Went to a district math pd yesterday to get our new updated math program materials (aligned with common core). The representatives of the math company came for the First half of the pd and then we had another speaker for the second half. They of course presented completely opposing views, but that's a whole other post. Any who, the second speaker taked a lot about the 8 mathematical practices from common core and how to use them to create rich math experiences in the classroom. Here is an example problem we worked on/talked about: the squirrel had to climb a 17 ft tree. Each day he climbed 5 ft and then fell down 2 ft because he was got tired. How many days would it take him to reach the top? I like the thinking that students should be given a problem, come up with strategies and solutions, and then share what they learned/ how they figured it out. Then the teacher teaches to fill in gaps and possibly to inroduce efficiency. ( of course the teacher is observing, asking probing questions while students are working and differentiating as needed.). Seems to be in line with the math I learned in college--cgi. So here is my thinking or what I'm kind of struggling with. Is this something that would be done on a daily basis? How would something like this be graded, especially if they may be working in groups? How could I do something along these lines with stations or centers? (thats what I was planning on implementing next year) Basically this frame of thought is teaching 'backwards' from what we've traditionally taught. I love the idea of this, letting students explore and figure out how to solve problems. I think it also translates well to what we are asked to do later in life. We are given problems to figure out, not taught what we need to know and then given a problem. Thoughts? Thanks!