I would use teacher pacing on these screens as well so that students can’t go ahead. The next four screens are also formative, and are more focused on multiplicity, where I find many students get tripped up when working with polynomials. Nothing crazy, just trying to see where student thinking is and help them do some informal work sketching and seeing sketches of polynomials. Then, I would pause and project a few examples anonymously to discuss why they are or are not polynomials, and show students a few different ideas of what the function could look like. I would use teacher pacing here, so that students can only work on these two screens and can’t go further ahead. They are meant to give me a rough idea of how my students conceptualize polynomials. The activity is linked here if you’d like to play along.īelow are the first two screens. I’m having trouble clearly articulating what I like about this activity that I don’t find in some others, but I’ll try to lay out what I was going for below. And I want it to stay laser focused on a few key ideas that I want to get across. I want this activity to provoke useful thinking, and to do so using tools like sketching and interactive Desmos graphs that are impossible with a pencil and paper or whiteboard and marker. There’s nothing very flashy about this activity, no high-engagement tasks that students will want to keep coming back to. My goal was to bridge some of the gaps between using vocabulary to describe polynomial functions and writing polynomial functions that meet certain conditions. I wanted to design a new activity, one that falls after Polygraph at the start of the unit but before students start doing more formal algebraic work. Students just end up fiddling with different functions until they find something that works, and in the process they may or may not learn what I want them to learn about polynomials. It can be great for certain features of polynomials, but can also suffer from some elements of task propensity. Students solve challenges where they need to build functions that meet certain conditions. I’ve previously used this Desmos activity. My polynomial units often feel flat and uninspired and I wanted to add a wider variety of activities. I spent a bunch of time this summer thinking about polynomials. They are valuable activities and I’m glad I am able to use them.īut in this post I want to offer an alternate perspective that tries to avoid the challenge of task propensity. They let students see math as a dynamic process, learning about objects that make sense and follow certain rules - and learning those rules is what learning math is all about. These activities are incredibly engaging - students love them, and are often asking for more. Marbleslides offers one paradigm for what Desmos activities can look like. They are likely to solve Marbleslides challenges through trial and error without paying attention to the structure of the mathematical objects they’re working with, or they get frustrated and use functions outside of the family I want them to learn about. At the same time, I find that a subset of students - usually the students who are already struggling - learn less than I would hope through these tasks. I love Marbleslides and I use variations on it often. Students solve challenges like the one above by rewriting the function so that when the balls drop, they capture all of the stars. I think the best example of task propensity is Marbleslides. I first learned about task propensity through this paper, and you can read the rest of my thinking on the topic here. I’m exploring how task propensity relates to Desmos activities and how this thinking could help me teach more thoughtfully with those tools. In short, they lose the forest for the trees. Task propensity refers to situations where students are so focused on the features of a specific task that they don’t generalize their thinking in a way that is useful to solve different problems in the future.
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