Khaled ALZUBİ

4721

The Effect of Using Multiple Mathematical Representations of Rational number concepts in Basic Grades Students in Jordan

This study, aimed at the effect of using multiple mathematical representations of rational number concept in basic grades students in jordan. The current study employed the content analysis approach to investigate the multiple mathematical representations and transitions among them in 8th Grade Mathematics Textbook. An observation method was used to analyses the teacher practices (n=35 observations), and record the representations and transitions. The results showed that there was an existence of symbol and verbal representations in the textbook and teachers' implementation. Meanwhile, the other three representations (pictures and figures, models and Cutters, and life situations) . And This study explored the nature of difficulties of eighth-grade students who struggled to build their conceptual understanding of early fraction ideas. interviews with Pre and post of students were conducted for a sufficient identification of the nature of the students’ difficulties. The study revealed The students also minimal use of informal ordering strategies that involve more conceptual than a procedural understanding of the concept of initial fraction ideas.
Keywords:

math representations, rational number concepts basic grades students in jordan,

PDF

___

  • Anthony, G., & Walshaw, M. (2009). Characteristics of Effective Teaching of Mathematics: A View from the West. Journal of Mathematics Education, 2(2), 147-164. Bal, A. (2015). Skills of Using and Transform Multiple Representations of the Prospective Teachers. Journal of Mathematical Behavior, 197(2015), 582-588. https://doi.org/10.1016/j.sbspro.2015.07.197
  • Bayazit, I. (2011). Prospective teachers’ inclination to single representation and their development of the function concept. Educational Research and Reviews, 6(5), 436- 446.
  • Cai, J., & Lester, F. (2005). Solution Representations and pedagogical representations in Chinese and U.S. classrooms. Journal of Mathematical Behavior, 24(3), 221-237. https://doi.org/10.1016/j.jmathb.2005. 09.003.
  • Doerr, H., & Lesh, R. (2011). Models and modelling perspectives on teaching and learning mathematics in the twenty-first century. In Trends in teaching and learning of mathematical modelling (pp. 247-268). Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0910-2_26.
  • Dreher, A., & Kuntze, S. (2015). Teachers’ professional knowledge and noticing: The case of multiple representations in the mathematics classroom. Educational Studies in Mathematics, 88(1), 89-114. https://doi.org/10.1007/s10649-014-9577-8.
  • Dwi. R, Subanji, P, Hidayanto, E., & Anwar, R. (2017). Process of Mathematical Representation Translation from Verbal into Graphic. Mathematic Education, 12(4), 367-381. Gagatsis, A., & Shiakalli, M. (2004). Ability to Translate from One Representation of the Concept of Function to Another and Mathematical Problem Solving. Educational Psychology, 24(5), 645-657. https://doi.org/10.1080/0144341042000262953.
  • Greeno, J., & Hall, B. (1997). Practicing Representation: Learning with and about Representational Forms. Phi Delta Kappa International, 78(5), 99-107. Hwang, W., Chen, N., Dung, J., & Yang, Y. (2007). Multiple Representation Skills and Creativity Effects on Mathematical Problem Solving using a Multimedia Whiteboard System. Educational Technology & Society, 10(2), 191-212.
  • Juersivich, N., Garofalo, G., & Fraser, V. (2009). Student Teachers’ Use of Technology- Generated Representations: Exemplars and Rationales. Journal of Technology and Teacher Education, 17(2), 149-173.
  • Koretsky, M., Keeler, J., Ivanovitch, J., & Cao, Y.(2018), The role of pedagogical tools in active learning: a case for sense-making. International Journal of STEM Education, 5(18), 2-20. https://doi.org/10.1186/s40594-018-0116-5.
  • Leinwand, S., & Ginsburg, A. (2007). Learning from Singapore Math: The United States could benefit from looking at five elements driving the program’s success. Educational Leadership, 65(3), 32-36.
  • Lesh, R, Post, T. & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. Retrieved on 28/2/2018 from http://www.cehd.umn.edu/ rationalnumberproject/87_5.html.
  • Lesh, R., & Harel, G. (2003). Problem solving, modeling, and local conceptual development. Mathematical thinking and learning, 5(2-3), 157-189. https://doi.org/10.1080/10986065.2003.9679998.
  • Lesh, R., & Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers, Mathematical Thinking and Learning, 5(2&3), 109–130. https://doi.org/10.1080/10986065.2003.9679996.
  • Lesh, R., Cramer, K., Doerr, H., Post, T. & Zawojewski, J. (2003). Using a translation model for curriculum development and classroom instruction. Retrieved on 5/1/2018, from: http://www.cehd.umn.edu/rationalnumberproject/03_1.html.
  • Santulli, T. (2009). Representations from the Real World. Mathematics teaching in the middle school, 14(8), 466-473.
  • Treffert-Thomas, S., Viirman, O., Hernandez-Martinez, P., & Rogovchenko, Y. (2017). Mathematics lecturers’ views on the teaching of mathematical modelling. Education, 22(4), 121-145.
  • Tripathi, P. (2008). Developing mathematical understanding through multiple representations. Mathematics Teaching in Middle School. 13(89), 438-445. Ulu, M. (2017). Examining the Mathematical Modeling Processes of Primary School 4th-Grade Students: Shopping Problem. Universal Journal of Educational Research, 5(4), 561-580. https://doi.org/10.13189/ujer.2017.050406.
  • Yan, Z., & Lianghuo, F. (2006). Focus on The Representation Of Problem Types In Intended Curriculum: A Comparison Of Selected Mathematics Textboks From Maibland China And The United States. International Journal of Science and Mathematics Education, 4(4), 609-626. https://doi.org/10.1007/s10763-006-9036-9.
  • You, Z., & Quinn, R. (2010). Prospective Elementary and Middle School Teachers’ Knowledge of Linear Functions: A Quantitative Approach. Journal of Mathematics Education, 3(1), 66-76.
  • Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier, (Ed.), Problems of representations in the teaching and learning of mathematics (pp. 33 – 40). Hillsdale, NJ: Lawrence Erlbaum.
  • Mack, N. (1990). Learning fractions with understanding: Building on informal knowledge. Journal for Research in Mathematics Education, 21, 16 – 32.
  • Mack, N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education, 26, 422-441.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis. Thousand Oaks, CA: Sage.
  • Moss, J. & Case, R. (1999). Developing children’s understanding of the rational numbers: A new model and an experimental curriculum. Journal for Research in Mathematics Education, 30, 122 – 147.
  • National Mathematics Advisory Panel (2008). Foundations for success: The final report of the national mathematics advisory panel. Washington D.C.: U. S. Department of Education.
  • Post, T., Behr, M., & Lesh, R. (1982). Interpretations of rational number concepts. In L. Silvey & J. Smart (Eds.), Mathematics for Grades 5-9, 1982 NCTM Yearbook (pp. 59-72). Reston, Virginia: NCTM.
  • Post, T., Wachsmuth, I., Lesh, R., & Behr, M. (1985). Order and equivalence of rational numbers: A cognitive analysis. Journal for Research in Mathematics Education, 16, 18-36.
  • Siemon, D., Beswick, K., Brady, K., Clark, J., Faragher, R., & Warren, E. (2015). Teaching Mathematics: Foundations to Middle Years (2nd Edition). South Melbourne, Victoria: Oxford University Press.
  • Silver, E. (1986). Using conceptual and procedural knowledge: A focus on relationships. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 181 – 198). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • U.S. Department of Education (2010). National Assessment of Educational Progress. National Center for Educational Statistics. Retrieved from http://nces.ed.gov/nationsreportcard/.
International Journal of Educational Research Review-Cover
  • Yayın Aralığı: Yılda 4 Sayı
  • Başlangıç: 2016
  • Yayıncı: Sakarya Üniversitesi
Arşiv
Sayıdaki Diğer Makaleler

Alı ALSHEHRİ, Majed Abdallah AL HARTHİ

Khaled ALZUBİ

Theodoto RESSA, Derek DANİELS, Sheri WELLS-JENSEN

Bülent KARAÇAR, İzzet KURBANOGLU

Kemal ABDULBASİT, Yilfashewa Seyoum MEKURİA

Mohammed Rashel UDDİN

Michael Nkwenti NDONGFACK

Eleanor GARINGAN

Peter Abayomi ONANUGA, Adebola IFAMUYIWA, Kehinde ALEBİOSU