Resources mentioned in this episode:

Beyond Answers: Exploring Mathematical Practices with Young Children by Mike Flynn

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Welcome fellow Recovering Traditionalists to Episode 38.  Today we are looking at how to help students Look for and Make Use of Structure.

Before we get into the episode I wanted to take a moment to say thank you.  We aren’t even to 40 episodes and we are almost at 100,000 downloads of this podcast!  Thank you so much for listening in and if you haven’t already, please make sure to subscribe.  The more subscribers the podcast has, the more downloads it gets, and then the algorithm behind the scenes starts to push the podcast out to get it in front of more educators.  Your subscription and downloads helps this podcast reach even more educators out there each week. So thank you so much for your support. Let’s get into the book I want to share with you.

Did you noticed that when the new standards came out there were no standards about Patterns in the early grades?

This came up in a private Facebook group that I do for my students of the Number Sense courses.  We were discussing why kids have a hard time with counting. Counting is all about looking for and using the patterns and that brought up the discussion about how the standards had no mention of investigating patterns in the early grades. 

When the standards came out, most teachers went to the grade level standards to find out what they needed to teach for their grade level.  Many people skipped the Standards for Mathematical Practice. These are 8 standards that describe how students should interact with mathematics at all grade levels, thus they were not inside each grade level because we should be doing them at all grade levels.

Math Practice #7 is Look for and Make Use of Structure and that is where you can find mention of patterns.  One of my favorite books about the Standards for Mathematical Practice is Beyond Answers by Mike Flynn.  I love this book because it’s written for primary grades teachers and gives lots of examples of young kids working on these big mathematical practices.  It’s so cool to read.

In Chapter 7, Mike talks about Math Practice #7: Look for and Make Use of Structure and he relates it to the movie the Matrix (which I’ll admit I’ve never actually watched).  He talks about how there are structures in our number system, in the properties of operations, in geometric shapes, and so much more. On page 151, Mike writes

“And like Neo in the beginning of the movie, students can interact in this mathematical world without really knowing about or understanding the intricacies of these structures.  In essence, they can have a very limited worldview of mathematics. However, if students are provided opportunities to explore the structures in meaningful ways, they can exploit them just like Neo does.”

He goes on to show what MP7 looks like through stories of kids in the classroom and then on page 154 he writes:

“More often than not, our wok around MP7 in the primary grades is subtle and spontaneous because it emerges from the work our students do in the moment.  When we notice students using structures, we can simply ask them about it as a way to draw their attention to the fact that there is something important about those ideas…..

Supporting MP7 really comes down to this:

  • Recognizing when students are working on an idea connected to structure and bringing the idea to the surface through questions and comments
  • Giving students opportunities to see and explore a structure in their own work or in tasks designed to highlight particular structures
  • Providing time for students to build an understanding of it
  • Supporting students as they apply their knowledge of the structure in novel task.

It is important to note that teachers and students do not need to name all the underlying mathematics to be able to see and use structure.  Many structures are easy to recognize, even if they aren’t always easy to express. Kindergarteners notice very early in their math work that when they add zero to a quantity, the amount does not change (5+0=5).  Although they apply this idea in their daily work, it’s safe to say they aren’t thinking about it as the additive-identity property (nor should they).”

This book gives much more detail and examples about MP7 as well as all the other Math Practices.

Now remember with all of these episodes I don’t go deep into the book or article because if this is an area you want to learn more about, then I want you to go learn it straight from the source.  We are all different learners and teachers and what I take away from a book or article might be different than what you take away. So if you want to learn more about implementing the Math Practice Standards, especially in the primary grades, then this book is for you.  I’ll link to it on the show notes page buildmathminds.com/38 and make sure you go there first if you want to get the book because Stenhouse has given me a discount code for you to use.  So go to buildmathminds.com/38 to get that code and buy the book. 

Also, for those of you who are members of Build Math Minds, Mike Flynn has done some trainings for us.  He’s done the Virtual Math Summit every year and he did a mini-course all about the math practices in the young grades.  You can find all those videos inside your BMM member area. For those of you who are not BMM members, you can get on the waitlist to join when we open up registration.  Just go to buildmathminds.com/bmm

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As you start off the school year, I want you to keep in mind what is really important as we're trying to teach mathematics to our students.