By Zachary Champagne and Michael Flynn, posted
March 14, 2016 –
As two educators who have attended and led a
myriad of online and facetoface professional development experiences, we have
come to realize that we get the most from these experiences, both in the moment
and over time, when we are challenged to engage in the mathematics. We
understand, and probably both held the position at one time, that this may seem
trivial to elementary school mathematics educators. However, it has become
clear to us that engaging and exploring the mathematical ideas embedded in our content
standards is essential to becoming better consumers of information and
practitioners in the classroom.
We would like to pose one simple idea—Doing
the math is important and can lead to a fundamental understanding of important
mathematical ideas. First, we would like to explain what we mean when we say, “Do
the math.” We will then pose our opinions and share experiences about why we
think this is important. In our followup blog entry, we will pose two examples
of math problems that are worth engaging in to deepen an understanding of two
topics in the Common Core State
Standards for Mathematics in elementary school.
When we say we are interested in doing the
math, we mean just that. We, as educators, should be “genuinely
curious” about the math that we teach. We should try
out problems that are connected to the work our students are doing and look for
connections to future content, explore a variety of models, and discuss our
ways of thinking with our peers in an effort to push our own thinking forward.
Thinking about the mathematics with which our
students will engage is critically important for a variety of reasons:

It allows us
to reflect on the prerequisite skills and concepts necessary to engage with the
math.

It lets us
consider a variety of pathways into the problem and the different
representations.

It helps us
anticipate pitfalls and places where students may get off track.

It deepens our
understanding of the content.

It presents an
opportunity to interact as learners with our colleagues as we genuinely explore
the content.
We have had experiences with this work in
different situations. One experience that stands out was an opportunity to
consider models and contexts for dividing fractions that gave us a much
stronger understanding of what it means and looks like to divide a fraction by
a whole number and a whole number by a fraction (5.NF.B.7.a), interacting with
the content from the standpoint of a learner through an authentic learning
experience. We found this work made us better educators because we had an enhanced
sense of how our students experience this work. Gaining a deeper understanding
of the content and ability to anticipate potential roadblocks for our students
allowed us to develop and plan better learning sequences.
So, at this point you may be asking yourself,
“What does this look like?” Well, first and foremost, it is not necessarily
just grabbing a problem from the textbook or curriculum materials that your
students will be using. This may be useful in some instances; however, we found
that asking authentic questions as learners is a good way to start. Building on
the example above, perhaps that learning experience could begin with a such a question
as, “What does a visual fraction model look like for dividing a fraction by a
whole number?” Or perhaps the question is, “What is a good story context for
dividing a fraction by a whole number?” After that comes the difficult part:
finding a good problem or model to help with understanding that content. We
don’t claim to have all the answers here.
Your
Turn
Now
it’s your turn. What is your view of doing the math as a means of professional
development? If there is a particular math problem that has recently challenged
you, tell us about it. In our next post, we will offer two example
problems that groups of teachers may wish to explore.
We want to hear from you! Post your comments
below or share your thoughts on Twitter @TCM_at_NCTM using #TCMtalk.
Zachary Champagne is an
Assistant in Research at the Florida Center for Research in Science,
Technology, Engineering, and Mathematics (FCRSTEM) at Florida State
University. Previously he taught fourth and fifth grade mathematics in
Jacksonville, Florida, for thirteen years. He is currently interested in
learning how young students think about mathematics and how to help them
understanding that mathematics makes sense. He tweets at @zakchamp. Michael
Flynn is the Director of Mathematics Leadership
Programs at Mount Holyoke College in South Hadley,
Massachusetts. Previously he taught second grade in
Southampton, Massachusetts, for fourteen years. He is currently interested in
how primary and elementary school students develop algebraic reasoning and how
teachers can support that work. He tweets at @mikeflynn55.