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Evidence #1: Math As A Second Language Portfolio Problem #1
This coordinate plane problem was the first portfolio problem I wrote up for VMI coursework. It also was my first experience with getting something wrong the first time and having a teacher ask me a question about an assumption I had made rather than showing me how to solve it. That was a great learning experience as a teacher.
Evidence #2: Math As a Second Language's Rope Problem
This was a confusing problem and you had to sort out the relevant from the irrelevant. Many word problems are presented to students with both important and unimportant information and students are expected to sort out which is which. This is an example that goes beyond pure mathematics and includes literacy and logic. It was a good reminder of what our students face when they are trying to figure out answers to word problems.
Evidence #3: Functions & Algebra's Coat Problem (from The Horse and Coat)
I look for real-life relevance in a lot of my math teaching. This was a great example of why functions are useful for both retailers and consumers to understand. Figuring out what the actual price of an item on sale is before you get to a counter is a practical skill and one my students can understand as a practical reason to learn math.
Evidence #4: Functions & Algebra's The 100 Meter Race
One of our VMI professors always encouraged us to create a graphical representation of our functions. I didn't for this problem and I probably should have as it was harder for me to understand this problem because I wasn't thinking of the function graphically. It was a good lesson to give credence to professors even if we don't understand why they are encouraging us to do something a certain way.
Evidence #5: Number Theory's The Broken Rock Problem
This was one of the first times I wasn't content to arrive at a correct solution but wanted to understand why and persisted until I understood why the math worked. It then became a goal for my teaching to have students not only understand how to solve a problem but why their solution works.
Evidence #6: Number Theory's Potato Base Poem Problem
I had heard of other bases than base ten before Number Theory but I don't remember actually having any experience with them. So this is a key example of something I learned from "scratch". Not only did I need to work through my understanding of bases, but also my approaches to the problem until I came to a resolution I that made me happy.
Evidence #7: Geometry's Three Circle Challenge
I chose the Three Circle Challenge for my portfolio because it's evidence of my persistence when faced with problems I would have given up on in the past. I also feel it's a good example of something I will eventually revisit after more time to deepen my understanding. We don't fully understand something until we can teach it ourselves.
Evidence #8: Geometry's The Fly and the Spider
This problem was one that led me down some wrong paths. It is also a great example of applying math in three dimensions, something that did not come naturally to me, and that I had to struggle through to gain understanding.
Evidence #9: Statistics II problems
Statistics was hard. I feel like I really need to revisit Statistics again. However, these problems were examples where I understood what I was doing (at least at the time) and was actually enjoying Statistics. It was a good reminder that even something challenging can be enjoyable when you have a grasp of what is going on. It also reminds me that even teachers struggle with math anxiety.
Evidence #10: Calculus's Maximizing the Profit of an Apartment House
I chose to include this because it was an example of a practical application of Calculus. Calculus was an extremely hard course for me and one of the courses at VMI that I would actually like to take again to help my understanding.