The Power of Popsicle Sticks

Content is not important to this post, but it sets the context. We looked at derivatives of exponential functions on Friday, starting with the derivative of y = e^x. We do this by looking at values of f(x) and f'(x) and then calculating the ratio of f'(x) to f(x). Today, we explored finding derivatives of exponential functions from first principles. I therefore didn't think there would be any issues when I asked them all to complete this:

And I might not have known that this was neither clear nor obvious had it not been for Popsicle sticks.

This is my tin of Popsicle sticks for my morning class. I have one for each of my afternoon classes as well. I generally go with the "no hands up except to ask a question" rule which means that the one or two extroverts in the class who have all the answers are not the only voices heard. I choose a name randomly to answer a question and then quite often choose another name to add thoughts to the first response. A response of "I don't know" is okay and is often followed by several other "I don't know"s which tells me that we all need to take a step back.

This morning's Popsicle sticks told me a lot. I went through a lot of sticks - there was a huge pile outside the tin - which means that there were many answers (some right, some not) to my questions and much "What do you think?" from me as I chose another name following each answer. When this happen I have them talk in their groups to see if they can make connections together before trying again. 

The Popsicle sticks help make my classroom a learning space where everyone has a voice and every voice is important. I do my utmost to make it a safe place where making mistakes is not only okay, but important. In addition to that, Popsicle sticks help me be a better teacher. They help me gauge the understanding in the room (I do thumbs up-sideways-down a lot, also) and help adjust the pace and choose what we need to practice in the moment. This is still a work in progress for me, but one that I think is important to help me grow as a teacher and to ensure that my students truly understand what we are doing, not merely mimic completed examples.

I first read about using Popsicle sticks in Dylan Wiliam's Embedded Formative Assessment. Here is a video about this strategy and here is his website.