This week in Mathematics for Elementary School Teachers, I was reintroduced to communicating and reasoning mathematically and problem solving. Thankfully much of the information was a refresher but at the same time, I was challenged in my thinking when I read through the material titled "Reasoning Mathematically." As I continued to read, I came across terms like "converse statements," "inverse statements," and "contrapositive statements." What? This threw me for a loop and took extra time to grasp. I found this clip from YouTube rather helpful:
A friend of mine is a high school math teacher and I have recently found out that he creates math songs and videos to help his students. I listened to it a few times and began to realize that math really is as easy as it appears at times; I need to stop over thinking things.
When reading further in the text, I was able to draw on the words themselves to help me understand the meaning of them. For example, when I have a conversation with someone, we are speaking back and forth to each other. Likewise, the converse of a conditional statement is formed by interchanging the hypothesis and conclusion. Back and forth. Another everyday example is found in my laundry room. When I invert my childrens' clothing before washing them, I am turning them inside out (or really right side in!) Again, the inverse of a conditional statement is formed by negating (opposite) both the hypothesis and conclusion. Finally, and probably resounds with many of you with teenagers, is when my children contradict every idea I may have. In essence they are attempting to have the same effect as the contrapositive of the original statement (idea). Not only are they telling me my idea isn't any fun, they are turning my idea around. The contrapositive of a conditional statement is formed by changing both the hypothesis and the conclusion and negating both.
This is what has helped me rejoin the math world and begin to understand mathematical vocabulary, which really is a part of my everyday life. Understanding the root of a word helps me to further comprehend the mathematical concept that lies behind it. After much studying and reviewing and watching videos, I am happy to say that I understand these terms and the logical reasoning attached to them. This week turned out to be a brainteaser for me until I was able to see the terms from real-life situations.
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