Since Fawn’s similar triangle lesson was so beautifully written here, I pretty much printed out her blog post and ran the class verbatim. I quickly realized that my students are not as enthusiastic problems solvers as Fawn’s and it’s because I don’t let them struggle enough. I’m working on it. They struggle a little, but at some point I jump in, and then kick myself later. This became evident to me as I compared my students reactions to Fawn’s descriptions. I got more of the “YOU’RE NOT HELPING ME!!” “It’s your job to help, you are not doing your job” types of comments. I stopped the class, we had a good group discussion on how they could be convincing that they found the exact point to hit the ball in order for it to go in the hole. They got back to work. They need more time. Some students figured out what to do right away: 
Others really were a mess. I am learning a lot, at least. We will continue on Monday. I’m sure it will be a success. 
Productive Failure
Day 104: Right triangle trig with words
I printed the questions on cards and gave a set to each group to encourage collaboration. I just gave them to the students. No instruction, no fancy schmancy notes. They learned through struggling and did great!
[update 2/28: Look! Research to support productive failure!]
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?
Crazy Math Teacher Lady 