What is CGI?
CGI / Common Core Math Frequently Asked Questions
by Tahnya Nodar
CGI: What is it?
Cognitive Guided Instruction (CGI) is the way we teach the new Common Core Math Standards. It is a philosophy of teaching, not a curriculum. It is a practice that has years of research behind it. It is based on the premise that all children come to the class already knowing something about math. We use what they know to help them solve problems. We learn multiple strategies to solve problems because we gain a deeper understanding of math concepts, when we can solve problems in different ways. This allows for multiple ways to access different problems in a way that makes sense to them.
What does it mean to develop an “Open Mindset” towards math?
In CGI we try to develop an “open mindset” towards math. This is where each student develops an identity as a mathematician rather than with a “closed mindset.” A person with a closed mindset towards math might think they are bad at math and will pretty much give up easily when faced with a challenging math problem. People with an open mindset might think they don’t know how to solve a problem “YET” or may think it might be solved if I approach it this way, why not give it a try? The open mindset is willing to take risks. It knows that mistakes are expected, respected and inspected and are critical to the learning process. Some of us adults have closed mindsets towards math. It is important to not vocalize those thoughts to our children.
Why use child generated strategies?
As teachers, once we see strategies that work well to solve different types of problems we showcase them. Students are learning from each other. These strategies are then collected and displayed so others may use them when facing similar problems. This is really important developmentally because some strategies utilize more concrete ways and others utilize more abstract ways to solve problems. Children conceptualize math problems differently than adults do. Using child generated strategies allows children to gain a deeper understanding of math concepts than teaching them adult strategies.
Why so much articulation of thinking?
A child, who can articulate clearly why a strategy works to others or who can explain why it is more or less efficient, is a child who clearly understands math concepts and properties. A child who is able to articulate a strategy can help the math learning community in class, as well. Explaining a concept makes it better for children to go back and check their work to figure out where mistakes were made. Accuracy is important. A child that writes only the answer and says, “I figured it out in my head,” cannot adequately retrace the steps to determine if the problem was solved correctly. A child that clearly understands the process of how he/she arrived at an answer, might also be able to apply the same knowledge towards a different type of math problem. Now those skills are starting to build and show different applications in different situations. This is what makes students mathematically powerful.
What is the role of the parents? How can they help their children with homework?
The good news for parents is the CGI approach to teaching math means that parents don’t need to play the role of ‘teacher’ when helping with math homework. All they need to do is ask questions to get the child to think about what they already know about math that could help them approach a problem. For example:
· “What is the question asking for?”
· “How can you represent the problem?”
· “What do you think you need to do to solve this? … Okay, Give it a try and see if it works?”
· “Can you explain to me what you did so far? Why did you decide to …?”
· “Are you successful with this strategy? Do you need to abandon this strategy and try a different strategy?”
· “Do you have the right materials to help you solve this?”
The rest is up to them! It is good to struggle and persevere! Give encouragement (Keep going! Don’t give up! I have confidence that you will find a way!) Tell them mathematicians sometimes spend years and years working on one problem!
What are “just right” number sets?
Not all people learn at the same pace or master every skill at the same time. We all have skills we are good at and skills that are not mastered, YET. Sometimes we are ready for a challenge and sometimes we need to practice using numbers that are easier to manage. All are okay!! We take the advice from Goldilocks and the Three Bears and try to find numbers that are “just right” for us, not too easy and not too hard. When children are really struggling, the first thing I ask them is, “Did you pick the number set that is “just right” for you?” Having multiple “just right” number sets is how we differentiate instruction for those children who need a little help and for those who need a challenge. By the way: you can have your child practice the same problems over again, if you feel they need the practice, by having them use a different number set. It becomes a whole new problem!