Instigator. Not a word we usually associate with something good. Often we speak of “problem” students as instigators of mischief.
The second module of the Making Math Moments workshop changed my perception of what it means to be an instigator. I already knew part of my job as a math teacher is to get students thinking about math. I also knew that I needed them to be curious about math in order to allow that thinking to occur. I preached this message to everyone who would listen for years.
The problem? I knew WHAT needed to happen but I lacked the knowledge of HOW to make it happen. How in the world can I get kids who have been abused by mathematics instruction in the past and who are terrified of math class to be curious?
My values and beliefs were not reflected in my practice.
I have to say this module’s content finally gave me the tools and structure to make this happen.
The past few weeks of school have been challenging for me. Combine the winter blues with a super long commute, lack of sleep, and random two-hour delays from days upon days of rain and wind and cold. I have been exhausted. I have been frustrated by the behavior choices of my students. I have been considering throwing in the towel. In fact, I had resorted to here’s your lesson, here’s some problems, we will talk about the answers tomorrow format just to have some sort of structure that limited the time students could {theoretically} be off task.
If you’ve read any of my posts, you might understand that this caused a tremendous internal battle for me. I know this isn’t the way to go if I really want my students to learn, but at the same time I didn’t have the energy to think about anything else. Only a few more days until spring break….let’s just get there.
One morning this week, as I previewed this 8th grade lesson on Exponent Review , I made a snap decision. I would enlarge the animation in the second slide so that students could not see the context or the growing numbers at the bottom of the screen and I would ask the students to Notice & Wonder. We watched the clip once to just see what was happening. Then I played it again before I asked them to make some notes to share.
Students Noticed:
More time = more dots
[The growing number of dots] Reminds me of asexual reproduction
Dots are orange
Dots are filling a square
Students Wondered:
Will it form a picture?
Is it {the number of dots} multiplying by itself?
How many dots?
Is it adding the same number {doubling} each time?
When did it stop multiplying?
Is this zooming out?
Is the number of dots being squared or cubed?
Pausing at each new frame, we watched again to see if any of our questions could be answered. We determined that in the first couple of changes, it was clear the number of dots was doubling. Of course, we didn’t take time to count how many were in the last image, but students were hooked. It was here that we paused to take in the context of the problem, how many coins we would have if the one we were given magically doubled in quantity each day for 28 days.
And then, something magical did happen. Students took on that pensive stare. Not the one that means they are on vacation somewhere in their minds, but the one that means they are really thinking and trying to make sense out of what they’ve just been told. Then, from a student who is particularly challenged in math I hear,
Wait. Can I do the math?
Asking for estimations…and reminding estimation comes BEFORE exact calculation…really gave me some insight into where students are in their understanding of number. The too low estimates ranged from 500 to one million while the too high list contained values from 1000 to one trillion.
After spending some time “doing the math,” we narrowed the estimates. A few students were low by one factor of two while another was one too high, but many of them were on target. They were curious about the “real” answer, so we came back together and talked about using an exponent to shorten the expression {the point of the lesson} and a couple of students used an “accuracy checker” {aka calculator} to verify calculations. Even though they wanted to know the exact number of coins, I wasn’t really concerned about that. The important thing to me was that I felt like they really understood how these exponent things work.
The rest of the week was spent applying the concept of exponents to powers of 10 and I presented this in a similar format. It took longer than I expected for us to get through the entire lesson (multiple days) but in the end I do believe they have a better understanding of the concept than if I had done a more traditional-to-me lesson. Hopefully, they will be able to transfer this understanding as we move to powers of powers next week.
Most of my students are slow math thinkers and slow workers in general so we have not yet “covered” as much content this year as we need to. Teaching in this curiosity format feels slow right now. It requires patience as students work through the ideas and arrive at their own place of understanding. Even so, I am beginning to see for myself how slowing down to spark curiosity can actually speed things up. I am already thinking ahead for next year and am interested to see how being a Curiosity Instigator from day one will change the math culture in my school.
I’m Curious…
Educators, are your lessons more traditional or more discovery based? How do you get your students interested in math?
Parents, do you use your child’s natural curiosity to dive into mathematical concepts and discussions?
What sparks your own curiosity in your daily life?
I’d love to hear your thoughts in the comments!
Until next time, let’s go make some meaningful math moments!
