Inspired by the concepts of 20% time, passion projects, and the great Genius Hour work happening in schools all over the world, I set out to explore what this would like for those of us who don't have our own class (and do math on a rotary schedule).
My hypothesis was this: our math curriculum (an incredibly balanced and strong one here in Ontario) is short on things like the history of math, or the math that makes the world work, or bigger topics that are a little outside the traditional elementary math box, like infinity or dividing by zero.
I wanted my students to explore some math of their choice, so I had to see what topics they were interested in first.
As I am #poweredbykids, I started by watching their brainstorming. My only question was this: "what's something you wonder about that can be answered with math?" I exaggerate little when I say that I could plan my entire math program by just letting them ask questions. Once the inquiry math mindset is open to them, all the old fears and hatred about math fall away. They become questioners, and they start to make meaningful and important connections to the math in the world around them.
The board (now called the Wonderwall) filled with stickys with questions like:
-was math discovered or created?
-I wonder what the last number is?
-is there a pattern that hasn't been thought of yet?
One student wondered how much of a certain substance Toronto's notorious may had consumed, but that question, while mathematical, could not be answered.
These were clearly the raw materials for something really good, but more work needed to be done. We took the odd question down to explore it, but mostly the board just sat like that, for a good two months. One day, reading the questions, it occurred to me what had happened with the brainstorming.
All the questions fell into one of three categories: Googleable, estimateable, or needing more exploration.
Once this realization happened, the hour of our greatest genius was upon us. We watched this astoundingly beautiful video on the beauty of math. I used Numberphile's video on cryptography to show how complicated mathematical concepts could be distilled into a carefully crafted explanation. I showed Kid President's Pep Talk. I explored dividing by zero with them to spark their minds.
As inquiry learning begins with questions, I gave them a simple organizer asking for a big question, and two sub questions that could be explored on the topic.
I discussed these with them, and offered feedback which would help focus the projects. We developed some simple success criteria for what the project could look like. The evaluation could not be pegged to a specific strand, as it usually is (although everything could broadly be said to be about number), so we mainly looked at evidence of mathematical thinking, and how it was communicated. The Ontario curriculum front matter, particularly the achievement chart, is the math teacher's best friend.
From there, they ran with it. The quality of a lot of the projects exceeded expectations. Topics ranged from things like types of infinity, to music in math, to statistical analysis of a number of sporting themes, like determining who will win the NBA championship. Activating the math of sports could be the topic for a whole other post. Students do amazing work when they are shown how much math is in their favourite sports.
One of the most memorable included a live demonstration of poker probability, in which the dealt hands (under the document camera), provided proof of the odds that were posted on a chart of the wall beside. Another sought to prove whether Santa Claus could make all his deliveries in a single night.
The only slight challenge I would say is helping your students make more research-based topics come alive (like infinity). Some projects were more research-based, and less based on mathematical technique, while the best of them had students actively developing their own mathematical technique to explore their topic.
I would encourage anyone to start on the road to #GeniusHour math. It's worth it. Too often (and for too long), we have let math ferment in its little silo. Strands and units create artificial boundaries that prevent students from making connections to their own lives. Math is seen as something that comes from teachers, in specific class periods, at specific times of day. Finally, we are too often the questioners in our math classrooms. Let your students be the questioners, and see what happens!