CGI Math Book Study (Part 1)

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A problem was posed to me recently, and I’d like to share it with you.

A teacher is taking 19 students on a field trip. The bus they are taking has seven seats. Student may sit two or three to a seat. How many students are sitting in each seat?

I’ll wait while you work on the problem…

Did you figure out the answer? How did you figure it out? Did you draw a picture? Count? Invent an algorithm? There are most likely many different solutions to this problem, but I’m not interested in solutions. I’m interested in your process and your reasoning.

Recently, I purchased the second edition of Children’s Mathematics: Cognitively Guided Instruction (2015, Thomas Carpenter, et al). My intention was to read it on my own, but a colleague offered to guide me through a book study. She’s a math coach, and knows this book well. I was so appreciative of her offer, and I jumped at the opportunity. My hope is to share my learning with you through this journey.

I was first introduced to CGI Math in 2015. At the time, I was teaching third grade at a public elementary school in my community. Teaching math has always made me nervous. Math itself makes me nervous! I’m not a “math person.” I did really well in math until second grade. Regrouping in subtraction was my first real mathematical challenge in school. I just could not understand it! My amazing teacher spent so much time working with me to show me how to “borrow from next door.” I didn’t completely understand why I had to do that, so I had trouble remembering to do it. At some point, I remember taking a quiz with 20 subtraction problems with regrouping, and I got all but one of them correct. My teacher helped me celebrate by giving me half a bagel with cream cheese. It was a good day. But, I continued to struggle with math for the rest of my academic career.

Up until I was introduced to CGI Math, I taught math the same way my teachers taught me to do math. I was taught to memorize facts and procedures. Sometimes I was successful, and sometimes I wasn’t. And, that translated to my students as well. But, when I heard of this cognitively guided instruction wizardry, I had to find out what it was all about. My early experiences involved a lot of trial and error — much like the relationship I’ve had with math nearly my entire life. Slowly, however, I started to see what the fuss was all about. I could see that my students could solve problems in their own way, with their own reasoning. I was never given the opportunity to reason my way through math. It’s made me wonder if my relationship with math would have been different if this method of instruction had been available to me. I have to say that I’m absolutely hooked into this type of instruction! Knowing that this could possibly save a student from a lifetime of thinking that they can’t do math has made me want to keep learning more about it!

So far, I’m in the early stages of the book study. My main take-aways have been that math is all about reasoning and process. I’m fascinated by the different ways students figure out how to solve problems. In the next few weeks, I will be learning more about different problem types and the various methods students use to reason through those problems. I’m looking forward to sharing all the bits of information I learn.

Until next time… HAPPY PROBLEM-SOLVING!