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Aug 21, 2023
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Abstract

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.

Keywords

Baseline assessment Enacted pedagogical content knowledge Learner outcomes Teaching strategies

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Author Biographies

Hanlie Botha, University of Pretoria

Department of Science, Mathematics and Technology Education

Corene Coetzee, University of Pretoria

Department of Science, Mathematics, and Technology Education

Liezell Zweers, University of Pretoria

Department of Science, Mathematics and Technology Education

References

  1. 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.

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. Department of Basic Education. (2011). Curriculum and Assessment Policy Statement. Intermediate Phase (Grades 4-6). Government Printers.

  8. Department of Basic Education. (2011). Curriculum and Assessment Policy Statement. Senior Phase (Grades 7-9). Government Printers.

  9. Department of Basic Education. (2014). The Annual National Assessment of 2014. Diagnostic Report Intermediate and Senior Phases Mathematics. Government Printers.

  10. Department of Basic Education. (2014). Framework for Improving Performance in Senior Phase ANA 2015-2019. Government Printers.

  11. Department of Basic Education. (2018). Mathematics teaching and learning framework for South Africa: Teaching mathematics for understanding. Government Printers.

  12. 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

  13. 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

  14. Fisher, D., Frey, N., & Hattie, J. (2017). Teaching literacy in the visible learning classroom, grades K-5. Corwin Press.

  15. 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

  16. Gooding, J., & Metz, B. (2011). From misconceptions to conceptual change. The Science Teacher, 78(4), 34-37.

  17. 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

  18. 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

  19. 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

  20. 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.

  21. 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

  22. 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

  23. 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

  24. 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.

  25. 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

  26. 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.

  27. Sadler, P. M., & Sonnert, G. (2016). Understanding misconceptions: Teaching and learning in middle school physical science. American Educator, 40(1), 26-32.

  28. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189x015002004

  29. 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

  30. 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

  31. Veal, W. R., & MaKinster, J. G. (1999). Pedagogical content knowledge taxonomies. The Electronic Journal for Research in Science & Mathematics Education, 3(4).

  32. Wright, B. D. (2003). Rack and stack: time 1 vs. time 2. Rasch measurement transactions, 17(1), 905-906.

  33. 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.