Mathematical Knowledge for Teaching in the Senior Phase: Entry-Level Teacher Candidates’ Subject Content Knowledge

Authors

DOI:

https://doi.org/10.57125/FED.2024.09.25.16

Keywords:

Baseline test, Entry-level, Mathematics knowledge, Senior phase mathematics, Teacher candidates, Subject content knowledge

Abstract

Having mathematical knowledge for teaching is now essential in defining the expertise of a mathematics teacher. Skilled and proficient educators in teaching are effective in attaining the intended educational objectives. Teaching is considered to be a noble profession as teachers rely on students' intellect as the main avenue of learning. It is a challenging role that demands dedication and hard work. Patience, respect, and sound judgment are qualities closely associated with teaching. In addition to sharing knowledge, teachers also reveal their own personalities, thoughts, principles, attitudes, and emotions. This paper reports on a study investigating the entry-level teacher candidates’ mathematics content knowledge for teaching in the senior phase. The study adopted a quantitative approach. A mathematical subject content knowledge baseline test for senior phase teacher candidates through Computer-Aided Mathematics Instruction (CAMI) was used to collect data. One hundred and eighty-five (185) teacher candidates who completed the Baseline Tests for all grades 7, 8, and 9 in the senior phase were selected for this paper. Purposive and convenience sampling were used in this paper. The data from the Baseline Test was analysed using descriptive statistics. Due to the inclusion of Baseline Tests in the CAMI package, every question on each grade was deemed valid. The CAMI Reports were then analysed using Microsoft Excel 2013. The findings suggested that at the entry-level, teacher candidates had limited and insufficient mathematics content knowledge and understanding. Therefore, teacher educators need to enhance the teacher candidates' comprehension of the mathematics they will be instructing in the senior phase. This paper recommends that the barriers in the teacher candidates' mathematics content knowledge and the understanding of the concepts should be addressed in the teacher education course.

References

Adelabu, F. M., & Alex, J. K. (2022). Mathematical knowledge for teaching in further education and training phase: Evidence from entry level student teachers’ baseline assessments. International Journal of Learning, Teaching and Educational Research, 21(8), 1–20. https://ijlter.myres.net/index.php/ijlter/article/view/1378

Adelabu, F. M., & Alex, J. K. (2023). Analysis of difficult concepts in Senior Phase Mathematics baseline assessments: First-year student teachers’ reflections. Research in Social Sciences and Technology, 8(4), 56–75. https://doi.org/10.46303/ressat.2023.20

Alex, J. (2019). The Preparation of secondary school mathematics teachers in South Africa: Prospective teachers’ student-level disciplinary content knowledge. Eurasia Journal of Mathematics, Science & Technology Education, 15(12), Article em1791. https://doi.org/10.29333/ejmste/105782

Alex, J., & Roberts, N. (2019, January). The need for relevant initial teacher education for primary mathematics: Evidence from the Primary Teacher Education project in South Africa. In N. Govender, R. Mudaly, T. Mthethwa, & A. Singh-Pillay (Eds.), Proceedings of the 27th Conference of the Southern African Association for Research in Mathematics, Science and Technology Education (pp. 59–72). Long Paper. https://www.jet.org.za/clearinghouse/projects/primted/resources/mathematics-resources-repository/alex-and-roberts-2019.pdf

Alex, J., & Trow, T. (2023). Entry level student teacher knowledge in school mathematics. In C. H. Stevenson-Milln (Ed.), Book of Proceedings of the 31st Annual Conference of the Southern African Association for Research in Mathematics, Science and Technology Education (pp. 14–29). University of the Free State. https://ujcontent.uj.ac.za/view/pdfCoverPage?instCode=27UOJ_INST&filePid=138519670007691&download=true#page=14

Al-Najjar, N., Al Bulushi, M. Y., Al Seyabi, F. A., Al-Balushi, S. M., Al-Harthi, A. S., & Emam, M. M. (2024). Perceived impact of initial student teaching practice on teachers’ teaching performance and professional skills: A retrospective study. Pedagogies: An International Journal. https://doi.org/10.1080/1554480X.2024.2331736

Altinok, N. (2013). The impact of teacher knowledge on student achievement in 14 sub-Saharan African countries. UNESCO. https://unesdoc.unesco.org/ark:/48223/pf0000225832

Askew, M., Bowie, L., & Venkat, H. (2019). Pre-service primary teachers’ mathematical content knowledge: An exploratory study. African Journal of Research in Mathematics, Science and Technology Education, 23(3), 286–297. https://doi.org/10.1080/18117295.2019.1682777

Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special?. Journal of Teacher Education, 59(5), 389–407. https://bibliotecadigital.mineduc.cl/handle/20.500.12365/17679

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. https://hdl.handle.net/10520/EJC151360

Bietenbeck, J., Piopiunik, M., & Wiederhold, S. (2018). Africa’s skill tragedy does teachers’ lack of knowledge lead to low student performance?. Journal of Human Resources, 53(3), 553–578. https://doi.org/10.3368/jhr.53.3.0616-8002R1

Boudersa, N. (2016). The importance of teachers' training programs and professional development in the Algerian educational context: Toward informed and effective teaching practices. Expériences Pédagogiques, 1(1), 71–84. https://www.asjp.cerist.dz/en/article/214956

Bowie, L., & Reed, Y. (2016). How much of What? An analysis of the espoused and enacted mathematics and English Curricula for intermediate phase teacher candidates at five South African universities. Perspectives in Education, 34(1), 102–119. https://doi.org/10.18820/2519593X/pie.v34i1.8

Danişman, Ş., & Tanişli, D. (2018). Examination of mathematics teachers’ pedagogical content knowledge of probability. MOJES: Malaysian Online Journal of Educational Sciences, 5(2), 16–34. https://ejournal.um.edu.my/index.php/MOJES/article/view/12622

Department of Basic Education. (2011). Curriculum and assessment policy statement grades 7–9 mathematics. https://www.education.gov.za/Curriculum/

Department of Basic Education. (2018). Mathematics teaching and learning framework for South Africa: Teaching mathematics for understanding. https://www.bridge.org.za/wp

Department of Basic Education. (2019). Report on the 2019 national senior certificate diagnostic report PART 1. https://www.education.gov.za/Portals

Department of Education and Training. (2017). Roles and responsibilities teaching service. Victoria State Government. https://www.education.vic.gov.au/Documents/pdf

Fonseca, K., Maseko, J., & Roberts, N. (2018). Students’ mathematical knowledge in a Bachelor of Education (Foundation or intermediate phase) programme. In R. Govender & K. Jonquière (Eds.), Proceedings of the 24th Annual National Congress of the Association for Mathematics Education of South Africa (pp. 124–139). https://t.ly/UKUW-

Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (Eds.). (2012). How to design and evaluate research in education (8th ed.). New York, NY: McGraw-Hill.

Gokalp, M. (2016). Investigating classroom teaching competencies of pre-service elementary mathematics teachers. Eurasia Journal of Mathematics, Science and Technology Education, 12(3), 503–512. https://doi.org/10.12973/eurasia.2016.1296a

Guerriero, S. (2014). Teachers’ pedagogical knowledge and the teaching profession: Background report and project objectives. OECD Publishing. https://search.oecd.org/education/ceri/Background_document_to_Symposium_ITEL-FINAL.pdf

Haegele, A. J., & Hodge, S. R. (2015). Quantitative methodology: A guide for emerging physical education and adapted physical education researchers. The Physical Educator, 72(5), 59–75. https://doi.org/10.18666/TPE-2015-V72-I5-6133

Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and instruction, 26(4), 430–511. http://doi.org/10.1080/07370000802177235

Jacinto, E. L., & Jakobsen, A. (2020). Mathematical knowledge for teaching: How do primary teacher candidates in Malawi understand it?. African Journal of Research in Mathematics, Science and Technology Education, 24(1), 31–40. https://doi.org/10.1080/18117295.2020.1735673

Johannsdottir, B. (2013). The mathematical content knowledge of prospective teachers in Iceland. Columbia University. https://academiccommons.columbia.edu/doi/10.7916/D8H99CG1/download

Lee, Y., Capraro, R. M., & Capraro, M. M. (2018). Mathematics teachers’ subject matter knowledge and pedagogical content knowledge in problem posing. International Electronic Journal of Mathematics Education, 13(2), 75–90. https://doi.org/10.12973/iejme/2698

Livy, S. (2014). Development and contributing factors in primary pre-service teachers’ mathematical content knowledge [Unpublished doctoral dissertation]. Deakin University. https://dro.deakin.edu.au/articles/thesis/Development_and_contributing_factors_in_primary_pre-service_teachers_mathematical_content_knowledge/21104050/1/files/37445458.pdf

Ma, L. (2010). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Routledge. https://doi.org/10.4324/9781003009443

Mji, A, & Makgato, M. (2006). Factors associated with high school learners’ poor performance: a spotlight on mathematics and physical science. South African Journal of Education, 26(2), 253–266. https://www.ajol.info/index.php/saje/article/view/25068

Montano, M. D. L. N. V. (2023). A comprehensive approach to the impact of job stress on women in the teaching profession. Interdisciplinary Rehabilitation/ Rehabilitacion Interdisciplinaria, 3, Article 56. https://doi.org/10.56294/ri202356

Narh-Kert, M. (2021). Predictive validity of entry-level mathematics: mathematical knowledge of pre-service teachers for teaching basic school mathematics in Ghana. Texila International Journal of Academic Research, 7(2), Article 003. https://doi.org/10.21522/TIJAR.2014.07.02.Art003

Norton, S. (2018). Middle school pre-service teachers' mathematics content knowledge and mathematical pedagogy content knowledge: Assessing and relating. Mathematics Education Research Group of Australasia. https://files.eric.ed.gov/fulltext/ED592511.pdf

Norton, S. (2019a). The relationship between mathematical content knowledge and mathematical pedagogical content knowledge of prospective primary teachers. Journal of Mathematics Teacher Education, 22(5), 489–514. https://doi.org/10.1007/s10857-018-9401-y

Norton, S. (2019b). Middle school mathematics pre-service teachers’ content knowledge, confidence, and self-efficacy. Teacher Development, 23(5), 529–548. https://doi.org/10.1080/13664530.2019.1668840

Olanoff, D. E. (2011). Mathematical knowledge for teaching teachers: The case of multiplication and division of fractions. Syracuse University. https://surface.syr.edu/cgi/viewcontent.cgi?article=1063&context=mat_etd

Özdil, G., & Kaçar, A. (2023). An investigation of the effect of a teaching experiment on the assessment literacy of pre-service mathematics teachers according to teacher competence standards. Turkish Journal of Mathematics Education, 4(2), 27–58. https://tujme.org/index.php/tujme/article/view/75

Pino-Fan, L. R., Assis, A., & Castro, W. F. (2015). Towards a methodology for the characterization of teachers’ didactic-mathematical knowledge. EURASIA Journal of Mathematics, Science and Technology Education, 11(6), 1429–1456. https://doi.org/10.12973/eurasia.2015.1403a

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), Article 1083. https://doi.org/10.15700/saje.v35n3a1083

Rach, S., & Ufer, S. (2020). Which prior mathematical knowledge is necessary for study success in the university study entrance phase? Results on a new model of knowledge levels based on a reanalysis of data from existing studies. International Journal of Research in Undergraduate Mathematics Education, 6(3), 375–403. https://doi.org/10.1007/s40753-020-00112-x

Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of educational psychology, 93(2), 346–362. https://doi.org/10.1037/0022-0663.93.2.346

Shirvani, H. (2015). Pre-service elementary teachers' mathematics content knowledge: A predictor of sixth graders' mathematics performance. International Journal of Instruction, 8(1), 133–142. https://eric.ed.gov/?id=EJ1085294

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. https://doi.org/10.3102/0013189X015002004

Siyepu, S. W., & Vimbelo, S. W. (2021). Pre-service teachers’ mathematical engagement in learning about the total surface areas of geometrical solids. South African Journal of Education, 41(2), 1–13. https://doi.org/10.15700/saje.v41n2a1837

Skaalvik, E. M., & Skaalvik, S. (2023). Shared goals and values in the teaching profession, job satisfaction and motivation to leave the teaching profession: The mediating role of psychological need satisfaction. Social Psychology of Education, 26(5), 1227–1244. https://doi.org/10.1007/s11218-023-09787-x

Spaull, N. (2011). A preliminary analysis of SACMEQ III South Africa. Stellenbosch: University of Stellenbosch. https://resep.sun.ac.za/wp-content/uploads/2017/10/wp-11-2011.pdf

Taylor, N. (2019). Inequalities in teacher knowledge in South Africa. In N. Spaull & J. Jansen (Eds.), South African schooling: The enigma of inequality (pp. 263–282). Cham: Springer. https://doi.org/10.1007/978-3-030-18811-5_14

Tichenor, M. S., & Tichenor, J. M. (2005). Understanding teachers' perspectives on professionalism. Professional Educator, 27, 89–95. https://eric.ed.gov/?id=EJ728484

Van der Sandt, S., & Nieuwoudt, H. D. (2003). Grade 7 teachers' and prospective teachers' content knowledge of geometry. South African Journal of Education, 23(3), 199–205. https://www.ajol.info/index.php/saje/article/view/24934

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

Venketsamy, R. (2022). Teacher’s needs for instructional support at early number sense: analysis in terms of (lens) the concerned based model for teacher development. Journal for the Education of Gifted Young Scientist, 10(1), 23–35. https://doi.org/10.17478/jegys.1053458

Venketsamy, R., & Hu, Z. (2022). Exploring challenges experienced by foundation phase teachers in using technology for teaching and learning: A South African case study. Journal for the Education of Gifted Young Scientists, 10(2), 221–238. https://doi.org/10.17478/jegys.1085660

Wong, T.-W., & Lai, Y.-C. (2012). Impact of entry-level mathematics subject-matter knowledge on teacher candidates' mathematics pedagogical content knowledge development and their mathematics teaching practice performance. Research in Mathematical Education, 16(1), 51–66. https://doi.org/10.7468/jksmed.2012.16.1.051

Downloads

Published

2024-07-26

How to Cite

Adelabu, F. M., & Alex, J. (2024). Mathematical Knowledge for Teaching in the Senior Phase: Entry-Level Teacher Candidates’ Subject Content Knowledge. Futurity Education, 4(3), 269–290. https://doi.org/10.57125/FED.2024.09.25.16