ELEMENTARY PRESERVICE TEACHERS’ KNOWLEDGE, PERCEPTIONS AND ATTITUDES TOWARDS FRACTIONS: A MIXED-ANALYSIS

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

Abstract


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.

Keywords


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

Full Text:

PDF

References


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

Refbacks

  • There are currently no refbacks.


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


Journal on Mathematics Education
Doctoral Program on Mathematics Education
Faculty of Teacher Training and Education, Universitas Sriwijaya
Kampus FKIP Bukit Besar
Jl. Srijaya Negara, Bukit Besar
Palembang - 30139
email: jme@unsri.ac.id

p-ISSN: 2087-8885 | e-ISSN: 2407-0610
Journal on Mathematics Education is licensed under a Creative Commons Attribution 4.0 International License

View My Stats