Article Sidebar

Download
PDF
Statistic
Read Counter : 293 Download : 159

Downloads

Download data is not yet available.

Main Article Content

Abstract

This study aimed to develop a specific Mathematical Content Knowledge (MCK) test focused on multiplication for pre-service mathematics teachers in Indonesia and Türkiye. No assessment tool exists to measure MCK related to multiplication among pre-service mathematics teachers. We used convenience sampling to obtain data from third- and fourth-year pre-service teachers in Indonesian and Turkish mathematics teacher education programs. The test items were administered to 423 Indonesian pre-service mathematics teachers and 413 Turkish pre-service mathematics teachers, and their responses were analyzed using factor analysis. The MCK test was found to be reliable, with 18 items that were grouped into four components: procedural knowledge of multiplication (C1), understanding of multiple representations (C2), conceptual knowledge of multiplication (C3), and anticipating students' thinking (C4). The study results suggest that a valid MCK test helps evaluate multiplication in these four components. Additionally, the study findings indicate that Indonesian pre-service teachers score higher in the C1 and C4 categories, while Turkish pre-service teachers score higher in the C2 and C3 categories.

Keywords

Comparative Studies Indonesia Mathematical Content Knowledge Test Multiplication Pre-Service Mathematics Teachers Türkiye

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite
Novikasari, I., & Dede, Y. (2024). Toward proficiency: Developing a multiplication mathematical content knowledge test for pre-service mathematics teachers in Indonesia and Türkiye. Journal on Mathematics Education, 15(1), 115–130. https://doi.org/10.22342/jme.v15i1.pp115-130
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX

References

  1. Alsina, A., Maurandi, A., Ferre, E., & Coronata, C. (2021). Validating an Instrument to Evaluate the Teaching of Mathematics Through Processes. International Journal of Science and Mathematics Education, 19(3), 559–577. https://doi.org/10.1007/s10763-020-10064-y
  2. Babadoğan, C., & Olkun, S. (2006). Program development models and reform in Turkish Primary School Mathematics curriculum. International Journal for Mathematics Teaching and Learning, 1–6. https://doi.org/10.1501/0003623
  3. Ball, D. L., Bass, H., Boerst, T., Cole, Y., Jacobs, J., Kim, Y., Lewis, J., Sleep, L., Suzuka, K., Thames, M., & Zopf, D. (2008). Developing Teachers ’ Mathematical Knowledge for Teaching Overview of session 1 . A larger perspective : why are we doing this, and. 734.
  4. Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing Mathematics for Teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29(1), 14–17. http://hdl.handle.net/2027.42/65072
  5. 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
  6. Beaton, D. E., Bombardier, C., Guillemin, F., & Ferraz, M. B. (2000). Guidelines for the process of cross-cultural adaptation of self-report measures. Spine, 25(24), 3186–3191. https://doi.org/10.1097/00007632-200012150-00014
  7. Beswick, K. (2019). The role of knowledge and beliefs in helping learners to progress their mathematical understanding. Journal of Mathematics Teacher Education, 22(2), 125–128. https://doi.org/10.1007/s10857-019-09432-5
  8. Burroughs, N., Gardner, J., Lee, Y., Guo, S., Touitou, I., Jansen, K., & Schmidt, W. (2019). Teacher Quality and Mean Student Outcomes: A Multi-model Approach. In Teaching for Excellence and Equity (Vol. 6, pp. 47–62). Springer. https://doi.org/10.1007/978-3-030-16151-4_5
  9. Busi, R., & Jacobbe, T. (2018). The Impact of Analyzing Student Work on Preservice Teachers’ Content Knowledge and Beliefs about Effective Mathematics Teaching. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1, 1–20.
  10. Cai, J., & Ni, Y. (2011). Investigating curricular effect on the teaching and learning of mathematics in a cultural context: Theoretical and methodological considerations. International Journal of Educational Research, 50(2), 65–70. https://doi.org/10.1016/j.ijer.2011.06.002
  11. Charalambous, C. Y., Hill, H. C., Chin, M. J., & McGinn, D. (2020). Mathematical content knowledge and knowledge for teaching: exploring their distinguishability and contribution to student learning. Journal of Mathematics Teacher Education, 23(6), 579–613. https://doi.org/10.1007/s10857-019-09443-2
  12. Christou, K. P., & Vamvakoussi, X. (2023). Natural number bias on evaluations of the effect of multiplication and division: the role of the type of numbers. Mathematics Education Research Journal, 35(3), 427-443.
  13. Copur-Gencturk, Y., Plowman, D., & Bai, H. (2019). Mathematics Teachers’ Learning: Identifying Key Learning Opportunities Linked to Teachers’ Knowledge Growth. American Educational Research Journal, 56(5), 1590–1628. https://doi.org/10.3102/0002831218820033
  14. Cox, A. (2005). What are communities of practice? A comparative review of four seminal works. Journal of Information Science, 31(6), 527–540. https://doi.org/10.1177/0165551505057016
  15. Dede, Y. (2012). Why is Mathematics Valuable ? A Comparison of Turkish and German Mathematics Teachers Por que a Matemática é Importante ? Uma Comparação entre Professores de Matemática Turcos e Alemães. Bolema, Rio Clarp, 26(44), 1171–1206.
  16. Ding, M. (2016). Developing preservice elementary teachers’ specialized content knowledge: the case of associative property. International Journal of STEM Education, 3(9), 1-19. https://doi.org/10.1186/s40594-016-0041-4
  17. Field, A. (2013). Discovering statistics using SPSS statistics, 4th edition. In Statistics. SAGE.
  18. Franklin, S. B., Gibson, D. J., Robertson, P. A., Pohlmann, J. T., & Fralish, J. S. (1995). Parallel Analysis: a method for determining significant principal components. Journal of Vegetation Science, 6(1), 99-106. https://doi.org/10.2307/3236261
  19. Ghazali, M., Idros, S. N., & McIntosh, A. (2004). From doing to understanding: An assessment of Malaysian primary pupils’ number sense with respect to multiplication. Journal of Science and Mathematics Education in Southeast Asia, 27(2), 92–111.
  20. Grossman, P. L. (1989). Learning to Teach without Teacher Education. Teachers College Record, 91(2), 191–208. https://doi.org/https://doi.org/10.1177/016146818909100201
  21. Hair, J. F., Anderson, R. E., Tatham, R. L., & Black, W. C. (1998). Multivariate data analysis with readings (5nd ed.). In Prentice-Hall, Upper Saddle River. Prentice Hall.
  22. Haladyna, T. M. (2004). Developing and validating multiple-choice test items. Routledge.
  23. Hickendorff, M., Torbeyns, J., & Verschaffel, L. (2019). Multi-digit addition, subtraction, multiplication, and division strategies. In International Handbook of Mathematical Learning Difficulties: From the Laboratory to the Classroom. https://doi.org/10.1007/978-3-319-97148-3_32
  24. Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. Elementary School Journal, 105(1), 11-30. https://doi.org/10.1086/428763
  25. Hino, K., & Kato, H. (2019). Teaching whole-number multiplication to promote children’s proportional reasoning: a practice-based perspective from Japan. ZDM - Mathematics Education. https://doi.org/10.1007/s11858-018-0993-6
  26. Huang, R., & Kulm, G. (2012). Prospective middle grade mathematics teachers’ knowledge of algebra for teaching. Journal of Mathematical Behavior. https://doi.org/10.1016/j.jmathb.2012.06.001
  27. Jager, J., Putnick, D. L., & Bornstein, M. H. (2017). More than just convenient: The scientific merits of homogeneous convenience samples. Monographs of the Society for Research in Child Development, 82(2), 13-30. https://doi.org/10.1111/mono.12296
  28. Jankvist, U. T., Clark, K. M., & Mosvold, R. (2020). Developing mathematical knowledge for teaching teachers: potentials of history of mathematics in teacher educator training. Journal of Mathematics Teacher Education, 23(3), 311–332. https://doi.org/10.1007/s10857-018-09424-x
  29. Kablan, Z., & Uğur, S. S. (2021). The relationship between routine and non-routine problem solving and learning styles. Educational Studies, 47(3), 328–343. https://doi.org/10.1080/03055698.2019.1701993
  30. Kaiser, H. (1974). An index of factorial simplicity. Psychometrika, 31–36. https://doi.org/10.1007/BF02291575
  31. Kawanaka, T., Stigler, J. W., & Hiebert, J. (2012). Studying mathematics classrooms in Germany, Japan and the United States: Lessons from timss videotape study. In G. Kaiser, E. Luna, & I. Huntley (Eds.), International Comparisons in Mathematics Education. Routledge. https://doi.org/10.4324/9780203012086-12
  32. Kemendikbud. (2013). Kompetensi Dasar. Kementerian Pendidikan dan Kebudayaan.
  33. Koponen, M., Asikainen, M. A., Viholainen, A., & Hirvonen, P. E. (2019). Using network analysis methods to investigate how future teachers conceptualize the links between the domains of teacher knowledge. Teaching and Teacher Education. https://doi.org/10.1016/j.tate.2018.12.010
  34. Kosko, K., & Singh, R. (2018). Elementary Children’s Multiplicative Reasoning: Initial Validation of a Written Assessment. Mathematics Educator.
  35. Krauss, S., Neubrand, M., Blum, W., & Baumert, J. (2008). The Professional Knowledge of German Secondary Mathematics Teachers: Investigations in the Context of the COACTIV Project. Online paper for the 11th International Congress on Mathematics Education (ICM 11) in Monterrey, Mexico (TSG 27).
  36. Larsson, K. (2016). Students' understandings of multiplication. Doctoral dissertation. Department of Mathematics and Science Education, Stockholm University.
  37. Levin, M. (2018). Conceptual and Procedural Knowledge During Strategy Construction: A Complex Knowledge Systems Perspective. Cognition and Instruction, 36(3), 247–278. https://doi.org/10.1080/07370008.2018.1464003
  38. Llinares, S. (2018). Mathematics teacher’s knowledge, knowledge-based reasoning, and contexts. Journal of Mathematics Teacher Education, 21, 1-3. https://doi.org/10.1007/s10857-018-9399-1
  39. Lorenzo-Seva, U. (1999). Promin: A method for oblique factor rotation. Multivariate Behavioral Research. https://doi.org/10.1207/S15327906MBR3403_3
  40. Ma, L. (2010). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States: Second Edition. Lawrence Erlbaum Associates. https://doi.org/10.4324/9780203856345
  41. Ma, L., & Kessel, C. (2018). The Theory of School Arithmetic: Whole Numbers. In New ICMI Study Series. https://doi.org/10.1007/978-3-319-63555-2_18
  42. Mack, N. K. (2000). Long-term effects of building on informal knowledge in a complex content domain: The case of multiplication of fractions. Paper Presented at the Annual Meeting of the American Educational Research Association (New Orleans, LA, April 27-28, 2000). https://doi.org/10.1016/s0732-3123(00)00050-x
  43. Max, B., & Amstutz, M. (2019). The Intersection of MET II Content Domains and Mathematical Knowledge for Teaching in Mathematics Content for Elementary Teachers Courses. Issues in the Undergraduate Mathematics Preparation of School Teachers.
  44. MEB. (2018). Matematik Dersi Öğretim Programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar) (p. 80). http://mufredat.meb.gov.tr
  45. Mohammadpour, E., & Maroofi, Y. (2023). A performance-based test to measure teachers’ mathematics and science content and pedagogical knowledge. Heliyon, 9(3), 1–11. https://doi.org/https://doi.org/10.1016/j.heliyon.2023.e13932
  46. Morris, A. K., & Hiebert, J. (2017). Effects of Teacher Preparation Courses: Do Graduates Use What They Learned to Plan Mathematics Lessons? American Educational Research Journal, 54(3), 524–567. https://doi.org/10.3102/0002831217695217
  47. Novikasari, I., & Dede, Y. (2021). Turkish Pre-Service Mathematics Teachers’ Beliefs in Multiplication. Journal on Mathematics Education, 12(3), 469–486. http://doi.org/10.22342/jme.12.3.14440.469-486
  48. Rittle-Johnson, B., & Schneider, M. (2014). Developing Conceptual and Procedural Knowledge of Mathematics. Oxford Handbook of Numerical Cognition, 1118–1134. https://doi.org/10.1093/oxfordhb/9780199642342.013.014
  49. Shulman, L. S. (1986). Those who understand: Knowledge Growth in Teaching. Educational Researcher, 15(2), 4–14. https://doi.org/https://doi.org/10.3102/0013189X015002004
  50. Sidney, P. G., Thompson, C. A., & Rivera, F. D. (2019). Number lines, but not area models, support children’s accuracy and conceptual models of fraction division. Contemporary Educational Psychology. https://doi.org/10.1016/j.cedpsych.2019.03.011
  51. Siemon, D., Izard, J., Breed, M., & Virgona, J. (2006). the Derivation of a Learning Assessment Framework for Multiplicative Thinking. Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education.
  52. Simon, M. A., Placa, N., Avitzur, A., & Kara, M. (2018). Promoting a concept of fraction-as-measure: A study of the Learning Through Activity research program. Journal of Mathematical Behavior. https://doi.org/10.1016/j.jmathb.2018.03.004
  53. Southwell, B., & Penglase, M. (2005). Mathematical Knowledge of Pre-Service Primary Teachers. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, 4, 209–216.
  54. Star, J. R. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36(5), 404–411.
  55. Star, J. R., & Stylianides, G. J. (2013). Procedural and conceptual knowledge: Exploring the gap between knowledge type and knowledge quality. Canadian journal of science, mathematics and technology education, 13, 169-181. https://doi.org/10.1080/14926156.2013.784828
  56. Tall, D., & Razali, M. R. (1993). Diagnosing students’ difficulties in learning mathematics. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739930240206
  57. Tatto, M. T., Schwille, J., Senk, S. L., 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.
  58. Valanides, N. (2000). Primary student teachers’understanding of the process and effects of distillation. Chemistry Education Research and Practice, 1(3), 355-364. https://doi.org/10.1039/A9RP90032B
  59. Venkat, H. (2015). Mathematical practices and mathematical modes of enquiry: same or different? International Journal of STEM Education, 2(1). https://doi.org/10.1186/s40594-015-0018-8
  60. Vistro-Yu, C. P. (2013). Cross-national studies on the teaching and learning of mathematics: Where do we go from here? ZDM - International Journal on Mathematics Education. https://doi.org/10.1007/s11858-013-0488-4
  61. Walter, J. G., & Gerson, H. (2007). Teachers’ personal agency: Making sense of slope through additive structures. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-006-9048-y
  62. Whitehead, A., & Walkowiak, T. (2017). Preservice Elementary Teachers’ Understanding of Operations for Fraction Multiplication and Division. International Journal for Mathematics Teaching and Learning, 18(3), 293–317.
  63. Wu, H. (2012). Teaching Fractions According to the Common Core Standards. 2011, 1–153.
  64. Zajda, J. (2021). Globalisation and education reforms: Creating effective learning environments (Vol. 25). Springer Nature.
  65. Zhang, S., Cao, Y., Wang, L., & Li, X. (2019). Characteristics of teaching and learning single-digit whole number multiplication in china: the case of the nine-times table. ZDM - Mathematics Education. https://doi.org/10.1007/s11858-018-01014-8