CONCEPT OF UNDERSTANDING IN EDUCATION FOR FIRST CLASSES OF EDUCATIONAL EDUCATION
DOI:
https://doi.org/10.5937/Keywords:
algebra, unknown, representations, textbookAbstract
The notion of an unknown number plays an important role in switching from arithmetic to an algebra, but it also represents a source of confusion that arises in algebra teaching. In previous research, the dominant view is that the unknown should be introduced in the teaching of arithmetic, gradually, while students acquire the skills in the account. In constructing the meaning of new concepts, a great deal of different representations were used. In this paper we are dealing with the analysis of the introduction of the term unknown in the textbooks for the first grade of elementary education from the aspect of marking the unknown, the way of reaching its value and the use of different representations. The research showed that there is no single position in the textbooks about marking the unknown and about how to find its value. Also, in some textbooks, insufficient attention is paid to the ways of representing this term.
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References
Brizuela, B., Blanton, M., Sawerey, K., Newman-Owens, A. & Gardiner, A. (2015). Children’s Use of Variables and Variable Notation to Represent Their Algebraic Ideas. Mathematical Thinking and Learning, Vol. 17: 34-63.
Cai, J. & Knuth, E. (2011). A Global Dialogue About Early Algebraization from Multiple Perspectives, Early Algebraization, In E. Cai & J. Knuth (Eds.), Early Algebraization (pp. vii – xi). Berlin-Heidelberg: Springer.
De Bock, D., Deprez, J., Van Dooren, W., Roelens, M. & Verschaffel, L. (2011).
Abstract or Concrete Examples in Learning Mathematics? A Replication and Elaboration of Kaminski, Sloutsky, and Heckler’s Study. Journal for Research in Mathematics Education, Vol 42. No. 2, 109-126.
Dreyfus, T. (1991a). Advanced mathematical thinking processes. In D. Tall (Ed.), Advanced mathematical thinking (pp. 25-41). Dordrecht: Kluwer Academic Publishers.
Filloy, E. & Rojano, T. (1989). The Transition from Arithmetic to Algebra. For the Learning of Mathematics, Vol. 9, No. 2, 19-25.
Goldstone, R. & Son, J. (2005). The Transfer of ScientificPrinciples Using Concrete and Idealized Simulations. The Journal of the Learning Sciences, Vol 14. 69-110.
Herscovics, N. & Linchevski, L. (1994). A Cognitive Gap between Arithemetic and Algebra. Educational Studies in Mathematics, Vol. 27, 59-78.
Hiebert, J., & Carpenter, T. (1992). Learning and teaching with understanding. In D.
Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65-97). New York: Macmillan.
Kaminski, J., Sloutsky, V. & Heckler, A. (2006). Do Children Need Concrete Instantiations to Learn an Abstract Concept? In R. Sun & N. Miyake (Eds.), Proceedings of the XXVIII Annual Conference of the Cognitive Science Society (pp. 411-416). Mahwah, NJ: Erlbaum.
Kaminski, J., Sloutsky, V. & Heckler, A. (2008). The Advantage of Abstract Examples in Learning Math. Science, Vol. 320, 454-455.
Kilpatrick, J. (2011). Commentary on Part I. In E. Cai & J. Knuth (Eds.), Early Algebraization (pp. 125-130). Berlin-Heidelberg: Springer.
Kuchemann, D. (1978). Children’s Undrestanding of Numerical Variables, Mathematics in School, Vol. 7, No. 4, 23–26.
Sfard, A. (2000). Simbolizing mathematical reality into being: How mathematical discourse and mathematical objects create each other. In P. Coob, K. Yackel, & K. McClain (Eds.), Simbolizing and communicating: Perspectives on Mathematical Discourse, Tools, and Instructional Design (pp. 37–98). Mahwh, NJ. Erlbaum.
Stacey, K. & MacGregor, M. (1999). Learning the Algebraic Method of Solving Problems. Journal of Mathematical Behavior, Vol. 18, No. 2, 149-167.
Russell, S. J., Schifter, D. & Bastable, V. (2011). Developing Algebraic Thinking in the Context of Arithmetic. In E. Cai & J. Knuth (Eds.), Early Algebraization (pp. 43 – 69). Berlin-Heidelberg: Springer.
Usiskin, Z. (1988). Conceptions about School Algebra and Uses of Variables. In A. F.
Coxford & A. P. Shulte (Eds.), The ideas of algebra, K-12 (1988 Yearbook of the National Council of Teachers of Mathematics, pp. 8-19). Reston, VA: NCTM.
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Иванчевић, И. & Тахировић, С. (2016). Математика. Уџбеник за први разред основне школе. Београд: Логос.
Јовановић-Лазић, М. & Дрнаревић, Д. (2010). Математика 1. Београд: Бигз.
Јосимовић С. (2016). Математика 1б. Уџбеник за први разред основне школе. Београд: Едука.
Милинковић, Ј. (2013). Математика 1. Уџбеник за првив разред основне школе. Београд: Креативни центар.
НП 1 - 2. Наставни програм за први и други разред разред. Службени гласник РС – Просветни гласник бр. 10/04.
PDTP (2004). Patterns, Functions, and Algebra for Elementary School Teachers. A Professional Development Training Program to Implement the 2001 Virginia Standards of Learning. Virginia Department of Education.
Поповић, Б., Вуловић, Н. Анокић, П. & Кандић, М. (2016). Маша и Раша. Математика 1. Уџбеник за први разред основне школе. Београд: Klett.
Тодоровић, З. & Огњановић, С. (2009). Математика 1. Уџбеник за први разред основне школе. Београд: Завод за уџбенике.
Ћук, М., Јевтић, З., Марковић, Б. (2011). Разиграна математика. Београд: Нова школа.
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