Algebra frustration applying skills

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?