Drawing in Math Class
Posted by Bowman Dickson
One of my favorite ways to start class is by putting out whiteboards with a problem paper-clipped at the top, and names of random groups. I love it most because every single person is engaged in mathematics within 30 seconds of class starting. In fact, students always ask me a minute or two before class starts “can we begin?” They can’t seem to resist the markers and the problem in front of them. Also, I found when I wanted to use whiteboards in the middle of class and put students in random groups that it just ate up a few minutes in each class, so this just feels more efficient (I’m kind of neurotic in terms of efficient use of class time).
Continuing my experiments with different modes of math whiteboarding, a great whiteboard warm up I tried was having them illustrate related rates type situations for objects that are changing in different ways. For example:
A pumpkin grows in a garden…
1. With a constant increase in the radius of the pumpkin
2. With a constant increase in the volume of the pumpkin
Then I had them describe what is happening to the rate of change of the important variables (so if dV/dt is constant, what is happening to dr/dt?). We then had a really good full class discussion where students explained their situation. I think this helped clarify for a lot of students the difference between “V” increasing and “dV/dt” increasing, or how just because “dV/dt” is decreasing it doesn’t mean the volume is decreasing.
This was part of a larger goal of mine to focus on big ideas and deep understanding this year – I’ve always asked students interpretation questions on tests (my final this past term had a crap-ton of writing) but I never felt like I actually directly taught them these sorts of things. For Related Rates, we solve all these problems and come up with all these numbers, but never actually talk about why they are interesting problems – the fact that as one aspect of a situation changes, another may change at a totally different rate, and that there is a relationship between all these rates that explain how things change the way they do. And honestly, I think this little activity made a huge difference – on the interpretation question on the Related Rates quiz, tons of students drew pictures to aid their explanations. 15 minutes well spent!
Posted on March 29, 2012, in Calculus, Related Rates, Whiteboarding and tagged Calculus, drawing, math art, rates of change, Related Rates. Bookmark the permalink. 5 Comments.
This sounds like a cool idea, but I feel like warmup time would actually be the hardest time to implement this activity. I’m wondering how you make it work. What is your beginning of class routine like normally, without whiteboards? Do the whiteboard groups determine their seats for the day? Do the first students to arrive ever finish the problem completely before their groupmates are present and ready to work? How much does the student who is not the “scribe” for the group contribute? I’m just trying to get an idea of how this would go down in my classroom. Thanks for the idea!!
Normally I have a “do it now” problem either posted on the board or printed out for them to glue in their notebooks relating to the previous day’s material or easing them into a new concept… we spend the first 3 or 4 minutes in silence working individually. Yeah, the whiteboards determine their seats for the day if I use it as a warmup (which is one of the only reasons I do it as a warmup… but I think you are right that this is not really an essentially warmup activity). I have never had a problem with kids finishing before group mates arrive (most calc problems worthy of activities like this take like 10 minutes to complete). The last question you asked (engaging if you aren’t the one writing) is the only one that I can’t really answer and is something that I totally struggle with. I have some activities that I have tried out that force the students to switch who is writing, or in some other way engage, and I try to keep the groups at 3 or less… but yeah that’s a problem I’ve been trying to fix for a while now. One thing I think I might try is having some sort of notebook component too to ensure that all students are writing. Thanks for the great questions.
I LOVE your idea to have the students DRAW a picture that would reflect related rates! Thanks for sharing the idea!
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