Understanding how children's mathematical thinking develops and reflection on how to help children build up their concepts from within (Carpenter 1999).
Children's Mathematics Cognitively Guided Instruction, Thomas P. Carpenter, 1999.
After attending a series of Cognitively Guided Instruction (CGI) sessions, provided by our district, it was a no brainer for me, this is the only way to teach math!! My students turned into little math investigators! They were exploring and discussing math and developing their own understating of addition, subtraction, multiplication, and division.
I promise, if you as a teacher have not tried CGI in your classroom then you have no idea all the math your students are truly capable of and already know!!
The hardest part, as a teacher, will be letting go of the teaching. Once you stop talking and start listening, you will finally be teaching! Seriously, I kept hearing this and it hit home one day when I was with a student who was just not getting the concept of what I was teaching. After trying several different strategies I eventually said, "Okay, you teach me." It became apparent, the misunderstanding, as he was explaining it to me. The CGI for his learning became simple once I stopped talking and started listening!!
Here is link to read more on CGI from the developers. Cognitively Guided Instruction: A Knowledge Base for Reform in Primary Mathematics Instruction
The most importan thing to know in CGI is; there are three levels of developmental strategies.
1. Direct Modeling Strategies- These kids must see exactly how the problem goes! They need to see every number.
2. Counting Strategies- These kids are FINGER counters. They dont necessarily need to see every number, but use a counting strategies to go up or down.
3. Number Fact- Theses kids know facts and know how to get to other facts from "derived facts".
A teacher needs to identify these students and place them into these category and then build their understanding of number sense to move them to the next step.
Don't tell your students how to start a problem. Only help them to "unpack" the problem. You might have to ask a question 10 ways to get them to figure out where they might need to start, but you have let THEM figure it out so they can own a strategie that works for THEM not YOU! Just remember, the one doing the talking is the one doing the learning! So teachers, STOP talking and START listening!
Below are examples of 3rd and 5th graders work, using CGI math problems. You can see the difference in strategies. They all got the answer but in 3 different ways.
|Counters and Direct Modeling|
|Direct Modler and Derived Facts|
Your job as a CGI teacher is guide their thinking and develop higher level thinkers through the use of inquiry! will be posting lessons and centers from my CGI classroom soon!