Eurasia Journal of Mathematics, Science and Technology Education

• Ahmad, A. W., & Shahrill, M. (2014). Improving post-secondary students’ algebraic skills in the learning of complex numbers. International Journal of Science and Research, 3(8), 273‑279.
• Anevska, K., Gogovska, V., & Malcheski, R. (2015). The role of complex numbers in interdisciplinary integration in mathematics teaching. Procedia–Social and Behavioral Sciences, 191, 2573-2577. https://doi.org/10.1016/j.sbspro.2015.04.553
• Anton, H. (2010). Elementary linear algebra. Wiley.
• Antwi, S. K., & Hamza, K. (2015). Qualitative and quantitative research paradigms in business research: A philosophical reflection. European Journal of Business and Management, 7(3), 217‑226.
• Arnon, I., Cottrill, J., Dubinsky, E., Oktac, A., Fuentes, S. R., Trigueros, M., & Weller, K. (2014). APOS theory. A framework for research and curriculum development in mathematics education. Springer. https://doi.org/10.1007/978-1-4614-7966-6
• Bansilal, S., Brijlall, D., & Trigueros, M. (2017). An APOS study on pre-service teachers’ understanding of injections and surjections. The Journal of Mathematical Behavior, 48, 22-37. https://doi.org/10.1016/j.jmathb.2017.08.002
• Bertram, C., & Christiansen, I. (2014). Understanding research: An introduction to reading research. Van Schaik.
• Bogomolny, M. (2007). Raising students’ understanding: Linear algebra. In Proceedings of the 31^st Conference of the International Group for the Psychology of Mathematics Education (pp. 65‑72).
• Borji, V., Erfani, H., & Font, V. (2020). A combined application of APOS and OSA to explore undergraduate students’ understanding of polar coordinates. International Journal of Mathematical Education in Science and Technology, 51(3), 405-423. https://doi.org/10.1080/0020739X.2019.1578904
• Brijlall, D. (2015). Innovative pedagogy: Implications of genetic decompositions for problem solving in management courses. Nitte Management Review, 23-31.
• Chauraya, M., & Brodie, K. (2018). Conversation in a professional learning community: An analysis of teacher learning opportunities in mathematics. Pythagoras, 39(1), a363. https://doi.org/10.4102/pythagoras.v39i1.363
• Cohen, L., Manion, L., & Morrison, K. (2011). Surveys, longitudinal, cross sectional and trend studies. Routledge.
• Corbin, J., & Strauss, A. (2008). Basics of qualitative research. SAGE.
• De Lima, R. N., & Tall, D. (2008). Procedural embodiment and magic in linear equations. Educational Studies in Mathematics, 67(1), 3-18. https://doi.org/10.1007/s10649-007-9086-0
• DeVries, D., & Arnon, I. (2004). Solution–What does it mean? Helping linear algebra students develop the concept while improving research tools. In Proceedings of the 28^th Conference of the International Group for the Psychology of Mathematics Education (pp. 55-62).
• Dorier, J. L., & Sierpinska, A. (2001). Research into the teaching and learning of linear algebra. In D. Holton, M. Artigue, U. Kirchgräber, J. Hillel, M. Niss, & A. Schoenfield (Eds.), The teaching and learning of mathematics at university level (pp. 255-273). Springer.
• Dubinsky, E. (1984). A constructivist theory of learning in undergraduate mathematics education research. In D. Hoton (Ed.), The teaching and learning of mathematics at university level: An ICMI study (pp. 275-282). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47231-7_25
• Dubinsky, E. (2004). Towards a theory of learning advanced mathematical concepts. In Proceedings of the 9^th International Congress on Mathematical Education (pp. 121‑123). Springer. https://doi.org/10.1007/1-4020-7910-9_17
• Dubinsky, E. D. (1997). Some thoughts on a first course in linear algebra at the college level. Purdue University Press.
• Dubinsky, E., & McDonald, M. A. (2001). APOS: A constructivist theory of learning in undergraduate mathematics education research. In D. Holton, M. Artigue, U. Kirchgräber, J. Hillel, M. Niss, & A. Schoenfield (Eds.), The teaching and learning of mathematics at university level (pp. 275-282). Springer. https://doi.org/10.1007/0-306-47231-7_25
• Dubinsky, E., & Wilson, R. T. (2013). High school students’ understanding of the function concept. The Journal of Mathematical Behavior, 32(1), 83-101. https://doi.org/10.1016/j.jmathb.2012.12.001
• Egan, K. (2008). Complex numbers. https://education.nsw.gov.au/teaching-and-learning/curriculum/mathematics/mathematics-curriculum-resources-k-12/Mathematics-11-12-resources/complex-numbers-1
• Foster, C. (2014). “Can’t you just tell us the rule?” Teaching procedures relationally. In S. Pope (Ed.), Proceedings of the 8^th British Congress of Mathematics Education, 34(2), 151-158. University of Nottingham.
• Habre, S. (2017). Students’ challenges with polar functions: Covariational reasoning and plotting in the polar coordinate system. International Journal of Mathematical Education in Science and Technology, 48(1), 48-66. https://doi.org/10.1080/0020739X.2016.1220027
• Hannah, J., Stewart, S., & Thomas, M. O. J. (2016). Developing conceptual understanding and definitional clarity in linear algebra through the three worlds of mathematical thinking. Teaching Mathematics and its Applications: An International Journal of the IMA, 35(4), 216-235. https://doi.org/10.1093/teamat/hrw001
• Hillel, J. (2000). Modes of description and the problem of representation in linear algebra. In J.-L. Dorier (Ed.), On the teaching of linear algebra (pp. 191-207). Kluwer Academic. https://doi.org/10.1007/0-306-47224-4_7
• Kazunga, C., & Bansilal, S. (2017). Zimbabwean in-service mathematics teachers’ understanding of matrix operations. The Journal of Mathematical Behavior, 47, 81-95. https://doi.org/10.1016/j.jmathb.2017.05.003
• Kazunga, C., & Bansilal, S. (2020). An APOS analysis of solving systems of equations using the inverse matrix method. Educational Studies in Mathematics, 103, 339-358. https://doi.org/10.1007/s10649-020-09935-6
• Klapsinou, A., & Gray, E. (1999). The intricate balance between abstract and concrete in linear algebra. PME Conference, 3, 3-153.
• Lev, F. M. (2006). Why is quantum physics based on complex numbers? Finite Fields and Their Applications, 12(3), 336-356. https://doi.org/10.1016/j.ffa.2005.07.006
• Maharaj, A. (2010). An APOS analysis of students’ understanding of the concept of a limit of a function. Pythagoras, 71, 41-51. https://doi.org/10.4102/pythagoras.v0i71.6
• Maharaj, A. (2015). A framework to gauge mathematical understanding: A case study on linear algebra concepts. International Journal of Educational Sciences, 11(2), 144-153. https://doi.org/10.1080/09751122.2015.11890385
• Moore, K. C., Paoletti, T., & Musgrave, S. (2014). Complexities in students’ construction of the polar coordinate system. The Journal of mathematical behavior, 36, 135-149. https://doi.org/10.1016/j.jmathb.2014.10.001
• Murphy, P. K., Greene, J. A., Allen, E., Baszczewski, S., Swearingen, A., Wei, L., & Butler, A. M. (2018). Fostering high school students’ conceptual understanding and argumentation performance in science through Quality Talk discussions. Science Education, 102(6), 1239-1264. https://doi.org/10.1002/sce.21471
• Mustafa, N., Ismail, Z., Tasir, Z., & Mohamad Said, M. N. H. (2016). A meta-analysis on effective strategies for integrated STEM education. Advanced Science Letters, 22(12), 4225-4228. https://doi.org/10.1166/asl.2016.8111
• Mutambara, L. H. N., & Bansilal, S. (2021). A case study of in-service teachers’ errors and misconceptions in linear combinations. International Journal of Mathematical Education in Science and Technology, 1-19. https://doi.org/10.1080/0020739X.2021.1913656
• Mynbaev, D. K., Bo, C. C., Rashvili, R. Y. K., & Liou-Mark, J. (2008). Support of study on engineering technology from physics and mathematics [Paper presentation]. The ASEE Mid-Atlantic Conference.
• Naidoo, K. (2007). First year students’ understanding of elementary concepts in differential calculus in a computer laboratory teaching environment. Journal of College Teaching and Learning, 4(9), 55-66. https://doi.org/10.19030/tlc.v4i9.1548
• Ndlovu, D., & Brijlall, D. (2015). Pre-service teachers’ mental constructions of concepts in matrix algebra. African Journal of Research in Mathematics, Science and Technology Education, 19(2), 1-16. https://doi.org/10.1080/10288457.2015.1028717
• Ndlovu, Z., & Brijlall, D. (2016). Pre-service mathematics teachers’ mental constructions of the determinant concept. International Journal of Educational Science, 14(2), 145-156. https://doi.org/10.1080/09751122.2016.11890488
• Nguyen, T. P. L., Nguyen, T. H., & Tran, T. K. (2020). STEM education in secondary schools: Teachers’ perspective towards sustainable development. Sustainability, 12(21), 8865. https://doi.org/10.3390/su12218865
• Nordlander, M. C., & Nordlander, E. (2012). On the concept image of complex numbers. International Journal of Mathematical Education in Science and Technology, 43(5), 627‑641.
• Salgado, H., & Trigueros, M. (2015). Teaching eigenvalues and eigenvectors using models and APOS theory. The Journal of Mathematical Behavior, 39, 100-120. https://doi.org/10.1016/j.jmathb.2015.06.005
• Siyepu, S. W. (2013). Students’ interpretations in learning derivatives in a university mathematics classroom. In Z. Davis, & S. Jaffer (Eds.), Proceedings of the 19^th Annual Congress of the Association for Mathematics Education of South Africa (pp. 183‑193).
• Stewart, S., & Thomas, M. O. J. (2010). Student learning of basis, span and linear independence in linear algebra. International Journal of Mathematical Education in Science and Technology, 41(2), 173-188. https://doi.org/10.1080/00207390903399620
• Stewart, S., Andrews-Larson, C., & Zandieh, M. (2019). Linear algebra teaching and learning: Themes from recent research and evolving research priorities. ZDM, 51(7), 1017-1030. https://doi.org/10.1007/s11858-019-01104-1
• Tall, D. (2014). Making sense of mathematical reasoning and proof. In M. N. Fried, & T. Dreyfus (Eds.), Mathematics & mathematics education: Searching for common ground (pp. 223-235). Springer. https://doi.org/10.1007/978-94-007-7473-5_13
• Tan, S. H., & Toh, T. L. (2013). On the teaching of the representation of complex numbers in the Argand diagram. Learning Science and Mathematics, 8, 75-86.
• Thibaut, L., Ceuppens, S., De Loof, H., De Meester, J., Goovaerts, L., Struyf, A., Boeve-dePauw, J., Dehaene, W., Deprez, J., De Cock, M., Hellinckx, L., Knipprath, H., Langie, G., Struyven, K., Van de Velde, D., Van Petegem, P., & Depaepe, F. (2018). Integrated STEM education: A systematic review of instructional practices in secondary education. European Journal of STEM Education, 3(1), 2. https://doi.org/10.20897/ejsteme/85525
• Trigueros, M. (2019). The development of a linear algebra schema: Learning as result of the use of a cognitive theory and models. ZDM, 51(7), 1055-1068. https://doi.org/10.1007/s11858-019-01064-6
• Wan, T., Emigh, P. J., & Shaffer, P. S. (2019). Probing student reasoning in relating relative phase and quantum phenomena. Physical Review Physics Education Research, 15(2), 020139. https://doi.org/10.1103/PhysRevPhysEducRes.15.020139
• Wawro, M. (2014). Student reasoning about the invertible matrix theorem in linear algebra. ZDM–The International Journal on Mathematics Education, 46(3), 389-406. https://doi.org/10.1007/s11858-014-0579-x
• Weller, K., Clark, J., Dubinsky, E., Loch, S., McDonald, M., & Merkovsky, R. (2003) Student performance and attitudes in courses based on APOS Theory and the ACE Teaching Cycle. In A. Selden, E. Dubinsky, G. Harel, & F. Hitt (Eds.), Research in Collegiate Mathematics Education V (pp. 97-131). American Mathematical Society, Providence.
• Weyer, R. S. (2010). APOS theory as a conceptualisation for understanding mathematics learning. Summation, 9-15.
• Widiyatmoko, A., & Shimizu, K. (2018). An overview of conceptual understanding in science education curriculum in Indonesia. Journal of Physics: Conference Series, 983(1), 012044. https://doi.org/10.1088/1742-6596/983/1/012044

APA

Mutambara, L. H. N., & Tsakeni, M. (2022). Cognitive obstacles in the learning of complex number concepts: A case study of in-service undergraduate physics student-teachers in Zimbabwe. Eurasia Journal of Mathematics, Science and Technology Education, 18(10), em2158. https://doi.org/10.29333/ejmste/12418

Vancouver

Mutambara LHN, Tsakeni M. Cognitive obstacles in the learning of complex number concepts: A case study of in-service undergraduate physics student-teachers in Zimbabwe. EURASIA J Math Sci Tech Ed. 2022;18(10):em2158. https://doi.org/10.29333/ejmste/12418

AMA

Mutambara LHN, Tsakeni M. Cognitive obstacles in the learning of complex number concepts: A case study of in-service undergraduate physics student-teachers in Zimbabwe. EURASIA J Math Sci Tech Ed. 2022;18(10), em2158. https://doi.org/10.29333/ejmste/12418

Chicago

Mutambara, Lillias Hamufari Natsai, and Maria Tsakeni. "Cognitive obstacles in the learning of complex number concepts: A case study of in-service undergraduate physics student-teachers in Zimbabwe". Eurasia Journal of Mathematics, Science and Technology Education 2022 18 no. 10 (2022): em2158. https://doi.org/10.29333/ejmste/12418

Harvard

Mutambara, L. H. N., and Tsakeni, M. (2022). Cognitive obstacles in the learning of complex number concepts: A case study of in-service undergraduate physics student-teachers in Zimbabwe. Eurasia Journal of Mathematics, Science and Technology Education, 18(10), em2158. https://doi.org/10.29333/ejmste/12418

MLA

Mutambara, Lillias Hamufari Natsai et al. "Cognitive obstacles in the learning of complex number concepts: A case study of in-service undergraduate physics student-teachers in Zimbabwe". Eurasia Journal of Mathematics, Science and Technology Education, vol. 18, no. 10, 2022, em2158. https://doi.org/10.29333/ejmste/12418