The Value of Noticing and Wondering in Math
Last Friday, our staff worked with math educator Annie Fetter (@MFAnnie) as a part of our professional development related to our TERC Investigations mathematics curriculum. Annie shared her observation that, like bumps in the road, often the goal with math is to find the right answer and be done. She has witnessed this mindset at many schools during teacher training sessions, particularly when it comes to state testing–where the focus is completing the worksheet, solving the word problem, finding the answer, and moving on.
At Miquon, we see things a little differently. We focus on sense-making over answer-getting.
To bolster this constructivist approach to mathematics, Annie led us through a discussion about the huge value that comes from noticing and wondering.
It sounds pretty different from what most of us did growing up, right?
Well, yes. Yes it is.
The idea behind noticing and wondering is simple. When learners take the time to really notice math problems and to consider the wide variety of strategies for solving those problems, they are actively engaging their critical thinking skills. As a result, they are better able to make sense of the math. In fact, they are better able to understand it.
Take a look at this image, and think about which one doesn’t belong. What makes each number different from the others?
Think about what you notice. What do you wonder? What do you know about 9, 16, 25, and 43? What do know about their relationship to one another? I am not going to tell you the answer. Instead, what I will tell you is that on Friday, Miquon staff were able to justify a rationale for why each of the options — 9, 16, 25, and 43 — didn’t belong. They did so by noticing, by wondering, and by putting their math knowledge to work.
How about this equation? How would you solve it?
Would you stack the numbers one on top of the other, like many of us were taught in school? Or would you add the 20 and the 40 and then the six and the nine? Or would you convert 26 to 25 and 49 to 50 to create an easier equation?
Of course any of these approaches work; they all yield the correct answer.
Consider, though, for a moment, all of the learning and value in working through all three approaches. In doing so, were you better able to understand these numbers and how they relate to one another? Unequivocally, we think so.
In reflecting on this idea of sense-making and looking back on the school year, we want to thank all of our amazing staff and our wonderful families for all the work you did to help us grow and stretch and better understand each other as a community. We appreciated the many ways in which you helped your children improve their understanding of the world around them and the times you resisted the urge to just get through to the answer.
Here at Miquon, we know that answer-getting is just skimming the surface. We would much rather walk the path with you and your children, take the time to notice and wonder, and make sense of the world around us together.
We wish you a lovely summer ahead, and we look forward to hearing all about your adventures when you return in the fall.
Resources for You and Your Family
- The New York Times article about the usefulness of noticing and wondering as tools for understanding and navigating the avalanche of data available to us in today’s world.
- The books, Which One Doesn’t Belong? and How Many? by Christopher Danielson this summer!
- The quick five minute video from Annie and the Math Forum.