I like to think I’m an entertaining story-teller. Even the driest of mathematical procedures (quadratic formula derivation, anyone?) can come to life when I’m in performance mode. But over the years I’ve lectured less and less, giving students more autonomy to follow their own paths of inquiry. Students work in small groups on real world scenarios, experimenting, drawing conclusions and solving complex problems while I facilitate, motivate and occasionally lecture. Here a few tips on how to drop the mic and let students pick it up in math class.
1) Ask Curious Questions
How much taller is a human compared to a carpenter ant? How much faster can a sailboat go if you double its length? How many trees per person are there in the world? If you flip two coins, are you more likely to get two heads or one head and one tail? If you double the radius of a pizza, how much more food do you get? What function is the best model for a car accelerating from a stop light, and why? Can you figure out the percentage of green m and m’s in the world from one bag?
Every student has an innate curiosity about how the world is put together. It can seem that the abstractions of algebra are outside daily experience, and yet there are ample opportunities to draw numbers from the real-world and spark excitement. The above questions can springboard into deep conversations about exponential notation, square root functions, probability, area, quadratic functions and sampling.
2) Not IKEA. Not Home Depot
Assembling a piece of furniture from IKEA is such a choreographed experience that creativity is a dead end by design. Conversely, if I walk into Home Depot to build a house without a blueprint the project will end before it begins. It’s important to find materials which strike the right balance between providing guidance and allowing students to experiment. Courage To Core math materials are classroom tested tools for algebra and geometry, and many other teachers are creating and selling great materials on Teachers Pay Teachers, Amazon and beyond which offer students the chance to actively engage in carefully guided experiments.
3) A Contained but Spacious Playground
A classroom which gives students greater autonomy to collaborate needs a structure. (See my prior post on how to create expectations and effectively play the role of facilitator in classrooms centered around group work.) Building a culture of self-directed students takes patient effort at the outset, but once groups are humming along it can be an efficient and effective learning structure and a great way for a teacher to observe each student in action.
4) Be the Lifeguard They Trust
In swim class when you were a little kid, you let that one lifeguard throw you in the deep end of the pool. He’d let you struggle when you were capable, but you knew he’d fish you out if you were in real trouble. Students need to know that they can visibly struggle with mathematics and that you’ll let them go at it as long as they need to. They also need to know that you’ll throw them a lifeline if their group is lost at sea. Finesse that line carefully.
5) The Calm Center of the Storm
Students are adept at following rules, but they are often even more adept at blurring the lines. Play at school can be an act of mild rebellion or it can be intrinsic to a learning environment that is designed to engage the voracious appetites of young minds. Once you allow students to engage more freely, the classroom can be a more productive yet more chaotic place. The usual distractions still interrupt work flow, but when group work is working, students take more responsibility for maintaining the work culture, and conversation and invention are steered toward productive ends.
6) Nothing Wrong Means Something’s Wrong
Once we have fired a curiosity with a good question and given them the basic rules of engagement, students need to experiment, fail, and experiment some more. The path of least resistance is also the path of least persistence. Mistakes are the necessary accidents on the path to deeper understanding. Of course, this process can take time…
7) Game Never Over
It can be tough to fit student-directed work into the rigid schedule of the school day, and tempting to sweep kids towards wrapping up when they are still deeply working in progress. As much as possible I don’t put time limits on activities, so that students can self-pace and own their hard fought success at the end of the proverbial day. In my experience, at the beginning of the year students are less efficient as they adapt to the structure but by the end of the year move through assignments efficiently and effectively.
A student-centered, collaborative classroom environment takes a bit of effort to set up, but the rewards are great. Students learn to communicate, collaborate, persevere, bounce back from failure, think creatively and problem solve more confidently. Check out my prior posts for more hints on how to implement a collaborative model in high school math class. If you drop the mic you may help more kids find their singing voice.