Blog #24 – GIVING CREDIT TO STUDENTS FOR INNOVATIVE SOLUTIONS
Something that I have done throughout my career, is giving credit to students for innovative solutions. I pride myself for constantly finding new ways of teaching a concept. I also love finding faster ways to solve certain problems. Yet, when a student in the classroom or online tutoring finds a unique solution I make sure that I tell them immediately. But, more importantly, I credit students for finding innovative solutions to problems that I am teaching. Let me cite a couple of examples. In the 1980’s I was trying to solve a Calculus limit problem, which required that I use a technique called “completing the square” on the numerator. A student in my class, Adrian Diazgonsenheimercuevasurraca, told me that I could factor the denominator which was x – 9. Since this was a linear term, I could not see how that would be possible. Adrian told me that x – 9 was equal to (x + the square root of 3)(x – the square root of 3). I was stunned by the way he factored x – 9. Using what he told me, I no longer had to complete the square for the numerator to solve the problem that I wanted to teach. That occurred 29 years ago, and every student that I have taught since then, has learned Adrian’s method and years later some have told me that they even remember his last name.
In another situation, I was finding the area under a curve using geometry. I traditionally used trapezoids. A student, Summer Cavin, told me that the formula for the area of a trapezoid could be used to find the area of a triangle. The formulas she referred to was that the area of a trapezoid was equal to (height)(sum of bases)/2. I did not think that the formula for the area of a trapezoid could be used to find the area of a triangle. So I asked her if she could explain how it was possible. She informed me that when using the area of a trapezoid formula to find the area of a triangle, I was to let one of the bases be zero. She correctly decided to let one base be 0, since the length of the vertex opposite the base of the triangle had no length. Since then, I have shared that with every student that I have taught and given Summer credit for it.
Sharing student’s innovative solutions inspires other students to attempt developing unique solutions. I have found that students love hearing stories about other students. My students have appreciated the fact that I give credit to others, although I am usually the one that unveils the Magic of Mathematics. To learn that Wizard apprentices also make phenomenal discoveries is inspirational. I encourage teachers to do what I have done. It is just one more tool that teachers can use to motivate a love of learning in general and a love of mathematics in particular.