FROM REALISTIC CONTENTS TO MATHEMATICAL MODELS. THE CASE OF LINEAR FUNCTIONS IN GRADE 10

PDF (ελληνικά)
Published: Oct 8, 2018
DOI: https://doi.org/10.12681/enedim.18763
Keywords:
Algebra Linear function Word problems Problem solving graphical representation senior high school
Ειρήνη Μικρώνη (Eirini Mikroni)
Department of Early Childhood Education, University of Patras
Κώστας Ζαχάρος (Kostas Zacharos)
Department of Early Childhood Education, University of Patras
Βασίλης Κόμης (Vasilis Komis)
Department of Early Childhood Education, University of Patras
Abstract

This study investigates students' ideas relating to transforming word problems in a mathematical 'language', which includes both, graphical and algebraic representations. The research question which we attempt to answer is whether students can move from verbal representation of a problem to typical mathematical 'language' such as the algebraic and graphical representations. In addition, we examine whether students prefer a certain type of representation, where they feel most competent.

The research was a case study and was carried out with the participation of 25 students in Grade 10 (first grade in 'Lykeion'). The subjects participated in a personal interview during which they were asked to solve linear word problems. The research data were analyzed using quantitative and qualitative methods.

It was found that the students in this study were generally able to transform word problems to algebraic and graphical representations. The findings, however, have shown some systematic faults in students thinking, such as the discontinuity in the graphical representations, the perception that the rate of change of a function means a negative slope in the graphical representation or another line from the beginning of the axes. In addition, in many cases, students were unable interpret graphical representations. Furthermore, students' work indicated that they were more familiar and preferred algebraic representations rather than using graphs.

Many researches point out to students’ ability to move from one type of representation to another, a competence that can emerge via students involvement with different representations of a problem. Consequently, students should be lead to work in environments of multiple representations, that is, environments that allow the representation of a problem and its solution in several ways: verbal, graphical and algebraic representation.

Article Details
  • Section
  • Articles
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors who publish with this journal agree to the following terms:

Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution licence that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g. post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

Authors are permitted and encouraged to post their work online (preferably in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).

 

 
Downloads
Download data is not yet available.
Author Biographies
Ειρήνη Μικρώνη (Eirini Mikroni), Department of Early Childhood Education, University of Patras
Post Graduate Stiudent
Κώστας Ζαχάρος (Kostas Zacharos), Department of Early Childhood Education, University of Patras
Assistant Professor
Βασίλης Κόμης (Vasilis Komis), Department of Early Childhood Education, University of Patras
Assistant Professor
References
Bell, Α., Brekke, G., & Swan, M. (1987). Diagnostic teaching: 4 graphical interpretations. Mathematics Teaching, 119, 56-60.
Dowling, P. (1998). The Sociology of Mathematics Education. Mathematical Myths/Pedagogic Texts, London: Falmer Press.
Dowling, P. (2001). Mathematics Education in Late Modernity: Beyond Myths and Fragmentation. In B. Atweh, H. Forgasz & B. Nebres (Eds.), Sociocultural Research on Mathematics Education (pp. 19-36), Lawrence Erlbaum Associates, Publishers, Mahwah, New Jersey, ZLondon.
Freudenthal, Η. (1983). Didactical Phenomenology of Mathematical Structures. D. Reidel Publishing Company, Dordrecht, Boston, Lancaster.
Gravemeijer, Κ. (1997). Commentary solving word problems: a case of modeling? Learning and Instruction, 7(4), 389-397.
Greer, B. (1997). Modelling reality in the mathematics classroom: The case of word problems. Learning and Instruction, 7, 293-307.
Hines, E. (2002). Developing the Concept of Linear Function: One Student's Experiences With Dynamic Physical Models, Journal of Mathematical Behavior, 20, 337-361.
Kaput, J. (1987). Representation Systems and Mathematics. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics (pp. 19-26), Hillsdale, NJ: Lawrence Erlbaum.
Kaput, J. (1991). Notations and representations as mediators of constructive processes. In E.Von Glasersfeld (Ed.) Radical constructivism in mathematics education (pp. 53-74), Kluwer Academic Publishers.
Kerslake, D. (1981). Graphs. In K. M. Hart (Ed.), Children's Understanding of Mathematical Concepts (pp. 11-16), John Murray, London.
Komis, V., Lavidas, K., Papageorgiou, V., Zacharos, K. & Politis, P. (2006). L'enseignement du tableur au collège en Grèce : étude de cas et implications pour une approche interdisciplinaire In Pochon L.-O., Bruillard E. & Maréchal Α., Apprendre (avec) les logiciels: Entre apprentissages scolaires et pratiques professionnelles (pp. 253-260), Neuchate- Lyon : IRDP - INRP.
Lesh, R., Post, T., & Behr, M. (1987). Representations and Translations Among Representations in Mathematics Learning and Problem Solving. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics (pp.33-40). Hillsdale Erlbaum.
Mevarech, Z. R, & Kramarsky, B. ( 1997). From verbal descriptions to graphic representations: stability and change in students' alternative conceptions. Educational Studies in Mathematics, 32, 229-263.
Molyneux-Hodgson, S., Rojano, T, Sutherland R., & Ursini, S. (1999). Mathematical Modelling: The Interaction of Culture and Practice, Educational Studies in Mathematics, 39, 167-183.
Moschkovich, J., Schoenfeld, A. H., & Arcavi, A. (1993). Aspects of understanding: On multiple perspectives and representations of inear relations and connections among them. In Τ A. Romberg, E. Fennema, & Τ. P. Carpenter (Eds.), Integrating research on the graphical representation of functions (pp. 69-100), Hillsdale, NJ: Lawrence Erlbaum Associates, NY.
Saljo, R. (1991). Learning and Mediation: Fitting Reality into a Table. Learning and Instruction, 1(3), 261-272.
Schorr, R. Y. (2003). Motion, speed, and other ideas that "should be put in books". Journal
of Mathematical Behavior, 22, 467-779.
Wubbels, T., Korthagen, F, & Broekman, H. (1997). Preparing Teachers for Realistic Mathematic Education. Educational Studies in Mathematics, 32, 1-28.
Most read articles by the same author(s)