Creativity: An Essential Element in Your Mathematics Classroom (continued)

While going through the classroom, that pupil asked me [the teacher] whether or not his solution was correct. I was forced to admit that it was. That is what you get when you don’t tell the pupils exactly what to do….” The teacher now reproaches himself for not having prevented this solution. He is obviously influenced by an insufficient understanding of what is mathematics, by the image of school as an institution for stuffing of brains…. (p. 88 (emphasis added))

Constant emphasis on sequential rules and algorithms may prevent the development of creativity, problem solving skills and spatial ability (Pehkonen, 1997). If we want to deepen our students’ understanding of mathematics, then we need to recognize that the mastery of rules, algorithms, rules and strategies is not the end goal of mathematics education. Our students should use these procedural tools to explore, test, revise and defend their solutions to meaningful problems.

Mathematics is meant to be performed, not just practiced. In sports, language arts, or music we practice to improve performance; not just for the sake of practice. Yet how often do our students see mathematics this way? Bogomolny’s (2000) comments capture the change we need to make in our classrooms to restore a love of mathematics and develop the mathematical potential of our students.

“Any” fruit of human endeavor shows creativity, if you think about it. The interesting question to me is this: Why is it that a student who is only playing other people’s music instinctively understands that those composers were creative, and that s/he might aspire to the same kind of creativity -- or, in English class, instinctively understands that those writers were creative, even when s/he is just reading their creations and answering quiz questions about them -- but doesn’t have the same instinctive understanding that Euclid and Newton and Pascal and Gauss and Euler were creative mathematicians? The most obvious answer has to do with the way these disciplines are taught.

Recommend Further Reading

Bogomolny, A. (Feb 2000). What is your answer to that question? Cut the Knot! Retrieved on August 15, 2006 from http://www.cut-the-knot.org/ ctk/Magic.shtml

Collection of papers presented at Int'l Comm on Mathematical Instruction-East Asia Regional Conference on Mathematics Education- 3 symposium on mathematical creativity. Available at http://www.math. ecnu.edu.cn/earcome3/SYM1.htm

Koshy, V. (2001). Teaching mathematics to able children. London: David Fulton Publishers.

Sheffield, L. J. (Ed.) (1999). Developing mathematically promising students. Reston, VA: National Council of Teachers of Mathematics.

Zentralblatt für Didaktik der Mathematik (International Reviews on Mathematical Education) (1997) Fostering of mathematical creativity. Available at http:// www.emis.de/journals/ZDM/zdm973i. html

References

Balka, D. S. (1974). Creative ability in mathematics. Arithmetic Teacher, 21, 633-636.

Bogomolny, A. (Feb 2000). What is your answer to that question? Cut the Knot! Retrieved on August 15, 2006 from http://www.cut-the-knot.org/ ctk/Magic.shtml