Introducing Geogebra

Back in the fall, I was thankful to have a one-on-one training session on Geogebra. A math professor whom I’m in touch with at the University of Nipissing generously offered his time to teach me how to use this free, open-sourced math software. It’s quite versatile and it can be used to create functions and draw geometric shapes.

Unfortunately, I’d forgotten about the software … it had always been on the back of my mind, but as other tasks piled up, it fell down on my priority list. Luckily, in February, all the high school math teachers were asked to attend a Geogebra training session. We were given three hours of “sandbox time” to play around with it and the principal made it a priority to get IT to install it in the computer labs … finally!

The week after my PD, I got my students onto the program right away . As each of our class periods is 50 minutes long, I gave them two short tasks to work on. The first task was quite simple: make a line drawing. Kids picked up pretty quickly on the difference between a line and a segment. They learned how to turn on/off the grid lines and/or the axes. They coloured the lines in, changed the thickness and figured out how to correct their mistakes and save their files.

Here’s one of the products by my student, J.:

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The second task required making an equilateral triangle. At first, I would just tell students to try making one on their own. Most of them would start with three line segments, and quickly realize that the side lengths vary far too much. Using the cursor, the sides could easily stretch, the side lengths would change and it would no longer be equal lengths on all three sides.

Subsequently, I showed them an easier way – we created two overlapping circles of the same radius, then drew the radii to form an equilateral triangle.

Altogether, our first session was a success. Next year, I will have to build some assignments for them to follow and have tasks that are presented within each of the units.

Extra tip: Some kids are awesome at picking new software up. It’s always a good idea to figure out who these kids are and space them around the classroom whenever you’re doing a new task. They can be great peer mentors and work as an extra helper when you find yourself running all over the place!

How Far We’ve Come

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.

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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!

Using Investigations

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.

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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!