# Casa di Mir Summer Mathematics: Adventure #10

###### Noticing and Wondering

As summer winds down and families turn to the start of school and fall activities, our last summer mathematics adventure is neither a destination, nor an activity, but rather a journey to a mindset of noticing and wondering about the world around us, and by extension, the mathematical ideas that help us understand that world.

Shifting to Noticing and Wondering. You may have read in earlier summer mathematics adventures, my frequent suggestions to ask your kids, “What do you notice? What do you wonder?” That’s an idea that I shamelessly stole from Annie Fetter at The Math Forum. The basic idea is to give your kids the space and time to think a little on their own, and formulate their own observations and questions about the world around them. If you are a parent who likes to answer every question that your kid poses as completely and correctly as possible, this might take some practice.

How do you do it? Here are two strategies.

1. When you are out and about with your kids, practice noticing and wondering out loud, and use this to draw them into the conversation.
2. When your kid poses a question, respond with a question and be open to whatever ideas he/she shares with you.

This helps build your children’s curiosity about the world around them and their belief in their own sense-making skills, both of which are essential for success in school mathematics and in life in general. I highly recommend taking a peek at Annie’s short presentation titled, Ever Wonder What They’d Notice?, a presentation at a conference for mathematics teachers. See https://www.youtube.com/watch?v=8BEzDHJ7ocQ.

Out and About. What places (besides school) do you go during the week with your kids in tow? What might you notice that could elicit some wondering?

• At the grocery store: “I notice that there are several different prices for milk. I wonder why some are more expensive than others, which one is the best deal, which one has the farthest-away expiration date…”
• On a walk around the neighborhood: “I notice that this house has pavers for its driveway. They are all different shapes and sizes of rectangles. I wonder how the measurements work together, how many pavers there are in the whole driveway, how long it took to install, how much it cost…”
• Walking through a parking lot: “I notice the parking spaces are slanted rather than perpendicular to the aisles. I wonder if these spaces are more or less slanted than those in other parking lots, how much space there is in each aisle for cars to back out, if the parking lot could fit more cars if the spaces were perpendicular…”
• Buying a book for a friend: “I notice there aren’t any graphic novels. I wonder what other kinds of reading your friend might like, what his interests are, how old he is, if he likes beautiful illustrations…”

Answering Questions with Questions.  This strategy has value for all kinds of questions, not just questions about school work. From the youngest kids’ wide-eyed wondering queries of “Why?” to your older kids’ exasperated queries of “Why?!?!” you can nearly always turn that question back to them and find some genuine thinking and understanding on their parts. Asking the question, “Well, why do YOU think it might be that way?” or “Well, what might be some reasons for that?” really pushes your kids to consider another perspective or even multiple perspectives and maybe even to think about cause-and-effect or actions-and-outcomes. These are very broad problem-solving skills that can powerfully impact their success in school mathematics and beyond.

Go forth, and notice and wonder with your kids.  Even if it’s slow-going at first, stick with it and prepare to be amazed by what your kids share with you.

About the author: Trisha Bergthold has been the middle school math teacher at Casa di Mir Montessori School since 2014. She holds a PhD in mathematics with emphases in curriculum and pedagogy. Prior to her work at Casa di Mir, she designed curriculum for kindergarten through college level. She also taught university-level mathematics courses for sixteen years.