When teaching math to children, what is YOUR goal? Is it helping your students get to the correct answer or what’s the math the student is supposed to learn from working on this problem. Before we go any further, please watch the following video.
One solution to just teaching answer getting is, CGI. Cognitive Guided Instruction is a way to teach mathematical reasoning that is developmentally appropriate. It is great because the types of word problems have been researched so that you can guide student thinking and understanding as they move through different types of word problems, eventually mastering concepts and improving mathematical reasoning. The goal is that students become independent problem solvers who can approach and solve a variety of word problems without relying on the teacher to tell them how to solve them. Who doesn’t want to encourage and inspire their students to be problem solvers?
You can help students develop computational fluency by having them frequently solve CGI type word problems and evaluate if their answer makes sense. The main focus at the K-2 level is addition and subtraction, but do not be afraid to use the multiplication and division just to help expand their thinking.
In the CGI classroom, there are different types of problems. Each of the different problem types requires different reasoning processes. Click to print out the types of problems.
Methods used to solve problems are broken into levels. It is important to understand that students will go through these levels as they develop their mathematical reasoning. The student moves from concrete mathematical reasoning to more abstract.
A child using a Counting On/Back strategy is able to hold a number in her/his mind and count on or back from that number while keeping track of the quantity that is added or subtracted using fingers, tally marks, or counters. They use aids such as number lines or hundreds charts to help keep track of their counting. Many students get “stuck” at this level, never really becoming automatic with their facts, instead relying on a variety of counting strategies or technology such as calculators or spreadsheets. That is why it is important to also work on math facts fluency as well.
In CGI, the goal at this level is to understand the action of addition, subtraction, multiplication and
division. After understanding the mathematical action, we will focus on how to record that action using math notation.
The first step in problem solving is… understanding the problem and making sure that it makes sense. For example, take this problem:
There are 125 sheep and 5 dogs in a flock. How old is the shepherd?
Now, watch this video of eight graders who were given this problem:
It is through daily discussions of problem solving that we hope to move students from direct modeling to counting strategies to using number facts to solve problems. If we rush this process the students may be copying our instruction with no understanding. If a student is stuck, reread the problem with them, have them talk it over with their friend, and if you need to suggest something, say that “last year, a student…” It should never come from you, the teacher, try to guide them but do not lead. It is important for you as the teacher to understand, the types of problems and where students are on the developmental level to help them learn math.
In the CGI classroom, some common components are:
- Problem solving is the focus on instruction, with children deciding how they should solve each problem.
- Many strategies are used to solve problems.
- Children communicate to their teachers and peers how they solved their problems.
- Each person’s thinking is important and respected by peers and teachers.
- Teachers understand children’s problem-solving strategies and use that knowledge to plan their instruction.
I want to share with you a Math Note Doodle I created to introduce students to word problem solving. I have included both versions, one that is filled out and one that can be filled out by the student it is up to you which one you prefer to use. As you introduce a word problem, you can talk about each of the components UNDERSTAND, PLAN, and SOLVE as they go through the steps. Add to the doodle notes as students come up with strategies (specifically in the SOLVE section.)
I hope I have encouraged you to dig deeper at Cognitive Guided Instruction for math and see how you can incorporate it in your classroom today.