Friday, June 6, 2014

What in the heck is "ALGEBRA" anyway?

A t-shirt with this saying was circulating Facebook and I couldn't resist making a comment. This is another indication we need to become an "I love math" generation!

I'd also argue that you probably did use algebra, but you didn't know it. I say that because in order to know you used algebra you'd have to know what it is.

Do we really know what Algebra is anyway? Go ahead....try to define it! Give it your best shot!

This has become one of my latest pet peeves. We use this word "algebra" like we understand what it is and what it means. but even for those of us who are trailblazers in the "I love math" generation, this word should give us pause.

What I know from working on 4K-12 math curriculum is that algebra begins actually as early as 1st grade. Some may say kindergarten, but I'd have to say developmentally one-to-one correspondence has to occur first and for some 5 and 6 year olds, that isn't happening quite yet.

So here is the Oxford definition of algebra, "The part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations." I'll summarize it as the transition from doing math concretely (such as counting) to more abstract representations. When I was trying to find a ale price and I knew the percent discount but not the dollar amount that would be taken off the original price, I had to use algebra. (Read Ann Taylor post)

I think for many of us the definition of algebra is what happened in our first year math class in high school that just so happened to be called "Algebra". (From this point forward in this blog I will capitalize the course title Algebra, but when referring to algebraic concepts it will be written with lowercase a - algebra.) Perhaps in that year you spent a lot of time factoring quadratic equations. We think that is what algebra is. I'll agree it is part of algebra, but algebra is so much more than that.

Folks, please always remember that Algebra I and Algebra II are course titles. That is it. Course titles that contain the teaching of mathematics. Some of which will be using algebraic concepts, some will use graphing, some geometry, etc. They are course titles. They actually could be called anything like HS Math 1 and HS Math 2. What you learned in high school in those first two courses isn't what you should tag algebra as being.

Remember that age old argument about should we teach Algebra in 8th grade. Guess what!!! We do! We teach algebra the concepts, (as stated above as early as 1st grade) but perhaps we didn't title the course Algebra.

This article is an example of an article that uses a random course title Algebra to make an argument without talking about what algebraic concepts are being referred to. The problem with this article is they don't ever get to the details of what is taught in each of these so called courses. In my experience working with 8th grade CCSS, much of what used to be called 8th grade Algebra or Algebra I in high school is now being taught in regular 8th grade math. In many districts however, they don't change the name of 8th grade math to reflect that. The first course is high school is still Algebra I, but the content that is taught within that course will be shifting to the topics normally found in Algebra II (or the second year course). Without going into tons of detail....the bottom line is this....

Algebra is the name of a course. It doesn't describe the content taught within that course. So you really have to be careful.  And if you step back even further to say what IS is much more than a course. It's the way you abstractly use mathematics to solve problems that you can't do using your fingers and toes. It is taking an idea and using a formula or equation figuring out how to solve it. That could mean mentally also, especially since most of us do math mentally on a day to day basis.

So.... did you use algebra today?

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