In this study, we developed an instrument for assessing teachers’ mathematics content knowledge (MCK) on ratio and proportion and examined the profile of Indonesian primary teacher’s MCK on this topic. The MCK items were administered to 271 Indonesian in-service primary teachers with a variety of educational backgrounds and teaching experiences. Teachers’ responses were analyzed by factor analysis and cluster analysis. The MCK instrument was found to have good acceptability in the reliability analysis with 3 factor components—meaning of proportional and non-proportional situations, number structures in situation, and figural representation—which was the main result of the study. With respect to the 3 factors, the teachers in the 3 assigned categories (“Good,” “Middle,” or “Low”) showed consistent performance on the items of the 3 factors. In particular, our results indicated that Indonesian in-service primary teachers had difficulty with the factor on figural representation, but they performed best on number structures in situation representing products of proportional reasoning.


Indonesia mathematics content knowledge proportional reasoning ratio and proportion 


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  1. Ahl, V. A., Moore, C. F. & Dixon, J. A. (1992). Development of intuitive and numerical proportional reasoning. Cognitive Development, 7, 81–108.CrossRefGoogle Scholar
  2. Alatorre, S., & Figueras, O. (2005). A developmental model for proportional reasoning in ratio comparison tasks. In H. L. Chick, H. L. & J. L. Vincent, (Eds.), Proceeding of the 29th conference of the International Group for the Psychology of Mathematics Education, Vol. 2 (pp. 25–32). Melbourne: PME.Google Scholar
  3. 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? The fall 2005 issue of American Educator, the quarterly Journal of the American Federation of Teachers, AFL-CIO.Google Scholar
  4. Barret, J. (2002). Working with novice teachers: Challenges for professional development mathematics. Teacher Education and Development Journal, 4, 15–27.Google Scholar
  5. Barrett, J., Jones, G., Mooney, E., Thornton, C., Cady, J. & Guinee, P., et al. (2002). Working with novice teachers: challenges for professional development. Mathematics Teacher Education and Development, 4, 15–27.Google Scholar
  6. Bayazit, I. (2013). Quality of the tasks in the new Turkish elementary mathematics textbooks: The case of proportional reasoning. International Journal of Science and Mathematics Education, 11, 651–682.CrossRefGoogle Scholar
  7. Beaton, D., Bombardier, C. & Ferraz, M. (2000). Guidelines for the process of cross-cultural adaptation of self-report measures. Spine, 25(24), 3186–3191.CrossRefGoogle Scholar
  8. Behr, M., Harel, G., Post, T. & Lesh, R. (1992). Rational number, ratio and proportion. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 296–333). NY: Macmillan Publishing.Google Scholar
  9. Ben-Chaim, D., Fey, J. T., Fitzgerald, W. M., Benedett, O. C. & Miller, J. (1998). Proportional reasoning among 7th grade students with different curricular experiences. Educational Studies in Mathematics, 36, 247–273.CrossRefGoogle Scholar
  10. Blömeke, S. & Delaney, S. (2012). Assessment of teacher knowledge across countries: A review of the state of research. ZDM, 44(3), 223–247.CrossRefGoogle Scholar
  11. Brink, J. V. D. & Streefland, L. (1979). Young children (6–8)-ratio and proportion. Educational Studies in Mathematics, 10, 403–420.CrossRefGoogle Scholar
  12. Chaim, D. B., Keret, Y., & Ilany, B. (2007). Designing and implementing authentic investigative proportional reasoning tasks: the impact on pre-service mathematics teachers’ content and pedagogical knowledge and attitudes. Journal of Mathematics Teacher Education, 10, 333–340Google Scholar
  13. Chaim, D. B., Keret, Y. Z. & Ilany, B. S. (2012). Research and teaching in mathematics teachers’ education: Pre- and in-service mathematics teachers of elementary and middle school classes. Rotterdam: Sense.Google Scholar
  14. Coakes, S. J. & Steed, L. G. (1997). SPSS analysis without anguish. Brisbane: John Wiley and Sons.Google Scholar
  15. Dole, S. (2008). Ratio tables to promote proportional reasoning in the primary classroom. Australian Primary Mathematics Classroom, 13(2), 19–22.Google Scholar
  16. Ebel, R. L. & Frisbie, D. A. (1986). Essentials of educational measurement. Englewood Cliffs: Prentice-Hall.Google Scholar
  17. Entwistle, N., Tait, H., & McCune, V. (2000). Patterns of response to an approaches to studying inventory across contrasting groups and contexts. European Journal of Psychology of Education, 15(1), 33–48.Google Scholar
  18. Fennema, E. & Franke, M. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning. NY: Macmillan.Google Scholar
  19. Fischbein, E. (1994). Tacit models. In D. Tirosh (Ed.), Implicit and explicit knowledge: An educational approach (pp. 96–110). Norwood: Ablex.Google Scholar
  20. Hair, J. F., Jr., Anderson, R. E., Tatham, R. L. & Black, W. C. (1998). Multivariate data analysis (5th ed.). Upper Saddle River: Prentice-Hall.Google Scholar
  21. Hart, K. M. (1981). Ratio and proportion. In K. M. Hart (Ed.), Children’s understanding of mathematics: 11–16. The CSMS Mathematics Team (pp. 88–101). London: John.Google Scholar
  22. Ilany, B-S., Keret, Y., & Ben-Chaim, D. (2004). Implementation of a model using authentic investigative activities for teaching ratio & proportion in pre-service teacher education. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 3, 81–88.Google Scholar
  23. Krauss, S., Baumert, J., & Blum, W. (2008). Secondary mathematics teachers’ pedagogical content knowledge and content knowledge: validation of the COACTIV constructs. ZDM Mathematics Education, 40, 873–892.Google Scholar
  24. Krauss S., Blum, W., Brunner, M., Neubrand, M., Baumert, J., Kunter, M., …, Elsner. J. (2013). Mathematics teachers’ domain specific professional knowledge: Conceptualization and test construction in COACTIV. In Kunter, M., Baumert, J., Blum, W., Klusmann, U., Krauss, S., Neubrand, M. (Eds.) 2013, VI, 378 p 31. Mathematics Teacher Education 8. NY: Springer Science + Business Media.Google Scholar
  25. Lamon, S. (1993). Ratio and proportion: Connecting content and children’s thinking. Journal for Research in Mathematics Education, 24(1), 41–61.CrossRefGoogle Scholar
  26. Lamon, S. J. (2007). Rational and proportional reasoning: Toward a theoretical framework for research. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 629–668). Charlottes: Information Age.Google Scholar
  27. Lawton, C. (1993). Contextual factors affecting errors in proportional reasoning. Journal for Research in Mathematics Education, 24(5), 460–466.Google Scholar
  28. Lesh, R., Post, T. & Behr, M. (1988). Proportional reasoning. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 93–118). Hillsdale: Lawrence Erlbaum Associates/National Council of Teachers of Mathematics.Google Scholar
  29. Livy, S. & Vale, C. (2011). First year pre-service teachers’ mathematical content knowledge: Methods of solution for a ratio question. Mathematics Teacher Education and Development, 13(2), 22–43.Google Scholar
  30. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. NJ: Lawrence Erlbaum Associates.Google Scholar
  31. Margarit, J., & Figueras, O. (2001) Ratio comparison: Performance on ratio in similarity tasks. Utrecht Netherlands: PME Conference Proceeding paper.Google Scholar
  32. Masters, J. (2012). Eight grade in-service teachers’ knowledge of proportional reasoning and functions: A secondary data analysis. International Journal for Mathematics Teaching & Learning [Published only in electronic form].February 3rd Issue. Retrieved from
  33. Peled, I. & Hershkovitz, S. (2004). Evolving research of mathematics teacher educators: The case of non-standard issues in solving standard problems. Journal of Mathematics Teacher Education, 7, 299–327.CrossRefGoogle Scholar
  34. Schmelzing, S., Driel, J. H. V., Juttner, M., Brandenbusch, S., Sandmann, A. & Neuhaus, B. J. (2013). Development, evaluation and validation of a paper-and-pencil test for measuring two components of biology teachers’ pedagogical content knowledge concerning the “cardiovascular system”. International Journal of Science and Mathematics Education, 11(6), 1369–1390.CrossRefGoogle Scholar
  35. Schmidt, S. H., Houang, R. & Cogan, L. S. (2011). Preparing future math teachers. Science, 332, 1266–1267.CrossRefGoogle Scholar
  36. Senk, S. L., Peck, R., Bankov, K., & Tatto, M. T. (2008). Conceptualizing and measuring mathematical knowledge for teaching: Issues from TEDS-M, an IEA cross-national study. Mexico: 11th International Congress of Mathematics Education.Google Scholar
  37. Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.CrossRefGoogle Scholar
  38. Thompson, B. & Levitov, J. E. (1985). Using microcomputers to score and evaluate test items. Collegiate Microcomputer, 3, 163–168.Google Scholar
  39. Thomson, S. & Fleming, N. (2004). Summing it up: Mathematics achievement in Australian schools in TIMSS 2002. Melbourne: Australian Council for Educational Research.Google Scholar
  40. Tirosh, D. & Graeber, A. O. (1990). Evoking cognitive conflict to explore pre-service teachers’ thinking about division. Journal for Research in Mathematics Education, 21(2), 98–108.CrossRefGoogle Scholar
  41. Tourniaire, F. & Pulos, S. (1985). Proportional reasoning: A review of the literature. Educational Studies in Mathematics, 16(2), 181–204.CrossRefGoogle Scholar
  42. Wiersma, W. & Jurs, S. G. (1990). Educational measurement and testing (2nd ed.). Boston: Allyn and Bacon.Google Scholar

Copyright information

© National Science Council, Taiwan 2014

Authors and Affiliations

  1. 1.National Taiwan Normal UniversityTaipeiTaiwan
  2. 2.The State University of SurabayaSurabayaIndonesia

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