Executable Functions of the Representations in Learning the Algebraic Concepts

Akram Daryaee; Ahmad Shahvarani; Abolfazl Tehranian; Farhad Hosseinzadeh Lotfi; Mohsen Rostamy-Malkhalifeh

doi:10.30827/pna.v13i1.6903

Autores/as

Akram Daryaee Islamic Azad University, Tehran,
Ahmad Shahvarani Islamic Azad University, Tehran,
Abolfazl Tehranian Islamic Azad University, Tehran,
Farhad Hosseinzadeh Lotfi Islamic Azad University, Tehran,
Mohsen Rostamy-Malkhalifeh Islamic Azad University, Tehran,

DOI:

https://doi.org/10.30827/pna.v13i1.6903

Palabras clave:

Álgebra, Aprendizaje, Representación gráfica, Representación numérica, Representación simbólica

Resumen

This study aimed to examine the role of multiple representations in learning algebraic concepts for high school students. Using the semi-experimental research method for teaching of numerical, symbolic, and graphical representations, and traditional teaching, 83 female students were selected from the tenth grade of a high school in Tehran. We concluded that there is a significant difference between the mean scores of mathematics in the control and experimental groups. Using the method based on different representations helped the students to become creative and provide similar Algebra examples; thereby analysis power will be increased.

Funciones ejecutables de las representaciones en el aprendizaje de los conceptos algebraicos

Este estudio tiene como objetivo examinar el papel de las representaciones múltiples en el aprendizaje de los conceptos algebraicos en estudiantes de educación secundaria. Se desarrolló una investigación semi-experimental para la enseñanza de representaciones numéricas, simbólicas y gráficas y la enseñanza tradicional, en este estudio participaron 83 estudiantes femeninas del décimo grado de una escuela secundaria en Teherán. Se concluyó que hay una diferencia significativa entre los puntajes promedio de matemáticas en el grupo control y los grupos ex- perimentales. El uso del método basado en diferentes representaciones ayudó a las estudiantes a ser creativas y proporcionar ejemplos de álgebra similares; por lo tanto, la capacidad de análisis aumentará.

Doi: 10.30827/pna.v13i1.6903

Handle: http://hdl.handle.net/10481/53993

Scopus record and citations

Descargas

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Biografía del autor/a

Farhad Hosseinzadeh Lotfi, Islamic Azad University, Tehran,

Código ORCID

Mohsen Rostamy-Malkhalifeh, Islamic Azad University, Tehran,

Código ORCID

Citas

Adu-Gyamfi, K., (2002). External Multiple Representations in Mathematics Teaching, Unpublished Thesis, Raleigh: North Carolina State University.

Blanton, M. & Kaput, J. (2003). Developing elementary teachers' “algebra eyes and ears”. Teaching Children Mathematics, 10(2), 70-77.

Brunner, M. E., Mayer, R. E., Moseley, B., Brar, T., Duran, R., Reed, B. S. & Webb, D. (1997). Learning by understanding: The role of multiple representations in learning algebra. American Educational Research Journal, 34(4), 663-689.

Cramer, K., &Bezuk, N. (1991). Multiplication of fractions: teaching for understanding. Arithmetic Teacher, 39(3), 34-37.

Davies, D. (1988). An algebra class unveils models of linear equations in three variables. In A. F. Coxford (Ed.), The Ideas of Algebra, K-12 (pp. 199-204). Reston, VA: NCTM.

DiSessa, A. A., Hammer, D. &Sherin, B. (1991). Inventing graphing: metarepresentational expertise in children. Journal of Mathematical Behavior, 10, 117-160.

Duval, R., (2006). A Cognitive Analysis of Problems of Comprehension in a Learning of Mathematics. Educational Studies in Mathematics, 61, 103-131.

Gouya, Z, Sereshti, H. (2006). Teaching calculus: existing problems and the role of technology. Journal of developments in Mathematics Education, No. 83. pp: 2 and 30 - 31. Office of Educational aids Publications, Organization of educational research and planning, Ministry of Education.

Herscovics, N. (1989). Cognitive obstacles encountered in the learning of algebra. In S. Wagner, & C. Kieran (Eds.), Research Issues in the Learning and Teaching of Algebra (pp.60-87). Virginia: NCTM Publications.

Janvier, C. (1987a). Conceptions and representations: The circle as an example In C. Janvier (Ed.), Problems of Representations in the Learning and Teaching of Mathematics (pp. 147-159). New Jersey: Lawrence Erlbaum Associates.

Janvier, C. (1987b). Representations and understanding: The notion of function as an example. In C. Janvier (Ed.), Problems of Representations in the Learning and Teaching of Mathematics (pp. 67-73). New Jersey: Lawrence Erlbaum Associates.

Kaput, J. J. (1986). Information technology and mathematics: Opening new representational windows. Journal of Mathematical Behavior, 5, 187-207.

Kaput, J. J. (1994). The representational roles of technology in connecting mathematics with authentic experience. In R. Biehler, R. W. Scholz, R. Strasser, & B. Winkelman (Eds.), Didactics in Mathematics as a Scientific Discipline (pp. 379-397). Netherlands: Kluwer Academic Publishers.

Kieran, C. (1989) The early learning of algebra: A structural perspective, In S. Wagner, & C. Kieran (Eds.), Research Issues in the Learning and Teaching of Algebra (pp. 33-57). Virginia: NCTM Publications.

Kieran, C. &Chalouh, L. (1992). Prealgebra: The transition from arithmetic to algebra. In D. T. Owens (Ed.), Research Ideas for the Classroom: Middle Grades Mathematics (pp. 59-71). New York: Macmillan.

Kilpatrick, J, Swafford, J. (2001). Helping children learn mathematics. [Trans] Mehdi Behzad and Zahra Gouya (2008), First edition, Fatemi publications, Tehran. pp. 32 - 38.

Koedinger, K. R., & Nathan, M. J. (2000). Teachers` and researchers` beliefs about the development of algebraic reasoning. Journal of Research in Mathematics Education, 31(2), 168-190.

Lesh, R. (1979). Mathematical learning disabilities: considerations for identification, diagnosis and remediaton. In R. Lesh, D. Mierkiewicz, & M. G. Kantowski (Eds.), Applied Mathematical Problem Solving. Ohio: ERIC/SMEAC.

Lesh, R., Post, T., & Behr, M. (1987b). 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). New Jersey: Lawrence Erlbaum Associates.

Lubinski, C. A. & Otto, A. D. (2002). Meaningful mathematical representations and early algebraic reasoning. Teaching Children Mathematics, 9(2), 76-91.

Murata, A., & Stewart, Ch. (2017). Facilitating Mathematical Practices through Visual Representations, Teaching Children Mathematics, pp. 404-412.

McGregor, M., & Price, E. (1999). An exploration of aspects of language proficiency and algebra learning. Journal of Research in Mathematics Education, 30(4), 449-467.

Moseley B. & Brunner M. E. (1997). Using multiple representations for conceptual change in pre-algebra: A comparison of variable usage with graphic and text based problems (pp.29-30). Washington DC: Office of Educational Research and Improvement.

NCTM. (2000). Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.

National Council of Teachers of Mathematics, (2000). Principles and Standards for School Mathematics (NCTM-2000) .pp :67-70, 360-363.

Ozgun-Koca S. (2001). Computer-based representations in mathematics classrooms: The effects of multiple linked and semi-linked representations on students’ learning of linear relationships. Unpublished doctoral dissertation, Ohio State University, USA.

Pape, S. J., &Tchoshanov, M. A. (2001). The role of representation (s) in developing mathematical understanding. Theory into Practice, 40(2), 118-127.

Pirie, S. E. B. & Martin, L. (1997). The equation, the whole equation and nothing but the equation! One approach to the teaching of linear equations. Educational Studies in Mathematics, 34, 159-181.

Post, T., Behr, M. J., &Lesh, R. (1988). Proportionality and the development of prealgebra understanding. In A. F. Coxford (Ed.), The Ideas of Algebra (pp.78-91). Reston, VA: NCTM.

Rau, M. A., & Matthews, P. G. (2017). How to make ‘more’ better? Principles for effective use of multiple representations to enhance student learning. ZDM - Mathematics Education. 49(4), 491-496.

Sauriol, J. (2013). Introducing Algebra through the Graphical Representation of Functions: A Study among LD Students, ProQuest LLC, Ph.D. Dissertation, Tufts University

Smith, E. (2004). Statis and change: Integrating patterns, functions and algebra throughout the K-12 curriculum. In J. Kilpatrick, W. G. Martin & D. Schifter (Eds.), A Research Companion to Principles and Standards for School Mathematics (pp. 136-151). Reston, VA: NCTM.

Tall, D.O., (1991), (Ed), Advanced Mathematical Thinking, Kluwer Academic Publishers, theNetherlands.

Tishman, S., & Perkins, D. (1997). The language of thinking. Phi Delta Kappan,78(5), 368-374.

van de Walle, J. A. (2001). Elementary and Middle School Mathematics: Teaching Developmentally. New York: Longman, Inc.

van Dyke, F., &Craine, T. (1997). Equivalent representations in the learning of algebra. Mathematics Teacher, 90, 616-619.

Wagner, S. (1983). What are these things called variables?, Mathematics Teacher, (474-479).

Wagner, S., & Kieran, C. (1999). An agenda for research on the learning and teaching of algebra. In B. Moses (Ed.), Algebraic Thinking, Grades K-12 (pp. 362-372). Reston, VA: National Council of Teachers of Mathematics.

Yerushalmy, M. & Gilead, S. (1997). Solving equations in a technological environment. The Mathematics Teacher, 90(2), 156-162.