| More


Views: 444 Downloads: 1043
Δημήτρης Μαρής (Dimitris Maris), Κωνσταντίνος Χρήστου (Konstantinos Christou)


Οι ρητοί αριθμοί αποτελούν μια από τις βασικότερες έννοιες στα μαθηματικά. Η έρευνα έχει εντοπίσει μεγάλες δυσκολίες στην κατανόησή τους και έχει καταγράψει πολλά λάθη, παρανοήσεις και αρνητικές στάσεις από τους μαθητές. Στην παρούσα μελέτη με τη χρήση της μαθηματικής λογοτεχνίας γίνεται προσπάθεια να αντιμετωπιστούν αυτές οι παρανοήσεις και οι στάσεις να γίνουν πιο θετικές. Ο πρώτος συγγραφέας του άρθρου έγραψε μια μαθηματική ιστορία με τίτλο "Ταξίδι προς το Μηδέν" που ασχολείται με τις έννοιες της διάταξης και της πυκνότητας των ρητών αριθμών. Η κατανόηση των ρητών πριν και μετά την ανάγνωση της ιστορίας ελέγχθηκε με ερωτηματολόγια και ατομικές ημιδομημένες συνεντεύξεις σε έξι μαθητές της Στ’ τάξης ενός δημοτικού σχολείου στην Ελλάδα. Τα αποτελέσματα έδειξαν ότι μια μαθηματική ιστορία θα μπορούσε να αντιμετωπίσει παρανοήσεις στους ρητούς και  να βελτιώσει τη στάση των μαθητών στους ρητούς.

Λέξεις κλειδιά

Μαθηματική λογοτεχνία, Ρητοί αριθμοί, Παρανοήσεις, Στάσεις

Πλήρες Κείμενο:

PDF (English)



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.


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.

Εισερχόμενη Αναφορά

  • Δεν υπάρχουν προς το παρόν εισερχόμενες αναφορές.

Copyright (c) 2019 Δημήτρης Μαρής (Dimitris Maris), Κωνσταντίνος Χρήστου (Konstantinos Christou)

Creative Commons License
Η χρήση του περιεχομένου καθορίζεται από την άδειαCreative Commons Attribution 4.0 International License.