CGI, or Cognitively Guided Instruction, is a student-centered strategy for teaching math. You start with what your students already know and build on their individual number sense and approach to problem solving at all levels. Research shows that CGI increases students' math success, teachers' math knowledge, and student problem solving achievement. In a CGI focused classroom, teachers pose thought provoking questions for students to solve using a variety of strategies. Students then must be able to explain their thought process for teachers to use their thoughts and strategies to guide further instruction. Now that we have discussed what CGI is, let's talk about how we can put the strategy into action in our upper elementary classrooms.

Step 1: Getting Started

First, start with a word problem covering your current topic or skill. The best approach is to project the word problem for everyone to see. (If you are the fun teacher, who has their students come to the floor for instruction, I would pull my students to the floor with nothing in their hands.) For my example, I am going to use an addition problem, but you would follow this same strategy with any skill.

Cheryl loves to draw using colorful markers. She has 156 colorful markers in her playroom. In her desk in the office, she has 271 colorful markers. How many total colorful markers does she have?

### Step 2: Analyze the Problem

Students need to read the word problem silently. I have them read it TWICE in their heads. When they finish, they give a thumbs up in front of their chest and wait quietly. Then, one person reads the problem out loud. Sometimes, I will choose a student to read, other times I will read the problem out loud to them.

Next, ask the class basic questions about the problem. What is happening in the problem? Is there any information we can cross out in the problem? What would the equation be? Now that they have thought more about it, ask them number sense problems. Is the answer going to be greater than ___? Is it going to be less than ___?

For our example, I would cross out the start of the problem. It is great that she loves drawing with colorful markers, but that has nothing to do with solving the problem. Students should say we are combining two amounts of markers, or adding markers from two places. The equation would be 156+271=M. For the number sense questions, I may ask if the answer will be greater than 500 markers or if it will be less than 300 markers.

### Step 3: Show me what you know!

Following our discussion, students are sent back to their seats to work the problems out independently. I love allowing students to use dry erase markers on their desks so they don't have to take anything else out. However, they could also use dry erase boards or just their notebooks. Students can use whatever strategy they are most comfortable with. As they get more confident with CGI, they will want to come up with more ways to solve the problem.

As students are working, the teacher walks around looking for different strategies that students are using to correctly solve the problem. The teacher wants to find three students who are using different leveled strategies, and solving the problem correctly.

1- Base ten

2 -Mix of strategies

3 -Advanced problem solver - uses the algorithm

I will write a 1, 2, or 3 on the students’ desk. This tells them they will be sharing with the class and allows them to look over their work to prepare. Some students will finish early. If they do, I will tell them to try and solve the problem another way while they wait (this is awesome for your advanced students).

### Step 4: Students become the teacher

Once most students have solved the problem, give a one minute finish up warning and then have everyone come back to the floor (if they started down there) or just have everyone put their writing utensils down. Call student "1" up to the board to work out the problem their way, then student "2", then student "3". As they get more comfortable with sharing and "teaching" their classmates, they will start explaining the process they are using. Encourage them to share their thought process. Students who may have done the problem wrong or only knew how to do it using a base ten strategy, now see their classmates work the problem out in a different way and get a chance to hear the problem explained.

It is important to remember that every student comes to class with some kind of math knowledge. They may not be on grade level or they may only be able to show what they know using base ten blocks. However, even while using the basic strategy, students can be successful. Using CGI often in your classroom allows all students to show what they know and build on their mathematical understanding. It all starts with number sense. Number sense questions are the foundation of mathematical knowledge.