PROBLEMS OF PUPILS IN DEVELOPMENT REPRESENTATION OF DIFFERENCE IN TEACHING MATHEMATICS
DOI:
https://doi.org/10.5937/Keywords:
representation of fractions, a problem, teaching of the mathematics on the beginner's level, methodical approachAbstract
This paper is based on theoretical analysis of the research in the field of fractions, with the special attention on students' problems with understanding the representation of fractions in the beginner's level of mathematics teaching. The aim of this paper is a solution of the problem which students encounter while trying to understand representations of fractions. The presented research used for this paper was a guidepost to obstacles students have to deal with while trying to understand the notion of fractions with the intention to overcome them. The paper consists of the two parts. The first one is dedicated to methodical approach of the content related to fractions. In the other part however, the attention is directed towards presentation of the relevant research related to the students' problems with understanding this notion. According to the previous theories and models we came to the following conclusions. Firstly, an adequate manipulation of representative models of the fraction will form the mental image of fraction, specially models from ordinary pupil’s life. Secondly, increasing of visual contents about fractions can be done by using a number line. Thirdly, while teaching this subject it is necessary to use innovative models of teaching because using of wide range of teaching systems contributes to better understanding of representations of fractions.
Downloads
References
Aksu, M. (1997). Student performance in dealnig with fractions. The Journal of Educational Research, 90, 375–380.
Arcavi, A. (2003). The role of visual representations in the learning of mathematics Educational studies in matematics, 52, 215–241. Netherlands: Academic Press.
Ball, D.(1990). The mathematical understanding that preservice teachers bring to teacher education. Elementary school journal, 90, 499–466.
Ball, D. (1993). Halves, pieces, and twoths: Constructing and using representational contexts in teaching fractions. In T. P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational numbers: An integration of research (pp. 157–196). Hillsdale, NJ: Lawrence Erlbaum.
Behr, M., Harel, G., Post, T. & Lesh, R. (1990). On the operator concept of rational numbers: Towards a semantic analysis.Paper presented at the Annual Meeting of the American Educational Research Association. Boston, MA.
Berlin, D. F. & White, A. L. (1995). ,,Connecting School Science and Mathematics”. In: Connecting Mathematics across the Curriculum, Ed. House, P. A. & Coxford, A. F., National Council of Teachers of Mathematics, 1995. Yearbook, Reston, Virginia.
Bonotto, C. (1991). Numeri razionali. Approcci diversi e relative sperimentazionididattiche. L’insegnamento della matematica e delle scienze integrate. 14, 7, 607–638.
Brown, A. (1993). A critical analysis of teaching rational number. In: Carpenter T.P., Fennema E., Romberg T.A.. (eds.) (1993). Rational numbers: as integration of research.
Hilsdale (N.J.): Lawrence Erlbaum. 197–218.
Galen, F., Feijs, E., Figueiredo, N., Gravemeijer, K., Herpen, E. & Keijzer, R. (2008).
Fractions, percentages, decimals and proportions: A learning-teaching trajectory for grade 4, 5 and 6. Rotterdam: Sense.
Gould, P. (2011). Developing an Understanding of the Size of Fractions. The Australian Association of Mathematics Teachers (pp.63–70).
Goldin, G. and Shteingold, N. (2001). Systems of representations and the development of mathematical; concepts. In: A. Cuoco and F. Curcio (Eds.), The roles of representations in school mathematics, 2001 Yearbook (pp.1–23). NCTM: Macmillan Publishing Company.
Duval, R. (1999). Representation,vision and visualization:Cognitive functionsin mathematical thinking. In F. Hitt, & M. Santos (Eds.), Pro-ceedings of the Twentyfirst Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 3–26). Columbus, Ohio: ERIC Clearinghouse for Science, Mathematics and Environmental Education.
Дејић, М. и Егерић, М. (2010). Методика наставе математике. Београд: Учитељски факултет.
Завод за вредновање квалитета образовања и васпитања (2011). Општи стандарди постигнућа – образовни стандарди за крај првог циклуса обавезног образовања из Математике, Београд.
Kieren T. E. (1988). Personal knowledge of rational numbers. Its intuitive and formal development. In: Hiebert J., Behr M. (eds.) (1988). Number concepts and operations in the middle grades. Reston (Va): NCTM-Lawrence Erlbaum Ass. 162–181.
Lazić, B. (2014). Propedevtičko uvođenje sadržaja o razlomcima u aritmetici za mlađe razrede osnovne škole (doktorska disertacija). Beograd: Učiteljski fakultet Univerziteta u Beogradu.
Милинковић, Ј. (2013). Увод у разломке, XXIX Специјализовани републички семинар за наставнике математике у основним и средњим школама, 11. 01. 2013. Београд: Математичко друштво ,,Архимедес“.
Милинковић, Ј. (2016). Огледи о учењу у настави математике, Београд: Учитељски факултет Универзитета у Београду.
Министарство просвете, науке и технолошког развоја Републике Србије (2015). Наставни програм за први циклус основног образовања и васпитања. http://www.zuov.gov.rs/poslovi/nastavni-planovi/nastavni-planovi-os-i-ss/
Мићић, В. (2010). Од природних до реалних бројева у старијим разредима основне школе, Настава математике, 239, (20–29). Београд: ДМС.
Post, T. R. & Cramer, K. A. (1989). Knowledge, representation, and quantitative thinking. In M. C. Reynolds (Ed.), Knowledge base for the beginning teacher (pp. 221–232). New York: Pergamon.
Првановић, С. (1958). Методски приручник за извођење наставе аритметике. Београд: Библиотека просветних радника.
Prediger, S. (2013). Focussing structural relations in the bar board – a design research study for fostering all students’ conceptual understanding of fractions. In B. Ubuz, C.
Haser & M. A. Mariotti (Eds.), Proceedings of the 8th Congress of the European Society for Research in mathematics Education, Antalya, 343–352.
Resnick, L. B. (1986). The development of mathematical intuition. In M. Perlmutter (Ed.), Percpetives on intellectual development: The Minnesota Symposia on Child Psychology (Vol. 19, pp. 159–194). Hillsdale, NJ: Lawrence Erlbaum.
Small, M. (2009). Teaching to the Big Ideas K-3, Mathfocus K-3, Nelson.
Strang, T. (1990). The fraction-concept in comprehensive school at grade-levels 3–6 in Finland. In G. Booker, P. Cobb & T. N. Mendicuti (Eds.), Proceedings of the 14th PME International Conference, 3,75–80.
Streefland L. (1990). Fractions in realistic mathematics education. Dordrecht: Kluwer.
Streefland L. (1991). Fractions in realistic mathematics education: a paradigm of developmental research. Dordrecht: Kluwer.
Streefland L. (1993). Fractions: a realistic approach. In: Carpenter T.P., Fennema E., Romberg T.A. (eds.) (1993). Rational numbers: an integration of research. Hillsdale (NJ): Lawrence Erlbaum Ass. 289–325.
Thompson, P. W. & Saldanha, L. A. (2003). Fractions and multiplicative reasoning. In J. Kilpatrick, W. G. Martin,& D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 95–113). Reston, VA: National Council of Teachers of Mathematics.
Tobias, J. M. (2013). Prospective elementary teachers’ development of fraction language for defining the whole. Journal of Math. Teacher Education, 16, 85–103.
Treffers, A. (1987). Three dimensions. A Model of Goal and Theory Descriptio in mathematics Instruction – the Wiskobas Project. Dordrecht: Reidel Publishing Company.
Fandiño, Pinilla M. I. (2007). Fractions: conceptual and didactic aspects. Acta Didactica Universitatis Comenianae. 7, 23–45.
Fosnot, C. T. & Dolk, M. (2002).Young Mathematicians at Work Constructing Fractions, Decimals, and Percents. Portsmouth: Heinemann.
Freudenthal, H. (1991). Revisiting mathematics education. China lectures. Dordrecht, the Netherlands: Kluwer Academic Publishers.
Herman, J., llucova, L., Kremsova, V., Pribyl, J., Ruppeldtova, J. & Simpson, A. et al. (2004). Images of fractions as proccesses and images of fractions in processes. In M. J. Heines & A. B.
Fuglestad (Eds.), Proceedings of the 28th PME International Conference, 4, 249–256.
Hannula, M. S. (2003). Locating frаction on a number line. In N. A. Patonan. B. J.
Dougheny, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 3, 17–24.
Charalambos, C. Y. & Pitta-Pantazi, D. (2005). Revisiting a theoretical model on fractions: Implications for teaching and research. In H. L. chick & J. L. Vincent (Eds.), Proceedings of the 29th PME International Conference, 2, 233–240.
Cramer, K. & Henry, A. (2002). „Using Manipulative Models to Build Number Sense for Addition and Fractions.” In Making Sense of Fractions, Ratios, and Proportions, Yearbook of the National Council of Teachers of Mathematics (NCTM), edited by Bonnie Litwiller and George Bright, pp. 41–48. Reston, VA: NCTM.
Ševčenko, I. N. (1967). Metodika nastave običnih razlomaka. Beograd: Jugoslovenski zavod za proučavanje školskih i prosvetnih pitanja.
Watanabe, T. (2006). Teaching and learning of fractions: A Japanese perceptive, Teaching Children Mathematics, 12(7), 368–372.
Witman, G. (2013). The consistency of students’ error patterns in solving computational problems with fractions. In B. Ubuz, C. Haser & M. A. Mariotti (Eds.), Proceedings of the 8th Congress of the European Society for Research in mathematics Education, Antalya, 393–402.
Downloads
Published
Issue
Section
License
Copyright (c) 2017 The Methodology Theory and Practice

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