I am writing this with next school year in mind. I don’t want this to happen anymore:

In my algebra 1 class, we have been working with polynomials. I would like it to be more real world / project based, but when we started this unit, I was so swamped, I had nothing to use, and I resorted back to my traditional ways. Adding, multiplying, factoring polynomials. They learned it like little monkeys, memorizing processes. This became evident when I gave them some application problems to work on in small groups with a sub while I was at NCTM Denver. IT WAS A DISASTER! They can multiply 2 binomials, buy cannot find the area of a square where each side is represented by a binomial. Actually, they flip out if the assignment is formatted differently then they expect.

While at NCTM, learning all about perplexity / Singapore teaching / PBL … I have the same dilemma in reverse in my mind…How do I help students to learn to apply their skills to multiple situations and relate the abstract to the concrete? Is the abstract not necessary as long as they can solve concrete problems?

Will they develop the ability / confidence to apply skills to new situations through their struggling if I use more PBL?

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[…] Original post by Crazy Math Teacher Lady. […]

At the very least, you can add in some structure that will help them move back down the ladder of abstraction. “How do you find the area of a square?” “What in this problem gives you the information you need to find the area of a square?”

But if you’re talking about what to do for next year, I’ve had more success when I start students out working with raw numbers first, then moving to the abstract form. If you haven’t already read them, check out Dan Meyer’s (blog.mrmeyer.com) posts on the Ladder of Abstraction (LOA in his quicklinks) and Grant Wiggins (http://grantwiggins.wordpress.com/2012/01/11/transfer-as-the-point-of-education/) has some good posts about teaching for transfer from early last year.