Journal of Mathematics and Science Teacher

• Ailing, W., & Bin, X. (2016). Logarithm concept teaching in teaching present reasons. International Journal of Research in Education Methodology, 7(4), 1302-1308. https://doi.org/10.24297/ijrem.v7i4.4352
• Alex, J. K. (2019). The preparation of secondary school mathematics teachers in South Africa: Prospective teachers’ student level disciplinary content knowledge. EURASIA Journal of Mathematics, Science and Technology Education, 15(12), em1971. https://doi.org/10.29333/ejmste/105782
• Ansah, I. (2016). Improving understanding of logarithms by using the approach of repeated division [Master’s thesis, University of Agder].
• 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. ttps://doi.org/10.1007/978-1-4614-7966-6
• Aziz, T. A., Pramudiani, P., & Purnomo, Y. W. (2017). How do college students solve logarithm questions. International Journal on Emerging Mathematics Education, 1(1), 25-40. https://doi.org/10.12928/ijeme.v1i1.5736
• Baker, W. (2021). The role of the teacher in facilitating the Aha! Moment. In B. Czarnocha, & W. Baker (Eds.), Creativity of an Aha! Moment and mathematics education (pp. 139-163). Brill. https://doi.org/10.1163/9789004446434_006
• Bansilal, S., Mkhwanazi, T., & Brijlall, D. (2014). An exploration of the common content knowledge of high school mathematics teachers. Perspectives in Education, 32(1), 34-50.
• Bekdemir, M. (2010). The pre-service teachers’ mathematics anxiety related to depth of negative experiences in mathematics classroom while they were students. Educational Studies in Mathematics, 75(3), 311-328. https://doi.org/10.1007/s10649-010-9260-7
• Bowen, P. W., Rose, R., & Pilkington, A. (2017). Mixed methods-theory and practice. Sequential, explanatory approach. International Journal of Quantitative and Qualitative Research Methods, 5(2), 10-27.
• Bronkhorst, H., Roorda, G., Suhre, C., & Goedhart, M. (2020). Logical reasoning in formal and everyday reasoning tasks. International Journal of Science and Mathematics Education, 18(8), 1673-1694. https://doi.org/10.1007/s10763-019-10039-8
• Campo-Meneses, K. G., Font, V., García-García, J., & Sánchez, A. (2021). Mathematical connections activated in high school students’ practice solving tasks on the exponential and logarithmic functions. EURASIA Journal of Mathematics, Science and Technology Education, 17(9), em1998. https://doi.org/10.29333/ejmste/11126
• Cangelosi, R., Madrid, S., Cooper, S., Olson, J., & Hartter, B. (2013). The negative sign and exponential expressions: Unveiling students’ persistent errors and misconceptions. Journal of Mathematical Behavior, 32(1), 69-82. https://doi.org/10.1016/j.jmathb.2012.10.002
• Celik, H. C., & Ozdemir, F. (2020). Mathematical thinking as a predictor of critical thinking dispositions of pre-service mathematics teachers. International Journal of Progressive Education, 16(4), 81-98. https://doi.org/10.29329/ijpe.2020.268.6
• Coetzer, T., Livingston, C., & Barnard, E. (2023). Eleven grade 1 teachers’ understandings of mathematical language in a South African context. Reading & Writing-Journal of the Reading Association of South Africa, 14(1), 409. https://doi.org/10.4102/rw.v14i1.409
• Creswell, J. W., & Plano Clark, V. L. (2017). Designing and conducting mixed methods research. SAGE.
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• Cuevas, G. J. (1984). Mathematics learning in English as a second language. Journal for Research in Mathematics Education, 15(2), 134-144. https://doi.org/10.5951/jresematheduc.15.2.0134
• Dall, N. (2023). Complex equation of maths education in South Africa. The UNESCO Courier, 2023(1), 22-23. https://doi.org/10.18356/22202293-2023-1-8
• Díaz-Berrios, T., & Martínez-Planell, R. (2022). High school student understanding of exponential and logarithmic functions. Journal of Mathematical Behavior, 66, 100953. https://doi.org/10.1016/j.jmathb.2022.100953
• Dintarini, M. (2018). Understanding logarithm: What are the difficulties that students have? In Proceedings of the 3^rd International Conference on Education, Sports, Arts and Management Engineering (pp. 239-241). Atlantis Press. https://doi.org/10.2991/amca-18.2018.65
• DoBE. (2012). National curriculum statement grades R-12. Department of Basic Education.
• Dubinsky, E., & McDonald, M. A. (2001). APOS: A constructivist theory of learning in undergraduate mathematics education research. In The teaching and learning of mathematics at university level (pp. 275-282). Springer. https://doi.org/10.1007/0-306-47231-7_25
• Espedal, B. (2015). A meaningful approach to logarithms: A design study on the introduction of logarithms through repeated division [Master’s thesis, University of Agder].
• Fair, D. L. (2019). School mathematics performance: A longitudinal case study [Doctoral dissertation, University of the Free State].
• Fermsjö, R. (2014). Exploring logarithms using number lines. Short Oral Communications, 308.
• Frketic, A. M., Berk, D., & Rossi, T. (2018). An investigation into college students’ learning about logarithmic functions: A thorny problem [Doctoral dissertation, University of Delaware]. https://doi.org/10.19080/PBSIJ.2019.10.555792
• Hine, G., & Thai, T. (2019). Pre-service mathematics teachers’ self-perceptions of readiness to teach secondary school mathematics. Mathematics Teacher Education and Development, 21(2), 64-86.
• Jojo, Z. (2011). An APOS exploration of conceptual understanding of the chain rule in calculus by first year engineering students [Doctoral dissertation, University of KwaZulu-Natal].
• Jojo, Z. (2019). Mathematics education system in South Africa. In G. Porto Jr (Ed.), Education systems around the world. IntechOpen. https://doi.org/10.5772/intechopen.85325
• Jooganah, K., & Williams, J. S. (2016). Contradictions between and within school and university activity systems helping to explain students’ difficulty with advanced mathematics. Teaching Mathematics and Its Applications: International Journal of the IMA, 35(3), 159-171. https://doi.org/10.1093/teamat/hrw014
• Kenney, R. (2005). Students’ understanding of logarithmic function notation. In Proceedings of the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.
• Kilpatrick, J., Swafford, J., & Findell, B. (2002). Adding it up: Helping children learn mathematics. The National Academies Press. https://doi.org/10.17226/9822
• Kuper, E., & Carlson, M. (2020). Foundational ways of thinking for understanding the idea of logarithm. Journal of Mathematical Behavior, 57, 100740. https://doi.org/10.1016/j.jmathb.2019.100740
• Maharaj, A. (2014). An APOS analysis of natural science students’ understanding of integration. Journal of Research in Mathematics Education, 3(1), 54-73. https://doi.org/10.4471/redimat.2014.40
• Meyer, D. (2018). What does fluency without understanding look like? https://blog.mrmeyer.com/2018/what-does-fluency-without-understanding-look-like/
• Mulqueeny, E. S. (2012). How do students acquire an understanding of logarithmic concepts? [Doctoral dissertation, Kent State University].
• Naidoo, K., & Naidoo, R. (2007). First year students understanding of elementary concepts in differential calculus in a computer laboratory teaching environment. Journal of College Teaching & Learning, 4(9), 55-70. https://doi.org/10.19030/tlc.v4i9.1548
• Ndlovu, Z., & 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), 156-171. https://doi.org/10.1080/10288457.2015.1028717
• Ndlovu, Z., & Brijlall, D. (2017). Pre-service mathematics teachers’ mental constructions of the determinant concept. International Journal of Educational Sciences, 14(1-2), 145-156. https://doi.org/10.1080/09751122.2016.11890488
• Ndlovu, Z., Amin, N., & Samuel, M. A. (2017). Examining pre-service teachers’ subject matter knowledge of school mathematics concepts. Journal of Education, 70, 46-72.
• Nga, N. T., Dung, T. M., Trung, L. T. B. T., Nguyen, T. T., Tong, D. H., Van, T. Q., & Uyen, B. P. (2023). The effectiveness of teaching derivatives in Vietnamese high schools using APOS theory and ACE learning cycle. European Journal of Educational Research, 12(1), 507-523. https://doi.org/10.12973/eu-jer.12.1.507
• Okoye-Ogbalu, I. (2019). Exploring pre-service mathematics teachers’ knowledge of logarithm in one of the universities in Kwazulu-Natal [Master’s thesis, University of KwaZulu Natal].
• Oktac, A. (2019). Mental constructions in linear algebra. ZDM-Mathematics Education, 51(7), 1043-1054. https://doi.org/10.1007/s11858-019-01037-9
• Ostler, E. (2013). Exploring logarithms with a ruler. The Mathematics Teacher, 106(9), 668-673. https://doi.org/10.5951/mathteacher.106.9.0668
• Peng, A., & Smida, H. (2015). Mathematical knowledge for teaching at the secondary level. In Proceedings of the 12^th International Congress on Mathematical Education: Intellectual and attitudinal challenges (pp. 507-512). Springer. https://doi.org/10.1007/978-3-319-12688-3_49
• Pournara, C., Hodgen, J., Adler, J., & Pillay, V. (2015). Can improving teachers’ knowledge of mathematics lead to gains in learners’ attainment in mathematics? South African Journal of Education, 35(3), 1083. https://doi.org/10.15700/saje.v35n3a1083
• Powney, J., & Watts, M. (2018). Interviewing in educational research. Routledge. https://doi.org/10.4324/9780429503740
• Pretorius, L. (2017). Effective teaching and learning: Working towards a new, all-inclusive paradigm for effective and successful teaching and learning in higher education and training. Educor Multidisciplinary Journal, 1(1), 6-29.
• Qi, F., Shi, X. T., & Liu, F. F. (2017). Expansions of the exponential and the logarithm of power series and applications. Arabian Journal of Mathematics, 6(2), 95-108. https://doi.org/10.1007/s40065-017-0166-4
• Rittle-Johnson, B. (2017). Developing mathematics knowledge. Child Development Perspectives, 11(3), 184-190. https://doi.org/10.1111/cdep.12229
• Rittle-Johnson, B. (2019). Iterative development of conceptual and procedural knowledge in mathematics learning and instruction. In J. Dunlosky, & K. A. Rawson (Eds.), The Cambridge handbook of cognition and education (pp. 124-147). Cambridge University Press. https://doi.org/10.1017/9781108235631.007
• Robertson, S. A., & Graven, M. (2020). Language as an including or excluding factor in mathematics teaching and learning. Mathematics Education Research Journal, 32(1), 77-101. https://doi.org/10.1007/s13394-019-00302-0
• Schoenfeld, A. H. (2020). Reframing teacher knowledge: A research and development agenda. ZDM: The International Journal on Mathematics Education, 52(2), 359-376. https://doi.org/10.1007/s11858-019-01057-5
• Shay, S. (2020). Why South Africa’s declining maths performance is a worry. UCT News. https://theconversation.com/why-south-africas-declining-maths-performance-is-a-worry-129563
• Siyepu, S. W. (2013). An exploration of students’ errors in derivatives in a university of technology. Journal of Mathematical Behavior, 32(3), 577-592. https://doi.org/10.1016/j.jmathb.2013.05.001
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• Spaull, N. (2019). Equity: A price too high to pay? In N. Spaull, & J. D. Jansen (Eds.), South African schooling: The enigma of inequality (pp. 1-24). Springer. https://doi.org/10.1007/978-3-030-18811-5_1
• Stewart, S., Epstein, J., & Troup, J. (2019). Leading students towards the formal world of mathematical thinking: A mathematician’s reflections on teaching eigentheory. International Journal of Mathematical Education in Science and Technology, 50(7), 1011-1023. https://doi.org/10.1080/0020739X.2019.1657598
• Tall, D. (2013). How humans learn to think mathematically: Exploring the three worlds of mathematics. Cambridge University Press. https://doi.org/10.1017/CBO9781139565202
• Taylor, N. (2021). The dream of Sisyphus: Mathematics education in South Africa. South African Journal of Childhood Education, 11(1), 1-12. https://doi.org/10.4102/sajce.v11i1.911
• Usiskin, Z. (2015). What does it mean to understand some Mathematics? In Proceedings of the 12^th International Congress on Mathematical Education (pp. 821-841). Springer. https://doi.org/10.1007/978-3-319-17187-6_46
• Venkat, H., & Spaull, N. (2015). What do we know about primary teachers’ mathematical content knowledge in South Africa? An analysis of SACMEQ 2007. International Journal of Educational Development, 41, 121-130. https://doi.org/10.1016/j.ijedudev.2015.02.002
• Villarreal-Calderon, R. (2012). Chopping logs: A look at the history and uses of logarithms. In B. Sriraman (Ed), Crossroads in the history of mathematics and mathematics education. Information Age Publishing.
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• Weber, C. (2016). Zugänge zum logarithmus–Operationale und strukturelle grundvorstellungen zum logarithmus [Making logarithm accessible–Operational and structural basic models for logarithm]. Journal für Mathematik-Didaktik [Journal for Mathematics Didactics], 37(1), 69-98. https://doi.org/10.1007/s13138-016-0104-6
• Weyer, R. S. (2010). APOS theory as a conceptualisation for understanding mathematics learning. Summation: Mathematics and computer science scholarship at Ripon, 3, 9-15.

APA

Okoye-Ogbalu, I., & Nnadozie, V. (2024). Subject competency and teacher knowledge: An exploration of second-year pre-service mathematics teachers’ difficulties in solving logarithmic problems using basic rules for logarithm. Journal of Mathematics and Science Teacher, 4(1), em054. https://doi.org/10.29333/mathsciteacher/13887

Vancouver

Okoye-Ogbalu I, Nnadozie V. Subject competency and teacher knowledge: An exploration of second-year pre-service mathematics teachers’ difficulties in solving logarithmic problems using basic rules for logarithm. Journal of Mathematics and Science Teacher. 2024;4(1):em054. https://doi.org/10.29333/mathsciteacher/13887

AMA

Okoye-Ogbalu I, Nnadozie V. Subject competency and teacher knowledge: An exploration of second-year pre-service mathematics teachers’ difficulties in solving logarithmic problems using basic rules for logarithm. Journal of Mathematics and Science Teacher. 2024;4(1), em054. https://doi.org/10.29333/mathsciteacher/13887

Chicago

Okoye-Ogbalu, Izuchukwu, and Victor Nnadozie. "Subject competency and teacher knowledge: An exploration of second-year pre-service mathematics teachers’ difficulties in solving logarithmic problems using basic rules for logarithm". Journal of Mathematics and Science Teacher 2024 4 no. 1 (2024): em054. https://doi.org/10.29333/mathsciteacher/13887

Harvard

Okoye-Ogbalu, I., and Nnadozie, V. (2024). Subject competency and teacher knowledge: An exploration of second-year pre-service mathematics teachers’ difficulties in solving logarithmic problems using basic rules for logarithm. Journal of Mathematics and Science Teacher, 4(1), em054. https://doi.org/10.29333/mathsciteacher/13887

MLA

Okoye-Ogbalu, Izuchukwu et al. "Subject competency and teacher knowledge: An exploration of second-year pre-service mathematics teachers’ difficulties in solving logarithmic problems using basic rules for logarithm". Journal of Mathematics and Science Teacher, vol. 4, no. 1, 2024, em054. https://doi.org/10.29333/mathsciteacher/13887