Learning by Doing
Trigonometry Proofs. That’s all I can say.
In Principles of Math 12, there is a unit called trigonometry (i.e. SOH CAH TOA) which involves trigonometric proofs. Although high school students have been familiarized with the fundamental concepts of trigonometry since Math 9, trigonometric proofs take a side step from what students have practiced with right angle triangles and ratios of sides.
When I taught Math 12, I would set up a framework for students to work with. There is no answer in the back of the book or a specific algorithm to complete a proof. There are “strategies” students can implement depending on what has been posed to them. In the end, all that the students have are some guidelines, a formula page, and prior knowledge.
The crazy thing about trigonometric proofs is that it looks simple when someone else (i.e. the teacher) completes the proof or when considering what you have to understand to complete a proof. Basically, you have a know how to refer to a formula page, manipulate algebraic expressions, and “do fractions.” Seems straight forward until you try one out yourself.
Solving your first, second, or third trigonometric proof is FRUSTRATING to say the least. You feel lost in the process. You guess and get lost. It does not become “straight forward” until you tried about 15-20 proofs. With deliberate practice and determination, the uphill climb suddenly plateaus. You reach this ah-ha moment with trig. proofs and it feels good.
Guess where I am with my dissertation? For months I felt completely lost with what I needed to do and what I wanted to write about. My first draft, second, and third drafts of my comprehensive proposal were BLAH. My fourth draft is better. Writing my ethics application has honed my thoughts and my writing. Ready for a fifth draft and it’s going to be better.
I have finally gotten to a place in my project where I have completed my first pilot interview and getting ready for my second… made revisions to my interview protocol… and it’s getting better. I am excited about what I am accomplishing and I feel that taking Educ 809 at SFU has given me the tools and self-confidence to move forward. I see the light…
You know what? Just like trigonometric proofs… I am LEARNING BY DOING. With both proofs and my dissertation, if you don’t engage, ask questions, or try… then you can never figure it out. It will never make sense. That’s how the marking scheme would normally work out on this unit test. My Math 12 students would either get an “A” or a failing mark.
Well, I have jumped in with two feet and I am going for it. I am the one who dictates my learning. Welcome to self-directed learning (Knowles, 1975) and I am learning by doing. I did not realize how dependent I was as a learner… waiting for the cues… looking for some reinforcement… I got stuck. Not any more… I am taking my learning into my own hands.
My new mantra: It’s 2012 or GO HOME.