PDA

View Full Version : What on earth are "Algebra Tiles?"

LateComer
11-10-2005, 10:22 AM
I saw a short piece on the news about parents going back to school to learn, among other things, algebra, so that they could help their children with homework. One parent talked about algebra tiles. I assumed that this is some kind of teaching tool, so I googled it and read a couple of pages about them and still don't understand what they're for or how they're supposed to teach algebra. In fact, it looks like it's just one more thing to learn on top of the math.

So, what's the deal on these things? Do they really help teach algebra? Are there any teachers who can give me some insight?

groman
11-10-2005, 11:07 AM
If one's an adult and they can't pickup high school algebra by just reading any book on the subject, perhaps they shouldn't have had children in the first place, but I digress...

Algebra tiles provide a visual way of representing variable multiplication, nothing more really. There's really nothing to learn there...

scr4
11-10-2005, 01:55 PM
As groman said, a tool for teaching the concept of multiplication. It's not enough to have them memorize "2x3=6", you need to teach what that means. A 2x3 tile represents, well, 2x3. That's 2 rows of 3 tiles each, or 3 rows of 2 tiles each. You can see visually that the area of this tile is 6 units.

I've also seen tiles for teaching the concept of digits (i.e the base-10 system). Number 32 is three 1x10 tiles and two 1x1 tiles. Number 120 is one 10x10 tile and two 1x10 tiles. And so on.

Giles
11-10-2005, 02:21 PM
That sounds like a misnomer: they really should be called "arithmetic tiles" or (given the level at which they are aimed) "number tiles".

Kimstu
11-10-2005, 02:35 PM
They're not arithmetic tiles because they don't actually represent specific numerical values (except for the unit). They allow you to visualize basic algebra operations like completing the square and so forth.

While I do find it handy to sketch little rectangles while explaining such algebra concepts, I'm not sure it's worth the trouble to create an actual set of physical manipulatives to represent that. You can see illustrations of the use of algebra tiles here (http://faculty.prairiestate.edu/skifowit/htdocs/manip/alg_tile.htm).

Giles
11-10-2005, 03:10 PM
Yes, Kimstu is right: they are used to model polynomials, so they are elementary algebra, not arithmetic.

TJdude825
11-10-2005, 06:46 PM
I've never used them, but I remember seeing a picture in my algebra book a couple years ago, that showed visually how to calculate (x+y)2

Basically, they have one tile which is x by x, another that's y by y, and two which are both x by y. Even if you don't know what x and y are exactly, it's easy to see that putting these four tiles together the right way will produce a square that's (x+y) on a side. Thus x2 + 2xy + y2 = (x+y)2

Although it might seem silly, I think these aren't necessarily a bad idea, because if a kid really knows what multiplication MEANS (not just how to do it) it will make things much easier for them down the road, for example, when they're told that "m2" is a unit of area, or when they're trying to learn definite integrals.

Bryan Ekers
11-10-2005, 06:52 PM
What's a "tile" ?

Carnac the Magnificent!
11-10-2005, 08:31 PM
If one's an adult and they can't pickup high school algebra by just reading any book on the subject, perhaps they shouldn't have had children in the first place, but I digress...

You're jesting, yes?

groman
11-10-2005, 09:16 PM
You're jesting, yes?

Not really, no. If you can't pick up high school algebra in about 3-4 hours as an adult there's probably something wrong. High school algebra is all about letters standing for numbers, dependent and independent. It can all be explained in about as long as it takes to do a cross word puzzle. The reason it takes two years in High School is because they are using an approach that leads to the greatest number of people retaining the knowledge for a long time - i.e. one concept at a time, repetition, repetition, repitition.

By the time you're an adult, you should already know how your own brain works and by looking at an explanation of something you should be able to understand the explanation (given that you have the definition of all terms handy).

The reason people go to college is because most advanced subjects are so vast that without experienced help you don't know what to read. With elementary algebra this is very well defined, because you can understand the entire subject in just a few hours. It's essentially four things: arithmetic, unknowns, functions and graphing.

Yes, it could be very challenging for a person unfamiliar with those concepts how to understand them, not because they're new concepts, but because that person doesn't know enough about learning to learn them quickly. If you're so hopelessly lost that you need an entire class sequence, you probably missed out on some key development in childhood. Ergo, probably shouldn't have children.

I'd rather not argue about this though, it's a rather sensitive subject for me, and I really don't mean to offend anybody, yet there's really no inoffensive ways to say "You shouldn't have children because ... ". People always take it personally. Hell, I would take it very personally, but it's just my opinion about the trends in the human population.

Wolfian
11-10-2005, 09:49 PM
Eine kliene minute-, er, -ten, Heir groman (http://boards.straightdope.com/sdmb/showthread.php?p=6784508#post6784508).