Math Education Concepts

Learning to rock-climb is changing how I’ll teach math.

Five years out of college—and taking a year off from teaching—I find myself in a precarious new position: dangling by ropes, 35 feet up a wall, a beginner again.

Learning to rock-climb is as exhausting and fun as I’d hoped. I’ve spent hours rising and falling, hauling my body from Point A to Point B, returning home too drained for anything but Facebook and Orange is the New Black. I’d half-forgotten how exhilarating and vulnerable it feels to begin something.

Because my mind exhales analogies (in much the same way that my body exhales CO2), I’m constantly drawing connections between rock-climbing and teaching math. In my own grunting and straining, I hear the graceless echo of my students’ efforts, but from the other side. Back in the classroom, I was the one holding the ropes, with two feet planted on flat, sturdy ground. I assured them not…

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Do They Get It? The Instantaneous Rate of Change Exactly

Today in calculus I wanted to check if students really understood what they were doing when they were finding the instantaneous rate of change. (We haven’t learned the word derivative yet, but this is the formal definition of the derivative.)

So I handed out this worked out problem.

And I had them next to each of the letters write a note answering the following individually (not as a group):

A: write what the expression represents graphically and conceptually

B: write what the notation $latex \lim_{h\rightarrow0}$ actually means. Why does it need to be there to calculate the instantaneous rate of change. (Be sure to address with h means.)

C: write what mathematical simplification is happening, and why were are allowed to do that

D: write what the reasoning is behind why were are allowed to make this mathematical move

E: explain what this number (-1) means, both conceptually and graphically

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Over the past few months I’ve been experimenting with guided math strategies in my classroom. One station in my classroom has been dubbed as the technology table. This table has been primarily used to differentiate  instruction to improve students’ understanding of mathematical concepts.  I’ve been using the tech table for the past few months with great success. There are five iPad apps that are used at this table.  Unlike many math apps that offer only demo versions, I’ve found the below apps to be useful in the classroom.

5 Dice

This app is the newest addition to my iPads for intervention list.  This app emphasizes order of operations for upper elementary and middle school students.  The game encourages students to use multiple dice to find the “target” number.  A whiteboard is built into the game for students to work out problem.  Progress reports can be emailed to the teacher for formative assessment…

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Tic, Tac, and Toe

Welcome to this week’s Math Munch!  We’re taking a look at several Tic-Toe-Toe related items.

To the right you can see a little Tic-Tac-Toe puzzle I found here.  If the board below shows a real game of Tic-Tac-Toe, then which player moved first?  Think. Think!!

Now let’s talk about the basic game itself.  Tic-Tac-Toe is fun for new players, but at some point, we can all get really good at it.  How good? Well, there’s a strategy, which if you follow without making mistakes, you will never lose!  Amazing, right?  So what’s the strategy?  The picture below shows half of it.  Here’s how to play if you’re X and get to move first. (instructions below.)

Strategy for X (1st player)

“Your move is given by the position of the largest red symbol on the grid. When your opponent picks a move, zoom in on the region of the…

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Why the math teacher in me loves the science teacher in me

I spend 9 months of the year being a math teacher and two weeks every year being a science teacher. As time goes, it is hardly a comparison, but I’m beginning to see those two science weeks as an absolutely essential part of supporting the rest of the math year.

For better or worse, my brain has but some boxes around the two disciplines. Science provides the contexts, math helps to generalize them. Science provides the data, math analyzes it. Science gives you a story to support evidence. Math gives you the tools to predict the future or to theorize the past.

I understand those are debatable points. The real borders between math and science are not nearly so cut-and-dry.

But I can’t get away from this generalization: science is story-telling. Some of the stories are exciting. Some of the stories are gruesome. Some of the stories are tragic. But, science has…

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