A Teacher's Guide to Using CGI Problem-Solving Strategies in the Classroom

 

If you're looking to spice up your math lessons and make problem-solving a blast for your students, CGI (Cognitively Guided Instruction) might just be the focus you're looking for. Here are some key strategies of this approach to help you along the way.

Direct Modeling

Direct modeling is a specific strategy in CGI where students use physical objects, drawings or their fingers to solve a mathematical problem. It's a great way to make abstract concepts concrete, especially for our youngest learners. It is often one of the first strategies that young children use when they are learning new math concepts. For example, in a kindergarten class the following problem was given:

 "There are 5 apples on the table. You get 3 more apples. How many apples do you have now?"

In direct modeling students might use counters to represent the apples. They place 5 counters on the table, then add 3 more counters. They count all the counters together to find the answer, which is 8.  The counters helps to visualize the problem and makes it easier for them to solve the problem.

Counting Strategies

Next, let's talk about counting strategies. These are a step up from direct modeling and help kids move toward more efficient problem-solving:

1. Counting All: For beginners, start with counting all the objects. If the problem is 5 + 3, they count all 8 objects from scratch.

2. Counting On: Encourage students to start with the larger number and count on. For example, if they have 5 + 3, they start at 5 and count "6, 7, 8."

3. Skip Counting: Teach them to count by twos, fives, or tens to solve problems faster. This is super handy for multiplication or larger addition problems.

Relational Thinking

Relational thinking helps students see the relationships between numbers and understand that they can break problems into smaller, more manageable parts:


1. Number Relationships: Show students how numbers relate to each other. For example, in 8 + 7, they can think of it as 8 + 2 + 5, knowing that 8 + 2 makes 10.

2. Decomposing Numbers: Practice breaking numbers into parts. With 14 - 6, they can decompose 14 into 10 + 4, making it easier to subtract 6.

3. Using Known Facts: Encourage them to use what they already know. If they know 5 + 5 = 10, then 5 + 6 is just one more, so 11.

Standard Algorithm

Finally, let's talk about the standard algorithm. This is the traditional step-by-step procedure for solving problems. While CGI emphasizes understanding over rote learning, the standard algorithm is still useful:

1. Start Simple: Begin with basic addition and subtraction problems. Show them the steps clearly.

2. Practice, Practice, Practice: Give plenty of practice with different problems. Use visual aids and examples to help them understand each step.

3. Connect to Understanding: Make sure students understand why each step works. Link the algorithm back to the concepts they've learned through direct modeling and relational thinking.


Using CGI strategies can transform your math lessons and help your students become confident problem-solvers. Give these strategies a try and watch your students' math skills soar! Happy teaching!