By Kasi Allen, posted March 14, 2016 —

Nearly thirty years ago, in my first algebra class, a frustrated ninth grader got my attention when she challenged me with this statement: “You know, I’m a really creative person, and I get to be creative in every class—every class, except MATH.”

Her words cut deep. In my heart of hearts, I knew she right. Mathematics, as she was experiencing it, rarely gave her a chance to let the creative juices flow. Rather than generating her own ideas, she felt forced to reproduce the ideas of others. As her teacher, I could see how my attempts at making math fun and engaging sometimes ran counter to making it meaningful.

I committed to helping my students see math differently. We started doing monthly projects; they involved tasks that ranged from researching the multicultural history of math, to analyzing city maps, to creating artwork from systems of inequalities. My students dedicated a different kind of energy to these more creative projects. The quality of the mathematics they generated never failed to impress me, especially complex calculations and graphs completed almost entirely by hand.

The next year, this same group of students, as tenth graders, proposed a search for “the number of unique triangles on a geoboard.” (See Kasi Allen, “The Geoboard Triangle Quest,” Mathematics Teacher, Sept. 2013, pp. 112–18.) When I wrote about the experience for MT, my goal was to inspire other teachers to make more space for student creativity in their math classes—in the hope of encouraging similar mathematical adventures. The exact answer to the question was secondary. In fact, perhaps better for the quest if it remained elusive?

However, once the article was published, readers embarked on their own geoboard triangle quests, making use of new technology not available when my students posed the original problem. (See “What’s Your Answer? Searching for Triangles,” by Michael S. Meagher, Michael Todd Harris, and S. Asli Özgün-Koca, MT March 2016, pp. 500–6.) As it turned out, my students and I had missed quite a few triangles. At first, I felt exposed and perhaps even irresponsible for not having “proven” the results before publication. It had been a long time since I had felt such negative emotions in connection to mathematics, and I knew that my reaction was really about being “wrong.”

In the months that followed, I exchanged some wonderful emails with Todd Edwards, and I urged him and his students forward. I am so grateful for their detailed and thorough work. We can now be certain that there are 79 triangles, not 72. On reflection, I realize how my fascination with the geoboard triangle quest has never been about the mathematics of the problem but about how the problem drew the mathematics out my students. The ideas were theirs; they were creating the math.

As a math educator, I know that answers and accuracy are important. However, too much focus on the right answer can have a chilling effect on creative problem solving and risk taking. What I want to remember from this experience is that one group’s mistake actually fueled another group’s creativity.

KASI ALLEN, kasi@lclark.edu, has worked in mathematics education for nearly thirty years as a teacher, researcher, and scholar. For the last decade, she has served as a professor of mathematics education in Oregon, teaching math content and methods to preservice K–12 teachers. Kasi loves helping people of all ages experience the power of having their own mathematical ideas. She is a math activist who studies math trauma and promotes teaching mathematics for social justice.