Now people are arguing over what constitutes a Big Idea. What idea is too big to be a Big Idea? That doesn’t even make sense. There are themes throughout mathematics that can be traced through grade levels. Number sense for example. Since it takes more than one year to cover all the aspects of number sense it is too big an idea? No, clearly not. Number sense must be learned as a person matures and begins to grasp concepts that they weren’t capable of before.

I think that the point that was made at the beginning is being lost in this discussion. The way that we teach Algebra (and for that matter most mathematics beginning in about 6th grade) is broken. We have lost our focus on teaching mathematical literacy by example and we have turned to teaching process. Mathematics has been boiled down to a set of rules to be memorized and rehearsed rather than explored.

Algebra is a tool, much like a wrench is a tool. If you asked a mechanic to take a course on the study of wrenches in which you analyzed the properties that make up the wrench and how it is formed you would loose many capable mechanics. If you teach a course where you use the wrenches to fix cars, and in doing so become familiar with the form and function of the wrench (as well as why you use a particular wrench for a particular task and why that wrench is made from the material it is made from and so on…) you produce a mechanic who has the ability to use his tools affectively. That is what we should be attempting to do with Algebra.

If we were to search long enough I do think that there is enough material in Algebra to come up with several Big Ideas that are worthy of learning in and of themselves. We certainly can search for Pretty Big Ideas and find them in Algebra as Chris Lusto would suggest. I am inclined to agree with Horner when he says that, “formal abstraction is an important theme of the course.” The ability to take a real world situation and express it as an equation should be a goal of any Algebra class. No matter what ideas you come up with the merits of them can certainly be debated, and it is open to personal opinion if they meet all the requirements.

I do not teach seventh or eight grade therefore some of the vocabulary thrown by Patrick was completely confusing and he got me lost. Then Wiggins brought it back when he said that big ideas should be understood by novices and experts alike. I decided to look at the big ideas of Algebra by just looking at the standards that I have to teach my fifth graders about Algebraic thinking. My fifth graders are required to understand the distributive property, Order of Operations, simple equations, and graphs. When I think of big ideas in Algebra I always come back to the fact that all this crazy equations have meaning. The equations are representing a story. WIth that said a big idea of algebra for me would be that values can be represented in different ways. My fifth graders learn that a variable takes the place of the value we are trying to solve for. I’m also thinking that patterns is one big idea in Algebra. If it wasn’t for mathematical patterns and observation, we wouldn’t come up with formulas to solve problems. Formulas are equations that were written based on a prediction about a certain pattern. A graph illustrates a pattern; therefore, an equation does too.

I’m still trying to wrap my head around the idea of Big Ideas but so far I think I have two. So are big ideas just main concepts that everybody should understand? Are we making these big ideas to difficult by over analyzing it?

There were a number of questions that came into my mind when Grant Wiggins proposed this challenge:
Does he already have the answer in mind?
Why 4? Why not 5 big ideas, or even just 1?
Other fields?…like physics? Business? Engineering?
Is he really even interested in the answer, or is he just proving that no one ever bothers to contemplate the real reason why algebra is uniquely important?

It’s made me think. I’ve had to look up the basic definition of algebra. It’s surprisingly brief. Most sources state that it’s a system of equations that uses variables to solve problems of unknown quantities. That’s it. So what is Grant Wiggins trying to do?

It’s been interesting to see how some of the discussions about Wiggins’ task have taken a different tack. Soccer? Creating and collapsing space in the soccer field is a big idea? That sounds more like a strategy. The big idea in soccer (and in most other games) is to make goals, to win the game.

The one statement that resonated with me about algebra was a quote in a post by Max Ray:
“…math is about “Creat[ing] structure when you’re building; look[ing] for structure when you’re exploring.”

Add to that a response to a post from Grant Wiggins:
“I always ask algebra teachers this question: do your students know what algebra does that arithmetic can’t do? Do your students know what analyses algebra enables that can’t be done with basic arithmetic?”

Therefore, my quest would be this; what will algebra do, that no other discipline can do, that will enable me to make sense of God’s creation?