### Internalization

Right now our math class is working with algebra tiles, fun little manipulatives that help with concepts like combining like terms, solving equations, and the distributive property. They're basically a set of squares and rectangles of different lengths. There are "ones" tiles that we use to measure everything else, but some lengths don't measure easily. So we call one unknown length "x" and the other unknown length "y." Each tile is named by its area, so the x tile, for example, has length x and width 1, while the x-squared tile has length and width x. I've never seen anything like them in algebra, and I really like the way they offer a tangible way of looking at variables.

The tiles hve different colors on each side. The pink/blue/green side (depending on the shape) denotes a positive number, while the red side denotes a negative. So for example, an x tile with the blue side up and a y tile with the red side up represents the expression x-y. However, when we draw pictures of the tiles on worksheets, assignments, etc. we can't use the actual colors, so the algebra tile people just use shaded/black or unshaded/white pictures to denote positive and negative. Guess which is positive and which is negative?

If you're like most people, you guessed that unshaded/white is positive and shaded/black is negative. But the algebra tile people flipped the script and declared that shaded/black tiles would denote positive numbers while the white/unshaded ones would be the negatives. I have to admit that this really confused me at first. The same was true for our kids. They complained about how difficult it was to interpret the pictures. "Why isn't white positive and black negative?" they wanted to know.

"Why wouldn't black be positive?" we asked. "Black is always negative," one student told me. How fascinating that in a classroom where there are at most three white students, the entire class would resist blackness representing something positive. My difficulty getting used to this system definitely made me reconsider my own internalization of racist attitudes, not to mention what this must mean for the identity development of all my students. I appreciate the thought that went into creating the algebra tiles and their notation--what an interesting and surprising way and place to challenge kids' ideas of race.

Unconvinced that this has anything to do with race? For more examples of the ways we equate blackness with negatives and whiteness with positives, check out pages 52-54 of Dean Keith Simonton's "Greatness: Who Makes History."

## 8 comments:

Wow-those tiles sound awesome. Can I play too?

It is a messed up world in which we live when we have to equate personal identity to classroom materials. But we do, and I can't figure out if that's a good idea or not. I have that luxury as a white person who had pretty good schooling all along.

A lot of disadvantaged kids are accused of not relating well to the rest of society, but maybe this is more a case of only relating to the "negative?"

To update my earlier comment, I have a few things to add.

1. Red is pretty standard for negative in the world of numbers. I think that the most intentional bias we can reasonably assume for the creators of the tiles is that they have spent too much time around accountants. ?

2. You might also be interested in Project Implicit

https://implicit.harvard.edu/implicit/

It is a project to study latent bias and you can even take some online tests. It's enlightening!

In Russia, red is positive and green is negative. When small kids are learning math and other things they have these two paddles - one red and one green - they hold up the red when the answer is correct and green when it is wrong. I was completely disoriented by this when I visited kindergartens. There are many color/psych connections that we don't think about.

Fascinating stuff. I have been asking kids what color they would choose. Even those who chose red or pink or blue for positive numbers select black or gray for negative numbers. Most can't say why they pick what they pick for positive but all agree that black is negative.

One of the math teachers here suggested that your tiles must come from Japan or somewhere else in East Asia. He said that white space is empty space, thus negative. While the black is filled in, closed and thus positive or whole. Interesting. Have you ever heard something like that?

The same teacher, who you may have met but really don't know, I think, heard how you were using this to help to discuss race, smiled (smugly, I suppose) and said, "She will make a great teacher." I have to agree with him.

I liked the book excerpt you included as well as swe (I finally figured out what that means) and her comments and the web connections. I have had friends take their tests and find some interesting things out about themselves.

Keep up the good work.

The tiles are not from an Asian country. The creators (or at least the creators of the notation) deliberately chose to represent black as positive and white as negative for the sole purpose of creating a counter-message to the usual color messages that students are used to.

Bravo for the company. I am doubly impressed when it is a conscious effort.

This is a great step in challenging the connections (in this case color and positivity/negativity) that children are taught to accept as

undeniabletruth.I'm so happy that you're entering this field (ps I totally brag to my friends about how smart you are)

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