Teaching the Perceptual Structure of Algebraic Expressions: Preliminary Findings from the Pushing Symbols Intervention

Building Bridges Across Cognitive Sciences Around the World - Proceedings of the 34th Annual Meeting of the Cognitive Science Society, CogSci 2012

Volumn , Issue , 2012, Pages 2156-2161

  Ottmar, Erin ^a   Landy, David ^a   Goldstone, Robert L ^b  

^a UNIVERSITY OF RICHMOND   (United States)

^b INDIANA UNIVERSITY   (United States)

Author keywords

Algebra education; learning; mathematical cognition; perception

Indexed keywords

SOFTWARE ENGINEERING; STUDENTS;

ALGEBRA EDUCATION; ALGEBRAIC EXPRESSION; ALGEBRAIC STRUCTURES; CHANGE-OVER TIME; LEARN+; LEARNING; MATHEMATICAL COGNITION; PHYSICAL OBJECTS; RESEARCH TEAMS; SYMBOL SYSTEMS;

ALGEBRA;

EID: 85048636079     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (28)

1. Alibali, M. W. & Nathan, M. J. (2007). Teachers' gestures as a means of scaffolding students' understanding: Evidence from an early algebra lesson. In Goldman, R., Pea, R., Barron, B. J., and Derry, S. (Eds.) Video Research in the Learning Sciences. Mahwah, NJ: Erlbaum.
2. Aleven, V., & Koedinger, K. R. (2002). An Effective Meta-cognitive Strategy: Learning by Doing and Explaining with a Computer-Based Cognitive Tutor. Cognitive Science, 26(2), 147-179.
3. Banerjee, R., & Subramaniam, K. (2011). Evolution of a teaching approach for beginning algebra. Educational Studies in Mathematics.
4. Bernardo, A. B., & Okagaki, L. (1994). Roles of symbolic knowledge and problem-information context in solving word problems. Journal of Educational Psychology, 86(2), 212–220.
5. Carey, S. (2009). The origin of concepts. New York: Oxford University Press.
6. Cheng, P.C.-H. Unlocking conceptual learning in mathematics and science with effective representational systems. Computers and Education, 33 (2-3). 109-130.
7. Cook, S., Mitchell, Z., & Goldin-Meadow, S. (2008). Gestering makes learning last. Cognition, 106(2), 1047-1058.
8. Dehaene, S. (1997). The number sense. New York: Oxford University Press.
9. Goldstone, R. L., Landy, D., & Son, J. Y. (2010). The education of perception. Topics in Cognitive Science, 2(2), 265-284.
10. Kaminski, J. A., Sloutsky, V. M., & Heckler, A. F. (2006). Effects of concreteness on representation: An explanation for differential transfer. In R. Sun & N. Miyake (Eds.), Proceedings of the XXVIII Annual Conference of the Cognitive Science Society.
11. Kellman, P. J., Massey, C. M., Roth, Z., Burke, T., Zucker, J., Saw, A., Aguero, K., & Wise, J. (2008).Perceptual learning and the technology of expertise: Studies in fraction learning and algebra. Pragmatics & Cognition, 16(2), 356–405.
12. Kirshner, D. (1989). The visual syntax of algebra. Journal for Research in Mathematics Education, 20(3), 274-287.
13. Kirshner, D., & Awtry, T. (2004). Visual salience of algebraic transformations. Journal for Research in Mathematics Education, 35(4), 224–257.
14. Koedinger, K. R., Alibali, M. W. and Nathan, M. J. (2008), Trade-Offs Between Grounded and Abstract Representations: Evidence From Algebra Problem Solving. Cognitive Science, 32: 366–397.
15. Kong, Q., Wong, N. & Lam, C. (2003). Student engagement in mathematics: Development of instrument and validation of construct. Mathematics Education Research Journal, 15(1), 4-21.
16. Landy, Allen, & Anderson (2011). Conceptual discontinuity involves recycling old processes in new domains. Behavioral and Brain Sciences, 34, 136-137
17. Landy, D., & Goldstone, R. L. (2010). Proximity and Precedence in Arithmetic. Quarterly Journal of Experimental Psychology.
18. Landy, D., & Goldstone, R. L. (2007). How abstract is symbolic thought? Journal of Experimental Psychology: Learning, Memory, and Cognition, 33(4), 720-733.
19. Marquis, J. (1988). Common mistakes in algebra. In A. F. Coxford & A. P. Shulte (Eds.), The ideas of algebra, K-12: National Council of Teachers of Mathematics Yearbook. Reston, VA: National Council of Teachers of Mathematics.
20. Martin, S. A., & Bassok, M. (2005). Effects of semantic cues on mathematical modeling: Evidence from word-problem solving and equation construction tasks. Memory & Cognition, 33(3), 471.
21. McNeil, N. M. (2008). Limitations to teaching children 2 +2 = 4: Typical arithmetic problems can hinder learning of mathematical equivalence. Child Development, 79., 1524-1537.
22. Midgley, C., Maehr, M. L., Hruda, L. Z., Anderman, E., Anderman, L., Freeman, K. E., et al. (2000). Manual for the Patterns of Adaptive Learning Scales: University of Michigan.
23. Nogueira de Lima, R. and Tall, D. (2008). Procedural embodiment and magic in linear equations. Educational Studies in Mathematics. 67 (1) 3-18.
24. Novick, L. R., & Catley, K. M. (2007). Understanding phylogenies in biology: The influence of a Gestalt perceptual principle. Journal of Experimental Psychology: Applied, 13, 197-223.
25. Palmer, S. E. (1999). Vision Science: Photons to phenomenology. Cambridge, MA: MIT Press.
26. Patsenko, E. G., & Altmann, A. M. (2010). How planful is routine behavior? A selective-attention model of performance in the Tower of Hanoi. Journal of Experimental Psychology: General, 139, 95-116.
27. Schwartz, D. L., & Black, J. B. (1996a). Analog imagery in mental model reasoning: Depictive models. Cognitive Psychology, 30(2), 154-219.
28. Sweller, J. (1994). Cognitive load theory, learning difficulty, and instructional design. Learning Instruction, 4.