What is C.G.I.?

At some point in your child’s education you will hear the term C.G.I.  No, Kindergarten may have changed drastically from when you were little, but they are not learning how to develop computer generated imagery. We’ll leave that to the experts at Pixar.  Here it means Cognitively Guided Instruction. Whoa!   Okay, to put it simply, it’s another way to teach math.

When you and I were growing up, the teacher likely taught arithmetic in the traditional format with algorithms that couldn’t be altered. You had to demonstrate two digit addition by carrying the one into the tens place, etc. We were forced to make connections to mathematical symbols like +, -, = and so forth before making connections to real world problems. Meaning that we had to learn that 2 + 2 = 4 before we thought about the fact that if I had two Barbies and my friend had two Barbies, that meant we had four Barbies altogether. C.G.I. instead allows kids to connect to their world first and then gradually make the connections to the mathematical symbols when they are developmentally ready.

C.G.I. also requires that the teacher listen to the child verbalize how they solved a math problem and use that information to guide their math instruction. Kids are way smarter than we give them credit for. They can figure out how to solve a multi-step math problem or a multiplication problem.   They may not use formal algorithms but they can solve their problems and explain how they did it!

Still confused? Let me explain how C.G.I. looked in my Kindergarten classroom. The class was given a story problem on a small sheet of paper.


Paul has 3 pieces of candy. James has 5 pieces of candy. How many pieces of candy do they have altogether?

We would paste this problem in our math journals. Then students were given a math toolkit to use to solve this problem if they wished. The beauty of C.G.I. is that students can work at their own developmental level to solve the problem.   Toolkits contain a variety of math manipulatives to help solve the problem, such as unifix cubes, teddy bear counters, bean counters, etc.   Yet, if they didn’t need a concrete visual representation to solve it, they could draw a picture in the journal. As the students were solving the problem, I, as the teacher, would walk around the room helping where needed and identifying student’s strategies. After a set amount of time, I would have several students using a variety of  strategies show their method for solving the problem to the class. This helped them verbalize their thinking and showed other students different ways to solve the problem. At the end, we would write the problem into the formal algorithm.    3 + 5 = 8

There are several types of story problems that your child will learn throughout the year including addition, subtraction, multiplication and division.  Some of these may even require several steps.  Basic addition and subtraction story types include:   Result Unknown 3 + 2 = __    Change Unknown- 3 + ___ = 5 Start Unknown- ___ + 2 = 5

At the beginning of the year, your child’s math time may consist of free exploration time with the math manipulatives. It may seem like playtime but this time is very important. At first, teddy bear counters will seem like toys to five-year-olds. Therefore, the teacher gives them time to basically get the “playing” out of their system. This way when it’s time to actual use these counters as tools in math, your child will have already made patterns, sorted them, made them talk, etc.

Now that I know, what do I do?

Create your own. Make up your own story problems using family members, neighbors and friends. Allow your child to create some as well. Use everyday household items for your child’s math toolkit and be sure to challenge your child with all types of story problems. Don’t get hung up on writing 2 + 2 = 4. It’s important that your child learns this eventually but first give her the chance to explain how she solved a problem in other ways.

Things to consider:

It’s never to early to practice math story problems as these will be on state assessments in years to come.


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Filed under 5 Year Olds, Questions

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