Main Article Content
Teaching is a challenging profession where teachers must create valuable learning opportunities to enhance learners’ conceptual understanding. Apart from mathematical content knowledge, teachers use their pedagogical content knowledge (PCK) that develops as they reflect on previously taught lessons and learner responses in assessments. International and national assessment studies showed that South African learners perform poorly in, among other topics, Measurement. Thus, we determined the gain in learner outcomes as revealed in a pre-and post-test on Measurement and studied one of the PCK domains, namely teachers’ enacted PCK as informed by the baseline assessment learner outcomes. The aim was to determine how teachers’ enacted PCK relate to learner outcomes. Underpinned by a social constructivist paradigm, the study used a mixed-method research approach. Data were gathered from a pre-and post-test written by 124 Grade 9 learners taught by two experienced mathematics teachers in a city school in South Africa. Findings revealed that although some improvements are evident after the topic has been taught, the test was still experienced as difficult by almost all the learners. However, from the observations, there is little evidence that the experienced teachers extensively used the baseline assessment outcomes to inform their teaching.
Baseline assessment Enacted pedagogical content knowledge Learner outcomes Teaching strategies
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
- Artzt, A. F., Armour-Thomas, E., Curcio, F. R., & Gurl, T. J. (2015). Becoming a reflective mathematics teacher: A guide for observations and self-assessment. Routledge.
- Blömeke, S., Suhl, U., & Kaiser, G. (2011). Teacher education effectiveness: Quality and equity of future primary teachers’ mathematics and mathematics pedagogical content knowledge. Journal of Teacher Education, 62(2), 154-171. https://doi.org/10.1177/0022487110386798
- Botha, J. J. (2012). Exploring mathematical literacy: The relationship between teachers’ knowledge and beliefs and their instructional practices. Doctoral dissertation, University of Pretoria. Retrieved from http://hdl.handle.net/2263/28984
- Carlson, J., Daehler, K. R., Alonzo, A. C., Barendsen, E., Berry, A., Borowski, A., Carpendale, J., Kam Ho Chan, K., Cooper, R., Friedrichsen, P., Gess-Newsome, J., Henze-Rietveld, I., Hume, A., Kirschner, S., Liepertz, S., Loughran, J., Mavhunga, E., Neumann, K., Nilsson, P., . . . Wilson, C. D. (2019). The refined consensus model of pedagogical content knowledge in science education. In A. Hume, R. Cooper, & A. Borowski (Eds.), Repositioning pedagogical content knowledge in teachers’ knowledge for teaching science (pp. 77-94). Springer Nature Singapore. https://doi.org/10.1007/978-981-13-5898-2_2
- Chan, K. K. H., Rollnick, M., & Gess-Newsome, J. (2019). A grand rubric for measuring science teachers’ pedagogical content knowledge. In A. Hume, R. Cooper, & A. Borowski (Eds.), Repositioning pedagogical content knowledge in teachers’ knowledge for teaching science (pp. 253-271). Springer Nature Singapore. https://doi.org/10.1007/978-981-13-5898-2_11
- Depaepe, F., Verschaffel, L., & Kelchtermans, G. (2013). Pedagogical content knowledge: A systematic review of the way in which the concept has pervaded mathematics educational research. Teaching and Teacher Education, 34, 12-25. https://doi.org/10.1016/j.tate.2013.03.001
- Department of Basic Education. (2011). Curriculum and Assessment Policy Statement. Intermediate Phase (Grades 4-6). Government Printers.
- Department of Basic Education. (2011). Curriculum and Assessment Policy Statement. Senior Phase (Grades 7-9). Government Printers.
- Department of Basic Education. (2014). The Annual National Assessment of 2014. Diagnostic Report Intermediate and Senior Phases Mathematics. Government Printers.
- Department of Basic Education. (2014). Framework for Improving Performance in Senior Phase ANA 2015-2019. Government Printers.
- Department of Basic Education. (2018). Mathematics teaching and learning framework for South Africa: Teaching mathematics for understanding. Government Printers.
- Dewey, J. (1933). How we think. A restatement of the relation of reflective thinking to the educative process. Heath & Co Publishers. https://opus4.kobv.de/opus4-Fromm/frontdoor/index/index/docId/7969
- Duit, R., & Treagust, D. F. (2003). Conceptual change: A powerful framework for improving science teaching and learning. International Journal of Science Education, 25(6), 671-688. https://doi.org/10.1080/09500690305016
- Fisher, D., Frey, N., & Hattie, J. (2017). Teaching literacy in the visible learning classroom, grades K-5. Corwin Press.
- Geddis, A. N. (1993). Transforming subject‐matter knowledge: the role of pedagogical content knowledge in learning to reflect on teaching. International Journal of Science Education, 15(6), 673-683. https://doi.org/10.1080/0950069930150605
- Gooding, J., & Metz, B. (2011). From misconceptions to conceptual change. The Science Teacher, 78(4), 34-37.
- Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specific knowledge of students. Journal for Research in Mathematics Education JRME, 39(4), 372-400. https://doi.org/10.5951/jresematheduc.39.4.0372
- Hodgen, J. (2011). Knowing and identity: A situated theory of mathematics knowledge in teaching. In T. Rowland & K. Ruthven (Eds.), Mathematical Knowledge in Teaching (pp. 27-42). Springer Netherlands. https://doi.org/10.1007/978-90-481-9766-8_3
- Ijeh, S. B., & Nkopodi, N. N. (2013). Developing a theoretical model for investigating the mathematics and science teachers’ PCK in South Africa and Zimbabwe. Mediterranean Journal of Social Sciences, 4(14), 473-479. https://doi.org/10.5901/mjss.2013.v4n14p473
- Kirschner, S., Taylor, J., Rollnick, M., Borowski, A., & Mavhunga, E. (2015). Gathering evidence for the validity of PCK measures: Connecting ideas to analytic approaces. In A. Berry, P. Friedrichsen, & J. Loughran (Eds.), Re-examining pedagogical content knowledge in science education (pp. 229). Routledge.
- Kriek, J., & Grayson, D. (2009). A holistic professional development model for South African physical science teachers. South African Journal of Education, 29(2), 185-203. https://journals.co.za/doi/abs/10.10520/EJC32199
- Mavhunga, E. (2019). Exposing pathways for developing teacher pedagogical content knowledge at the topic level in science. In A. Hume, R. Cooper, & A. Borowski (Eds.), Repositioning pedagogical content knowledge in teachers’ knowledge for teaching science (pp. 131-150). Springer Nature Singapore. https://doi.org/10.1007/978-981-13-5898-2_5
- Mavhunga, E., & Rollnick, M. (2013). Improving PCK of chemical equilibrium in pre-service teachers. African Journal of Research in Mathematics, Science and Technology Education, 17(1-2), 113-125. https://doi.org/10.1080/10288457.2013.828406
- Mosimege, M., Beku, U., Juan, A., Hannan, S., Prinsloo, C. H., Harvey, J., & Zulu, N. (2016). TIMSS Item Diagnostic Report: South Africa Grade 9 Mathematics. Human Sciences Research Council Printers.
- Pedro, J. (2006). Taking reflection into the real world of teaching. Kappa Delta Pi Record, 42(3), 129-132. https://doi.org/10.1080/00228958.2006.10516449
- Reddy, V., Prinsloo, C., Visser, M., Arends, F., Harvey, J., Hannan, S., Namome, C., Sekhejane, P., & Zulu, N. (2020). TIMSS 2019: Highlights of the Western Cape province grade 9 results in mathematics and science. HSRC.
- Sadler, P. M., & Sonnert, G. (2016). Understanding misconceptions: Teaching and learning in middle school physical science. American Educator, 40(1), 26-32.
- Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189x015002004
- Sisman, G. T., & Aksu, M. (2016). A study on sixth grade students’ misconceptions and errors in spatial measurement: Length, area, and volume. International Journal of Science and Mathematics Education, 14(7), 1293-1319. https://doi.org/10.1007/s10763-015-9642-5
- Tariq, V. N. (2008). Defining the problem: Mathematical errors and misconceptions exhibited by first-year bioscience undergraduates. International Journal of Mathematical Education in Science and Technology, 39(7), 889-904. https://doi.org/10.1080/00207390802136511
- Veal, W. R., & MaKinster, J. G. (1999). Pedagogical content knowledge taxonomies. The Electronic Journal for Research in Science & Mathematics Education, 3(4).
- Wright, B. D. (2003). Rack and stack: time 1 vs. time 2. Rasch measurement transactions, 17(1), 905-906.
- Wright, B. D., & Mok, M. M. C. (2004). An overview of the family of Rasch measurement models. Introduction to Rasch measurement, 1(1), 1-24.