How Middle School Students Deal
with Rational Numbers? A Mixed
Methods Research Study

Sebahat Yetim; Ramazan Alkan

doi:10.12973/eurasia.2013.9211a

How Middle School Students Deal with Rational Numbers? A Mixed Methods Research Study

Full Text (PDF)

Sebahat Yetim ¹ ^* , Ramazan Alkan ¹

More Detail

¹ Gazi Üniversitesi, TURKEY^* Corresponding Author

Abstract

The aim of this study was to identify 7th grade students’ common mistakes and/or misconceptions about representing rational numbers in different forms. Seventy-three 7th grade students participated in this study. We utilized a diagnostic test with 8 questions in order to determine common student mistakes. For identifying misconceptions, we conducted interviews with 25 of the participants purposefully chosen from among the ones who made mistakes more frequently. The data analysis showed that students had difficulties especially in determining rational numbers, relating rational numbers with decimals, representing rational numbers, and rational-number division. Moreover, the current study also revealed students’ misconceptions about dividing by zero and division of integers (with + – signs). The results suggest that using concrete materials and multiple representations would be more beneficial for overcoming these difficulties and for a sound understanding of the abstract nature of rational numbers.

Keywords

mixed methods research
rational numbers
common mistakes
misconceptions

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2013, Volume 9, Issue 2, 213-221

https://doi.org/10.12973/eurasia.2013.9211a

Publication date: 14 Dec 2013

Article Views: 1888

Article Downloads: 2345

Open Access References How to cite this article

References

Aksu, M. (1997). Student performance in dealing with fraction. Journal of Education Research, 90(6), 375-380.
Alajmi, A. H. (2012). How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan, and Kuwait. Educational Studies in Mathematics, 79(2), 239-261.
Altun, M. (1998). Mathematics teaching in education faculties and primary education pre- service teachers. Erkam Typography, Bursa, Turkey.
Başgün, M., & Ersoy, Y. (2000). Numbers and arithmetic: The difficulties and misconceptions in teaching fractions and decimal numbers. IV. Science Teaching Congress, Symposium Book, Ministry of Education Publication, Ankara, Turkey. pp 604-608.
Bell, A. W. (1982). Diagnosing students’ misconceptions. The Australian Mathematics Teacher, 38(1), 6-10.
Bright, G.W., Behr, M.J., Post, T.R. & Wachsmuth, I., (1988). Identifying fractions on number lines, Journal for Research in Mathematics Education. 19(3), 215-232.
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.
Eaton, J. F., Anderson, C. W., & Smith, E. L. (1983). Students' misconceptions interfere with learning: Case studies of fifth-grade students (Research Rep. No. 128). East Lansing, MI: Institute for Research on Teaching.
Ersoy. Y., & Ardahan, H. (2003). Teaching of fractions in primary schools II editing of diagnostic activities. Web: http://www.matder.org.tr/bilim/ioko2tyed.asp?ID=49, 27.04.2005.
Farrell, M. A. (1992). Implementing the professional standards for teaching mathematics: Learning from your students. The Mathematics Teacher, 85(8), 656-659.
Fraenkel, J. R., & Wallen, N. E. (2006). How to design and evaluate research in education. A Business Unit of the McGraw-Hill Companies.
Gardner, H. G. (1991). The unschooled mind. New York: Basic Books.
Gürbüz, R. (2007). Students’ and their teachers’ opinions about the instruction based on the materials on probability subject. Journal of Kastamonu Faculty of Education, 15(1), 259-270.
Guy, R. (2012). Overcoming misconceptions in neurophysiology learning: an approach using colorcoded animations. Advances in Physiology Education, 36(3), 226-228.
Hart, K. M., Brown, M.L., Kuchermann, D.E., Kerslach, D., Ruddoock G., & and Mccartney, M. (1998). Children’s Understanding of Mathematics. In K.M. Hart (Ed.), The CSMS mathematics team (pp. 11-16). Antony Rowe Limited.
Haser, Ç., & Ubuz, B. (2001). The conceptual understanding of fractions and processing skills of 5th grade students. IV. Science Teaching Congress, Symposium Book, Ministry of Education Publication, Ankara, Turkey, pp: 609-612.
Haser, Ç., & Ubuz, B. (2002). The conceptual and processing skills with fractions. Education and Science, 27(126): 53-61.
Hesse-Biber, S. N. (2010). Mixed methods research: Merging theory with practice. Guilford Publication.
Hiebert, J., & Wearne, D. (1986). Procedures over concepts: The acquisition of decimal number knowledge. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 197-223). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
Hudson Hawkins, V. (2008). The effects of math manipulatives on student achievement in mathematics. (Unpublished dissertation). Minneapolis, MN: Cappella University.
Karasar, N. (1999). Scientific research methods. Nobel Typography, Ankara, Turkey.
Kerslake, D. (1986). Fractions: Children’s strategies and mistakes. A Report of the Strategies and Mistakes in Secondary Mathematics Project. Windsor: NFER-Nelson.
Kieren, T. E. (1976). On the mathematical, cognitive and instructional foundations of rational numbers. In R. A. Lesh (Ed.), Number and measurement (pp 101-144). Columbus Publishing.
Küçük A. & Demir, B. (2009). A Study on Some Misperceived Concepts in the Teaching of Mathematics in 6th-8th Grades. Journal of Dicle University Ziya Gökalp Faculty of Education, 13, 97-112.
Lamon, S.J. (2001). Presenting and representing: From fractions to rational numbers.In A. Cuoco (Ed.), Problems of representation in the teaching and learning mathematics (pp. 41-58) Hillsdale, NJ: Lawrence Erlbaum Associates.
Margulies, S. (1993). Tips for beginners: Algebraic atrocities. Mathematics Teacher, 86(1), 40-41.
Moseley, B. (2005). Student’s early mathematical representation knowledge: The effects of emphasizing single or multiple perspectives of the rational number domain in problem solving. Educational Studies in Mathematics, 60(1), 37-69.
Moseley, B. J., Okamoto, Y., & Ishida, J. (2007). Comparing US and Japanese elementary school teachers’ facility for linking rational number representations. International Journal of Science & Mathematics Education, 5(1), 165–185.
Moss, J., & Case, R. (1999). Developing children’s understanding of the rational numbers: A new model and an experimental curriculum. Journal of Research in Mathematics Education, 30(2), 122-147.
Olkun, S., & Toluk, Z. (2001). Teaching mathematics in primary education:1-5th grades. Artım Typography, Ankara, Turkey.
Özmantar, M. F., Bingölbali. E., & Akkoç. H. (Ed.). (2008). Matematiksel kavram yanılgıları ve çözüm önerileri. Ankara: Pegem A.
Perso, T. (1992). Making the most of errors. The Australian Mathematics Teacher, 48(2), 12-14.
Pesen, C. (2008). Kesirlerin sayı doğrusu üzerindeki gösteriminde öğrencilerin öğrenme güçlükleri ve kavram yanılgıları. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 9(15), 157-168.
Seyhan, S., & Gür, H. (2004). The Misconception of 7th ad Grades Regarding to Decimal Numbers. Association of Mathematicians,http://www.matder.org.tr/bilim/gshg.a sp?ID=76.
Shaughnessy, J. M. (1992). Research in probability and statistics: Reflections and directions. In D. A. Grouws, (Ed.), Handbook of research in mathematics teaching and learning (pp. 465-494). New York: Macmillan.
Siegler, R. S. et al. 2010. Developing effective fractions instruction: A practice guide. Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.
Siegler, R. S. Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fraction development. Cognitive psychology, 62, 273–296.
Sirotic, N. & Zazkis, R. (2004) Making sense of irrational numbers : focusing on representation, in Proceedings of 28th International Conference for Pyschology of Mathematics Education.
Smith, J. P., diSessa, A. A. and Roscheile, J. (1993). Misconceptions reconceived: A constructivist analysis of knowledge in transition. The Journal of the Learning Sciences, 3(2), 115-163.
Stafylidou, S., & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and Instruction, 14, 503–518.
Şandır, H., Ubuz B., & Argün, Z. (2007). 9th grade students’ difficulties in arithmetic operations, ordering numbers, solving equations and inequalities. Journal of Hacettepe University Faculty of Education, 32, 274-281.
Şiap, İ., & Duru, A. (2004). Skills of using geometrical models in fractions. Journal of Kastamonu Education, 12(1), 89-96.
Tirosh, D., Tsamir, P., & Hershkovitz, S. (2008). Insights into children’s intuitions of addition, subtraction, multiplication, and division. In A. Cockburn & G. Littler (Eds.), Mathematical misconceptions. New Delhi: Sage Publications.
Toluk, Z. (2000). The process of primary sschool students to relate the division with rational numbers. Bogazici University Journal of Education, 19(2), 32-57.
Vergnaud, G. (1983). Multiplicative structures. In R. Lesh and M. Landau (Eds). Acquisition of mathematics concepts and processes. 92-126. New York: Academic Pres.
Yetim, S. & Alkan, R. (2010). İlköğretim 7. sınıf öğrencilerinin rasyonel sayılar ve bu sayıların sayı doğrusundaki gösterimleri konusundaki yaygın yanlışları ve kavram yanılgıları (Common mistakes and misconceptions of 7th grade students about the rational numbers and placement of the rational numbers on the number line). Kırgızistan Türkiye Manas Üniversitesi Fen Bilimleri Dergisi, 2(11), 87-109.
Yetkin, E., 2003. Student Difficulties In Learning Elementary Mathematics. ERIC Digest, ERIC Clearinghouse for Science Mathematics and Environmental Education.

How to cite this article

APA

Yetim, S., & Alkan, R. (2013). How Middle School Students Deal with Rational Numbers? A Mixed Methods Research Study. Eurasia Journal of Mathematics, Science and Technology Education, 9(2), 213-221. https://doi.org/10.12973/eurasia.2013.9211a

Vancouver

Yetim S, Alkan R. How Middle School Students Deal with Rational Numbers? A Mixed Methods Research Study. EURASIA J Math Sci Tech Ed. 2013;9(2):213-21. https://doi.org/10.12973/eurasia.2013.9211a

AMA

Yetim S, Alkan R. How Middle School Students Deal with Rational Numbers? A Mixed Methods Research Study. EURASIA J Math Sci Tech Ed. 2013;9(2), 213-221. https://doi.org/10.12973/eurasia.2013.9211a

Chicago

Yetim, Sebahat, and Ramazan Alkan. "How Middle School Students Deal with Rational Numbers? A Mixed Methods Research Study". Eurasia Journal of Mathematics, Science and Technology Education 2013 9 no. 2 (2013): 213-221. https://doi.org/10.12973/eurasia.2013.9211a

Harvard

Yetim, S., and Alkan, R. (2013). How Middle School Students Deal with Rational Numbers? A Mixed Methods Research Study. Eurasia Journal of Mathematics, Science and Technology Education, 9(2), pp. 213-221. https://doi.org/10.12973/eurasia.2013.9211a

MLA

Yetim, Sebahat et al. "How Middle School Students Deal with Rational Numbers? A Mixed Methods Research Study". Eurasia Journal of Mathematics, Science and Technology Education, vol. 9, no. 2, 2013, pp. 213-221. https://doi.org/10.12973/eurasia.2013.9211a