About six years ago, I was a naive teacher who was starting out my formal teacher career in an inner-city school in east end Toronto. My first lesson involved showing Grade 7 students that the interior angles of any triangle add up to 180 degrees. I made lots of newbie mistakes. I gave out the scissors first. I didn’t instruct the kids not to make straight cuts on the angles. In the end, no one was listening and everyone had hacked up triangles, but not a single child knew what was going on! It was a pretty big disaster and I laugh now when I think back on it.
Fast forward to 2016.
I pull this lesson out for a Friday morning before the bell. I know what to do and how to execute it all without needing to write it down. I know what materials I need and I can see all the pitfalls ahead before they even happen. A lot happens subconsciously now.
And it’s amazing to be reminded of how far you’ve come. Often, we don’t realize our own progress. We can take our skills for granted. At the odd moment, you are reminded of how long you’ve been in the classroom.
It was nice to have a reminder of my progress this morning when B., a tutor who has been helping in my math classes for the past three weeks, gave me a compliment. I don’t recall what was said prior, but he told me that my classroom was the best math class he had ever been to. My students are engaged and are listening. They are focused and they are working. That is not the norm, he said.
I felt flattered and to be honest, I can’t remember if I said thank you in return! To be clear, I enjoy positive feedback, but I have, in the past, a terrible habit of dismissing compliments when I receive them. I will brush them off, I won’t look people in the eye or I will silently stare back awkwardly in silence. Of course, we all like compliments. I simply just don’t know how to react to them!
But it was nice. I appreciated it. And it just made it that much more of an excellent teaching day!
Over the past two days, both the Sec 4 and Sec 5 students have been reviewing integers. Yesterday, we learned how to add integers and today, we spent a good amount of time discussing how subtract positive and negative integers.
About 60% of the students were able to master both concepts fairly well by the end of class. I have to say that’s pretty good, considering our periods are only 50 minutes! I used dual coloured foam chips; we use red for negative and white for positive.
I model how I subtract or add on the Smartboard with this convenient website from McGraw Hill. I walk around and ask students to do it themselves. Some of them get confused at first because they’re reluctant to participate, but I model how I count – touching a “zero sum” with two fingers and saying “zero” – with my hands. Once they start doing it, the gears start turing and they get their “aha” moments.
Of course, adding integers with chips is easy.
But how the heck do you subtract 7 from -2? You start with two red chips and then …?
I won’t go into a lengthy explanation. This video below explains it pretty well:
It just felt great to see the kids really eating up the math!
At the end of the day, I dug around YouTube to see if I could spice up my lesson a bit and came across this lovely gem, PBS Math Club! They’re not cheesy or lame; on the contrary, the series is professionally done and the actors and actresses are pretty hip young teenagers who can hold their own. Check it out! There’s a pretty good definitely of adding and subtracting positive and negative, using an analogy of how much good and evil is happening in the city of Gotham!
I will have to play this tomorrow in class before we practice our skills with Integer Wars. The kids are really gonna get a kick out of this!
*It’s especially important for Second Language Learners to watch videos with closed captioning where possible. I myself watched a lot of Frasier as a teenager and learned a lot of good words that way!
During my summer course, our instructor made us do a few math investigations. This is the idea that students explore a concept on their own and try to come up with a mathematical rule, versus having the teacher prattling on about what one needs to memorize.
It’s easy, as a teacher, to revert back to the good ol’ lecture.
We do it all the time. While it’s necessary once in a while, it’s boring for the kids if it happens day in and day out. Not only that, but engagement often isn’t there. An investigation allows students to develop deeper learning. How often have you learned something in life because you discovered it on your own?
So I have made it a goal this year to trust my students more, and give them the ability to start exploring on their own, rather than delivering a boring lecture and telling them to memorize all the exponent rules. Too often I hear teachers in the north say, “Oh, they’re not capable of it” or “It’ll take too much time.”
Even I’ve said these words myself.
But what does that say about us as instructors, mentors and educators when we’ve simply decided that “they can’t” but that we don’t even provide them the opportunity in the first place?
This morning, I gave it a go. We looked at what happens when exponents of the same base were multiplied together?
And guess what?!
They got it!
That’s really all there is to it. Trust your kids. Let them think on their own. Stop holding their hand. Give them the chance.
Where can you find math investigations? You can look through the resources at the National Council of Teachers of Mathematics (NCTM), such as this investigation into the Law of Sines. The Ontario Association of Mathematics Education (OAME) also has an abundance of lesson plans (K-12) that are structured as investigations.
Quotient rule next week!