The Rookery

Today we had our first math talk.  It's a technique that I learned more about while taking an on-line course from Jo Boaler this summer.  The focus of her research is shifting math students from a fixed mindset about their math ability to a growth model which enables them to learn math more effectively.  (Here's her book, What's Math Got to do With It?)

In a math talk, students answer use mental computation to solve a problem.  Individuals then explain the path they took to the answer.  Students who are able to articulate their approaches are better able to generalize that approach to new problems.  Further, students learn new ways to think about number by listening to others.

To me, these talks illustrate clearly that math is a creative process.  Even when we are arriving at a single "right" answer (which is certainly not how most of math works) our brains take us on different journeys.  Once children perceive math as a creative process, it becomes less intimidating.  There is no secret one way to do something.  It honors the work of figuring things out.  And, importantly, "failure" might just be a side step on the journey…maybe even a necessary detour.  It's not a dead end.

So today we gave it a go.  I put a pattern of dots on the board and asked the students to count the dots and to pay careful attention to the path their brains took to get the answer.  Did they group dots?  How did they group them?  What were they thinking.  The dots are at the beginning of this post.  Take a moment to count them.

The Herons shared more than twelve different ways of counting the ten dots.  They listened carefully to each other's approaches and often built off of one another's responses.  "Mine was like ______'s except that I did ________."

As the teacher, I listen I try to record each child's approach on the board.  I often have to ask clarifying questions and children will often correct my understanding of their thinking.  I'm using images and equations to show models of their thinking — a skill they will all be working to develop this year.  Click on the below image to expand it and see if you can find your approach among those shared by the Herons (I could go on for paragraphs about the different approaches…perhaps another blog):

Cathy and the Robins did a very similar number talk this morning and in the afternoon, we swapped classes.  I asked the Robins to count our dots and then did a shortened number talk with them.  The Robins were very interested in approaches the Herons' took and compared them to the ones their class had used.  At the end of our short discussion, I asked how many students had counted my dots differently based on the approaches they had heard as part of the number talk that morning.  Many students shared they had tried a different way.  Almost all of the children reported being surprised at how many different pathways there were to the same answer.  Many said they expected almost everyone to use the one they had used.

That means a single fifteen minute discussion had begun to shift their ideas about math.  It was very exciting.  Future number talks will include mental computation of more complex problems but we'll develop that complexity slowly, building trust and a repertoire of techniques as we go.