### LATENT CLUSTER ANALYSIS OF INSTRUCTIONAL PRACTICES REPORTED BY HIGH- AND LOW-PERFORMING MATHEMATICS TEACHERS IN FOUR COUNTRIES

#### Abstract

Using Trends in International Mathematics and Science Study (TIMSS) 2011 eighth-grade international dataset, this study explored the profiles of instructional practices reported by high- and low-performing mathematics teachers across the US, Finland, Korea, and Russia. Concepts of conceptual teaching and procedural teaching were used to frame the design of the current study. Latent cluster analysis was applied in the investigation of the profiles of mathematics teachers’ instructional practices across the four education systems. It was found that all mathematics teachers in the high- and low-performing groups used procedurally as well as conceptually oriented practices in their teaching. However, one group of high-performing mathematics teachers from the U.S. sample and all the high-performing teachers from Finland, Korea, and Russia showed more frequent use of conceptually oriented practices than their corresponding low-performing teachers. Another group of U.S. high-performing mathematics teachers showed a distinctive procedurally oriented pattern, which presented a rather different picture. Such results provide useful suggestions for practitioners and policy makers in their effort to improve mathematics teaching and learning in the US and in other countries as well.

#### Keywords

#### References

Abdullah, A.S. (2017). Ethnomathematics in perspective of sundanese culture. Journal on Mathematics Education, 8(1), 1-16.

Aud, S., Hussar, W., Planty, M., Snyder, T., Bianco, K., Fox, M., & Drake, L. (2010). The condition of education 2010 (NCES 2010-028). Washington, DC: National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education.

Carpenter, T.P., Fennema, E., Peterson, P.L., Chiang, C., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499-531.

Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatley, G., Trigatti, B., & Perlwitz, M. (1991). Assessment of a problem-centered second-grade mathematics project. Journal for Research in Mathematics Education, 22(1), 3-29.

Collins, L.M., & Lanza, S.T. (2010). Latent class and latent transition analysis: With applications in the social, behavioral, and health sciences. Hoboken, NJ: John Wiley & Sons.

Desimone, L.M., Smith, T., Baker, D., & Ueno, K. (2005). Assessing barriers to the reform of U.S. mathematics instruction from an international perspective. American Educational Research Journal, 42(3), 501-535.

Ferguson, R., & Ladd, H. (1996). How and why money matters: An analysis of Alabama schools. in H. Ladd (ed.), Holding schools accountable, (pp. 265-298). Washington, DC: Brookings institution.

Fleischman, H.L., Hopstock, P.J., Pelczar, M.P., & Shelley, B.E. (2010). Highlights from PISA 2009: Performance of U.S. 15-Year-Old Students in Reading, Mathematics, and Science Literacy in an International Context (NCES 2011-004). Washington, DC: U.S. Department of Education.

Foy, P., Arora, A., & Stanco, G.M. (Eds.). (2013). TIMSS 2011 user guide for the international database. Boston, MA: TIMSS & PIRLS International Study Center.

Gamoran, A. (2001). Beyond curriculum wars: Content and understanding in mathematics. In T. Loveless (Ed.), The great curriculum debate: how should we teach reading and math? (pp.134-162). Washington, DC: Brookings Institution.

Geary, D. (1994). Children’s mathematical development: Research and practical applications. Washington, DC: American Psychological Association.

Gonzales, P., Williams, T., Jocelyn, L., Roey, S., Kastberg, D., & Brenwald, S. (2009). Highlights from TIMSS 2007: Mathematics and science achievement of U.S. fourth- and eighth-grade students in an international context (NCES 2009–001 Revised). Washington, DC: National Center for Education Statistics.

Greeno, J., Collins, A., & Resnick, L. (1996). Cognition and learning. In D. Berliner & R. Calfee (Eds.), Handbook of educational psychology (pp. 15-46). New York, NY: Macmillan.

Goldhaber, D., & Brewer, D. (2000). Does teacher certification matter? High school teacher certification status and student achievement. Educational Evaluation and Policy Analysis, 22(2), 129-145.

Hamilton, L.S., & Martinez, J.F. (2007). What can TIMSS surveys tell us about mathematics reforms of the 1990s? In T. Loveless (Ed.), Lessons learned: What international assessments tell us about mathematics achievement (pp. 127–174). Washington, DC: Brookings Institution.

Hiebert, J., Carpenter, T.P., Fennema, E., Fuson, K., Human, P., Murray, & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher, 25(4), 12-21.

International Association for the Evaluation of Educational Achievement (IEA). (2011). TIMSS 2011 eighth grade mathematics teacher questionnaire. Hamburg, Germany: IEA Data Processing and Research Center.

Karp, A., & Vogeli, B.R (Eds). (2010). Russian mathematics education: History and world significance. Hackensack, NJ: World Scientific Publishing.

Kim, J., Han, I., Park, M., & Lee, J (Eds). (2013). Mathematics education in Korea: Contemporary trends in researches in Korea. Hackensack, NJ: World Scientific Publishing.

Le, V.N., Lockwood, J.R., Stecher, B.M., Hamilton, L.S. & Martinez, J.F. (2009). A longitudinal investigation of the relationship between teachers’ self-reports of reform-oriented instruction and mathematics and science achievement. Educational Evaluation and Policy Analysis, 31(3), 200-220.

Lo, Y., Mendell, N.R., & Rubin, D.B. (2001). Testing the number of components in a normal mixture. Biometrika, 88(3), 767-778.

Martin, M.O., & Mullis, I.V.S. (Eds.). (2012). Methods and procedures in TIMSS and PIRLS 2011. Chestnut Hill, MA: TIMSS & PIRLS International Study Center.

Mullis, I.V.S., Martin, M.O., Ruddock, G.J., O’Sullivan, C.Y., Arora, A., & Erberber, E. (2005). TIMSS 2007 assessment frameworks. Chestnut Hill, MA: TIMSS & PIRLS International Study Center.

Mullis, I.V.S., Martin, M.O., Smith, T.A., Garden, R.A., Gregory, K.D., González, E.J., ..., & O’Connor, K.M. (2003). TIMSS assessment frameworks and specifications: 2003 (2nd ed.). Chestnut Hill, MA: TIMSS & PIRLS International Study Center.

Mullis, I.V.S., Martin, M.O., Ruddock, G.J., O'Sullivan, C.Y., & Preuschoff, C. (2009). TIMSS 2011 assessment frameworks. Chestnut Hill, MA: TIMSS & PIRLS International Study Center.

Muthén, L.K., & Muthén, B.O. (1998-2012). Mplus user’s guide (7th ed.). Los Angeles, CA: Muthén & Muthén.

National Council of Teachers of Mathematics (NCTM). (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.

National Council of Teachers of Mathematics (NCTM). (1991). Professional standards for teaching mathematics. Reston, VA: NCTM.

National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: NCTM.

National Council of Teachers of Mathematics. (2014). Principles to action: Ensuring mathematical success for all. Reston, VA: NCTM.

National Mathematics Advisory Panel. (2008). Foundations for success. Washington, DC: U.S. Department of Education.

Organization for Economic Co-operation and Development (OECD). (2004). The quality of the teaching workforce. Paris, France: OECD.

Organization for Economic Co-operation and Development (OECD). (2005). Teachers matter: Attracting, developing and retaining effective teachers. Paris, France: OECD.

Prahmana, R.C.I, Zulkardi, & Hartono, Y. (2012). Learning multiplication using Indonesian traditional game in third grade. Journal on Mathematics Education, 3(2), 115-132.

Ramaswamy, V., DeSarbo, W.S., Reibstein, D.J., & Robinson, W.T. (1993). An empirical pooling approach for estimating marketing mix elasticities with PIMS data. Marketing Science, 12(1), 103-124.

Rivkin, S., Hanushek, E., & Kain, J. (2005). Teachers, schools, and academic achievement. Econometrica, 73(2), 417-458.

Romberg, T.A. (1990). Evidence which supports NCTM's Curriculum and Evaluation Standards for School Mathematics. School Science and Mathematics, 90(6), 466-479.

Schneider, B., Carnoy, M., Kilpatrick, J., Schmidt, W. H., & Shavelson, R. J. (2007). Estimating causal effects using experimental and observational designs (report from the Governing Board of the American Educational Research Association Grants Program). Washington, DC: American Educational Research Association.

Schwerdt, G., & Wuppermann, A. C. (2011). Is traditional teaching really all that bad? A within-student between-subject approach. Economics of Education Review, 30(2), 365-379.

Stigler, J.W., & Hiebert, J. (2009). The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. New York, NY: Free Press.

Tabachnick, B.G., & Fidell, L.S. (2013). Using multivariate statistics (6th ed.). Boston, MA: Pearson.

Thompson, S. (2001). The authentic standards movement and its evil twin. Phi Delta Kappan, 82(5), 358-362.

Wu, H. (1999). Basic skills versus conceptual understanding: A bogus dichotomy in mathematics education. American Educator, 23(3), 1-7.

Zuzovsky, R. (2013). What works where? The relationship between instructional variables and schools’ mean scores in mathematics and science in low-, medium-, and high-achieving countries. Large-scale Assessments in Education, 1(2), 1-19.

### Refbacks

- There are currently no refbacks.

**Journal on Mathematics Education**

Kampus FKIP Bukit Besar

Jl. Srijaya Negara, Bukit Besar

Palembang - 30139

p-ISSN: 2087-8885 | e-ISSN: 2407-0610

Journal on Mathematics Education is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License

View My Stats

**Indexed in:**