For the math fair, my partner Vicky and I created a "Touching Circles" problem-solving activity. The activity was designed for a primary grade level but could be modified in such a way to challenge the elementary learner as well. The main objective of the "Touching Circles" activity was to fill a large size triangle with red, yellow and blue circles without having a same color circle touch vertically, horizontally or diagonally. The triangle was divided into three different levels so that problem-solvers could be challenged accordingly. Vicky and I had also provided problem-solvers with four different extensions to the "Touching Circles" activity. The extensions included filling a hexagon with the same three color circles (again, without having them touch), finding the shape (either a circle or a pentagon) that could not be filled without having a same color circle touch, and filling another triangle plus a rectangle in the same way but with an extra color of green added. The extensions allowed problem-solvers to think outside of the initial problem but to maintain a focus on patterns and relationships. As problem-solvers explored patterns and relationships in how the different color circles could be arranged accordingly, an increased understanding of predictability occurred. A positive response was received by my fellow classmates as individuals appeared quite eager to complete the problem. The "Touching Circles" problem-solving activity was presented in a visually appealing and interactive style and so drew problem-solvers in.
Initially, I remained with the "Touching Circles" problem-solving activity while Vicky set off to tackle the other activities presented in the classroom. By remaining at the activity, I learned three important lessons regarding the context of the primary/elementary classroom. First, as individuals began to circulate the classroom to have a go at the problem-solving activities, I thought about how people would be attracted to activities that were visually appealing, perhaps activities that were presented by close friends or simply activities that seemed to catch a curious eye. In the context of the primary/elementary classroom, it was reinforced for me that math has to be made engaging and meaningful to students to garner success. Just as my fellow classmates and I had chosen to participate in activities that appealed to us, students will engage more so with the task at hand if it is presented in a motivating and engaging way. Also, I discovered just how tempting it is to simply give the answer to somebody when they have not quite understood the concept yet. However, as hard as it may have been, I refrained from giving anyone (okay, maybe just one! ) the answer. Nonetheless, I realize in the context of the primary/elementary classroom, that it is more beneficial to allow students to struggle through a problem to make sense of the task at hand. Students need to be given the tools to know how to use their knowledge in application of other problems and situations. I also learned the value of limiting my use of "praise phrases." As individuals discovered a solution to my problem, I would eagerly say "yay!" or "you found a pattern!" In doing so, I allowed for problem-solvers to ask of themselves the question "I found a pattern...could there be another one?" The same idea can be applied to young students. When told specifically what was considered to be a "good job" students are enabled to then think more critically of their positve behaviours and themselves.
When it was my turn to circulate the classroom, I left all my fears and hesitations about math aside and confidently approached each problem. The first problem I approached, I amazed myself with my own determination to find a solution. And I did. Each new problem I then attempted, I had even more confidence to do so, and most importantly, I had fun! At one particular problem-solving activity, I was told that I had found a new strategy that was not thought of previously. My self-confidence in my ability to do math soared and I realized in that moment that I would never approach math in the same grudging way again. I want my future students to feel that way about math, and to feel confident, even when in doubt.
All in all, I feel the math fair experience was a great success! If I were to facilitate this particular problem-solving activity again, I would use a combination of colors and numbers. As the extensions followed the same sequence as the original problem, problem-solvers were not adequately given the opportunity to extend their newfound knowledge to advanced patterns and relationships.
The ideas and approaches explored in class and the math fair experience itself has really opened my eyes to my ability to teach math in the primary/elementary classroom. I no longer think "fear" when I think of math; I now think "possibility." The math fair experience allowed me to open myself up to new ideas and personally take on the positive attitude about math that I wish to instill in my future students.
I believe a math fair would be most applicable in the context of the primary/elementary classroom as well. I believe a math fair experience would give students the excitement and motivation to engage in mathematics problems with little fear or hesitation.
