As I have been feverishly working to finish my CGI subtraction resource this week, I had some discussions with teachers about CGI and realized that not everyone is familiar with "Cognitively Guided Instruction"! I attended the University of Wisconsin during the development of CGI, so I "grew up" teaching with it!
For today's "Texts on Tuesdays", I thought I would share some resources that you might be interested in if you ARE wanting to learn more about how children learn to solve problems.
What is CGI?
Cognitively Guided Instruction is an approach to teaching math developed at the University of Wisconsin in the late 1980's and early 1990's (yes, this is when I was there!). It is based on using students' own thinking as the foundation for instruction...in other words, teachers base what THEY do off what the students already know. The researchers (Carpenter, Fennema, and more) base their work on the assumption that students come to school with a certain amount of informal understanding about numbers and math. The teacher's job is to learn what students know already, build upon it, and help students make connections between real-world math "stories"/experiences and--eventually--the abstract symbols we use to represent math (like +, =, etc).
This is VERY different than how math is traditional taught where we start very early by teaching the abstract symbol ("+) and then try to attach meaning to it. In other words...we need to teach math IN a REAL WORLD CONTEXT well before we introduce those abstract symbols! By immersing students in story problems from the day they enter our schools, we can better help them understand math and help them to be better problem solvers with better number sense. The implications for us as teachers is that we need to become experts in "reading" our students, learning what they know (see why mathematical discourse will be so important?!?), and then making smart educational decisions for them.
So...CGI is really critical in the early years...but for ME, as a fourth grade teacher, I feel I need to backtrack with some of my strugglers to give them some of these experiences. I worked to organize my thoughts and created some problems to create an "intervention" group of sorts...and as I kept going, it grew and grew. I wanted sets of word problems that were "real world"...I wanted students to be able to select "just right" numbers to use--so different levels could use the same problems...I wanted BIG sized problems to use for teaching. THIS was born!
Here are a few snapshots!
|Blank pages to glue problems to use as assessments...the rest of the problems got glued into math journals|
|Students pick the numbers that are the right size for them...|
|Full sized problems to use as teaching tools|
|Love watching how students solve the problems...and then use as a part of our mathematical discourse|
So...I had great success with helping my students recognize the six different types of addition problems when I worked with them in small groups, so I have gone ahead and made the same resource with subtraction AND have bundled the two together for anyone who is interested. The individual resources are on sale today...and the bundle is always discounted by quite a bit.
Anyhoo..thought I'd share! I really hope you take the time to read up about CGI...there are tons of articles and sources out there...especially if you teach primary grades or struggling mathematicians! Keep on learning, everyone!