I was visiting the Great Lakes Science center with family during high school. I was busy reading information printed on a horizontal rotating triangular prism - the three sides had facts about the phenomenon being demonstrated at the exhibit, though I don't remember what the exhibit was about. While I was reading, a younger student came along and stood in front of me to view the exhibit. He barely paid any attention to me; his attention was piqued when he placed his hand flat on the prism and it rotated slightly under the weight. He then proceeded to flick the prism as hard as he could to see how fast he could make it turn. That was how he spent a couple of minutes while I looked on, flabbergasted by both his lack of interest in the flashing exhibit in front of him and the fact that all the exhibit inspired him to do was to challenge himself to a spinning competition. Once he was satisfied that he had peaked in the spinning task, he went off to a new exhibit.
I was pretty annoyed as a sixteen year old science enthusiast. How dare he not take the time to read what was printed at the exhibit? Not even try? There was so much good knowledge there to be learned - why bother coming to the museum if you weren't going to try to learn something new? The best part for me was coming and playing with the exhibits and then seeing what science principle was being demonstrated. This was (as I understood it at the time) what science was all about.
For me, this was not something that was limited to museum visits. I had a pretty good arrangement for doing investigation at home as well. I was always able and encouraged to go outside and explore in the woods, burn stuff with magnifying glasses (not of course while doing the previous activity), and do experiments mixing things in the kitchen. I am incredibly grateful that my mom allowed me to do these experiments in spite of my frequent habit of rushing away afterwards without cleaning up. I didn't realize at the time how unique it was that she let me do some of the things I did, and probably would have cleaned up myself more often if I had. (I did do so marginally more often after a particularly stern chat about the difficulties of removing hardened candle wax from the good silverware. She clearly explained that the experiments would stop if I didn't do this sort of cleaning myself.) The other major time I realized I should be grateful was when I accidentally removed the gold coating on a fork during an electroplating experiment. (Sorry mom.)
One that sticks in my mind was after I first learned about objects from space reentering the atmosphere and burning up. I didn't understand how metal objects could burn - I had seen metal melt before on TV, but could it really burn? I took a penny and some cooking tongs to the gas stove and held the penny in the flame for a long time. I was able to see the penny get hot and ultimately glow. I had a bowl of cold water there to drop the penny into afterwards. The colored patterns on its surface reminded me of a picture in a magazine that showed the oxidation patterns on a sample of material that had survived reentry. I also tried wires and aluminum foil in the flame, and the way both materials twisted around themselves and changed both in appearance and material properties gave me some insight into what it meant for metal to burn.
Was there a goal? Not really. I didn't write up a lab report or keep a notebook recording my observations. These were just experiences in which I explored what I could do with the stuff in front of me. I did get the sense that this sort of thing was distinctly different from what I was doing in school because there was no assessment. I don't know if she ever talked to others about her son "playing on the stove" as she called it. At the time I objected to her calling it that because I thought it made it sound like I was being reckless. I had a purpose to my experiments. I was creating meaning on my own as I had done throughout my Montessori elementary education. And I was careful when carrying out these investigations.
Years later, I have a different understanding the role of play in learning. I really like this TED talk by Stuart Brown that talks about some of the reasons why play is important. Much of what I have learned about building with LEGO is in the context of playing in an unguided way. Another major influence on my philosophy on play was K.C. Cole's book Something Incredibly Wonderful Happens, which I heard about during the summer before teaching biology for the first time to ninth graders. The book describes physicist Frank Oppenheimer (brother of Robert Oppenheimer) and the full story of his life as a father, rancher, teacher, and ultimately creator of the world class Exploratorium.
I have visited the Exploratorium twice. There is no other museum in the world that has influenced me in such a visceral way as that museum. as I can still picture numerous things at that museum and what I learned from doing the exhibits. Reading about Frank and his process of seeing the museum as vital was really important to defining something that I think I hadn't officially acknowledged in the preceding six years I had been teaching.
First, some Frank Oppenheimer quotes from a speech he gave upon receiving an award from the American Association of Museums, along with my thoughts:
Many people who talk about the discovery method of teaching are really talking about arranging a lesson or an experiment so that students discover what they are supposed to discover. That is not an exploration. The whole tradition of exploration is being lost for entire generations.
There is a role for discovery in our classrooms. This is not, as is often thought, the expectation that students will spontaneously figure out Newton's laws or the quadratic formula. These are instead carefully designed activities through which students arrive at an idea. Our world needs more interactivity. People, not just students, are spending less time constructing their own understanding, and more time (since we are all inherently busy) hoping that others can explain things to us since it will invariably be faster this way.
If one of the things, however, we want to teach students is how to construct their own understanding, this is not going to come from giving them information and then telling them how to use it. Any way we can engage students to interact with the material actively instead of merely receiving content moves us closer to that goal.
It is, therefore, more important than ever that museums assume the responsibility for providing the opportunities for exploration that are lacking for both city and suburban dwellers. It would be fine, indeed, if they would, but it will take a bit of doing to do so properly. If museums are too unstructured, too unmanageable, people get lost and simply want to get back to home base. On the other hand, if they are too rigid, too structured or too channeled, there are no possibilities for individual choice or discovery.
It may be useful to note that these quotes are from 1982. Certainly these issues are no different nearly thirty years later. If lesson activities for students are too unstructured, they may have no idea of the learning goal, what they are supposed to figure out, or how to get from one point to another. They get lost. They get cranky. They would rather just be told information. This, however, is the opposite extreme. While some students demand the structure, there are serious limitations to the quality of learning experiences under a classroom model that is too rigid.
Exploring, like doing basic research, is often fruitless. Nothing comes of it. But also like basic research, as distinct from applied or directed research, exploring enables one to divert attention from preconceived paths to pursue some intriguing lead: a fragrance, a sight or smell, an interesting street or cave, an open meadow encountered suddenly in the woods or a patch of flowers that leads one off the trail, or even a hole in the ground! Often it is precisely as a result of aimless exploration that one does become intensely directed and preoccupied.
A museum that allows exploration does not have to be disorganized either physically or conceptually. It does, however, mean that the museum must contain a lot of which people can readily miss, so that discovery becomes something of a surprise, a triumph, not so much of personal achievement as of personal satisfaction. It is the kind of satisfaction that invariably leads me to tell someone about the experience.
When people in a museum find something that engages them, that moment of engagement is what justifies the museum's existence. That may be what the visitor remembers about their museum experience. It may also be the sort of experience that causes the visitor to come back, and ideally, bring a friend or child. A well designed exhibit involves its visitors in its operation, tries to engage them, and along the way provides interesting information in the off chance a visitor is interested. A good museum has many of these experiences.
Here is the key idea that changed the way I decorate my classroom, organize my lessons, and structure my time with students:
You cannot entirely control what your students will get out of their time with you.
I have spent lots of time designing what I thought were perfect lessons only to have students remember the fact that I used colors in my handout, even months later, because that was what stuck with them.
You can tell them what you want them to get out of an activity. You can assess that they got out of the activity what you wanted them to get out of it. You can also try to tell them why something should be interesting to them. (Not recommended) None of these work well, at least authentically well when it comes to evaluating our use of an activity to reach specific learning goals.
What you can do is provide a range of activities, approaches, and experiences for your students. Providing students a chance to play in your classroom is one of the most powerful tools in our tool chest. You can't play incorrectly. You can't get playing wrong. Play is one of the few times when the only judgments being made belong to the individual that is playing. In the world of math education where students still see math as a class where there is always a right answer, and that right answers are inherently worth more than wrong answers, we need play more than ever.
What does play look like? Not like the majority of lessons I do, admittedly, but I'm working on that. The real reason this doesn't happen as often as I want it to is that it doesn't necessarily feel productive. I force myself to push through this because I've had the idea of clear learning goals and measurable objectives drilled into my head from the moment I started teaching. The problem is that real learning doesn't look like this. When we figure things out, it isn't with the end goal in mind. Unstructured time to just be in the presence of an idea that motivates itself is enough to get students to think as they do during play.
The biggest tool that we have at our disposal though is the use of technology. I've seen students discover by accident that when you hit the equal sign on some calculators, it repeats the previous operation with the answer. What do most students do when they discover this after multiplying? They hit it a bunch of times until the calculator overflows. Sometimes they will do the same thing with multiplying a decimal, and the number of zeroes to the right of the decimal point increases. Is there a lesson on place value or exponential functions there? Sure. The moment you tell them that though, it suddenly ceases to be exploration and starts becoming Math Class.
It's also easy to create a Geogebra sketch of a quadrilateral with measured angles and tell students to "play" with it for five minutes. The goal is not to have them discover the sum of the interior angles is 360 degrees, though they might observe that. The goal is instead to give them a chance to interact with a mathematical object and have an experience that is all their own. Then start the lesson. See what happens. This is exactly what Noah Podolefsky from the PhET physics simulation project at the University of Colorado recommends students be allowed to do for 5 - 10 minutes before telling students what you want them to use the simulation to do.
The other aspect of this is in decorating my classroom. I don't want so much on the walls that students will be continually distracted. I do want things that create interesting learning experiences without much effort. I hung a spring between two corners of the room as an example of a catenary curve - students don't care about that. They do walk by it all the time and make it bounce up and down. Sometimes they see how long it takes for the vibrations to die down. Sometimes they hang things on it to see how it changes the droop in the overall spring. I have a bicycle wheel that normally is used as a demonstration of conservation of angular momentum. Students have instead spun it and observed that it stays upright like a top on the table. I have a checker board with checkers, the game Set, little metal puzzles, and a bunch of other things that don't require a whole lot of explanation to be interesting. It's amazing to see how the students use their down time to interact with these objects and with each other - it makes my classroom the same safe learning environment of a museum. The dream is to create this environment during every single lesson.
Looking back, the kid that stepped in front of my at the Great Lakes Science Center wasn't learning what the exhibit designers intended him to learn. He was, however, constructing his own knowledge when he spun the prism as fast he could. He might have gotten some notion of what feels different about a force and a torque. He might have seen that the rotation only increased in speed while his hand was in contact with it - an intuitive concept related to Newton's 2nd law.
Or not. It was pretty hypocritical of me to judge and potentially hamper his learning process when so many others (including my mom, who had many good, flammable reasons to do so) did not. He wasn't using the museum wrong - I was. He was just doing what came naturally.
Entirety of Frank Oppenheimer's speech to the American Association of Museums, 1982 can be found here.
I also find myself going back to this article written by Oppenheimer about teaching as a quick reminder of all sorts of important ideas.