Τα διαγράμματα στην επίλυση προβλημάτων: δυσκολίες στη δημιουργία και στη χρήση τους από μαθητές της Δ’ Δημοτικού


Δημοσιευμένα: Dec 18, 2023
Λέξεις-κλειδιά:
επίλυση μαθηματικού προβλήματος (ΕΜΠ) λεκτικό πρόβλημα διαγράμματα στην ΕΜΠ δυσκολίες χρήσης διαγραμμάτων
Άννα Μπακαλίδου
Μαριάννα Τζεκάκη
Περίληψη

Η παρούσα έρευνα εξετάζει τις δυσκολίες με τις οποίες οι μαθητές έρχονται αντιμέτωποι, όταν χρησιμοποιούν ή δημιουργούν διαγράμματα για να επιλύσουν λεκτικά προβλήματα αθροιστικής δομής μίας πράξης πριν και μετά από μια διδακτική παρέμβαση για τη χρήση διαγραμμάτων. Για τη διερεύνηση των δυσκολιών δόθηκαν δύο τεστ (αρχικό και τελικό) σε 45 μαθητές της Δ’ δημοτικού, οι οποίοι κλήθηκαν να επιλύσουν τρία προβλήματα με την παρότρυνση να σχεδιάσουν διαγράμματα και να τα χρησιμοποιήσουν. Οι δυσκολίες ταξινομήθηκαν σε τρεις κατηγορίες αναφορικά με την κατανόηση της έννοιας, τη δημιουργία και τη χρήση ενός διαγράμματος. Τα αποτελέσματα έδειξαν ότι αρχικά όλοι οι μαθητές δυσκολεύονται να κατανόησουν την έννοια του διαγράμματος κι αντίστοιχα να το χρησιμοποιήσουν. Μετά τη διδακτική παρέμβαση οι δυσκολίες των μαθητών περιορίστηκαν και αφορούσαν κυρίως τη δημιουργία ενός διαγράμματος ως προς τη συμπλήρωση των δεδομένων-ζητούμενου στη σωστή θέση ή τη χρήση του κυρίως σε προβλήματα Σύγκρισης και Αλλαγής.

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Αναφορές
Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215-241.
Bakar, K., Way, J., & Bobis, J. (2016). Young Children’s Drawings in Problem Solving. In B. White, M. Chinnappan, & S. Trenholm (Eds.), Opening up Mathematics Education Research (Proceedings of the 39th Annual Conference of the Mathematics Education Research Group of Australasia) (pp. 86-93). Adelaide: MERGA.
Boonen, A., van Wesel, F., Jolles, J., & van der Schoot, M. (2014). The role of visual representation type, spatial ability, and reading comprehension in word problem solving: An item-level analysis in elementary school children. International Journal of Educational Research, 68, 15-26.
Carpenter, T., Hiebert, J., & Moser, J. (1981). Problem Structure and First-Grade Children's Initial Solution Processes for Simple Addition and Subtraction Problems. Journal for Research in Mathematics Education, 12(1), 27-39.
Chan, W. W. L., & Kwan, J. L. Y. (2021). Pathways to word problem solving: The mediating roles of schema construction and mathematical vocabulary. Contemporary Educational Psychology, 65, 1-12.
Christou, C., & Philippou, G. (1998). The Developmental Nature of Ability to Solve One-Step Word Problems. Journal for Research in Mathematics Education, 29(4), 436-442.
Collins, A., Joseph, D., & Bielaczyc, K. (2004). Design Research: Theoretical and Methodological Issues. Journal of the Learning Sciences, 13(1), 15-42.
Diezmann, C. (1999). Assessing diagram quality: Making a difference to representation. Proceedings of the 22nd Annual Conference of Mathematics Education Research Group of Australasia, (pp. 185-191). Adelaide.
Diezmann, C. (2000). Making Sense with Diagrams: Students’ Difficulties with Feature-Similar Problems. Proceedings of the 23rd Annual Conference of Mathematics Education Research Group of Australasia, (pp. 228-234). Freemantle.
Diezmann, C. (2000). The difficulties students experience in generating diagrams for novel problems. In T. Nakahara, & M. Koyama (Eds.), Proceedings 25th Annual Conference of the International Group for the Psychology of Mathematics Education, (pp. 241-248). Hiroshima, Japan.
Diezmann, C., & English, L. (2001). Promoting the use of diagrams as tools for thinking. In A. Cuoco (Ed.), The Roles of Representation in School Mathematics: 2001 Yearbook (pp. 77-89). National Council of Teachers of Mathematics, Virginia, USA.
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of Mathematics. Educational Studies in Mathematics, 61, 103-131.
Fagnant, A., & Vlassis, J. (2013). Schematic representations in arithmetical problem solving: Analysis of their impact on grade 4 students. Educational Studies in Mathematics, 84, 149-168.
Fischbein, E. (2002). Tacit Models and Infinity. Educational Studies, 48, 309-329.
Fuson, K. (1992). Research on whole number addition and subtraction. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning. A Project of the National Council of Teachers of Mathematics (pp. 243-275). Reston, Virginia: National Council of Teachers of Mathematics.
Gagatsis, A., & Elia, I. (2004). The effects of different modes of representation on mathematical problem solving. In M. Hoines, & A. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education: Vol. 2, (pp. 447-454). Bergen, Norway.
Goldin, G., & Kaput, J. (1996). A joint perspective on the idea of representation in learning and doing mathematics. In L. Steffe, P. Nesher, P. Cobb, G. Goldin, & B. Greer (Eds.), Theories of Mathematical Learning (pp. 397-430). Mahwah, NJ: Erlbaum.
Gravemeijer, K., & Cobb, P. (2006). Design Research from the Learning Design Perspective. In J. van den Akker, B. Bannan, A. E. Kelly, N. Nieveen, & T. Plomp (Eds.), Educational Design Research (pp. 73-112). Enschede, Netherlands: Netherlands Institute for Curriculum Development (SLO).
Hegarty, M., & Kozhevnikov, M. (1999). Types of Visual-Spatial Representations and Mathematical Problem Solving. Journal of Educational Psychology, 91(4), 684-689.
Jonassen, D. (2003). Designing Research-Based Instruction for Story Problems. Educational Psychology Review, 15(3), 267-296.
Lowrie, T. (2020). The utility of diagrams in elementary problem solving. Cognitive Development, 55, 1-12.
Lowrie, T., & Diezmann, C. (2005). Fourth-grade students’ performance on graphical languages in Mathematics. In H. Chick, & J. Vincent (Eds.), Proceedings 30th Annual Conference of the International Group for the Psychology of Mathematics Education: Vol. 3, (pp. 265-272). Melbourne: PME.
Lowrie, T., & Diezmann, C. (2007). Solving Graphics Problems: Student Performance in Junior Grades. The Journal of Educational Research, 100(6), 369-378.
Lowrie, T., & Kay, R. (2001). Relationship Between Visual and Nonvisual Solution Methods and Difficulty in Elementary Mathematics. The Journal of Educational Research, 94(4), 248-255.
Manalo, E., & Uesaka, Y. (2006). Quantity and quality of diagrams used in math word problem solving: A comparison between New Zealand and Japanese students. Refereed papers of the NZARE (New Zealand Association for Research in Education) National Conference 2006. New Zealand: Wellington.
Marshall, S. (1995). Schemas in Problem Solving. New York: Cambridge.
Mayer, R., & Hegarty, M. (1996). The Process of Understanding Mathematical Problems. In R. Stenberg, & T. Ben-Zeev (Eds.), The Nature of Mathematical Thinking (pp. 29-53). Mahwah, NJ: L. Erlbaum Associates.
Nesher, P., Greeno, J., & Riley, M. (1982). The Development of Semantic Categories for Addition and Subtraction. Educational Studies in Mathematics, 13(4), 373-394.
Nesher, P. (1986). Learning Mathematics: A Cognitive Perspective. American Psychologist, 41(10), 1114–1122.
Pantziara, M., Gagatsis, A., & Pitta-Pantazi, D. (2004). The use of diagrams in solving non routine problems. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education: Vol. 3, (pp. 489-496). Bergen, Norway .
Polya, G. (1957). How to solve it? Princeton, NJ: Princeton University Press.
Pongsakdi, N., Kajamies, A., Veermans, K., Lertola, K., Vauras, M., & Lehtinen , E. (2020). What makes mathematical word problem solving challenging? Exploring the roles of word problem characteristics, text comprehension, and arithmetic skills. ZDM Mathematics Education, 52, 33-44.
Riley, M., Greeno, J., & Heller, J. (1983). Development of Children's Problem-Solving Ability in Arithmetic. In H. Ginsburg (Ed.), The Development of Mathematical Thinking (pp. 153-196). New York: Academic Press.
Saundry, C., & Nicol, C. (2006). Drawing as problem-solving: Young children's mathematical reasoning through pictures. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education: Vol. 5, (pp. 57-63). Prague: PME.
Schoenfeld, A. H. (1985). Mathematical Problem Solving. Orlando: Academic Press.
Uesaka, Y., Manalo, E., & Ichikawa, S. (2007). What kinds of perceptions and daily learning behaviors promote students’ use of diagrams in mathematics problem solving? Learning and Instruction, 17, 322-335.
Van de Walle, J. (2007). Διδάσκοντας Μαθηματικά. Θεσσαλονίκη: Επίκεντρο.
van Garderen, D., & Montague, M. (2003). Visual-Spatial Representation, Mathematical Problem Solving, and Students of Varying Abilities. Learning Disabilities Research & Practice, 18(4), 246–254.
van Garderen, D., Scheuermann, A., & Jackson, C. (2013). Examining How Students With Diverse Abilities Use Diagrams to Solve Mathematics Word Problems. Learning Disability Quarterly, 36(3), 145-160.
van Garderen, D., Scheuermann, A., & Poch, A. (2014). Challenges students identified with a learning disability and as high-achieving experience when using diagrams as a visualization tool to solve mathematics word problems, ZDM Mathematics Education, 46(1), 135-149.
Vergnaud, G. (1982). Cognitive and Developmental Psychology and Research in Mathematics Education: Some Theoretical and Methodological Issues. For the Learning of Mathematics, 3(2), 31-41.
Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse: Swets and Zeitlinger.
Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word problems in mathematics education: a survey, ZDM Mathematics Education, 52, 1-16.
Willis, G., & Fuson, K. (1988). Teaching Children to Use Schematic Drawings to Solve Addition and Subtraction Word Problems. Journal of Educational Psychology, 80(2), 192-201.
Ηλία, Ι., & Γαγάτσης, Α. (2004). Η εικόνα στην επίλυση προβλήματος: Αρωγός ή εμπόδιο;. Λευκωσία: Πανεπιστήμιο Κύπρου (ΙΠΕ).
Τζεκάκη, Μ. (2007). Μικρά παιδιά μεγάλα μαθηματικά νοήματα. Αθήνα: Gutenberg.
Χαραλάμπους, Χ. (2003). Επίλυση μαθηματικών προβλημάτων με βάση τη Θεωρία Σχήματος: Εμβαθύνοντας στην εφαρμογή μιας καινοτομίας (Ανέκδοτη μεταπτυχιακή διατριβή). Πανεπιστήμιο Κύπρου, Λευκωσία.
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