Examining the Effect of Problem Classification and Number Structures on Proportional Reasoning

Öz

The main purpose of this study is to examine sixth grade students' problem classification abilities on proportional reasoning problems and whether problem solving strategies and success rates change with problem type and number structure of the problems. This study considered 165 randomly selected students of grade six studying in middle schools in a southern province of Turkey during academic year 2013-2014. A problem test including proportional (missing value, numerical comparison, and qualitative prediction and comparison problems) and non-proportional word problems was designed as a data collecting tool for the research. Number structures that involve within integer, between integer, both within and between integer and non-integer relations were also included in the problem test. The subjects of the study were divided into two groups. Half of the students solved the problem test first and then did the classification task (SC-condition), while the other half solved the problems in the reverse order (CS-condition). Strategies used in solving problems with different types and number structures were identified by evaluating students’ answers on problems. Besides, comparisons among different categories Descriptive data analysis methods were used for this purpose.  Analysis show that the problem classification skills of sixth grade students are in average level, and problem type, and number structure of the problems affect the problem solving success.

Anahtar Kelimeler

• Problem Solving,Proportional Reasoning,Problem Classification,Problem Solving Strategies,Number Structures of Problems

Kaynakça

1. Aladağ, A. (2009), İlköğretim öğrencilerinin orantısal akıl yürütmeye dayalı sözel problemler ile gerçekçi cevap gerektiren problemleri çözme becerilerinin incelenmesi, Yüksek Lisans Tezi, Çukurova Üniversitesi Sosyal Bilimler Enstitüsü, Adana
2. Aleman, B. P. (2007), The effect of a proportional reasoing based test preparation instructional treatment on mathematics achievement of eight grade students, Faculty of the college of Education, University of Houston
3. Bart, W., Post, T., Behr, M., Lesh, R. (1994), “A Diagnostic Analysis Of A Proportional Reasoning Test Item: An Introduction To The Properties Of A Semi-Dense Item”, Focus on Learning Problems in Mathematics, 16(3), 1-11.
4. Baxter, G. P., Junker, B. A. (2001), Case study in proportional reasoning. Paper presented at the annual meeting of National Council of Mathematics for Measurement in Education Seattle, Washington
5. Baykul, Y. (2009), İlköğretimde matematik öğretimi 6-8. Sınıflar, Pegem Akademi
6. Ben-Chaim, D., Fey, J., Fitzgerald, W., Benedetto, C., Miller, J. (1998), Proportional reasoning among 7th grade students with different curricular experiences, Educational Studies in Mathematics, 36: 247-273
7. Cramer, K., Post T. (1993), “Connecting Research To Teaching Proportional Reasoning” Mathematics Teacher,(86), S. 5, ss. 404 – 407.
8. De Bock, D., Van Dooren, W., Janssens, D., Verschaffel, L. (2002), “Improper Use Of Linear Reasoning: An In-Depth Study Of The Nature And The Irresistibility of Secondary School Students’ Errors”, Educational Studies In Mathematics, 50: 311-334.

9. De Bock, D., De Bolle, E., Janssens, D., Van Dooren, W., Verschaffel, L. (2003), Secondary School Students' Improper Proportional Reasoning: The Role Of Direct Versus Indirect Measures, Pme Conference, 2, no. Conf 27, (2003): 293-300
10. Duatepe A., Akkuş-Çıkla O., Kayhan M. (2005), “Orantısal Akıl Yürütme Gerektiren Sorularda Öğrencilerin Kullandıkları Çözüm Stratejilerinin Soru Türlerine Göre Değişiminin İncelenmesi”, Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 28: 73-81
11. Johnson, G. J. (2010), Proportionality in middle-school mathematics textbooks, Doctor of Philosophy, Department of Secondary Education College of Education, University of South Florida
12. Hoogland, K.; Bakker, A.; Koning, J. de; Gravemeijer, K. (2012), Comparing students' results on word problems with their results on image-rich numeracy problems, 12th International Congress on Mathematical Education Program Name XX-YY-zz (pp. abcde-fghij) 8 July – 15 July, 2012, COEX, Seoul, Korea
13. Karplus, R., Pulos, S., Stage, E. K. (1983), Early adolescents’ proportional reasoning on rate problems. Educational Studies in Mathematics, 14, 219-234
14. Lamon, S. J. (1993). Ratio and proportion: Children's cognitive and metacognitive processes Rational numbers: An integration of research (pp. 131-156). Hillsdale, NJ.: Lawrence Erlbaum Associates.
15. Langrall, C. W., Swafford, J. (2000), “Three Balloons for Two Dollars: Developing Proportional Reasoning”, Mathematics Teaching in the Middle School, 6 – 254.
16. Lesh, R., Post, T., Behr, M. (1988), “Proportional Reasoning. J. Hiebert & M. Behr (Eds.) Number Concepts and Operations in the Middle Grades”, 93-118, Reston, VA: Lawrence Erlbaum & National Council of Teachers of Mathematics
17. McIntosh, M. B. (2013), Developing Proportional Reasoning in Middle School Students, Masters of Mathematics, College of Science, The University of Utah
18. MEB (2013), Ortaokul Matematik Dersi (5, 6, 7 ve 8. Sınıflar) Öğretim Programı, Ankara: MEB Yayınları
19. Misailidou, C., Williams, J. (2003), Diagnostic assessment of children’s proportional reasoning, Journal of Mathematical Behavior, v22 n3 (2003): 335-368
20. National Council of Teachers of Mathematics (2000) Principles and Standards for School Mathematics, National Council of Teachers of Mathematics, Reston, VA.
21. Silver, E. A. (1979). Student perceptions of relatedness among mathematical verbal problems. Journal for Research in Mathematics Education, 10, 195–210.
22. Singh, P. (2000), “Understanding The Concepts Of Proportion And Ratio Constructed By Two Grade Six Students”, Educational Studies In Mathematics, 43, 271-292.
23. Steinthorsdottir, O. B. (2006), Proportional reasoning variable influencing the problems difficulty level and one’s use of problem solving strategies, Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (30th, Prague, Czech Republic, July 16-21, 2006). Volume 5
24. Tourniaire, F., Pulos, S. (1985), Proportional Reasoning: A Review of the Literature, Educational Studies in Mathematics, v16 n2 (May, 1985): 181-204
25. Tourniaire, F. (1986), Proportions in Elementary School, Educational Studies in Mathematics, v17 n4 (Nov., 1986): 401-412
26. Van Dooren, W., De Bock, D., Hessels, A., Janssens, D., Verschaffel, L. (2005), Not Everything Is Proportional: Effects of Age and Problem Type on Propensities for Overgeneralization, Cognition and Instruction, v23 n1 (2005): 57-86
27. Van Dooren, W., De Bock, D., Verschaffel, L. (2010), From Addition to Multiplication … and Back: The Development of Students' Additive and Multiplicative Reasoning Skills, Cognition and Instruction, 28, no. 3 (2010): 360-381
28. Van Dooren, W. De Bock, D. Vleugels, K. Verschaffel, L. (2010), Just Answering … or Thinking? Contrasting Pupils' Solutions and Classifications of Missing-Value Word Problems, Mathematical Thinking and Learning, 12:1, 20-35