Extending Children's Mathmatics

Summer Professional Development: I don't know about the rest of you teachers out there, but I've done quite a bit of Summer PD ever since I started teaching.  This summer I've spent a total of 9 days in PD out of my 5 weeks of summer (courtesy of the non-traditional calendar I work on).  The first five were spent in Technology training that I wrote about here.  This past week I spent 4 days in math training.  I'm in year 2 of Extending Children's Mathematics. This is a totally different way of teaching math than how I learned in school.  The basics of the training is teaching multiplication, division, and fractions through word problems.  It's also the concept of not actually "teaching" the students how to solve the problems but rather facilitating a variety of problem solving that students come up with. Instead of teaching the method and then giving word problems, you give word problems first and explore the different ways kids solve and use their methods to extend kids' thinking.

This is the book that we are working with

 

We spent a lot of time exploring A TON of ways to solve one problems.  At times is was repetitive, but I did quite a lot out of it.  Last year in Year 1 we talked about how a multiplication problem should be set up to describe groups of something.  So 6 groups of 7 puppies should always be written as 6 x 7.  I never saw it as a big deal which way the problem was written because of the communative property.  Our trainer opened my eyes to see the difference between 7 houses with 2 people in each vs. 2 houses with 7 people in each. What do you think? I also spent a lot of time thinking what numbers to put into problems instead of just pulling numbers out of a hat. :)

 I have 3 more day of training to go to throughout the year where we will analyze student work and get to see this type of teaching in action in a real classroom.  I've really learned a lot, but I'm going to try to enjoy my last week off next week with my little girl.  My building opens on Monday, so I plan on spending some time up there, but hopefully not too much.

How do you teach math? What different things have you tried in the past? What do plan on doing this year?