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Exploring Different Solving Techniques

During class, we were given a fairly simple problem involving solving for maximum area of a box. We were asked to solve the problem among our desk groups. Fairly quickly, we were able to find a solution using algebraic methods. Based on our group's advanced background in mathematics, this problem appeared trivial and was not difficult to solve. We were then asked to come up with at least one other method of solving the same problem. This should have been easy - right? Wrong. Thinking outside of what we knew proved to be more difficult than I thought. I was stumped when it came to figuring out another way of solving. One of my group members suggested using a table of values and more of a trial-and-error method to come up with a solution. This seemed so tedious and unnecessary to me, given that I already solved the problem much quicker using my own method. However, we went ahead and used the new method and came up with an identical answer.

This made me think - why would anyone solve the problem using trial-and-error when there was a much more efficient solution available? Well, if someone hadn't yet learned a more advanced method, then  how would they go about the problem? This is the way in which students will think. Some of them will have never encountered problems like the ones that I as a teacher will present to them. Even if they are familiar with the concept of the problem, every student learns differently and has different ways of achieving a correct answer. This is something I need to keep in mind as I prepare for my teaching block. It is hard to go back and rewind the knowledge of mathematics that I have. I immediately skip to the most recent, most-efficient method of computing, often forgetting how I would have even solved the same problem in high school. However, it is so important to be aware of the many ways in which a student can perceive a problem and the many ways in which they may solve it. A different method does not mean an incorrect method, it simply means the student thought about the problem in a different way. As I journey through this course I hope to challenge myself to think outside of what I know and how I do math in order to understand how my students will do math. Having an open mind to multiple solving techniques will help me to connect with my students' various learning needs and styles and to understand how they are coming up with their solutions.

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