Roslinda Rosli, Dianne Goldsby, Mary Margaret Capraro, Anthony J Onwuegbuzie, Robert M Capraro, Elsa Gonzalez Y Gonzalez


Previous research has shown knowledge, perceptions, and attitudes are essential factors during mathematics classroom instruction. The current study examined the effects of a 3-week fraction instructional unit using concrete models, problem-solving, and problem-posing to improve elementary preservice teachers’ knowledge, perceptions and attitudes towards fractions. A quasi-experiment design was implemented to gather data via closed-ended, open-ended, and essay tasks from a convenience sampling of 71 female elementary preservice teachers during pre- and post-assessments. The study discovered that the select preservice teachers were weak in the content knowledge specifically on unit-whole, part-whole, equivalent area, arithmetic operations, and ordering fractional values. In contrast, the incorporation of concrete models, problem-solving and problem-posing was effective in improving the preservice teachers’ level of pedagogical content knowledge, perceptions and attitudes towards fractions. Implications of the results and suggestions are discussed.


Elementary School; Problem Posing; Teacher Preparation Program; Preservice Teachers; Mixed Methods

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Ball, D. L. (1993). Halves, pieces, and twoths: Constructing and using representational contexts in teaching fractions. In Carpenter, T. P., Fennema, E., Romberg, T. A. (Eds.). Rational numbers: An integration of research (pp.157-195). Hillsdale, NJ: Erlbaum.

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://dx.doi.org/10.1177/0022487108324554.

Barnett-Clarke, C., Fisher, W., Marks, R., & Ross, S. (2010). Developing essential understanding of rational number: Grades 3-5. Reston, VA: The National Council of Teachers of Mathematics.

Collins, K. M. T., Onwuegbuzie, A. J., & Jiao, Q. G. (2007). A mixed methods investigation of mixed methods sampling designs in social and health science research. Journal of Mixed Methods Research, 1(3), 267-294. http://dx.doi.org/10.1177/1558689807299526.

Collins, K. M. T., Onwuegbuzie, A. J., & Sutton, I. L. (2006). A model incorporating the rationale and purpose for conducting mixed methods research in special education and beyond. Learning Disabilities: A Contemporary Journal, 4(1), 67-100.

Cramer, K., & Wyberg, T. (2009). Efficacy of different concrete models for teaching the part-whole construct for fractions. Mathematical Thinking and Learning, 11(4), 226-257. http://dx.doi.org/10.1080/10986060903246479.

Erlandson, D. A., Harris, E. L., Skipper, B. L & Allen, S. D. (1993). Doing naturalistic inquiry: A guide to methods. Newbury Park, CA: Sage.

Empson, S. B. (2002). Organizing diversity in early fraction thinking. In B. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios and proportions: 2002 Yearbook (pp. 29-40). Reston, VA: National Council of Teachers of Mathematics.

Glaser, B. (1965). The constant comparative method of qualitative analysis. Social Problems, 12(4), 436-445. http://dx.doi.org/10.2307/798843.

Hill, H. C. (2010). The nature and predictors of elementary teachers’ mathematical knowledge for teaching. Journal for Research in Mathematics Education. 41(5), 513-545.

IBM Corp. (2013). IBM SPSS Statistics for Windows, Version 21.0 [Computer software]. Armonk, NY: IBM Corp.).

Jaccard, J., & Guilamo–Ramos, V. (2002). Analysis of variance frameworks in clinical child and adolescent psychology: Issues and recommendations. Journal of Clinical Child and Adolescent Psychology, 31(1), 130 –146. http://dx.doi.org/10.1207/S15374424JCCP3101_15.

Johnson, B., & Christensen, L. (2012). Educational research: Quantitative, qualitative, and mixed approaches (4th ed.). Boston, MA: Sage.

Johnson, R. B., & Turner, L. A. (2003). Data collection strategies in mixed methods research. In A. Tashakkori, & C. Teddlie (Eds.), Handbook of mixed methods in social and behavioral research (pp. 297-319). Thousand Oaks, CA: Sage.

Kane, R., Sandretto, S., & Heath, C. (2002). Telling half the story: A critical review of research on the teaching beliefs and practices of university academics. Review of Educational Research, 72(2), 177–228. http://dx.doi.org/10.3102/00346543072002177.

Lamon, S. J. (1999). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. Mahwah, NJ: Erlbaum.

Learning Mathematics for Teaching. (2008). Mathematical knowledge for teaching measures: Rational number. Ann Arbor, MI: Author.

Lin, C. (2010). Web-based instruction on preservice teachers’ knowledge of fraction operations. School Science and Mathematics, 110(2), 59-70. http://dx.doi.org/10.1111/j.1949-8594.2009.00010.x.

Lincoln, Y., & Guba, E. (1985). Naturalistic inquiry. Newbury Park, CA: Sage.

Llinares, S. (2002). Participation and rei?cation in learning to teach. The role of knowledge and beliefs. In G. Leder, E. Pehkonen, & G. To ?rner (Eds.), Beliefs: A hidden variable in mathematics education (pp. 195–210). Dordrecht, The Netherlands: Kluwer.

Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum.

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

Newton, K. J. (2008). An extensive analysis of preservice elementary teachers’ knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110. http://dx.doi.org/10.3102/0002831208320851.

Onwuegbuzie, A. J. (2003). Expanding the framework of internal and external validity in quantitative research. Research in the Schools, 10(1), 71-90.

Onwuegbuzie, A. J., Johnson, R. B., & Collins, K. M. T. (2009). A call for mixed analysis: A philosophical framework for combining qualitative and quantitative. International Journal of Multiple Research Approaches, 3(2), 114-139. http://dx.doi.org/10.3102/000283120832085110.5172/mra.3.2.114.

Onwuegbuzie, A. J., & Teddlie, C. (2003). A framework for analyzing data in mixed methods research. In A. Tashakkori & C. Teddlie (Eds.), Handbook of mixed methods in social and behavioral research (pp. 351–383). Thousand Oaks, CA: Sage.

Osana, H. P., & Royea, D. A. (2011). Obstacles and challenges in preservice teachers’ explorations with fractions: A view from a small-scale intervention study. Journal of Mathematical Behavior, 30(4), 333-352. http://dx.doi.org/10.1016/j.jmathb.2011.07.001.

Piaget, J. (1964). Part I: Cognitive development in children: Piaget development and learning. Journal of Research in Science Teaching, 2(3), 176-186. http://dx.doi.org/10.1002/tea.3660020306

Provalis Research. (2009). QDA Miner 3.2. User‘s guide. Montreal, QC, Canada: Author.

Sarama, J., & Clements, D. H. (2009). "Concrete" computer manipulatives in mathematics education. Child Development Perspectives, 3(3), 145-150. http://dx.doi.org/10.1111/j.1750-8606.2009.00095.x.

Shadish, W. R., Cook, T. D., & Campbell, D. T. (2002). Experimental and quasi-experimental designs for generalized causal inference. Boston, MA: Houghton Mifflin.

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. http://dx.doi.org/10.3102/0013189X015002004.

Sowder, J. T., Philipp, R. A., Armstrong, B. E., & Schappelle, B. P. (1998). Middle-grade teachers’ mathematical knowledge and its relationship to instruction: A research monograph. New York, NY: State University of New York.

Teddlie, C., & Tashakkori, A. (2006). A general typology of research designs featuring mixed methods. Research in the Schools, 13(1), 12-28.

Thompson, P. W. (1994). Concrete materials and teaching for mathematical understanding. Arithmetic Teacher, 41(9), 556-558.

Timmerman, M. (2004). The influences of three interventions on prospective elementary teachers’ beliefs about the knowledge base needed for teaching mathematics. School Science and Mathematics, 104(8), 369-382. http://dx.doi.org/10.1111/j.1949-8594.2004.tb18003.x.

White, A. L., Way, J., Perry, B., & Southwell, B. (2005). Mathematical attitudes, beliefs and achievement in primary pre-service mathematics teacher education. Mathematics Teacher Education and Development, 7, 33-52.

DOI: https://doi.org/10.22342/jme.11.1.9482.59-76


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Journal on Mathematics Education
Program S3(Doktor) Pendidikan Matematika FKIP Universitas Sriwijaya
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Jl. Srijaya Negara, Bukit Besar
Palembang - 30139
email: jme@unsri.ac.id

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