RESEARCH PAPER
Modelling Opportunities to Learn, Mathematical Belief and Knowledge for Teaching among Pre-service Teachers
 
More details
Hide details
1
University of Malaya Faculty of Education, Kuala Lumpur, MALAYSIA
 
 
Online publication date: 2019-04-08
 
 
Publication date: 2019-04-08
 
 
EURASIA J. Math., Sci Tech. Ed 2019;15(7):em1724
 
KEYWORDS
ABSTRACT
Issues about low level of mathematical knowledge for teaching among pre-service teachers has raised the question on the effectiveness of the mathematics teacher education program which has been planned and implemented by the Malaysian Institute of Teacher Education (MITE). This study was conducted to identify factors that affect mathematical knowledge for teaching (MKT) among pre-service teachers in Institute of Teacher Education (ITE). The influence of mathematical belief and opportunity to learn (OTL) have been tested to explain the factors affecting MKT. Using a structured questionnaire together with paper and pencil test adapted from the literature reviewed, data were collected from 105 pre-service teachers in MITE. Data were analysed using SmartPLS version 3.0. The result of the structural equation model indicated that OTL-Practicum (β=0.491, p<0.001) and OTL-Program (β=0.368, p<0.001) has a positive relationship with mathematical knowledge for teaching. Besides that, the result for the impact of OTL on mathematical belief, it showed that OTL-Practicum (β=0.208, p<0.001) and OTL-Program (β=0.243, p<0.001) has a positive relationship with constructivist belief, whereas OTL-Program was negatively related to traditional belief (β=-0.283, p<0.001). Overall, the model explained 53.9% of the variance in mathematical knowledge for teaching. Implications from these findings to the ITE were further elaborated.
REFERENCES (63)
1.
Acharya, A. S., Prakash, A., Saxena, P., & Nigam, A. (2013). Sampling : Why and How of it? Indian Journal of Medical Specialities, 4(2), 330–333. http://doi.org/10.7713/ijms.20....
 
2.
Adnan M., Abdullah M. F. N. L., & Che Ahmad C. N. (2014). Aplikasi Model Persamaan Berstruktur dalam Menilai Kepercayaan dan Pengetahuan Konseptual Guru Matematik Sekolah Rendah. Jurnal Pendidikan Matematik, 2(1), 32–50.
 
3.
Akkoç, H., & Yesildere, S. (2010). Investigating development of pre-service elementary mathematics teachers’ pedagogical content knowledge through a school practicum course. Procedia - Social and Behavioral Sciences, 2(2), 1410–1415. http://doi.org/10.1016/j.sbspr....
 
4.
Austin, J. (2015). Prospective Teachers’ Personal Mathematics Teacher Efficacy Beliefs and Mathematical Knowledge for Teaching. Mathematics Education, 10(1), 17–36. http://doi.org/10.12973/mathed....
 
5.
Ayieko R. A. (2014). The Influence of Opportunity to Learn to Teach Mathematics on Pre-service Teachers’ Knowledge and Belief: A Comparative Study. Michigan State University.
 
6.
Ball, D. L. (2000). Bridging Practices: Intertwining Content and Pedagogy in Teaching and Learning to Teach. Journal of Teacher Education, 51(3), 241–247. http://doi.org/10.1177/0022487....
 
7.
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. http://doi.org/10.1177/0022487....
 
8.
Beswick, K. (2012). Teachers’ beliefs about school mathematics and mathematicians’ mathematics and their relationship to practice. Educational Studies in Mathematics, 79(1), 127–147. http://doi.org/10.1007/s10649-....
 
9.
Blömeke, S., Jenßen, L., Grassmann, M., Dunekacke, S., & Wedekind, H. (2016). Process Mediates Structure: The Relation Between Preschool Teacher Education and Preschool Teachers’ Knowledge. Journal of Educational Psychology, 109(3), 338–354. http://doi.org/10.1037/edu0000....
 
10.
Bloom, B. S., Englehard, M. D., Furst, E. J., Hill, W. H., & Krathwohl, D. R. (1956). Taxonomy of educational objectives: The classification of educational goals: Handbook I, cognitive domain. New York (Vol. 16). http://doi.org/10.1300/J104v03....
 
11.
Carroll, J. (1963). A model of school learning. Teachers College Record, 64, 723–733.
 
12.
Considine, J., Botti, M., & Thomas, S. (2005). Design, format, validity and reliability of multiple choice questions for use in nursing research and education. Collegian, 12(1), 19–24. http://doi.org/10.1016/S1322-7....
 
13.
Cross, D. I. (2009). Alignment, cohesion, and change: Examining mathematics teachers’ belief structures and their influence on instructional practices. Journal of Mathematics Teacher Education, 12(5), 325–346. http://doi.org/10.1007/s10857-....
 
14.
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. http://doi.org/10.1016/j.tate.....
 
15.
Ernest, P. (1989). The Knowledge, Beliefs and Attitudes of the Mathematics Teacher: a model. Journal of Education for Teaching: International Research and Pedagogy, 15(1), 13–33. http://doi.org/10.1080/0260747....
 
16.
Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 147–164).
 
17.
Fitzallen, N. (2015). STEM education: What does mathematics have to offer? 38th Annual Conference of the Mathematics Education Research Group of Australasia, (June), 237–244.
 
18.
Fornell, C., & Larcker, D. F. (1981). Evaluating Structural Equation Models with Unobservable Variables and Measurement Error. Journal of Marketing Research, 18(1), 39. http://doi.org/10.2307/3151312.
 
19.
Goos, M. (2013). Knowledge for teaching secondary school mathematics: what counts? International Journal of Mathematical Education in Science and Technology, 44(7), 972–983. http://doi.org/10.1080/0020739....
 
20.
Hair, J. F. J., Hult, G. T. M., Ringle, C. M., & Sarstedt, M. (2017). A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM). SAGE Publications Ltd.
 
21.
Hair, J. F., Ringle, C. M., & Sarstedt, M. (2011). PLS-SEM: Indeed a Silver Bullet. Journal of Marketing Theory and Practice, 19(2), 139–152. http://doi.org/10.2753/MTP1069....
 
22.
Hassan N., & Ismail Z. (2008). Pengetahuan Pedagogi Kandungan Guru Pelatih Matematik Sekolah Menengah. Seminar Kebangsaan Pendidikan Sains Dan Matematik, 1–14.
 
23.
Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 65–97).
 
24.
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, 39(4), 372–400. http://doi.org/Article.
 
25.
Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of Teachers’ Mathematical Knowledge for Teaching on Student Achievement. American Educational Research Journal, 42(2), 371–406.
 
26.
Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing Measures of Teachers’ Mathematics Knowledge for Teaching. The Elementary School Journal, 105(1), 11–30.
 
27.
Holmes, V. (2012). Depth of Teachers’ Knowledge : Frameworks for Teachers ‘ Knowledge of Mathematics. Journal of STEM Education, 13(1), 55–71.
 
28.
Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1–55. http://doi.org/10.1080/1070551....
 
29.
Hulland, J. (2002). Use of partial least squares (PLS) in strategic management research: A review of four recent studies. Strategic Management Journal, 8(2), 195–204. http://doi.org/10.1002/smj.43l.
 
30.
Kleickmann, T., Richter, D., Kunter, M., Elsner, J., Besser, M., Krauss, S., & Baumert, J. (2013). Teachers’ Content Knowledge and Pedagogical Content Knowledge : The Role of Structural Differences in Teacher Education. Journal of Teacher Education, 64(1), 90–106. http://doi.org/10.1177/0022487....
 
31.
Konig, J., Tachtsoglou, S., Lammerding, S., Straub, S., Nold, G., & Rohde, A. (2017). The Role of Opportunities to Learn in Teacher Preparation for EFL Teachers’ Pedagogical Content Knowledge. The Modern Language Journal, 101(1), 1–19. http://doi.org/10.1111/modl.12....
 
32.
Kul, U., & Celik, S. (2017). Exploration of Pre- service Teachers ‘ Beliefs in relation to Mathematics Teaching Activities in Classroom-based Setting. International Journal of Research in Education and Science (IJRES), 3(1), 245–257.
 
33.
Leinhardt, G., & Greeno, J. G. (1986). The cognitive skill of teaching. Journal of Educational Psychology, 78(2), 75–95. http://doi.org/10.1037/0022-06....
 
34.
Leong K. E., Chew C. M, & Abdul Rahim S. S. (2015). Understanding Malaysian pre-service teachers mathematical content knowledge and pedagogical content knowledge. Eurasia Journal of Mathematics, Science and Technology Education, 11(2), 363–370. http://doi.org/10.12973/eurasi....
 
35.
Lim, C. P., & Chai, C. S. (2008). Teachers’ pedagogical beliefs and their planning and conduct of computer-mediated classroom lessons. British Journal of Educational Technology, 39(5), 807–828. http://doi.org/10.1111/j.1467-....
 
36.
Livy, S., & Downton, A. (2018). Exploring experiences for assisting primary pre-service teachers to extend their knowledge of student strategies and reasoning. Journal of Mathematical Behavior, (November 2016), 1–11. http://doi.org/10.1016/j.jmath....
 
37.
Meschede, N., Fiebranz, A., Möller, K., & Steffensky, M. (2017). Teachers’ professional vision, pedagogical content knowledge and beliefs: On its relation and differences between pre-service and in-service teachers. Teaching and Teacher Education, 66, 158–170. http://doi.org/10.1016/j.tate.....
 
38.
Mohd Yusof Y., & Zakaria E. (2015). The Integration of Teacher’s Pedagogical Content Knowledge Components in Teaching Linear Equation. International Education Studies, 8(11), 26–33. http://doi.org/10.5539/ies.v8n....
 
39.
NCTM. (2000). Principles and Standards for School Mathematics. United States of America: The National Council of Teachers of Mathematics, Inc.
 
40.
Pajares, M. F. (1992). Teachers’ Beliefs and Educational Research: Cleaning Up a Messy Construct. Review of Educational Research, 62(3), 307–332. http://doi.org/10.3102/0034654....
 
41.
Philipp, R. A., Ambrose, R., Lamb, L. L. C., Sowder, J. T., Schappelle, B. P., Sowder, L., … Nickerson, S. (2007). Effects of Early Field Experiences on the Mathematical Content Knowledge and Beliefs of Prospective Elementary School Teachers: An Experimental Study. Journal for Research in Mathematics Education, 38(5), 438–476. http://doi.org/10.2307/3003496....
 
42.
Philippou, G., & Christou, C. (2002). A Study of the Mathematics Teaching Efficacy Belief of a Primary Teachers. In Beliefs: A Hidden Variable in Mathematics Education? (pp. 211–231). Netherlands: Kluwer Academic Publishers.
 
43.
Porter, A. C. (2002). Measuring the content of instruction: Uses in research and practice. Educational Researcher, 31(7), 3–14. http://doi.org/10.3102/0013189....
 
44.
Qian, H., & Youngs, P. (2016). The effect of teacher education programs on future elementary mathematics teachers’ knowledge: a five-country analysis using TEDS-M data. Journal of Mathematics Teacher Education, 19(4), 371–396. http://doi.org/10.1007/s10857-....
 
45.
Ren, L., & Smith, W. M. (2017). Teacher characteristics and contextual factors: links to early primary teachers’ mathematical beliefs and attitudes. Journal of Mathematics Teacher Education, pp. 1–30. http://doi.org/10.1007/s10857-....
 
46.
Richardson, V. (1996). The role of attitudes and beliefs in learning to teach.
 
47.
Shulman, L. S. (1986). Those who understand: knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
 
48.
Shulman, L. S. (1987). Knowledge and Teaching: Foundations of the New Reform. Harvard Educational Review, 57(1), 1–21.
 
49.
Si-Mui Sim, & Raja Isaiah Rasiah. (2006). Relationship between item difficulty and discrimination indices in true/false-type multiple choice questions of a para-clinical multidisciplinary paper. Annals of the Academy of Medicine Singapore, 35(2), 67–71.
 
50.
Skemp, R. R. (1978). Relational Understanding and Instrumental Understanding. The Arithmetic Teacher, 26(3), 9–15. http://doi.org/10.1017/CBO9781....
 
51.
Suffian H., & Abdul Rahman S. (2010). Teachers’ choice and use of examples in the teaching and learning of mathematics in primary school and their relations to teacher’s pedagogical content knowledge (PCK). Procedia - Social and Behavioral Sciences, 8(5), 312–316. http://doi.org/10.1016/j.sbspr....
 
52.
Swars, S., Hart, L. C., Smith, S. Z., Smith, M. E., & Tolar, T. (2007). A Longitudinal Study of Elementary Pre-service Teachers’ Mathematics Beliefs and Content Knowledge. School Science and Mathematics, 107(8), 325–335. http://doi.org/10.1111/j.1949-....
 
53.
Tatto, M. T. (2013). The Teacher Education and Development Study in Mathematics (TEDS-M): Policy, Practice, and Readiness to Teach Primary and Secondary Mathematics in 17 Countries. Technical Report. http://doi.org/10.1038/nn.2116.
 
54.
Tatto, M. T., Peck, R., Schwille, J., Bankov, K., Senk, S. L., Rodriguez, M., … Rowley, G. (2012). Policy, Practice, and Readiness to Teach Primary and Secondary Mathematics in 17 Countries: Findings from the IEA Teacher Education and Development Study in Mathematics (TEDS-M-M). International Association for the Evaluation of Educational Achievement. Retrieved from http://eric.ed.gov/?id=ED54238....
 
55.
Tatto, M. T., Rodriguez, M., & Lu, Y. (2015). The Influence of Teacher Education on Mathematics Teaching Knowledge: Local Implementation of Global Ideals. Promoting and Sustaining a Quality Teacher Workforce, 27(1), 279–331. http://doi.org/10.1108/IJBM-07....
 
56.
Tatto, M. T., Senk, S. L., & Rowley, G. (2008). Teacher Education and Development Study in Mathematics (TEDS-M).
 
57.
Tengku Zainal T. Z., Mustapha R., & Habib A. R. (2009). Pengetahuan Pedagogi Isi Kandungan Guru Matematik bagi Tajuk Pecahan : Kajian Kes di Sekolah Rendah. Jurnal Pendidikan Malaysia, 34(1), 131–153.
 
58.
Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. Handbook of Research on Mathematics Teaching and Learning, 127–146.
 
59.
Ting-Ying Wang, & Shu-Jyh Tang. (2013). Profiles of Opportunities To Learn for Teds-M Future Secondary Mathematics Teachers. International Journal of Science and Mathematics Education, 11(4), 847–877. http://doi.org/10.1007/s10763-....
 
60.
Toh T. L., Berinderjeet K., & Koay P. L. (2009). Singapore Pre-service Secondary Mathematics Teachers’ Content Knowledge : Findings from an International Comparative Study. The Mathematics Educator, 1–22.
 
61.
Wasserman, N. H. (2018). Knowledge of nonlocal mathematics for teaching. Journal of Mathematical Behavior, 49(November 2017), 116–128. http://doi.org/10.1016/j.jmath....
 
62.
Zakaria E., Halim L., Abdullah K., Mohd Nordin N., Mohamad N. S., & Daud M. Y. (2009). Pembangunan instrumen kepercayaan guru-guru pra-perkhidmatan terhadap matematik, pengajaran matematik dan pembelajaran matematik. Laporan Penyelidikan. Fakulti Pendidikan UKM.
 
63.
Zulkpli Z., Mohamed M., & Abdullah A. H. (2017). Assessing Mathematics Teachers’ Knowledge in Teaching Thinking Skills. Sains Humanika, 9(1–4), 83–87. http://doi.org/10.11113/sh.v9n....
 
eISSN:1305-8223
ISSN:1305-8215
Journals System - logo
Scroll to top