Have you ever tried to teach a 3-yr-old how to ride a tricycle?
Now take that same thought, with the same 3-yr-old but the tricycle has only one wheel! Crazy right?!?! This is how I expected my students to become computationally fluent in my early years of teaching. Sadly, I only gave my students one wheel to merrily ride down the road towards computational fluency and the wheel’s name was knowing facts. With only one wheel I think you can estimate how far they got.
Unfortunately I never let my students use or put into practice the other two wheels they probably needed more than the only wheel they had…flexible thinking and estimation. Estimation is a key component to reasoning mathematically yet it was a skill I seldom had my students employ in the elementary classroom (and I kick myself to this day because of it!). I would even say it is one of my best kept secrets until now. I have since learned that students must be given the opportunity to explore the relative size of quantities in the real world. Give any first grade student a pile of about 70 counters and ask them how many are counters are in the pile? The typical response is a teen number, maybe they’ll say “twenty-thirty-nine”, or one million. There is no rhyme, reason, or thought in their estimation and as an educator this saddened me. But then I realized, why should a student care about their estimate if it is undervalued by the teacher and never discussed by peers.
It is the aforementioned statement that drastically shifted my thinking as a teacher. For years, there was a low tolerance for errors in my classroom and that’s where I had it all wrong. I came to notice that the right answer didn’t tell me anything about what a student knew or how they were thinking. I came to realize that if I had my students make and share estimations before tackling a problem or ever picking up their pencil, I would gain far more insight into my students mathematical thinking. In order to get my students thinking and invested in the math I needed to have them estimate… and the more they estimated, the more the other 2 wheels naturally developed. I think it’s time we stop teaching students to ride tricycles with one wheel!
Now if you just realized that you need to start having your students estimate more than you currently do (like once a month), you have to check out @mr_stadel’s wicked awesome estimation station located at http://www.estimation180.com/. Start helping your students become computationally fluent but remember…estimation is only part of the trike!