Slide 1: This is Emily Kresiak and we’re here in the third unit in the sequence about helping you help teach math.
We’re going to consider what it means to “teach math” and also where a special education paraprofessional fits in. That’s the big picture we want to paint in this webinar. Subsequent units will go into detail about most of the things we mention today.
Slide 2: You won’t be surprised to hear that teaching math comes out of an understanding of what math is, which the Old Guy talked about in the Unit 1 webinar. You might have seen it. But here’s the recap about what math is: math is a way of thinking logically about the world using numbers and shapes (or, actually, space).
Math, in short, is thinking. And teaching math means helping kids think. That is the Big Picture in a nutshell. But let’s fill out the picture.
Slide 3: Of course, what we meant is thinking mathematically. Thinking mathematically—that must be something only really smart people can do. It’s not true.
In fact, you do think mathematically in some ways, but you just don’t realize it. Probably no one ever told you. But when you compare qualities or classify things or estimate how much of something you need, you are thinking mathematically. In these situations, you have to be logical enough to get a solution that works for you.
Anyhow, what’s important in mathematical thinking—as in all kinds of learning and understanding—is ideas.
Slide 4: Creating space for ideas in the classroom is difficult, however. Ideas are delicate. Introducing them and dealing with them requires a lot of trust and a lot of conversation.
So how we treat kids is very important, and especially so, we think, in math class. That understanding is one half of teaching math.
Slide 5: The other half is the math.
Mathematics itself is a structure of related ideas. So those relationships of ideas to each other is also important. And that’s where mathematical ideas really start to get interesting.
What does a mathematical idea look like? How would you recognize one on the street or in the classroom? What would you hear if a mathematical idea “spoke to you?”
Slide 6: In fact, really teaching math is about helping math ideas speak to kids—to really mean something important to them. It’s a great goal, and it doesn’t seem to be easy to pull off.
What people mean when they say things like “I’m not good at math” is that math doesn’t speak to them. This reaction was part of what we dealt with in Unit 2 when we considered math attitudes and anxiety.
Teaching should generate excitement about mathematical ideas. Not fear.
Slide 7: Note that we’ve already come a very long way into the Big Picture of math instruction! And it’s easy to understand.
Here’s where we are now: Math instruction is about helping kids think, understanding and using mathematical ideas about space and number, relating those ideas to each other: and liking it and looking for more.
How can you, as a special education paraprofessional, help the kids you work with in this sort of way?
Slide 8: Your actual teaching assignments will probably entail reinforcing math lessons. And that often means re-teaching something you’ve seen taught.
Even if you are doing something simple like drilling a kid on math facts, you can add bits and pieces of what you know about the related ideas. For many kids, too much drilling actually creates fear, and makes things worse!
Slide 9: All of this will take a bit of work, and that’s why this unit has a toolkit. It explains the different sorts of math kids can learn, so you can answer questions like “What is arithmetic?” and “What is algebra?” and “What is calculus?”
This webinar is shorter than some of the others because big ideas need to be packaged up small. If you can’t explain the Big Idea in a few words, it’s not a big idea (not yet). Its ability to fit in a small package is what makes a big idea so powerful. Rather like the idea of equality and the idea of zero.
Slide 10: The Big Idea:
Math instruction should inspire students to think mathematically: to engage ideas about space and number and to explore the relationships of those ideas to each other.
Slide 11: Saying a lot more would be too much. But remember the words:
These words have teachers and students active together doing things. That’s teaching, and it includes teaching math.
Slide 12: Once more, anyone who teaches math (you included) should
- inspire – to demonstrate to students what’s exciting and interesting in the lesson
- think – to help students understand the ideas involved
- engage – to get students active and attentive
- explore – to share with students questions and wonderment