Evaluation of Teachers’ Problem Solving Strategies Impressionability by the Semantic Types of proportional problems

Document Type : Research Paper

Authors

1 PhD student. department of mathematics Education. faculty of Basic Science. Central Tehran Branch. Islamic Azad Univercity.Tehran. Iran

2 Assistant Professor / Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

3 , Professor / Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran. Iran

4 PhD, Organization for Educational Research and Planning (Research Institute for Education), Data Manager of TIMSS and PIRLS of Iran, Tehran, Iran

Abstract

Abstract
In a cognitive sense, the concept of proportionality and the requirement for the development of proportional thinking are complex and teaching them needs concept-based approaches. Studying the perceptional quality in teachers amounts to how learners develop conceptual structures.. The goal of this study was to consider the teachers’ and prospective teachers selected strategies in teaching proportional problems solving activity and the impressionability of 4 semantic problems types. Convenient sampling was used to select three independent groups of subjects, including 180 elementary school teachers, middle school math teachers, and prospective teachers who participated in the study voluntarily. The research tools included one author-made test, contained 12 tasks including direct proportional word problems (missing value and comparison). The content validity of the test was approved by professors of "mathematics education" and "test construction". The results showed significant differences between 3 independent groups in applying the strategies leading to correct solving among the semantic problem types. In addition, the rate of using proportional reasoning strategies among these semantic types didn’t follow similar patterns. In order for the development of future teachers, attention to the consequences of delayed emergence of students' proportional thinking should be employed in the design of educational curriculum.

Keywords


Aleman, B. P. (2007). The effect of a proportional reasoning-based test preparation instructional treatment on mathematics achievement of eight grade students. A dissertation submitted in partial fulfillment of the requirements for degree of Doctor of Education. Faculty of the college of Education, University of Houston. URL: https://www.proquest.com/openview/034a8f2147716897c8aaf1bf035f74d6/1?pq-origsite=gscholar&cbl=18750
Artut, P. D., Pelen, M. S. (2015). 6th grade gtudents’ golution gtrategies on proportional reasoning problems. Journal of Procedia-Social and Behavioral Sciences, 197(11), 113-119. https://doi.org/10.1016/j.sbspro.2015.07.066
Ben-Chaim, D., Keret, Y., & Ilany, B. (2012). Ratio and proportion: Research and teaching in mathematics teachers’ education. pre-and in-service mathematics teachers of elementary and middle school classes. Rotterdam, the Netherlands: Sense.
Ben-Chaim, D., Keret, Y., & Ilany, B. S. (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 Education10(4), 333-340. https://doi.org/0.1007/s10857-007-9052-x
Charalambos, Y., Hill, H., Ball, D. (2011). Prospective teachers' learning to provide instructional explanations: How does it look and what might it take? Journal of Mathematics Teacher Education, 14(6), 441-463. https://doi.org/10.1007/s10857-011-9182-z
Clark, M. R., Berenson, S. B.& Cavey. L. O. (2003). A comparison of ratios and fractions and their roles as tools in proportional reasoning. Journal of Mathematical Behavior. 22(3): 297-317. https://doi.org/10.1016/S0732-3123(03)00023-3
Cramer, K. A., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications: Middle grades mathematics. In Research ideas for the classroom: Middle grades mathematics (pp.159-178), New York: Macmillan.
Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. Teachers College Press, Teachers College, Columbia University.
Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specific knowledge of students. Journal for research in mathematics education, 39(4), 372-400. https://doi.org/ 10.5951/jresematheduc.39.4.0372
Hines, E., McMahon, M. T. (2005). Interpreting middle school students' proportional reasoning strategies: Observations from preservice teachers. School Science and Mathematics105(2), 88-105. https://doi.org/10.1111/j.1949-8594.2005.tb18041.x
Howe, C., Luthman, S., Ruthven, k., Mercer, N., Hofman, R., Ilies, S., & Guardia, P. (2015). Rational number and proportional reasoning in early secondary school: towards principled improvement in mathematics. Research in Mathematics Education. 17(1), 38-56. https://doi.org/10.1080/14794802.2015.1019914
Howe, C., T. Nunes, and P. Bryant. (2011). Rational number and proportional reasoning: Using intensive quantities to promote achievement in mathematics and science. International Journal of Science and Mathematics Education, 9(2), 391-417. https://doi.org/10.1007/s10763-010-9249-9
Lamon, S, J. (1993). Ratio and proportion: Connecting content and children's thinking. Journal for research in mathematics education, 24(1), 41-61. https://doi.org/10.2307/749385
Lamon, S, J. (1996) .The development of unitizing: Its role in childeren's patitionings strategies. Journal for Research in Mathematics Education, 27(2), 170-193. https://doi.org/10.5951/jresematheduc.27.2.0170
Lamon, S, J. (1999). Teaching fractions and ratios for understanding: Essentiol content knowledge and instructional strategies for teachers. Mahwah. NJ: Lawrence Erlbaum.
Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. Second handbook of research on mathematics teaching and learning1, 629-667. Reston, VA: NCTM
Lim, K. H. (2009). Burning the candle at just one end. Using nonproportional examples helps students determine when proportional strategies apply. Mathematics Teaching in the MiddleSchool, 14(8): 492–500. https://doi.org/10.5951/MTMS.14.8.0492
Lo, J. J., & Watanabe, T. (1997). Developing ratio and proportion schemes: A story of a fifth grader. Journal for research in mathematics education, 28(2), 216-236.  https://doi.org/10.2307/749762
Lobato J. Orrill, H, Ch. Druken, B., Jacobson, E. ( 2011). Middle school teachers’ knowledge of proportional reasoning for teaching. in Annual Meeting of the American Educational Research Association (AERA), New Orleans, LA. Abstract retrieved from http://www. kaputcenter. umassd. edu/ downloads/ products/ workshops/ AERA2011/ Lobato_Orrill_Druk en_Erikson_AERA_July12-13.
Nagar, G. G., Weiland, T., Orrill, C. H, & Burke, J. P. (2015). Teachers’ understanding of ratios and their cinnections to fractions. Hands book of PMENA-37. Bartell, T.G., Bieda, K. N., Putnam, R.T., Bradfield, K., & Dominguez, H.(Eds), pp 764-771. (Proceedings of the 37th Annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. East Lansing, MI: Michigan State University).
NCTM (1989). National Council of Teachers of mathematics. Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics. URL: https://nap.nationalacademies.org/read/5844/chapter/5
NCTM (2013). Research Brief: Teaching Ratio and Proportion in the Middle Grades. Available from: https://www.nctm.org
Orrill, C. H., & Burke, J. P. (2013). Fine-grained analysis of teacher knowledge: proportion and geometry. Hands book of PMENA-35. Martinez, M. & Castro Superfine, A. (Eds.), pp 605-612. (Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Chicago, IL: University of Illinois at Chicago).
Parish, L. (2010). Facilitating the Development of Proportional Reasoning through Teaching Ratio. Mathematics Education Research Group of Australasia, 469-476. URL: https://files.eric.ed.gov/fulltext/ED520962.pdf
Pearce, D. L., Bruun, F., Skinner, K., & Lopez-Mohler, C. (2013). What Teachers Say About Student Difficulties Solving Mathematical Word Problems in Grades 2-5. International Electronic Journal of Mathematics Education, 8(1),3-19. https://doi.org/10.29333/iejme/271
Pitta-Pantazi, D., & Christou, C. (2011). The structure of prospective kindergarten teachers’ proportional reasoning. Journal of Mathematics Teacher Education14(2), 149-169. https://doi.org/10.1007/s10857-011-9175-y
Radford, L. (2011). Grade two students’ non-symbolic algebraic thinking. In Early algebraization Springer, Berlin, Heidelberg.
Riley, K. R. (2010). Teachers’ understanding of proportional reasoning. In Proceedings of the 32nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 6, 1055-1061.
Ruiz Ledesma, E. F. R. (2011). Primary and Secondary Teachers’ Knowledge, Interpretation, and Approaches to Students Errors about Ratio and Proportion Topics. Creative Education, 2(03), 264-269. https://doi.org/10.4236/ce.2011.23035
Ruiz Ledesma, E. F. R. (2013). Activities to learn the proportion concept using technology. Journal of International Review of Social Sciences and Humanities, 5(1), 175-184.
Sen, C., Guler, G. (2017). Effect of Strategy Teaching for the Solution of Ratio Problems on Students' Proportional Reasoning Skills. Malaysian Online Journal of Educational Sciences, 5(2)1-15. URL: https://mojem.um.edu.my/index.php/MOJES/article/view/12621
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
Silvestre, A. I. da Ponte J. P. (2012). Missing value and comparison problems: What pupils know before the teaching of proportion? PNA, 6(3), 73-83.
Son, J. W. (2013). How preservice teachers interpret and respond to student errors: ratio and proportion in similar rectangles. Educational studies in mathematics84(1), 49-70. https://doi.org/10.1111/j.1949-8594.2009.00005.x
Spanoudi, A., & Misailidou, C. (2015). Teachers encountering challenging word problems: How do they solve them?
Tourniaire, F., & Pulos, S. (1985). Proportional reasoning: A review of the literature. Educational studies in Mathematics, 16(2), 181-204. https://doi.org/10.1007/s10649-012-9393-y