Session Information
ERG SES C 06, Mathematics Education
Parallel Paper Session
Contribution
The concept of variable is a center point in mathematics from elementary schools to college because understanding this concept provides a transition from arithmetic to algebra (Kuchemann, 1978; Philipp, 1992).While the goal of arithmetic which is to find numerical answers, the main focus of school algebra is to find general methods and rules and to use algebraic symbols and language in order to express these rules in a general form (Booth, 1988). In contrast to the importance of variables and their heavily usages in algebra, many of studies show that students are generally confused while passing from arithmetic to algebra in their learning processes due to the concept of variable having different meanings in different context (MacGregor & Stacey, 1997; Schoenfeld & Arcavi, 1988; Ursini &Trigueros, 2001).
In fact, there are some questions to be answered in order to overcome students’ difficulties and misconceptions concerning with the concept of variable: What is the origin of the notions of unknown and variable? How are these concepts developed? At this point, history of mathematics can provide a reasonable perspective to look at the concept in terms of teaching and learning of algebra in schools. After examining the context related to exchange of money in trading or inheritances in ancient civilization, I understood why people need to negative numbers, complex numbers, unknown, matrix or decimal fractions. As a result, it can be said mathematics is a human endeavor which has spanned over four thousand years (Katz, 2000; 2007). By blending historical and psychological perspectives, historical developments can be used as a tool in order to predict students’ behaviors because there is an analogy between historical and individual development (Sfard, 1991; 1995).
According to Sfard (1995), phylogenic and ontological approaches to mathematics reveal similarities between historical and individual construction of knowledge. In a similar way, Gallardo (2000) emphasizes the use of historical-critical analysis for learning and teaching of algebra because the corresponding notions of “epistemological obstacles” serve as central elements that link the domains of history and education. Furthermore, it provides a great opportunity to determine misconceptions of students. As a result, this methodology can be used for teacher training programs at universities. By this means, teacher will be more conscious about students’ behaviors whenever they confront a new concept which has different meaning from previous learning such as transition unknown to variable. Many of teachers are always complaining their students’ difficulties while teaching the concepts of “variable” and “unknown”. The historical analysis emphasizes that the notions of unknown and variable have a totally different origin and evolution. Even if both the concepts deal with numbers, their processes of conceptualizations seem to be entirely different (Radford, 2000). In other words, mathematics history constructs a bridge from the past to the future. From this perspective, the purpose of this article is to provide a theoretical framework about using history of mathematics in learning and teaching of the concept of variable.
Method
Expected Outcomes
References
Gallardo, A. (2000). Historical-epistemological analysis in mathematics education: Two works in didactics of algebra. In R. Sutherland, T. Rojano, A. Bell, & R. Lins (Eds.), Perspective on School Algebra (pp. 121-139). Dordrecht, The Netherlands: Kluwer Academic Publishers. Katz, V.J. (2000). Using History to Teach the Mathematics. An International Perspective. The Mathematics Association of America. Washington: DC. Katz, V. J. (2007). Stages in the history of algebra with implications for teaching. Educational Studies in Mathematics, 66, 185-201.doi:10.1007/s10649-006-9023-7. Kuchmann, D. (1978). Children’s understanding of numerical variables. Mathematics in School, 7(4). MacGregor, M., & Stacey, K. (1997). Students’ understanding of algebraic notation. Educational Studies in Mathematics, 33, 1-19. Philipp, R. A. (1992). The many uses of algebraic variables. Mathematics Teacher, 85(7), 560. Schoenfeld, A. H., & Arcavi, A. (1988). On the meaning of variable. Mathematics Teacher, 81, 420-427. Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1-36. Sfard, A. (1992). Operational origins of mathematical objects and the quandary of Reification: The case of function. In Harel, G., & Dubinsky, E., (Eds.), The concept of function: Aspects of epistemology and pedagogy MAA Notes Vol. 25. Washington, DC: Mathematical Association of American. Sfard, A. (1995). The development of algebra: Confronting historical and psychological perspectives. Journal of Mathematical Behavior, 14, 15-39. Sfard, A., & Linchevski, L. (1994). The gains and the pitfalls of reification: The case of algebra. Educational Studies in Mathematics, 26, 191-228. Ursini, S., & Trigueros, M., (2001). A model for the uses of variable in elementary algebra. In Van den Heuvel-Panhuizen, M. (Ed.), Proceedings of the 25th conference of the international group for the psychology of mathematics education, 4, 327–334. Utrecht, Netherlands: Freudenthal Institute.
Search the ECER Programme
- Search for keywords and phrases in "Text Search"
- Restrict in which part of the abstracts to search in "Where to search"
- Search for authors and in the respective field.
- For planning your conference attendance you may want to use the conference app, which will be issued some weeks before the conference
- If you are a session chair, best look up your chairing duties in the conference system (Conftool) or the app.