For me, math journals and contextual problems that press student thinking are my favorite fruits of this class. I ask my kids to do some heavy duty problem solving and to show it in as many ways as they can. I started a wikispace as an educational tool for parents to see how kids are problem- solving on their own in meaningful ways. I post the contextual problems and the kids' solutions on the wiki. I'd love for you to see what they've been doing. Look here to check it out. It also explains my math journals in more detail.
Here are a few problems that we've recently worked on. See if you can dissect their strategies.
Miss McMorrow's class started out with some stars from the lunch lady. She gave them 10 more. They ended up with 17 stars. How many stars did they start with?
Miss McMorrow was lifting weights at the gym. While working her calves, she used 45 pounds, 25 pounds, and 5 pounds. How much weight did she lift altogether?
They amaze me!