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Monday, November 23, 2009

Why Algebra Tiles?

Algebra tiles provide a concrete, visual manner to "see" equations. They are part and parcel of the approach to math that exalts the value of multiple representations and a variety of approaches towards solving problems.

They are not a crutch, but they do serve students who have significant difficulties dealing with algebra on a purely symbolic level. For students who are able to navigate the symbology, these same tiles stretch the mind to "justify" why the moves they have learned "work". For all students, the tiles continually reinforce the concept of negatives as "opposites" because each time they cross a region on the mat, the students is obligated to flip them, thus showing their opposite. That is a concept that is easily lost to beginning algebra students as they rush to "solve" equations.

Later in the course, when we look at factoring polynomials, these tiles will no longer feel "backwards" but will actually provide key support for all students to feel successful at this difficult task.

Finally, these tiles reinforce the very true interconnectedness between algebra and geometry as well as arithmetic in general as the rectangle model we are using (known as "array" model) is an excellent basis to understand multiplication/division and fractions.

I notice that students who accept the tiles as a part of algebra are more successful down the line when we come to use them for more complicated concepts. In particular, many MANY 8th grades make simple errors as the “rush” along the path towards “solving” equations. The tiles kind of make them slow down and justify their moves.

And yet, I must admit, my students resist the use of tiles year after year. They often say they are more confused about what algebra means when they use them. Usually when I ask them to take out the tiles, there is an adolescent groan in the room.

This year I made my best effort to ignore this because I know that the tiles present algebra concepts very concretely. In particular, I like how the tiles, on tile mats, oblige the students to consider the real meaning of negative numbers (as opposites). I have begun to see my students make intuitive decisions about how to solve for variables rather than procedural ones. However, they still complain.

I have my theories why, but what do you think is happening with them?

1 comment:

Sean Nash said...

Disclaimer: not a math teacher.

Rules are relatively easy. Battling through a constructivist understanding = not easy. However, you're shooting for deep understanding... you're shooting for real transfer. No?

Stick with the tiles. They are used to traditional? Don't abandon the really sequential, linear folks who cling to the list of steps. Battle away at bringing them along. But push the constructivist approach. God knows I wish that could have happened for me.

Sean