International Electronic Journal of Mathematics Education

International Electronic Journal of Mathematics Education
Pre-service Secondary Teachers’ Mathematical Pedagogical Content Knowledge Self-concept related to their Content Knowledge of Functions and Students
AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: Sintema EJ, Marbán JM. Pre-service Secondary Teachers’ Mathematical Pedagogical Content Knowledge Self-concept related to their Content Knowledge of Functions and Students. INT ELECT J MATH ED. 2020;15(3), em0598. https://doi.org/10.29333/iejme/8327
APA 6th edition
In-text citation: (Sintema & Marbán, 2020)
Reference: Sintema, E. J., & Marbán, J. M. (2020). Pre-service Secondary Teachers’ Mathematical Pedagogical Content Knowledge Self-concept related to their Content Knowledge of Functions and Students. International Electronic Journal of Mathematics Education, 15(3), em0598. https://doi.org/10.29333/iejme/8327
Chicago
In-text citation: (Sintema and Marbán, 2020)
Reference: Sintema, Edgar John, and José M. Marbán. "Pre-service Secondary Teachers’ Mathematical Pedagogical Content Knowledge Self-concept related to their Content Knowledge of Functions and Students". International Electronic Journal of Mathematics Education 2020 15 no. 3 (2020): em0598. https://doi.org/10.29333/iejme/8327
Harvard
In-text citation: (Sintema and Marbán, 2020)
Reference: Sintema, E. J., and Marbán, J. M. (2020). Pre-service Secondary Teachers’ Mathematical Pedagogical Content Knowledge Self-concept related to their Content Knowledge of Functions and Students. International Electronic Journal of Mathematics Education, 15(3), em0598. https://doi.org/10.29333/iejme/8327
MLA
In-text citation: (Sintema and Marbán, 2020)
Reference: Sintema, Edgar John et al. "Pre-service Secondary Teachers’ Mathematical Pedagogical Content Knowledge Self-concept related to their Content Knowledge of Functions and Students". International Electronic Journal of Mathematics Education, vol. 15, no. 3, 2020, em0598. https://doi.org/10.29333/iejme/8327
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Sintema EJ, Marbán JM. Pre-service Secondary Teachers’ Mathematical Pedagogical Content Knowledge Self-concept related to their Content Knowledge of Functions and Students. INT ELECT J MATH ED. 2020;15(3):em0598. https://doi.org/10.29333/iejme/8327

Abstract

Pre-service teachers’ beliefs, attitudes, and values about mathematics have a significant influence on their self-concept about mathematics as a subject and determine how confident they are to teach it. The purpose of this study was to examine Zambian pre-service secondary mathematics teachers’ pedagogical content knowledge self-concept about the function concept in relation to their knowledge of content and students. Data was collected from 150 pre-service teachers using a sequential approach in two phases. The first, quantitative phase, involved 150 pre-service teachers who responded to a functions survey and a mathematical pedagogical content knowledge survey. The second, qualitative phase, involved two pre-service teachers who were purposively selected from phase one to respond to vignettes and interviews for an in-depth understanding of their knowledge. Results of the study revealed that pre-service teachers’ level of their pedagogical content knowledge self-concept was low. They would not be confident enough to teach the function concept in secondary school. Results further revealed that their knowledge of content and students was weak. A weak correlative relationship between pre-service teachers’ KMLS and KM was revealed whereas a moderate correlative relationship of their KL and KC was revealed. It was further revealed that there was no significant correlative relationship between KTS and their knowledge of the function concept Thus, pre-service teachers needed to improve before leaving university for them to effectively teach secondary school concepts.

References

  • Aksu, Z., & Kul, Ü. (2016). Exploring Mathematics Teachers’ Pedagogical Content Knowledge in the Context of Knowledge of Students. Journal of Education and Practice, 7(30), 35-42.
  • Alrwaished, N., Alkandari, A., & Alhashem, F. (2017). Exploring In- and Pre-Service Science and Mathematics Teachers’ Technology, Pedagogy, and Content Knowledge (TPACK): What Next? Eurasia Journal of Mathematics, Science and Technology Education, 13(9), 6113-6131. https://doi.org/10.12973/eurasia.2017.01053a
  • Aziz, T. A., & Kurniasih, M. D. (2019). External representation flexibility of domain and range of function. Journal on Mathematics Education, 10(1), 143-156. https://doi.org/10.22342/jme.10.1.5257.143-156
  • Bagozzi, R. P., & Yi, Y. (1988). On the evaluation of structural equation models. Journal of Academy of Marketing Science, 16(1), 74-94. https://doi.org/10.1007/BF02723327
  • Bates, A. B., Latham, N., & Kim, J. A. (2011). Linking preservice teachers’ mathematics Self‐Efficacy and mathematics teaching efficacy to their mathematical performance. School Science and Mathematics, 111(7), 325-333. https://doi.org/10.1111/j.1949-8594.2011.00095.x
  • Beswick, K., & Goos, M. (2012). Measuring Pre-Service Primary Teachers’ Knowledge for Teaching Mathematics. Mathematics Teacher Education and Development, 14(2), 70-90.
  • Blömeke, S., Busse, A., Kaiser, G., König, J., & Suhl, U. (2016). The relation between content-specific and general teacher knowledge and skills. Teaching and Teacher Education, 56, 35-46. https://doi.org/10.1016/j.tate.2016.02.003
  • Carlson, J., & Daehler, K. R. (2019). The refined consensus model of pedagogical content knowledge in science education. In Repositioning pedagogical content knowledge in teachers’ knowledge for teaching science (pp. 77-92). Springer, Singapore. https://doi.org/10.1007/978-981-13-5898-2_2
  • Chin, W. W. (1998). The partial least squares approach to structural equation modeling. Modern Methods for Business Research, 295(2), 295-336.
  • da Costa, D. A. (2020). Knowledge to Teach and Knowledge for Teaching in Teacher Education Research. Pedagogical Research, 5(3), em0059. https://doi.org/10.29333/pr/7936
  • de Sousa Magalhaes, S., Fernandes Malloy-Diniz, L., & Cavalheiro Hamdan, A. (2012). Validity convergent and reliability test-retest of the rey auditory Verbal Learning Test. Clinical Neuropsychiatry
  • Dorko, A., & Weber, E. (2014). Generalising calculus ideas from two dimensions to three: How multivariable calculus students think about domain and range. Research in Mathematics Education, 16(3), 269-287. https://doi.org/10.1080/14794802.2014.919873
  • Duran, M., & Usak, M. (2015). Examining the pedagogical content knowledge of science teachers who have different teaching experience about acids and bases. Oxidation Communications, 38(1A), 540-557.
  • Elia, I., Panaoura, A., Eracleous, A., & Gagatsis, A. (2007). Relations between secondary pupils’ conceptions about functions and problem solving in different representations. International Journal of Science and Mathematics Education, 5(3), 533-556. https://doi.org/10.1007/s10763-006-9054-7
  • Elmahdi, I., & Fawzi, H. (2019). Pre-service Teachers’ Perception of Readiness to Teach in Light of Teachers’ Standards. American Journal of Educational Research, 7(4), 304-308.
  • Even, R. (1990). Subject-matter knowledge for teaching and the case of functions. Education studies in mathematics education, 21(6), 521-544. https://doi.org/10.1007/BF00315943
  • Even, R. (1992). The inverse function: Prospective teachers’ use of “undoing”. International Journal of Mathematical Education in Science and Technology, 23(4), 557-562. https://doi.org/10.1080/0020739X.1992.10715689
  • Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for research in mathematics education, 24(2), 94-116. https://doi.org/10.2307/749215
  • Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147- 164). New York: Macmillan.
  • Fornell, C. G., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18(1), 38-50. https://doi.org/10.1177/002224378101800104
  • Gagatsis, A., & Shiakalli, M. (2004). Ability to translate from one representation of the concept of a function to another and mathematical problem solving. An International Journal of Experimental Educational Psychology, 24(5), 645-957. https://doi.org/10.1080/0144341042000262953
  • Garson, G. D. (2016). Partial least squares: regression & structural equation models Asheboro. North Carolina: Statistical Associates Publishing.
  • Gess-Newsome, J. (2015). A model of teacher professional knowledge and skill including PCK: Results of the thinking from the PCK Summit. In A. Berry, P. Friedrichsen, & J. Loughram (Eds.), Re-examining pedagogical content knowledge in Science Education (pp. 28-42). New York: Routledge.
  • Gold, A. H., Malhotra, A., & Sergas, A. H. (2001). Knowledge management: an organizational capabilities perspective. Journal of Management Information Systems, 18(1), 185-214. https://doi.org/10.1080/07421222.2001.11045669
  • Gresham, G. (2009). An examination of mathematics teacher efficacy and mathematics anxiety in elementary pre-service teachers. The Journal of Classroom Interaction, 22-38.
  • Hair J. F., Sarstedt, M., Pieper, T. M., & Ringle, C. M. (2012). The use of partial least squares structural equation modeling in strategic management research: a review of past practices and recommendations for future applications, Long Range planning, 5(6), 320-340. https://doi.org/10.1016/j.lrp.2012.09.008
  • Hair Jr, J. F., Sarstedt, M., Hopkins, L., & Kuppelwieser, V. G. (2014). Partial least squares structural equation modeling (PLS-SEM). European Business Review. https://doi.org/10.1016/j.jfbs.2014.01.002
  • Henseler, J., Ringle, C. M., & Sarstedt, M. (2015). A new criterion for assessing discriminant validity in variance-based structural equation modeling. Journal of Academy of Marketing Science, 42(1), 115-135. https://doi.org/10.1007/s11747-014-0403-8
  • Henseler, J., Ringle, C. M., & Sinkovics, R. R. (2009). The use of partial least squares path modeling in international marketing, Advances in International Marketing, 20, 277-320. https://doi.org/10.1108/S1474-7979(2009)0000020014
  • 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.
  • Hitt, F. (1998). Difficulties in the articulation of different representations linked to the concept of a function. The Journal of Mathematics Behavior, 17(1), 123-134. https://doi.org/10.1016/S0732-3123(99)80064-9
  • Hu, L. T., & Bentler, P. M. (1998). Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification, Psychological Methods, 3(4), 424. https://doi.org/10.1037/1082-989X.3.4.424
  • Huang, R., & Kulm, G. (2012). Prospective middle grade mathematics teachers’ knowledge of algebra for teaching. The Journal of Mathematics Behavior, 31(4), 417-430. https://doi.org/10.1016/j.jmathb.2012.06.001
  • Jeffery, T. D., Hobson, L. D., Conoyer, S. J., Miller, K. E., & Leach, L. F. (2018). Examining EC-6 Pre-Service Teachers’ Perceptions of Self-Efficacy in Teaching Mathematics. Issues in the Undergraduate Mathematics Preparation of School Teachers, 5.
  • Kim, S. (2018). Technological, Pedagogical, and Content Knowledge (TPACK) and Beliefs of Pre-service Secondary Mathematics Teachers: Examining the Relationships. Eurasia Journal of Mathematics, Science and Technology Education, 14(10), em1590. https://doi.org/10.29333/ejmste/93179
  • Kline, R. B. (2011). Principles and practice of structural equation modeling, 93rd ed), Guilford Press.
  • Kontorovich, I. (2017). Students’ confusions with reciprocal and inverse functions. International Journal of Mathematical Education in Science and Technology, 48(2), 278-284. https://doi.org/10.1080/0020739X.2016.1223361
  • 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
  • Leinhardt, G., Zaslavsky, O., & Stein, M. S. (1990). Functions, graphs and graphing: Tasks, learning, and teaching. Review of Educational Research, 1, 1-64. https://doi.org/10.3102/00346543060001001
  • Loewenberg Ball, D., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special?. Journal of teacher education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
  • Magnusson, S., Krajcik, J., & Borko, H. (1999). Nature, sources, and development of pedagogical content knowledge for science teaching. In Examining pedagogical content knowledge (pp. 95-132). Springer, Dordrecht. https://doi.org/10.1007/0-306-47217-1_4
  • Malambo, P. (2016). Exploring Zambian mathematics student teachers’ content knowledge of functions and trigonometry for secondary schools (Doctoral dissertation), University of Pretoria.
  • Malambo, P., Van Putten, S., Botha, J. J., & Stols, G. H. (2019). Dysfunctional functions: the case of Zambian mathematics education students. Eurasia Journal of Mathematics, Science and Technology Education, 15(1), em1651. https://doi.org/10.29333/ejmste/99510
  • Marban, J. M., & Sintema, E. J. (2020). Pre-service secondary teachers’ of the function concept: A cluster analysis approach. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 5(1), 38-53. https://doi.org/10.23917/jramathedu.v5.i1.9703
  • Marks, R. (1990). Pedagogical content knowledge: From a mathematical case to a modified conception. Journal of teacher education, 41(3), 3-11. https://doi.org/10.1177/002248719004100302
  • Martínez-Planell, R., Gaisman, M. T., & McGee, D. (2015). On students’ understanding of the differential calculus of functions of two variables. The Journal of Mathematical Behavior, 38, 57-86. https://doi.org/10.1016/j.jmathb.2015.03.003
  • Matos, J. M. (2020). Construing Professional Knowledge of Secondary School Teachers of Mathematics: A Historical Perspective. Pedagogical Research, 5(3), em0058. https://doi.org/10.29333/pr/7898
  • Ministry of Education (2013). “O” level Mathematics Syllabus (Grades 10 t0 12), Lusaka, Zambia: Zambia Curriculum Development Centre.
  • Newton, K. J., Leonard, J., Evans, B. R., & Eastburn, J. A. (2012). Preservice elementary teachers’ mathematics content knowledge and teacher efficacy. School Science and Mathematics, 112(5), 289-299. https://doi.org/10.1111/j.1949-8594.2012.00145.x
  • Ohanian, R. (1990). Construction and validation of a measure celebrity endosers’ perceived expertise, trustworthiness, and attractiveness. Journal of advertising, 19(3), 39-52. https://doi.org/10.1080/00913367.1990.10673191
  • Ozgen, C. (2010). Pre-service secondary mathematics teachers’ pedagogical content knowledge of composite and inverse functions (Doctoral Dissertation), Middle East Technical University.
  • Ozkan, E. M., & Unal, H. (2009). Misconceptions in Calculus-1: Engineering students’ misconception in the process of finding domain of a function. Procedia Social and Behavioral Sciences, 1(1), 1792-1796. https://doi.org/10.1016/j.sbspro.2009.01.317
  • Polit, D. F., & Beck, C. T. (2004). Nursing research: Principles and methods (7th ed.) Philadelphia: Lippincott, Williams, & Wilkin.
  • Polit, D.F., Beck, C.T., & Owen, S.V. (2007). Is the CVI an acceptable indicator of content validity? Appraisa and recommendations. Research in Nursing & Health, 30, 459-467. https://doi.org/10.1002/nur.20199
  • Sánchez-Jiménez, E. (2020). The Methodology of Mathematics and the Emergence of a Proto Discipline. Pedagogical Research, 5(3), em0064. https://doi.org/10.29333/pr/8201
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
  • Shulman, L. S. (1987). Knowledge and Teaching: Foundations of the New Reforms. Harvard Educational Review, 57, 1-22. https://doi.org/10.17763/haer.57.1.j463w79r56455411
  • Sintema, E. J., Phiri, P. A., & Marban, J. M. (2018). Zambian mathematics pre-service secondary mathematics teachers’ knowledge of the function concept: Theoretical framework and a literature review with implications for Zambia. Journal of Global Research in Education and Social Sciences, 12(3), 133-147.
  • Teo T. S., Srivastava, S. C., & Jiang, L. (2008). Trust and electronic government success: an empirical study. Journal of Management Information Systems, 25(3), 99-132. https://doi.org/10.2753/MIS0742-1222250303
  • Ubah, I. J. A., & Bansilal, S. (2018). Pre-service mathematics teachers’ knowledge of mathematics for teaching: quadratic functions. Problems of Education in the 21st Century, Problems of Education in the 21st Century, 76(6), 847-863. https://doi.org/10.33225/pec/18.76.847
  • Usak, M., Ozden, M., & Eilks, I. (2011). A case study of beginning science teachers’ subject matter (SMK) and pedagogical content knowledge (PCK) of teaching chemical re action in Turkey. European Journal of Teacher Education, 34(4), 407-429. https://doi.org/10.1080/02619768.2011.592977
  • Usak, M., Ulker, R., Oztas, F., & Terzi, I. (2013). The Effects of Professors’ Pedagogical Content Knowledge on Elementary Teacher Candidates’ Attitude and Achievement Regarding Biology. The Anthropologist, 16(1-2), 251-261. https://doi.org/10.1080/09720073.2013.11891353
  • Wasserman, N. H. (2017). Making sense of abstract algebra: Exploring secondary teachers’ understanding of inverse functions in relation to its group structure. International Journal of Mathematical Education in Science and Technology, 19(3), 181-201. https://doi.org/10.1080/10986065.2017.1328635
  • Watson, A., Ayalon, M., & Lerman, S. (2018). Comparison of students’ understanding of functions in classes following English and Israel national curricula. Education Studies in Mathematics, 97(3), 255-272. https://doi.org/10.1007/s10649-017-9798-8
  • You, Z. (2010). Preservice teachers’ knowledge of linear functions within multiple representation modes (Doctoral dissertation), Texas A & M University.

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.