What I love about inquiry, besides everything, is being able to see how kids think. Today, I gave my students the locker problem as part of our mathematical number and problem solving focus. It’s an open-ended, inquiry-based, mathematical problem. Last year, my students spent almost a week on the problem. They skyped with another class about it. They were involved. I tried it again with my class this year, and after one hour, there was already so much already coming out. Just listening in on the students gives me insight into how they’re thinking, and I like it. Here’s the locker problem:
There are 100 lockers in our hallways. Each August, the school caretakers add a fresh coat of paint to the lockers and replace the broken nameplates. The lockers are numbered 1 to 100.
There is a silly tradition at our school. We celebrate the first day of school with this routine. The first student runs down the hall opening every locker. The second student closes every second locker, beginning with locker number 2. The third student reverses the position of every third locker, beginning with locker number 3. The fourth student changes the position of every fourth locker, beginning with locker number 4. This continues until the 100th student goes, changing the position of the 100th locker.
At the end of this ritual, which locker doors are open?
We’ve been studying factors and multiples, so students had the vocabulary to discuss the problem. I pointed out manipulatives we had available, including 100 charts and tiles. I read the problem to them, but after that, I let them loose in groups of 3. From then on out, I watched. I listened. I videotaped and took some pictures.
What I heard and saw was:
- mathematical vocabulary
- revision of plans
- natural problem solving strategies that hadn’t been directly instructed
- use of manipulatives
- Beginnings of some “ah ha” moments
One girl, for example, who is new to English, was able to predict, in English, how the number 1 would of course remain open since it wouldn’t be touched again. Another student started thinking about patterns and how that might help. Another group broke the 100 lockers into 3 groups so they could work with a smaller problem. Another group divided 100 into 3 so they could each work on a part of the problem and then come together as a whole at the end–divvying up the work. Some went out in the hallway to look at the lockers to see if that might give them some ideas. Others tried one strategy for a while, failed, and then tried a different one.
A great recent post recently by A.J. Juliani discussed the benefits of 20% time and inquiry-based teaching. One quote in his post was from Edutopia on inquiry-based research: “Research shows that such inquiry-based teaching is not so much about seeking the right answer but about developing inquiring minds, and it can yield significant benefits.” And as the research points out, involvement leads to understanding.
I agree. The locker problem seems to be a prime example. The kids are involved, and they’re drawing their own conclusions. It’s hard, but I refrain from pointing them in any direction, so they’re solving their own problems. They’re thinking like inquirers and scientists, trying one thing, and when it doesn’t work, trying another. They’re asking questions. They’re revising. They’re talking about Math without even thinking about it.
Schools are beginning to jump on the idea of 20% time because it gives students time to inquire. There’s a big movement, encapsulated in part here and through Twitter @geniushour.
Do you do inquiry? Have you tried 20% time or genius hour? How does it affect your classroom? If inquiry leads to so much learning, shouldn’t we be doing it 100% of the time?