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

Mathematical creatively can be thought of as “the ability to see new relationships between techniques and areas of application and to make associations between possibly unrelated ideas” (Tammadge as cited in Haylock, 1987, p. 60). Balka’s 1974 article in the Arithmetic Teacher, Creative Ability in Mathematics, is frequently cited in literature on mathematical creativity. In this brief, three-page article, Balka offers five attributes of creativity. These attributes, qualities we must strive to develop in all students, are the ability to:

1. Formulate mathematical hypotheses
2. Determine patterns
3. Break from established mindsets to obtain solutions in a mathematical situation
4. Sense what is missing and ask questions
5. Consider and evaluate unusual mathematical ideas, to think through the consequence from a mathematical situation (divergent)

At the 2006 NAGC national convention, I offered sample activities for each of these attributes. A copy of that presentation, The Essence of Mathematics, is available on my web site at http://www.edci. purdue.edu/elmann/. There you will also find links to some of my favorite mathematics education resources that you may find useful. Two other programs that emphasize mathematical creativity are Project M3: Mentoring Mathematical Minds (http://www.projectm3.org) and Extending Process Skills for Able Mathematicians (http://www.franassisi.rbkc.sch.uk/curriculum/ centre_for_excellence.htm). Finally, Rachel McAnallen, is a name very familiar to the veterans of the University of Connecticut’s CONFRATUE (http://www. gifted.uconn.edu/confratu.html), Purdue University’s DISCOVER! (http://www.geri. soe.purdue.edu/profdev/discover institute/ default.html) or Edufest (http://www. edufeast.org), her website (http://www. mathchannel.com/) offers a wealth of information to help you instill in your students a love of the wonders of mathematics.

Students often tell me they are no good at math. My response is, “How do you know?” to which they reply with comments about performance in school or difficulty in solving problems quickly. Over the years, these students have learned to equate mathematics with algorithms, the learning of rules, and ability to find the answer the teacher is expecting. A sixth grader’s comment that, “It doesn’t make much sense. But, we are in math class, so I guess it does here,” or a calculus student’s comment that, “In math, I do things just the opposite way from what I think it should be and it almost always works” (Linquist, as cited in Heibert et al., 1997, p. vii), are illustrative of the impact such instruction can have. If taught that there is only one right answer or only one correct method, a student’s concept of mathematics as only the application of mathematical techniques is reinforced.

The way we teach mathematics is a significant contributor to this perception. Köhler (1997) illustrates this point in a discussion with an elementary classroom teacher about a student who had arrived at the correct answer in an unexpected way. Rather than delight in the student’s creativity, the teacher responded: