I want to share a question with you that has been clanking around my brain for a while. At first I wasn’t even sure if I wanted or was even “allowed” to share and write about this question, but it’s one I keep coming back to. It’s a question that makes me feel somewhat vulnerable. And it’s one I’d love to hear your thoughts about, so please feel free to leave a comment even if, like me, your ideas around this question aren’t fully developed either.
Is there room for math that isn’t hard?
One reason I wasn’t sure I wanted to write about this topic is because I really believe in teaching students to work hard to figure out mathematical ideas. I believe that math can be challenging and also enjoyable. I teach teachers and students that doing challenging work is what helps us construct new understanding. I really believe in the power of the “make sense of problems and persevere in solving them” (CCSS.Math.Practice.MP1) I believe that much of math learning will occur in this way. And yet, I keep coming back to this question. Should all math be rigorous? Should we persevere through all tasks? Or is there a room for something else too?
When imagining strong math communities, I like to consider analogies to literacy communities. In reading workshops, teachers spend time a good amount of time engaging children in read-alouds in which a primary purpose is learning to love books and enjoy reading. As a kindergarten teacher I often read Mo Willems’ Piggie and Elephant books not because they were rigorous, but because it’s fun to read the speech bubbles using the voices we imagine Piggie and Elephant would use. We lingered to laugh for a few moments on the page of David Shannon’s No David that shows David’s naked bottom as he runs down the street naked. In reading workshops book browsing is encouraged. Children squirrel away Lego encyclopedias in their book boxes to pore over with friends. They linger over photographs of animals and come up with their own wonderings like, “Why are reptiles bumpy?” “Why do pigs have curly tails?”
In reading workshop, children should not spend the majority of their independent reading time engaged in books that are difficult for them. Richard Allington’s research indicates that children should be spending the great majority of their reading time engaged in books at their independent level, books they understand and can read accurately. Children need to read and re-read. (This is one quick Allington article, but his work on the topic is much more extensive than this.)
So, I’m wondering, is there a math equivalent of this? If children subsist on a diet that consists only of difficult math, will they learn to enjoy it? Will they learn to pursue it beyond the walls of the classroom? I say that with the huge caveat that I believe challenging and difficult math can be engaging and fun. But I also believe there is space for math that is not terribly difficult, but is very enjoyable.
Strategy games (like Rush Hour, for example) can be extremely challenging. While playing Railroad Rush Hour recently, 5th grader Kevin told me, “I’m only on the first challenge. And it’s already hard. I can’t do it.” He stuck with it though, and figured it out. Kevin moved on to other Rush Hour challenge cards, but a few days later I noticed he was working on that first card again.
“Kevin, didn’t you do that one the other day”” I asked.
“Yes,” replied Kevin matter-of-factly. “But I like to go back to ones I’ve already done and think about it again. It’s fun.”
Was what Kevin was doing the problem solving equivalent of re-reading a favorite book?
This weekend I spent some time at the grocery store with my daughter watching an employee make a giant batch of guacamole. I watched with fascination. “I wonder how many avocados are in that bowl. How many containers of guacamole will that make?” I considered a few ideas in my mind. How much space would ten avocados take up? So, how many groups of ten avocados? I engaged lightly and playfully with the idea. The avocados offered an invitation, rather than a specific task to complete.
I held my almost-two-year-old up to see the giant batch of guacamole. “How many avocados are in there, Lulu?” (She loves avocados!)
“One and one and one and one!” (That’s what her counting sounds like now.) “Dos!” (That means any quantity more than one in her world.”)
It wasn’t hard. For me or for Lulu. But it was kind of fun to think about. I love looking for math in my life. I hope to inspire that in her and the teachers and students with whom I work. I hope to offer invitations to engage in mathematics. Sometimes in difficult mathematics and sometimes in something less serious.
So, is there space for this in our classrooms? Time for engaging, but not terribly difficult math? What other opportunities do children have to just wonder about math? To browse math? To engage in math play? To relax into math, the way one relaxes into a book. Is this important? Is this a thing in math? Is it something professional mathematicians do? Is it something everyone does as they wonder about their world?
I’d love to hear your thoughts.