I recently had the opportunity to hang out with an old girlfriend. She was my first crush. She heavily influenced the person I am today. Periodically I would think about her but she launched herself back into my life about a month ago… and I’m smitten!

Like a fine wine she improved with age. Seeing her again made me remember all the reasons I fell in love with her in the first place. She connected with me like no other. I felt smarter each time we hung out. Every time I’d drop her off, I couldn’t wait to pick her up the next day and listen to her stories. Together we’ve developed some amazing children. If you’ve read Cognitively Guided Instruction then we’ve dated the same book… and I’m glad “she gets around!”

I posted about CGI a while back and Katherine Bryant asked if I’d take a sneak peek at the 2nd Edition of *Children’s Mathematics *(released next month)… and I’m so happy she did. After my 2nd go around I can’t help but think how CGI has changed me as an educator.

The biggest thing I came to realize is that students struggle with word problems because they don’t understand what’s actually happening. I found that most students focused only on numbers and never took the opportunity to understand what the context of the problem was asking.

So what usually happened was quantities were embraced, while the context was ignored. I learned that ** understanding the context of the problem should ALWAYS supersede the importance placed on quantities.** Today that goes without saying! CGI hyper-focused this idea for me which empowered my students’ mathematical reasoning. Here’s an example of how:

I’d put a problem on the board and cover the numbers. This frustrated students because they were so fixated on the quantities, but over time it drastically improved my students’ contextual understanding of the quantities…and what to do with them.

Students were asked to set up an equation using the Post-its as variables to explain what the context was asking OR how to solve the problem. This took a lot of time but it was time well spent. When I witnessed students setting up their equations before writing down numbers I was amazed.

After students set up their equation and we’d talked about it for a minute. Then I’d remove the Post-its from the original problem and watch them model through manipluatives or representations. I didn’t realize it then but I was engaging my students in patient problem solving. The information required to solve the problem was time released.

My takeaways:

- It was much easier for me to transition to Common Core and embrace the Standards for Mathematical Practice because they encompass everything that is CGI. Problem solving is at the heart of every CGI classroom. It asks that students construct their own understanding and urges teachers to let go. This screams SMP#1.
- As students are making sense of the problem they are continually contextualizing and decontextualizing numbers then asked to share/support their understanding (SMP#2). The list goes on as all 8 SMPs are strongly connected to the teaching practices employed within CGI.
- I wish CGI had the initials BP (Best Practice). In education, acronyms and programs come and go. For me, Cognitively Guided Instruction is not a program or an acronym…it’s what is best for kids! I’ve learned that the best way to find out what a student knows is to have them share and explain while I listen, observe and ask questions. These are all key components of a CGI classroom.

Many K-5 teachers have read* Children’s Mathematics* but that was before the implementation of Common Core. I would strongly suggest another go around through the lens of CCSS and the SMPs. Only this time bring a friend or create a book study!

Thanks Katherine for the opportunity to preview the new edition! Thanks Turtle for lending me the 1st edition that I never returned. Thank you Dr Ovrick for introducing me to CGI at UGA. And thanks Mike for teaching me the mighty power of a 3×3 piece of paper!

Much love my friends!

Graham, what suggestions would you given to someone trying to implement this practice in middle school? I’ve implemented the use of the 3 read strategy, which worked for many students, but not all. I still have some students who do not connect quantities to meaning.

Hi Jenise,

I would think that this idea works in middle school as well. The best thing I can suggest is give it a try and see how it goes. Maybe show your students Robert’s video to see if that will help drive home the importance of a understand in a context. http://robertkaplinsky.com/how-old-is-the-shepherd/ video and see where.

If you do either, please let me know how it goes.

Graham

Active listening’s companion is active engagement with the material. I see this example as removing the barrier to active engagement. I think it is a great way to engage students in word problems!

Completely agree Cleargrace! Whenever we can remove barriers we make the task accessible for students. Removing the barriers allows for multiple entry points which is where I’ve lost a lot of students in the past. Now if I could just go back and apologize to them.

I love that you are emphasizing understanding!!! Does this mean I need to take my cute “key words” poster down? yes!!! Students are completely eliminating SMP #1 by relying on inconsistent tricks. Very well said gfletchy!

Thanks Katie. I still struggle in having students build stamina when it comes to problem solving. I’m continually reminding myself to be purposeful when selecting a tasks and how I present them to students.

I had also come to this conclusion. I love your way of teaching this “without the numbers!”