Some of you will read this and wonder, seriously, this person is a teacher and didn’t know that?!? But I am being honest and open, admitting that when I am closed minded, I fail as a teacher, each day I must keep my eyes open to seeing new strategies and my ears open to hearing others’ ideas in order to succeed as a learner…
I’m not sure it’s a matter of not knowing, but more that I hadn’t taken a moment to think about a concept outside the procedures I learned as a student. I was the “model student” following directions, copying notes, doing what teachers told me to do. And I didn’t question it. I just did it. I didn’t ask why. And that makes me sad.
I believe that’s how I ruined math for so many students, telling them, this is the way, as opposed to allowing them to grapple with it themselves, encouraging them to notice patterns and develop their own ‘set of rules.’ And that makes me sad, too.
Last year, I remember a tweet about solving systems by elimination-most of us can do the steps correctly, but do we ever pause to wonder WHY it works? I am not sure the question had ever been posed to me. I sat down, reading posts, solving problems until I was comfortable with the why.
Yesterday, I read Glenn’s post Never Tell Me It Can’t Be Done. Again, we get so fixated on the process we’ve been ‘taught’ or even used to teach that we never allow ourselves to grapple and play with the math. When we take the time to see beyond the procedures, the cool things of math begin to show up. Truth is, the coolness has always been there, we just didn’t take the time to see it.
Glenn’s post reminded me of an encounter earlier this year. I had a colleague tell me I could not take my students outside, using pictures of classmates and their shadows to introduce trig ratios. Why not? Because my idea was just similar triangles. Seriously? This teacher is talented and smart, but the truth is, when we are so fixated on teaching the checklist of skills and procedures, we don’t allow ourselves to enjoy the math. By thinking inside the box, teaching our content as a series of disjointed skills, our students are missing out on opportunities to see the beauty and connections math has to offer.
Just this morning as I read Making Math Meaningful’s Boat on a River, I had one of those duh!?! moments. Why had I never presented tangent ratio specifically as slope?!? Seriously? Its like one of those things you know, you understand, but at that moment I asked myself, what was I thinking?
Another instance was 2 years ago, when students were matching cards of equivalent radical expressions, rational exponents, integer terms…I overheard a student explain to his classmate, “you want one-third of the factors, when its a cube-root. Its three-fourths of the factors when…” Seriously? I knew that, but why didn’t I make it that easy? Because I was caught up in telling students the procedures and rules rather than allowing them to see the patterns and connections.
Or the time a student explained to a classmate, the sign change for the center of a circle as a transformation…”what it takes to move the center back to the starting point, the vales that make it 0^2+0^2″ Yep. Been THAT teacher who gave them the equation of a circle, saying this crazy thing happens with the signs of the center, without explaining the WHY. At some point, in my early years of teaching, I am embarrassed to admit, I am not sure I even knew the WHY.
I have been a teacher who claimed to use inquiry learning for years. The truth is, I often would steer students to ‘my way’ in the end. That makes me sad. At some point I realized my way wasn’t always best/easiest to understand. Although at the time, it seemed easier for me to have them all doing it the same way. 😦
I realize many have voiced issues with the CCSS. For me, deconstructing those standards has forced me to think about the math, looking for connections, asking why, investigating tasks to see if they offer opportunities for students to answer the why.
Being intentional with the Mathematical Practices, I am learning to listen to my students more and that its okay to admit I am not sure if their idea will always work, but then sitting alongside them to experiment with their strategy/idea, modeling a bit of productive struggle, high-fiving or asking questions to move their thinking forward.
I am not embarrassed to admit, I don’t know all the answers, its an opportunity to learn something new and share it!
Pam Wilson, NBCT
5 Practices for Orchestrating Productive Mathematical Discussions, Smith & Stein
Teach Like a Pirate, Dave Burgess
From Ashes to Honor, Loree Lough