“All I Really Need to Know I Learned in 4th Grade” and Mathematical Freedom


Our 6th grade Math/Science Teacher, Becky Bob-Waksberg, presented this talk, “All I Really Need to Know I Learned in 4th Grade” at the Ignite event at CMC South 2017 in Palm Springs, CA as part of one the keynote events. Ignite sessions are dynamic, fast-paced, and inspirational 5-minute talks from the best mathematical and teaching experts in the nation. Each speaker gets five minutes, using 20 slides that audo advance every 15 seconds, whether they’re ready or not! Luckily for us, they got video recording of the talk so we get a peak inside of her thinking! Read on for some of her reflections on “Math Talks” and mathematical freedom.

This past weekend I presented at the California Mathematics Council conference and got the opportunity to hear Jo Boaler speak. She shared her research about how much more students are able to think and learn in math when they feel ‘mathematically free.’ It got me thinking about the times I see our 6th graders show a sense of mathematical freedom.

On the first day of 6th grade, students walk into the math classroom to see the number 24 written on the board followed by the instruction, “Record anything you can think of about this number.” Some students don’t believe the instructions at first.

“Anything? Really anything?” they ask.

My answer: “Anything.”

As they work I walk around and share out some of what I’m seeing, such as, “I see students finding factors; I see students using addition and subtraction; I see students thinking about where they see this number out in the world.” Students then share with a partner and write down at least one new idea. I then call on some students to share out with the class and, once again, students must write down a new idea.

We start class with this warm-up routine every day. We call it Math Talk.

There are two main expectations for Math Talk: students need to use up all the work time they are given (there is no such thing as being ‘done’), and they need to challenge themselves.

Within this simple routine are some of the hallmarks of our mathematics program:

  • Tasks are low-floor high-ceiling: every student can enter the task, and there are also limitless levels of challenge embedded within it.
  • There are multiple paths to correctness: I sometimes hear a myth about math that there is always one right answer. In reality, there are often multiple correct answers depending on the context, and there are almost always multiple strategies for getting to the same answer. When we share ideas in Math Talk, we practice the truth that the correctness of an answer lies in the reasoning and explanation.
  • Knowledge is socially constructed: Humans learn from and build on the thinking of others. In Math Talk, students try out ideas they’ve heard from peers on previous days, and trends even arise – last year, showing everything on a number line became all the rage.
  • Mathematics centers on curiosity: Mathematicians pose problems and then work at solving them. In Math Talk, students take ownership over deciding what they want to find out about the prompt.

One of the joys of my job is hearing fresh ideas and ways of thinking that I never would have thought of myself. The more mathematically free my students feel, the more energized I become in my teaching and my own mathematical thinking (because yes, the rumors are true – I solve math problems for fun).

The next time you find your family with a few free minutes, try it out: what could you write about 24? You might be surprised with what you come up with yourself, and you might be really surprised by what you learn from your child!