MATHEMATICAL LITERATURE AS A TOOL FOR UNDERSTANDING RATIONAL NUMBERS

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Published: Dec 5, 2019
DOI: https://doi.org/10.12681/enedim.21967
Keywords:
Mathematical Literature Rational Numbers Misconceptions Attitudes
Δημήτρης Μαρής (Dimitris Maris)
University of Athens
Κωνσταντίνος Χρήστου (Konstantinos Christou)
University of Western Macedonia
Abstract

Rational numbers are a cornerstone of mathematics and mathematics education. Mathematics education research has identified great difficulties understanding rational numbers and has recorded a variety of errors, misconceptions and negative attitudes towards them. In this study an attempt to use Mathematical literature as a mean to address certain difficulties, misunderstandings and attitudes with rational numbers. The first author has written a mathematical story named "Ταξίδι προς το Μηδέν (Traveling to zero)" approaching ordering and density of rational numbers in an alternative way. In order to test this story as an educational instrument, questionnaires were given to 6th graders from Greece, in pre/post test design and individual semi-structured interviews were conducted. The results showed that a mathematical story could help students address their misconceptions with rational numbers and also to improve their attitudes towards them.

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Author Biographies
Δημήτρης Μαρής (Dimitris Maris), University of Athens
Post Graduate Program od Mathematics Education
Κωνσταντίνος Χρήστου (Konstantinos Christou), University of Western Macedonia
Ass. Professor
References
Ξενόγλωσση:
Abbott, E. A. (2006). Flatland: A romance of many dimensions. OUP Oxford.
Beer, G. (1990). Translation or transformation? The relations of literature and science. Notes and Records of the Royal Society of London, 44(1), 81-99.
Bintz, W. P. (2002). Using literature to support mathematical thinking in middle school. Middle School Journal, 34(2), 25-32.
Cartwright, J. (2007). Science and Literature: Towards a conceptual framework. Science & education, 16(2), 115-139.
Casey, B., Erkut, S., Ceder, I., & Young, J. M. (2008). Use of storytelling context to improve girls' and boys' geometry skills in Kindergarden. Journal of Applied Developmental Psychology, 29(1), 29-48.
Casey, B., Kersh, J. E., & Young, J. M. (2004). Storytelling sagas: An effective medium for teaching early childhood mathematics. Early Childhood research Quarterly, 19(1), 167-172.
Christou K.P and Prokopou, A (in press). Using refutational text to address the Multiplication Makes Bigger misconception. Educational Journal of the University of Patras. UNESCO Chair.
Christou, K. P. (2015). Natural number bias in operations with missing numbers. ZDM, 47(5), 747-758.
Common Core State Standards Initiative (2019), Standards for Mathematical Practice, Grade 6, The Number System. Retrieved from: http://www.corestandards.org/Math/Content/6
Copple, C., & Βredekamp, S. (2009). Developmentally appropriate practive in early childhood programs serving children from birth through age 8. ERIC.
Cramer, K. A., Post, T. R., & & delMas, R. C. (2002). Initial fraction learning by fourth- and fifth-grade students: a comparison of the effects of using commercial curricula with the effects of using the rational project curriculum. Journal for Research in Mathematics Education, 33, 111-144.
Khoury, H. A., & Zazkis, R. (1994). On fractions and non-standard representantions: Preservice teachers' concepts. Educational Studies in Mathematics, 27, 191-204.
Killpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up. Helping children learn mathematics. Washington, DC: National Academy Press.
Levine, G. (1988). Darwin and the novelists: patterns of science in Victorian fiction. University of Chicago Press.
Lim, S. Y., & Chapman, E. (2013). Development of a short form of the attitudes toward mathematics inventory. Educational Studies in Mathematics, 82(1), 145-164.
Li, Y., Chen, X., & & An, S. (2009). Conceptualizing and organizing content for teaching and learning in selected Chinesem Japanese and US mathematics textbooks: the case of fraction division. ZDM - The International Journal on Mathematics Education, 41, 908-826.
Maloney, A. P. (2014). Learning over time: Learning trajectories in mathematics education. IAP.
Martinie, S. L., & Bay-Williams, J. M. (2003). Using literature to engage Students in proportional reasoning. Mathematics Teaching in the Middle School, 9(3), 142-148.
Mazzocco, M. M., & Devlin, K. T. (2008). Parts and 'holes': gaps in rational number sense among children with vs. without mathematical learning disabilities. Developmental Science, 11, 681-691.
McMullen, J. L.-S. (2015). Modeling the developmental trajectories of rational number concept (s). Learning and Instruction, 37, 14-20.
Moskal, B. M., & Magone, M. E. (2000). Making Sense of what students know: Examining the referents, relationships and modes students displayed in response to a decimal task. Educational Studies in Mathematics, (43), 313-335.
Moss, J. (2005). Pipes, tubes, and beakers: New approaches to teaching the rational-number system. In M.S. Donovan & J.D. Bransford (Eds.). How students learn: Mathematics in the classroom, DC: National Academic Press, 121-162.
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(2), 122-147.
Naumann, B. (2005). Introduction: Science and Literature. Science in context, 18(4), 511-523.
Ni, Y. & Zhou, Y. D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27-52.
Resnick, L. B., Nesher, P., Leonard, F., Magone, M., Omanson, S., & Peled, I. (1989). Conceptual bases of arithmetic errors: The case of decimal fractions. Journal for research in mathematics education, 8-27.
Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273-296.
Smith, C. L., Solomon, G. E., & Carey, S. (2005). Never getting to zero: Elementary school students’ understanding of the infinite divisibility of number and matter. Cognitive Psychology, 101-140.
Sriraman, B. (2003). Mathematics and Literature: Synonyms, Antonyms or the Perfect Amalgam? Australian Mathematics Teacher, The, 59(4), 26.
Sriraman, B. (2004). Mathematics and Literature (the sequel): Imagination as a pathway to Advanced Mathematical Ideas and Philosophy. Australian Mathematics Teacher, 60(1), 17-23.
Stafylidou, S., & Vosniadou, S. (2004). The development of students' understanding of the numerical value of fractions. Learning and Instruction, 14, 503-518.
Stewart, I. E. (2010). Flatterland: Like Flatland, only more so. ReadHowYouWant.com.
Usnick, V., & McCarthy, J. (1998). Turning adolescents onto mathematics through literature. Middle School Journal, 29(4), 50-54.
Vamvakoussi, X., Christou, K. P., & Vosniadou, S. (2018). Bridging Psychological and Educational Research on Rational Number Knowledge. Journal of Numerical Cognition, 4(1), 84-106.
Vamvakoussi, X., Van Dooren, W., & Verschaffel, L. (2012). Naturally biased? In search for reaction time evidence for a natural number bias in adults. The Journal of Mathematical Behaviour, 31, 344-355.
Vamvakoussi, X., & Vosniadou, S. (2010). How Many Decimals Are There Between Two Fractions, Aspects of Secondary School Students' Understanding of Rational Numbers and Their Notation. Cognition and instruction, 28(2), 181-209.
Vamvakoussi, X., & Vosniadou, S. (2012). Βridging the gap between the dense and the discrete: The number line and the “rubber line” bridging analogy. Mathematical Thinking and Learning, 14, 265-284.
Van Hoof, J., Janssen, R., Verschaffel, L., & Van Dooren, W. (2015). Inhibiting natural knowledge in fourth graders: towards a comprehensive test instrument. ZDM, 47(5), 849-857.
Vosniadou, S., Vamvakoussi, X., & Skopeliti, E. (2008). The framework theory approach to conceptual change. In S. Vosniadou (Ed.). Handbook of reasearch on conceptual change, 3-34.
Zazkis, R., & Liljedahl, P. (2009). Τeaching mathematics as storytelling. Sense Publishers.
Ελληνική:
Μιχαηλίδης, Τ. (2007). Από τον Αισχύλο στους μεταμοντέρνους: μαθηματική λογοτεχνία.
Παιδαγωγικό Ινστιτούτο (2011). Νέο Πρόγραμμα Σπουδών, Επιστημονικό πεδίο: Προσχολική-Πρώτη Σχολική Ηλικία (Β’ μέρος). Ανακτήθηκε από: http://ebooks.edu.gr/info/newps
Φιλίππου, Γ., & Χρίστου, Κ. (2001). Συναισθηματικοί παράγοντες και μάθηση των μαθηματικών. Αθήνα: Ατραπός.
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