'Tis the night before Thanksgiving and I've got somethin' good for ya!
This year, I'm getting some intense training on CGI (Cognitively Guided Instruction), a research-based instructional method for teaching mathematics that focuses solely on conceptual understanding and children's natural ability to reason mathematically.
Why? You guessed it! Our new Common Core Standards are shaking things up! My school has pretty much shifted exclusively to Common Core and this program is part of that shift. (We did CCCS Writing last year as a 'taste'.) It's enough to make me sneeze!
Regardless of grade level, the new CCCS include new "Standards for Mathematical Practice". They aren't skill or content specific, but rather guidelines for how students should think about and interact with mathematics. I've listed them here.
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
These standards are the driving force of our new approach to mathematics. Rather than focusing just on the content, we're using these standards to guide our teaching practice. CGI is a huge part of that shift.
So what's a girl to do?
I'm no CGI expert by any means but in order to understand it better, I've narrowed down what I've learned so far into three categories. These key points could help you if you're interested in trying out some similar practice in your classroom. (You might already do some of it, since CGI has been around for quite some time!)
1. Writing problems
CGI has specific problem types - and depending on the problem type, the difficulty increases. Click the picture for a free chart download. (Note: I only recreated this chart, it is originally from the book Cognitively Guided Instruction, which I highly recommend.)
2. Let them find their strategy.
Instead of dictating to students which problem solving strategy they should use, the goal is to allow students to use whatever manipulatives or strategy they prefer. It's a little scary at first - and you typically have base ten blocks and linking cubes cluttering up every corner, but eventually the students begin to strategize about methods that will work best for each specific problem.
We're using a problem solving notebook.
As the students 'discovered' ways to solve problems, I kept an ongoing anchor chart displaying their strategies. We continually added to the chart. Things like 'Draw a picture' and 'Counters' were the first to appear, but later they got creative with strategies like 'Color coding' and 'grouping by tens'.
I was so excited to see that even without me telling them, they really DID come up with smart strategies! This is definitely a shift in teaching compared to our old CA Standards-based curriculum, where everything was taught 'teacher-down", direct-instruction.
3. Let 'em talk about it
So after the students work through one problem, a handful share their thinking with the class. I have mine show their work under the document camera. All the students discuss the presenter's thinking and strategy, asking questions and making comments about their classmate's thinking.
It's HARD at first. Mostly because they have no idea what they are doing - and they say next to nothing. But they do eventually get there, and the discussions are pretty cool! In my seven years of teaching, I've never experienced anything quite like it.
If you use CGI, I'd love to know how it works in your room! I'm really enjoying it and can't wait to blog about some of the lessons that have naturally evolved from the discussion.
I'm excited to share more as I learn more.
But for now, I will turn off my freakish type A teacher personality and go toast my bread to make stuffing.