“The problem is that most of the middle school teachers don’t have a specialty in math.”

When I heard that statement, I knew it bothered me.  But at the time, I was unable to articulate exactly why.  There are a lot of problems with education, many more with math specifically.  But I know that pointing the finger squarely at the grades below is both unproductive and damaging.  Not only that, but when we are convince ourselves that groups of teachers lack certain “necessary” content knowledge, we close our minds to anything else they can teach us.

I’ve had a busy couple of weeks at AFT Thinking Mathematics training for 9 days and then straight on to Twitter Math Camp for another 5.  Both of those experiences will change my teaching for the better, and I found a common theme throughout:  Listen to what elementary and middle school teachers can teach you about mathematics pedagogy.

We talk about connecting representations of mathematics like graphs, tables, and equations.  But how often do we connect what kids do in elementary grades to what they experience in high school?  We lament in high school about kids lacking number sense, but how do our classroom routines support and build on the number sense kids have created through the primary grades?

Notice the similarities between the Ten Principles of Thinking Mathematics and the NCTM Math Teaching Practices:

Credit: AFT

Credit: NCTM

I know those are dense, but they are the foundation of what we need to do in order to improve mathematics education.  Every shift we make needs to be based in these principles/practices.  And the ideas need to connect from counting to arithmetic to algebra to calculus and all the places in between.  We can no longer be complacent in teaching as we were taught.  Doing so means committing negligence toward a generation of students who need a deeper understanding of mathematics in order to use it successfully in the world they create.

Tracy Zager brought it all home for me with her keynote at Twitter Math Camp.  Here is her blog post with the link to the slides and the video.  I heard the same things the research had been telling me over and over in Baltimore:  We need to listen to each other.  There isn’t a hierarchy of teaching from elementary through post-secondary.  The conversations between vertical groups of teachers are important – even necessary – to helping our students develop as mathematicians.

Here are some pictures from the AFT Thinking Mathematics Training (credit:  AFT)