I’m teaching Statistics this year to a group of seniors who are energetic, interested, and, well, seniors. They are most interested in class when they are being drawn in by our class activities. Today, I planned an exercise to lead us to a discussion about standard deviation. After bouncing around ideas about what numerical data we could collect within our classroom, we decided on number of siblings. I put our data up on the Smartboard, and began to calculate some of the representative numbers we have been discussing, including the mean. I then created a column to look at how far each data point varied from the mean, and summed that column. The sum was zero so I asked about why that might be the case, and whether that implied anything about our data. A few kids had some thoughts to share but as a whole, the group was not entirely sure. Then, someone suggested changing our data. We tweaked the information from someone who had 1 sibling to change them to having 37 siblings. Our column sum was still zero! How could this be? The uproar in the room as we played around with putting different numbers in our data set to see if we still had a column sum of zero was impressive. I still felt a pull to progress with the lesson I had planned, so I did mention the term standard deviation before they walked out the door, but I keep thinking about that noisy moment.
In this course, kids have an opportunity to talk and think about math, without always needing to do the calculations by hand. There are some students in the room for whom this opportunity is freeing, and it allows them to show me (and themselves) that they are capable of doing many things in a math classroom. Earlier in the year, we had an equally lively discussion following a homework assignment where I asked them to watch this TED talk, featuring Peter Donnelly, Part of the talk focuses on tossing a fair coin numerous times, and how frequently the pattern of “heads-tails-heads” would occur, versus “heads-tails-tails”. As we shared our thoughts on the footage, the students got riled up, debating Donnelly’s theory with their own sense of what would (or should) happen. Almost every students was involved, and it was loud! This may have been our second or third day of class for the year, and it seemed to bode well for what our Statistics class would be.
In teaching this course, after having taught for over seventeen years, I am letting go of some of the emphasis on algebraic detail which has been part of every other math class I have taught. However, I find myself mulling over how much I have gained, already, in the first month of the year. My students are getting loud, debating about math. They are shocked when a cell in a spreadsheet stays zero, even when we change our data. For perhaps the first time in their math lives, they are seeing math that draws them in, makes them want to ask questions, participate, and push back. How can this energy be carried over into other classes? How can I share out and remember what is working well, so that I learn as much as I can from this experience too? As I ponder these questions, mostly I am just thinking about how much I enjoy what I do.