, B Tatira Education Sciences 14 (12), 1332 , 2024 2024 Citations: 9
Creation of Innovative Teaching Spaces with Gamma Tutor: A Techno-Blended Model for Rural Mathematics Teaching. FM Adelabu, JK Alex, A Ngwabe, B Tatira, S Boateng Journal of Education and e-Learning Research 9 (4), 249-257 , 2022 2022 Citations: 9
In-service mathematics teachers' perceptions of GeoGebra integrative training materials: The case of geometry teaching IY Marange, B Tatira EURASIA Journal of Mathematics, Science and Technology Education 21 (2), 1 , 2025 2025 Citations: 7
Higher education for public good: Perspectives in the new academic landscape in South Africa NS Matsiliza AOSIS , 2023 2023 Citations: 6
Defining formative electronic assessment in undergraduate mathematics: A reflective approach B Tatira, I Kariyana International Journal of Learning, Teaching and Educational Research 21 (7 … , 2022 2022 Citations: 6
A Review of the Implementation of Technology-Enhanced Heutagogy in Mathematics Teacher Education A Mukuka, B Tatira Education Sciences 15 (7), 822 , 2025 2025 Citations: 5
Exploring Grade 11 Learners' Understanding of Trigonometric Equations: An Evaluation of a Remedial Teaching Intervention. V Tunzana, A Mukuka, B Tatira Mathematics Teaching Research Journal 17 (2), 80-103 , 2025 2025 Citations: 5
Analysis of pre-service mathematics teachers’ proof comprehension through Toulmin’s argumentation model A Mukuka, B Tatira Journal on Mathematics Education 16 (1), 111-130 , 2025 2025 Citations: 5
Unpacking pre-service teachers’ conceptualization of logarithmic differentiation through the APOS theory B Tatira, A Mukuka Eurasia Journal of Mathematics, Science and Technology Education 20 (12), em2541 , 2024 2024 Citations: 5
Schema Development in Solving Systems of Linear Equations Using the Triad Framework. B Tatira Mathematics Teaching Research Journal 16 (1), 167-189 , 2024 2024 Citations: 5
Undergraduate students’ understanding of the application of integral calculus in kinematics B Tatira Eurasia Journal of Mathematics, Science and Technology Education 21 (3), 2601 , 2025 2025 Citations: 4
Analysis of preservice teachers’ understanding of solving trigonometric equations: A perspective through actions, processes, objects, and schemas theory B Mukuka, A., & Tatira Pythagoras 45 (1), 1-15 , 2025 2025 Citations: 4
Undergraduate students’ abstractions of kinematics in differential calculus B Tatira Eurasia Journal of Mathematics, Science and Technology Education 20 (9), em2497 , 2024 2024 Citations: 4
A survey of Mathematics Pre-service teachers’ end-of-teaching practice reflections of Educational contexts B Tatira International Journal of Learning Teaching and Educational Research , 2023 2023 Citations: 4
