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Video series prior videos
#1: Why you shouldn’t teach math through a textbook
#2: How to Teach Elementary Math Without a Textbook
#3: Creating School Change When Others Don’t Want To
#4: Components of Number Sense in PreK-2
#5: Components of Number Sense in 3rd-5th
#6: Teaching Math through Story Problems
#7: Math Practice: Building Math Fluency through Games (releases 10-17)

• Download the Guide to Teaching Elementary Math Without a Textbook
• Teacher’s Guide to CGI from the University of Wisconsin Oshkosh
• Cognitively Guided Instruction: A Knowledge Base for Reform in Primary Mathematics Instruction by Carpenter, Fennema, and Franke.
• Children’s Mathematics: Cognitively Guided Instruction by Carpenter, Fennema, Franke, Levi, Empson
• 5 Practices for Orchestrating Productive Discussion by Smith & Stein
• Robert Kaplinsky’s How Old is The Shepherd? Video
• Dan Meyer’s TED talk – Math Class Needs a Makeover

It is not teaching kids steps and tricks to solve problems, like CUBES and Key Words. Those things need to go away. 

It is not saving the story problem for the end of the lesson after the kids have done 20 bare problems, just so kids get that real world connection. 

I’m a believer in using context, or story problems, to teach the mathematics. We don’t add in the story problem at the end to help kids see a connection to it, we start with story problems to begin with.

Cognitively Guided Instruction – What teaching math with story problems should look like

The basic premise of CGI, this is a summary version of it, but the idea is that you give kids a problem in context without any instruction and you just let them solve it using their own intuitive understanding of the mathematics and you watch to see how they approach it. And then, what they discovered is this progression that kids go through with their solution strategies for addition, subtraction, multiplication, and division, and that progression is something you need to watch for as kids are solving the problems and then you help guide them to more advanced solution strategies as you see that they are ready for it. But one of the things that is underlying Cognitively Guided Instruction is this idea of the problem types.

I’m not going to go too deep into it. I’ll show a picture here of the CGI problem types for addition and subtraction. 

There’s also one for multiplication and division and you can find them very easily by Googling “CGI Problem Types Chart.”

I’ll also link below to some of my favorite. These problem types have kind of gotten used in the wrong way, I guess I should say, is that often times we look at these problem types and we teach kids how to solve each of the different problem types. The idea of the problem types is to understand them for ourselves as teachers because the type of problem that we give students will partly determine the solution strategy they use. There are kids who will solve problems in one problem type and then you give them the exact same numbers in a different problem type and they can’t solve it. 

So, if you want to learn even more about Cognitively Guided Instruction, I’ll link to one of their research articles and I’ll link to the book that details it out for you guys underneath this video. But I just want to give you one quick example of why the story problem type makes a difference. So let’s use this example:

“Sierra has some money. She earns $17. Now she has $36. How much money did she begin with?” 

To adults that seems like we could pull out the numbers and subtract, which is why our textbooks will often put that kind of a story problem in a subtraction lesson because yes, you can take 36 and subtract 17 and get your answer, but that problem is not a subtraction problem to kids. 

To children, it’s basically, she has some, so like you could put a X, you could put a circle there, whatever you want to put, she has some. She got 17 more, so you add 17 and now you’re at 36. To them that is not a subtraction problem. They need to figure out what to add, what added to 17 gets them to 36. 

They’re not seeing it as subtraction and yes, later down the road, yeah, we want them to see all of those relationships and be able to use subtraction to solve it, but if we jump straight to, just solve this with subtraction.  This is where kids start to become what my friend Graham Fletcher calls Number Pluckers. They just start plucking out the numbers and trying to operate on them, thinking that it doesn’t need to make sense. I just need to perform some kind of operation. 

So the premise of CGI is to really understand kids’ solution strategies, give them problems based upon the problem types and where you think that they would be able to solve things and then you watch to see how they’re solving it. How are they intuitively thinking about that problem? 

Now the other cool part about knowing the problem types is that once you know those problem types, you could really put in any numbers that you want. 

You could take Sierra’s problem there that I just had and you could replace it with some with decimals. You could even put fraction in there. You could even make it single digit, right? It just depends upon what your students are working on. You could totally use that same story problem, just replace the numbers to be something that’s appropriate for your students at the time. 

Now another key component to teaching with story problems in mathematics is really what I like to refer to as the missing piece. 

5 Practices – The missing piece of teaching math with story problems

Once they solved a problem, I would have kids come up and show and tell about the strategy that they used to solve the problem. Then they would go sit down. Another kid would come up and show and tell about their strategy, another kid would show and tell, and then I would just end the lesson. 

But one of the key pieces to using story problems in your classroom is the discussion that needs to happen about the different solution strategies. Once you have kids share, the powerful piece is connecting those strategies. If kids are feeling, if you see kids kind of toning out when kids are sharing their strategies, it’s because they aren’t seeing the connectedness between it.  

So one of the jobs for us as teachers when we’re teaching through story problems is yes, letting kids share, but then weaving the thread of connectedness. Helping kids see how this strategy is similar to this strategy. How are they alike, how are they different, what do you see? And build relationships around solution strategies. Don’t just do the show and tell. 

One of the best ways I ever learned to do this was from the book, 5 Practices. Now I just call it the five practices but it’s the 5 Practices for Orchestrating Productive Mathematical Discussions and I’ll link to that below this video as well. It walks you through how to make that time be the most productive that it can be and it’s such a powerful piece. And most of us are doing it incorrectly, I know I was. So that book really helped me out. But it’s all about monitoring for certain solutions, picking the ones that you want to come up so that you can weave that connectedness for the students.

Where to get tasks to help you teach math with story problems

That’s one of the most powerful ways to do it because you can write them using your kids, your students names. You can write them using number sets that are appropriate for them. What kind of numbers should you have in there? And context that matter to your students. 

Every year there’s a new fad coming around. Video games, whatever it is that your students are interested in, write story problems using those contexts. So, create your own. The other thing is, it doesn’t have to be story problems like the typical story problem frameworks, there are lots of cool ways that you can encompass this problem solving atmosphere in your classroom. 

One of my other favorites is through the use of Three-Act Math Tasks. Now Graham Fletcher is one of the leading experts in that for elementary school. Upper grades, Dan Meyer was one of the first people to get started in that from junior high and high school, but I’ll link to Graham’s site where he lists all of his Three-Act Math Tasks that you can use with elementary students. 

The last thing I’m going to link to underneath this video is how to modify your textbook. One of my favorite videos that got me started in this was Dan Meyer’s TED Talk about how the math classroom needs a makeover and he talks about how he modifies a high school textbook, but that gave me so many ideas about how to modify textbooks in the elementary and middle school as well. 

All of those will be linked below this video and I also want to remind you that there is a guide that I have available for teaching math without a textbook that I would love for you to go check out that you can get your hands on and it talks you through all of this whole video series. And don’t forget the rest of the videos are linked below this video. 

I hope that this video has built your mind around how to teach mathematics through story problems because they are one of the best ways to build your students’ math minds. Have a great day.

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