بررسی درک رویه ای و ساختاری دانش آموزان دوره متوسطه اول در عبارت های جبری

[1] Ladson-Billings G. Just what is critical race theory and what’s it doing in a nice field like education? International Journal of Qualitative Studies in Education. 1998; 11(1): 7-24.

[2] Asghari N. Developing a model to enhance elementary teachers’ ability to foster functional thinking and algebraic reasoning in elementary students. CSTP. 2014; 2(3): 141-162. Persian.

[3] Kieran C. The learning and teaching of school algebra, In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 271-290). Reston, V A: NCTM; 1992.

[4] Bell A. Problem solving approached to algebra: Two aspects. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 167-186). Dordrecht: Kluwer; 1996.

[5] Kaput JJ. A research base supporting long term algebra reform. In D. T. Owens, M. K. Reed, & G. M. Millsaps (Eds.), Proceedings of the Seventeenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 7194). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education; 1995.

[6] Kaput JK. Transforming algebra from an engine of inequity to an engine of mathematical power by “algebrafying” the K-12 curriculum. Dartmouth, MA: National Center for Improving Student Learning and Achievement in Mathematics and Science; 2000.

[7] Sfard A, Linchevski L. The gains and the pitfalls of reification? The case of algebra. Educational Studies in Mathematics. 1994; 26(26): 191–228.

[8] Küchemann D. Algebra in K. Hart (Ed.), Children uderstanding of mathematics: 11–16 (pp. 102–119). London: Murray; 1981.

[9] MacGregor M, Stacey K. Students understanding of algebraic notation: 11-15. Educational Studies in Mathematics. 1997; 33: 1–19.

[10] Philipp RA. The many uses of algebraic variables, Mathematics Teacher. 1992; 85: 7, 557–561.

[11] Stephens AC. Developing students’ understandings of variable, Mathematics Teaching in the Middle School. 2005; 11(2): 96-100

[12] Wagner, S. What are these things called variables? Mathematics Teacher. 1983; 76: 474478.

[13] Swan M. Making sense of algebra. Mathematics Teaching. 2000; 171: 16-19

[14] Van Ameron B. Focusing on informal strategies when linking arithmetic to early algebra. Educational Studies in Mathematics. 2003; 54: 63 - 75.

[15] Liebenberg R, Linchevski L, Oliver A, Sasman M. Laying the foundation for algebra: developing an understanding of structure. Proceedings of the Fourth Annual Congress of the Association for Mathematics Education of South Africa (pp. 276-282). Pietersburg, South Africa; 1998

[16] Banerjee R, Subramaniam K. Evolution of a teaching approach for beginning algebra. Educational Studies in Mathematics. 2011; 80: 351–367.

[17] Booth LR, Watson J. Learning and teaching algebra. The Australian Mathematics Teacher. 1990; 46(3): 12-14

[18] Carraher DW, Schliemann AD, Schwartz JL. Early algebra is not the same as algebra early. In In J. Kaput. D. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 235-272). New York: Lawrence Erlbaum; 2008.

[19] Novotná J, Hoch M. How structure sense for algebraic expressions or equations is related to structure sense for abstract algebra. Mathematics Education Research Journal. 2008; 20(2): 93-104.

[20] Warren E. The role of arithmetic structure in the transition from arithme=tic to algebra. Mathematics Education Research Journal. 2003; 15: 122-137.

[21] Kieran C. The Learning and Teaching of School Algebra. In D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 390-419). New York: Macmillan Publishing Company; 1992.

[22] Welder RM. Improving algebra preparation: Implications from research on student misconceptions and difficulties. School Science and Mathematics. 2012; 112(4): 255 – 264.

[23] Sfard A. Reification as the birth of metaphor. For the Learning of Mathematics. 1994; 14(1): 44-55.

[24] Capraro MM, Joffrion H. Algebraic equations: Can middleschool students meaningfully translate from words to mathematical symbols? Reading Psychology. 2006; 27: 147-164

[25] National Council of Teachers of Mathematics. Principles and Standards for School Mathematics. Reston, VA: NCTM; 2000.

[26] Sfard A. On the dual nature of mathematical conceptions: reflections on process and objects as different sides of the same coin. Educational Studies in Mathematics. 1991; 22: 1-36.

[27] Kieran C. Learning and teaching algebra at the middle school through college levels. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 707–762). Charlotte, NC: Information Age; 2007.

[28] Kieran C. The changing face of school algebra. In C. Alsina, J. Alvarez, B. Hodgson, C. Laborde, & A. Pérez (Eds.), 8th International Congress on Mathematical Education: Selected lectures (pp. 271-290). Seville, Spain: S.A.E.M. Thales; 1996.

[29] Radford L. The historical origins of algebraic thinking. In R. Sutherland, T. Rojano, A. Bell, & R. Lins (Eds.), Perspectives on school algebra (pp. 13-36). Dordrecht, the Netherlands: Kluwer Academic; 2001.

[30] Kieran C. The core of Algebra: Reflections on its main activities. In: Stacey K., Chick H., Kendal M. (Eds), The Future of the Teaching and Learning of Algebra (The 12thICMI Study. New ICMI Study Series, vol 8.) Springer, Dordrecht; 2004.