A Discussion about Errors in Algebra for Creation of Learning Object

Abstract

This Article reports the results of a research with 333 freshmen students of Differential Calculus, for whom it was applied a test with questions about basic mathematics. The question analysed in this article involves basic algebra. The students made mistakes in operations and algebraic properties that are essential for the continuity of their studies in Calculus, especially to solve exercises of limits and derivatives. Then, we sought to some theoretical constructs to discuss the errors, such as concept image, symbol sense, structure sense and algebraic insight. The main difficulties observed are related to the distributive property of multiplication over addiction. In this paper we propose the creation of a learning object, in accordance to the principles of multimodality to help students overcome their difficulties in algebra.

 

 

 

 

Keywords

• Error analysis, Distributive property, Algebra learning, Elementary school

References

1. Arcavi, A. (1994). Symbol sense: informal sense-making in formal mathematics. For the Learning of Mathematics, 14 (3), 24-35.
2. Artigue, M. (2004). L´enseignement du calcul aujourd´hui: problèmes, defis et perspectives. Reperes IREM, 54, 23-39.
3. Bardin, L. (1979). Análise de conteşdo. Lisboa: Edições 70.
4. Borba, M. C., & Penteado, M. G. (2007). Informática e Educação Matemática. Belo Horizonte: Editora Autêntica.
5. Cabral, T. C. B., & Baldino, R. R. (2004). O ensino de matemática em um curso de engenharia de sistemas digitais. In H. N. Cury (Org.), Disciplinas matemáticas em cursos superiores: reflexões, relatos, propostas (pp. 139-186). Porto Alegre: EDIPUCS.
6. Fey, J. T. (1990). Quantity. in L. A. Steen (Ed.), On the shoulders of giants: new approaches to numeracy (pp. 61-94). Washington: National Academy Press.
7. Giraldo, V. (2004). Descrições e conflitos computacionais: o caso da derivada. Tese de Doutorado em Engenharia de Sistemas e Computação, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil.
8. Hardy, N. (2009). Students´perceptions of institutional practices: the case of limits of functions in college level Calculus courses. Educational Studies in Mathematics, 72 (3), 341-358.

9. Hoch, M., & Dreyfus, T. (2004). Structure sense in high school algebra: the effects of brackets. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Bergen, Norway, 3 (pp. 49-56).
10. IEEE Learning Technology Standards Committee (LTSC). Draft Standard for Learning Object Metadata, Institute of Electrical and Electronics Engineers, Inc, 2000.
11. Kirshner, D., & Awtry, T. (2004). Visual salience of algebraic transformations. Journal for Research in Mathematics Education, 35 (4), 224-257.
12. Pierce, R., & Stacey, K. (2001). A framework for algebraic insight. Proceedings of the 24th Annual MERGA Conference, http://www.merga.net.au/documents/RR_Pierce&Stacey.pdf. Australia. Retrieved June, 02, 2013 from
13. Pierce, R., & Stacey, K. (2004). Monitoring progress in algebra in a CAS active context: symbol sense, algebraic insight and algebraic expectation. The International Journal for Technology in Mathematics Education, 11(1), 3-12.
14. Porter, M. K., & Masingila, J. O. (2000). Examining the effects of writing on conceptual and procedural knowledge in Calculus. Educational Studies in Mathematics, 42, 165-177.
15. Roswell, J., & Walsh, M. (2011). Rethinking literacy education in new times: multimodality, multiliteracies, & new literacies. Brock Education, 21 (1), 53-62.
16. Tall, D. (1992). Students´difficulties in calculus. Proceedings of the 7th International Congress on Mathematical Education, Quebéc, Canada.
17. Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151–169.
18. The University of the State of New York. Regents High School Examination. Integrated Algebra. January 28, 2010. Retrieved June, 05, 2013 from http://www.nysedregents.org/IntegratedAlgebra/archive/ 20100128exam.pdf.
19. Wiley, D. A. (2000). Connecting learning objects to instructional design theory: A definition, a metaphor, and a taxonomy. In D. A. Wiley (Ed.), The Instructional Use of Learning Objects: Online Version. Retrieved June 28, 2013, from http://reusability.org/read/chapters/wiley.doc.
20. Zazkis, R. (2005). Representing numbers: prime and irrational. International Journal of Mathematical Education in Science and Technology, 36 (2-3). 207-218.