Pengaruh Faktor Peluang untuk Belajar dan Kepercayaan Efikasi Terhadap Pengetahuan Matematik untuk Pengajaran (The Influence of Opportunities to Learn and Efficacy Belief Factor Towards Mathematical Knowledge for Teaching)
Main Article Content
Abstract
The present study investigates the influence of opportunities to learn (OTL) and mathematics teaching efficacy beliefs (MTEB) towards mathematical knowledge for teaching (MKT). Using a structured questionnaire together with paper and pencil test adapted from the literature reviewed, data were collected from 187 pre-service elementary teachers in Institute of Teacher Education (ITE) Malaysia. Data were analysed using SmartPLS 3.0. The result of the structural equation model indicated that both OTLPracticum (? = 0.395, p < 0.001) and OTL-Program (? = 0.324, p < 0.001) was positively related to MKT. The second regression analysis was to examine the impact of mathematics teaching efficacy belief on the MKT. The results showed that mathematics teaching outcome expectancy belief (MTOEB) (? = 0.322, p < 0.001) was positively related to MKT, whereas personal mathematics teaching efficacy belief (? = 0.017, p > 0.1) was not related to MKT. Overall, the belief and OTL factors explaining a total of 54% variance in MKT. Implications from these findings to the successful teacher’s education program implementation in Malaysia were further elaborated.
Kajian ini dijalankan untuk menguji pengaruh faktor peluang untuk belajar (PUB) dan kepercayaan efikasi pengajaran matematik (KEPM) terhadap pengetahuan matematik untuk pengajaran (PMUP). Data telah dikumpul daripada 187 orang guru pra perkhidmatan di Institut Pendidikan Guru (IPG) Malaysia dengan menggunakan borang soal selidik beserta ujian pensel dan kertas yang diadaptasi daripada kajian terdahulu. Analisis data telah dijalankan menggunakan perisian SmartPLS 3.0. Dapatan daripada analisis model persamaan berstruktur yang telah dijalankan menunjukkan kedua-dua faktor PUBPraktikum (? = 0.395, p < 0.001) dan PUB-Program (? = 0.324, p < 0.001) mempunyai perkaitan yang positif dengan PMUP. Analisis regresi yang kedua adalah untuk menguji pengaruh faktor kepercayaan efikasi pengajaran matematik terhadap PMUP. Dapatan menunjukkan Kepercayaan Jangkaan Hasil Pengajaran Matematik (KJHPM) (? = 0.322, p < 0.001) mempunyai perkaitan yang positif dengan PMUP, manakala faktor Kepercayaan Efikasi Pengajaran Matematik Peribadi (KEPMP) (? = 0.017, p > 0.1) pula didapati tidak mempunyai perkaitan dengan PMUP. Secara keseluruhan, kedua-dua faktor kepercayaan dan PUB menjelaskan sebanyak 54% varians di dalam PMUP. Implikasi kajian ini ke atas kejayaan pelaksanaan program pendidikan guru di Malaysia telah dihuraikan dengan lebih lanjut.
Article Details

This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Adamson, B. (2012). International comparative studies in teaching and teacher education. Teaching and Teacher Education, 28(5), 641–648. https://doi.org/10.1016/j.tate.2012.02.003
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. https://doi.org/DOI:10.1016/j.sbspro.2010.03.210
Alrajhi, M., Aldhafri, S., Alkharusi, H., Albusaidi, S., Alkharusi, B., Ambusaidi, A., & Alhosni, K. (2017). The predictive effects of math teachers’ emotional intelligence on their perceived self-efficacy beliefs. Teaching and Teacher Education, 67, 378–388. https://doi.org/10.1016/j.tate.2017.07.003
Austin, J. (2015). Prospective teachers’ personal mathematics teacher efficacy beliefs and mathematical knowledge for teaching. Mathematics Education, 10(1), 17–36. https://doi.org/10.12973/mathedu.2015.102a
Ayieko R. A. (2014). The influence of opportunity to learn to teach mathematics on pre-service teachers’ knowledge and belief: A comparative study. Unpublished doctoral dissertation, Michigan State University.
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://doi.org/10.1177/0022487108324554
Bandura, A. (1989a). Human agency in social cognitive theory. The American Psychologist, 44(9), 1175–1184. https://doi.org/10.1037/0003-066x.44.9.1175
Bandura, A. (1989b). Social cognitive theory. Annals of Child Development, 6, 1–6.
Barnard-Brak, L., Lan, W. Y., & Yang, Z. (2018). Differences in mathematics achievement according to opportunity to learn: A 4pL item response theory examination. Studies in Educational Evaluation, 56(August 2017), 1–7. https://doi.org/10.1016/j.stueduc.2017.11.002
Berger, J. L., Girardet, C., Vaudroz, C., & Crahay, M. (2018). Teaching experience, teachers’ beliefs, and self-reported classroom management practices: A coherent network. SAGE Open, 8(1), 1–12. https://doi.org/10.1177/2158244017754119
Blazar, D. (2015). Effective teaching in elementary mathematics: Identifying classroom practices that support student achievement. Economics of Education Review, 48, 16–29. https://doi.org/10.1016/j.econedurev.2015.05.005
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. https://doi.org/10.1037/edu0000147
Blömeke, S., Suhl, U., Kaiser, G., & Döhrmann, M. (2012). Family background, entry selectivity and opportunities to learn: What matters in primary teacher education? An international comparison of fifteen countries. Teaching and Teacher Education, 28(1), 44–55. https://doi.org/10.1016/j.tate.2011.08.006
Buchholtz, N. F. (2017). The acquisition of mathematics pedagogical content knowledge in university mathematics education courses: Results of a mixed methods study on the effectiveness of teacher education in Germany. ZDM - Mathematics Education, 49(2), 249–264. https://doi.org/10.1007/s11858-017-0849-5
Dunekacke, S., Jenben, L., Eilerts, K., & Blomeke, S. (2016). Epistemological beliefs of prospective preschool teachers and their relation to knowledge, perception, and planning abilities in the field of mathematics: A process model. ZDM - Mathematics Education, 48(1–2), 125–137. https://doi.org/10.1007/s11858-015-0711-6
Ekstam, U., Korhonen, J., Linnanmäki, K., & Aunio, P. (2017). Special education preservice teachers’ interest, subject knowledge, and teacher efficacy beliefs in mathematics. Teaching and Teacher Education, 63, 338–345. https://doi.org/10.1016/j.tate.2017.01.009
Enochs, L. G., Smith, P. L., & Huinker, D. (2000). Establishing factorial validity of the mathematics teaching efficacy beliefs instrument. School Science and Mathematics, 100(4), 194–202.
Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18(1), 39–50. https://doi.org/10.2307/3151312
Gerasimova, E., Shcherbatykh, S., Savvina, O., Simonovskaya, G., Masina, O., Trofimova, E., & Tarasova, O. (2017). Coexistence of theory and practice in training the future mathematics teacher: The experience of the Russian education system. Eurasia Journal of Mathematics, Science and Technology Education, 8223(12), 7695–7705. https://doi.org/10.12973/ejmste/80359
Goos, M. (2013). Knowledge for teaching secondary school mathematics: What counts? International Journal of Mathematical Education in Science and Technology, 44(7), 972–983. https://doi.org/10.1080/0020739X.2013.826387
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.
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.
Hine, G. S. C. (2015). Strengthening pre-service teachers’ mathematical content knowledge. Teaching and Learning Forum, 12(4), 1–11.
Irvin, M., Byun, S., Smiley, W. S., & Hutchins, B. C. (2017). Relation of opportunity to learn advanced math to the educational attainment of rural youth. American Journal of Education, 123(3), 475–510. https://doi.org/10.1086/691231
Kementerian Kewangan Malaysia. (2017). Bajet 2017. Putrajaya: Author.
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. https://doi.org/10.1177/0022487112460398
Kleickmann, T., Richter, D., Kunter, M., Elsner, J., Besser, M., Krauss, S., Cheo, M., & Baumert, J. (2015). Content knowledge and pedagogical content knowledge in Taiwanese and German mathematics teachers. Teaching and Teacher Education, 46, 115–126. https://doi.org/10.1016/j.tate.2014.11.004
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. https://doi.org/10.1111/modl.12383
Leong K. E., Chew C. M, & Abdul Rahim S. S. (2015). Understanding Malaysian preservice teachers mathematical content knowledge and pedagogical content knowledge. Eurasia Journal of Mathematics, Science and Technology Education, 11(2), 363–370. https://doi.org/10.12973/eurasia.2015.1346a
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, 51(September), 1–11. https://doi.org/10.1016/j.jmathb.2017.11.004
Livy, S., Vale, C., & Herbert, S. (2016). Developing primary pre-service teachers’ mathematical content knowledge during practicum teaching. Australian Journal of Teacher Education, 41(2), 152–173. https://doi.org/10.14221/ajte.2016v41n2.10
Lotter, C. R., Thompson, S., Dickenson, T. S., Smiley, W. F., Blue, G., & Rea, M. (2016). The impact of a practice-teaching professional development model on teachers’ inquiry instruction and inquiry efficacy beliefs. International Journal of Science and Mathematics Education, 16(2), 255–273. https://doi.org/10.1007/s10763-016-9779-x
Mohd Tajudin, N., Chinnapan, M., & Saad, N. S. (2017). Relationship between mathematics teacher subject matter knowledge, pedagogical content knowledge and professional development needs. Proceedings of the International Conference on Education, Mathematics and Science 2016 (ICEMS2016) in Conjunction with 4th International Postgraduate Conference on Science and Mathematics 2016 (IPCSM2016) 1847(1), 030001. https://doi.org/10.1063/1.4983878
Mohd Yusof, Y., & Zakaria, E. (2010). Investigating secondary mathematics teachers’ pedagogical content knowledge: A case study. Journal of Education and Sociology, March, 32–39.
Mosvold, R., & Fauskanger, J. (2014). Teachers’ beliefs about mathematical horizon content knowledge. International Journal of Mathematics Teaching and Learning, September, 1–9.
Mu, G. M., Liang, W., Lu, L., & Huang, D. (2018). Building pedagogical content knowledge within professional learning communities: An approach to counteracting regional education inequality. Teaching and Teacher Education, 73, 24–34. https://doi.org/10.1016/j.tate.2018.03.006
Murray, E., Durkin, K., Chao, T., & Star, J. R. (2018). Exploring connections between content knowledge, pedagogical content knowledge, and the opportunities to learn mathematics: Findings from the TEDS-M dataset. Mathematics Teacher Education and Development, 20(March), 4–22.
Newton, K. J., Evans, B. R., Eastburn, J. A, & Leonard, J. (2007). Preservice elementary teachers’ mathematics content knowledge and teacher efficacy. School Science and Mathematics, 112(5), 289–299.
Norton, S. J. (2017). Primary mathematics trainee teacher confidence and its relationship to mathematical knowledge. Australian Journal of Teacher Education, 42(2), 47–61.
Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory (Vol. 3). Mc Graw Hill Inc.
Oppermann, E., Anders, Y., & Hachfeld, A. (2016). The influence of preschool teachers’ content knowledge and mathematical ability beliefs on their sensitivity to mathematics in children’s play. Teaching and Teacher Education, 58, 174–184. https://doi.org/10.1016/j.tate.2016.05.004
Pape, S. J., Prosser, S. K., Griffin, C. C., Fichtman Dana, N., Algina, J., & Bae, J. (2015). Prime online: Developing grades 3–5 teachers’ content knowledge for teaching mathematics in an online professional development program. Contemporary Issues in Technology and Teacher Education, 15(1), 14–43.
Philippou, G., & Christou, C. (2002). A study of the mathematics teaching efficacy belief of a primary teachers. In G. C.
Leder, E. Pehkonen, E., & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 211–231). Netherlands: Kluwer Academic Publishers.
Polit, D. F., & Beck, C. T. (2006). The content validity index: Are you sure you know what’s being reported? Critique and recommendations. Research in Nursing and Health, 29(5), 489–497. https://doi.org/10.1002/nur.20147
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. https://doi.org/10.1007/s10857-014-9297-0
Ren, Y., Wang, J., & Hu, L. (2017). Multi-valued stochastic differential equations driven by G-Brownian motion. International Journal of Control, 90(5), 1132–1154.
Sanchez-Franco, M. J., & Roldán, J. L. (2010). Expressive aesthetics to ease perceived community support: Exploring personal innovativeness and routinised behaviour as moderators in Tuenti. Computers in Human Behavior, 26(6), 1445–1457. https://doi.org/10.1016/j.chb.2010.04.023
Shahbari, J. A. (2017). Mathematical and pedagogical knowledge amongst first- and second-grade in-service and pre-service mathematics teachers. International Journal for Mathematics Teaching and Learning, 18(1), 41–65.
Shi, Q. (2016). Interrelationships among teacher self-efficacy, collective teacher efficacy, and teachers’ pedagogical content knowledge. Unpublished doctoral dissertation, University of Nevada, Las Vegas.
Shirvani, H. (2015). Pre-service elementary teachers’ mathematics content knowledge: A predictor of sixth graders’ mathematics performance. International Journal of Instruction, 8(1), 132–142. Retrieved from http://www.scopus.com/inward/record.url?eid=2-s2.0-84921932931&partnerID=tZOtx3y1
Simsek, N., & Boz, N. (2016). Analysis of pedagogical content knowledge studies in the context of mathematics education in Turkey: A meta-synthesis study. Educational Sciences: Theory & Practice, 16(3), 799–826. https://doi.org/10.12738/estp.2016.3.0382
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. https://doi.org/10.1111/j.1949-8594.2007.tb17797.x
Swars, S. L., Smith, S. Z., Smith, M. E., & Hart, L. C. (2009). A longitudinal study of effects of a developmental teacher preparation program on elementary prospective teachers’ mathematics beliefs. Journal of Mathematics Teacher Education, 12(1), 47–66. https://doi.org/10.1007/s10857-008-9092-x
Tatto, M. T., Peck, R., Schwille, J., Bankov, K., Senk, S. L., Rodriguez, M., Ingvarson, L., Reckase, 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=ED542380
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. https://doi.org/10.1108/IJBM-07-2013-0069
Tatto, M. T., Schwille, J., Senk, S., Ingvarson, L., Peck, R., & Rowley, G. (2008). Teacher Education and Development Study in Mathematics (TEDS-M): Policy, practice, and readiness to teach primary and secondary mathematics. Conceptual framework. East Lansing, MI: Teacher Education and Development International Study Center, College of Education, Michigan State University.
Thanheiser, E., Browning, C., Edson, A., Kastberg, S., & Lo, J.-J. (2013). Building a knowledge base: Understanding prospective elementary teachers’ mathematical content knowledge. International Journal for Mathematics Teaching and Learning, 9(July), 1–34.
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.
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
Zulkpli Z., Mohamed M., & Abdullah A. H. (2017). Assessing mathematics teachers’ knowledge in teaching thinking skills. Sains Humanika, 9(1–4), 83–87. https://doi.org/10.11113/sh.v9n1-4.1129