Imagine…
Imagine a math class where 2nd grade students solve only 1 or 2 problems a day.
This class has no worksheets, textbooks, required homework, or teacher’s guide, yet by the end of the first semester, most 2nd grade students are able solve addition, subtraction, multiplication, division and simple algebraic word problems. The students always show their work, and they always explain in writing the exact steps used to solve the problem.
This math class is not a fantasy, nor is it part of a gifted and talented program. I worked in this classroom and witnessed the magic with my own eyes. Nearly 25 years have passed, and I still look back at that experience with amazement.
My Experience
In the fall of 2001, I student taught in a second grade classroom at William Ford Elementary School in Dearborn, Michigan. No Child Left Behind had not been implemented yet, and Common Core was still a few years aways. Teachers in my area had fewer curriculum demands, smaller class sizes, more paraprofessional help, and a lot more creative freedom.
Most of the students in the class were bilingual, spoke only Arabic at home, and had at least one parent who did not speak English yet. Some had been born in the US, and others recently immigrated here.
How could a group of 7 and 8 year old ESL students perform so well in math when they only had to solve one or two problems each day?
CGI
My supervising teacher, Kris McKinnon, used an approach to math called Cognitively Guided Instruction (CGI). She believed that writing was integral to every topic she covered, including math, and CGI was a great fit for her classroom.
Here’s how it worked:
- Before the children arrived, the teacher wrote a word problem on a whiteboard. After the students put away their belongings and submitted the lunch count and attendance, they copied the word problem into a designated math notebook and got to work solving it.
- After the students solved the problem, they were required to write down the steps they used to solve it using words like first, next, and then. (This teacher taught the same class in 1st grade, so the kids already had experience with CGI before I came along. A lot of pre-teaching took place the prior year.)
- Each day at least 3 children would have to stand at the front of the classroom and show the other kids step by step how they solved the problem. The 3 children usually represented 3 different ways to solve the problem. Perhaps one child drew a picture to solve the problem, one used a number sentence to solve the problem, and one used manipulatives to solve the problem.
Examples
Personalized Instruction
There were many ways Kris personalized instruction for her students:
Quick workers could:
- receive an additional problem with larger numbers or more complexity
- write their own problem and exchange it with another quick student
- mentor students who were struggling with the work
Challenged workers could:
- meet with the teacher or another adult in a small group to work on the problem
- meet with a student mentor 1:1
- receive a similar word problem with smaller numbers or less complexity
Think about all the different things the kids practiced during “math.” Not only were they practicing problem solving skills, they were also reading, writing, communicating, learning from peers, seeing different problem solving methods and more!
This type of math can easily be reproduced at home. Start with small, age appropriate numbers. Make adjustments for your kid as needed. Maybe you write the problem in yellow highlighter, and your kid traces the letters. Maybe your kid dictates the steps he or she used, and you write those steps down. Get creative! Perhaps you start by focusing on just one part of the process and add another part in a few weeks. As long as your child gets to read, write, problem solve, and verbally explain what he or she is doing, you’re doing a good job!
Learn more about CGI:
Here is what AI has to say about CGI:
Here is more from Heinemann:
https://blog.heinemann.com/what-is-cognitively-guided-instruction