CGI Charts

Is it Day 2 and there are already so many amazing things happening during CGI. Students are showing so much tenacity with their approach to problem solving - even if that means drawing and counting lots of circles!

During the discourse, the teacher records student strategies on chart paper so students can reference the strategies shared when they do other problems of the same type. It is very intentional that the chart is not created on a smart board or white board. We want students to be able to see the strategies and use them.

Most of our teachers have at least 2 classes per day and the organization of this can feel pretty overwhelming. Mr. F at KALE came up with an amazing display to keep his charts organized for students. He has room for a weeks worth of charts from both of his classes and clips to easily put the most current problem on the top of the stack. Thanks for sharing your great system!

Awesome Resource: Word Problem Generator

Last week in Boston, I was able to hear Greg Tang speak and it was incredible! I could have listened to him talk about strong math instruction all day. Besides being a great speaker and mathematical thinker, Greg Tang also write children's books about math. If you have not checked them out, I highly recommend them. A few of my favorites...

During his talk, he shared a new free resource on his website. 

With this tool, you can select an operation, problem time, location of the unknown, and the number range. You can either print a list of problems or you can display to project and work on together as a class. Students can also use this independently. There is a hint button that will give them a model to help solve. It is a really awesome tool!

Cognitively Guided Instruction: Introduction

One of the most helpful resources in learning more about CGI is the book Children's Mathematics: Cognitively Guided Instruction. They recently came out with a new edition and it is full of incredible resources. As I really spend time on each chapter, I will share with you key takeaways, as I know teachers don't always have the time to read through entire books about teaching strategies :)

Introduction: The book starts by explaining the ideas behind CGI and the goals of teaching math in this way. It does not promise to provide a model for the perfect CGI classroom, because each one is unique. Rather, the goal of the book is to give teachers the chance to collaboratively and independently make sense of the principles in relation to their own classes and teaching styles. In elementary school we are learning about whole numbers which should provide a foundation for learning about fractions and decimals, and lead to a seamless transition to learning algebra. 

The introduction really just set the stage for how to approach the reading and principles that will be presented, stay tuned for chapter 1 that focuses on children thinking and problem types...

CGI Charts & Number Lines

Yesterday, I spent the morning at KAO and was amazed by the awesome job they are doing with CGI story problems. Kindergarten can be especially challenging, because everything is new to them but kindergartners were digging in with so many different strategies and couldn't wait to tell you all about them.

In our PD last week we talked a lot about how to get kids to try out other strategies and one idea Ms.R came up with was providing students with a number line. We didn't want to print the number line on the paper because that would choose their strategy for them, so they decided to put number lines on the table alongside the cubes that students can write on and tape to their papers.

So many students were doing great work with the number line and many were drawing their own rather than using the print out. It has really increased the use of different strategies in their room!

Here are the charts from the 2 classes that show all the amazing strategies that these Kindergartners are coming up with:

Also, notice the great idea around taping another chart paper over the first, so you do not have to re write the problem for both classes. Nice time saving trick for teachers who have 2 classes per day :)

So excited to see how these students continue to grow as mathematicians!

Cognitively Guided Instruction Book Study

Since winter break, many more teachers have begun working on a CGI problem solving block. It is so exciting to see the work that our students are doing, all the strategies that they are showing, and the conversations that they are having about Math. With all these new trials, there have been many questions come up that have pushed my own knowledge of CGI.

I got the newest CGI book a couple months ago and reading it has been on my list for quite some time. I know that there are some amazing things in it and I cannot wait to learn more about CGI and continue to work with our teachers. I am going to read each chapter and create a post with a summary of that chapter, key takeaways, and some questions to think about. I think it will be really helpful to have a reference for what is in the book and where to find information about certain topics. I will begin reading and posting tomorrow and go chapter by chapter through the book.

Please feel free to order the book and read along with me :)

Planning for CGI

Cognitively Guided Instruction is not as based in planning as the traditional math lesson. The most important aspects of planning for an effective CGI lesson is selecting a problem and anticipating students responses.

Selecting the problem can be challenging because you want to make sure it is a realistic, familiar context and that students can solve in multiple ways and share their thinking. Anticipating responses ensures that you know where the lesson is going and which student work samples you will highlight to get at the learning goal for the day.

According to the newest version of Children's Mathematics: Cognitively Guided Instruction, the prepared CGI teacher:

• Chooses problem contexts that are accessible
• Ensures students have tool available to them to support their thinking
• Encourages students to do what makes sense to them
• Makes sure all students have a way to get started 

So much of CGI is adjusting instruction in the moment and changing course for the next day based on what students did today, this makes the planing process pretty basic. 

Here is an example template that can be used to plan for the lesson:

Here is the link to download a copy. 

Here is an example of a completed template for Kindergarten. 

Happy planning!

CGI Problem Solving: Recording and Posting Strategies

Across campuses, most teachers are implementing student led problem solving times. Some campuses are doing it following the CGI model, others are doing Worthy tasks, and others are doing a problem of the day.

All are great ways to make sure that your students are applying their math skills and thinking critically about math problems on a daily basis. The use of technology in the classroom is amazing - engages students, is time efficient, and allows for less prep work. While going over problems and sharing strategies, showing student work using a power point, white board, or doc cam accomplishes the same goal as charting it out on chart paper. The difference comes in students being able to reference strategies. Students need to be able to go back and reference past successful strategies to help solve more complex problems. Here are some examples from KIPP Houston of how they chart and organize past charts.

Using Cubes for Problem Solving

This week Mrs. Doyle and I had a great chance to see some CGI problem solving in action. KIPP DC has done a lot of work this year to push their students thinking and problem solving skills. One big takeaway we had is that students need cubes to directly model the problem. Understanding the context of the problem and being able to show what is happening is crucial for student understanding.

The cubes should be readily available and in towers of ten, of all the same color. We keep them in towers of ten to help students with base ten thinking. When they always start with groups of ten, they are much more likely to use base ten strategies to make counting and operations more efficient.

Cubes should always be out and being used during story problem time for K-2 and can be easily stored and hassle free!

As you can see, 1 black cube got mixed into the blue cube box. You have to really work with students on keeping them organized and putting them back into tens at the end of the lesson, but that can definitely do it!