Hi, readers of sporadic blog! I’m starting the second course of a Master’s in Math Education, and this one involves weekly journaling (or, according to the dictionary, journalizing? ha ha Chrome spellcheck redlines both of them, as well as “redlines”). So I’m going to do my journal entries here for y’all to read.
The course is with Peter Liljedahl, who is gaining some well-deserved internet cred for his research and work in promoting ‘Thinking Classrooms’. This is the second time I’ve taken a course with him, and as was expected we spent our in-class time working on some good problems in visibly random groups on some whiteboards. Makes for a lot of on-your-feet time by the end of a long evening class, but it’s awfully fun.
Okay, now for the content that the prof was actually hoping for.
Respond to the following questions:
- What is mathematics?
- How does someone best learn mathematics?
- How does someone best teach mathematics?
- Did Peter teach today?
Right, nothing too challenging …
Mathematics is a collection of disciplines which attempt to create interesting rules and see how far they can logically go. These rules are often, but not necessarily, related to shape and number.
Someone best learns mathematics by doing mathematics. Which is a total dodge, because I’m not going to answer how one best does mathematics.
One best teaches mathematics by creating a situation and an environment where the learner can focus on doing mathematics, so as to best learn mathematics.
Did Peter teach? Sure. Did he teach mathematics? Perhaps, although was that his goal?
Okay, but no, really. We participated in doing some mathematics. Did we learn something new? Hmm. For those who weren’t there, let me recap one of the tasks we engaged in.
Say you’ve got a jar, 20 cm high, 6cm radius. It’s mostly full of water. So now we’re going to take a smaller jar, 18 cm high, 5cm radius, and sloooooowly push it into the bigger jar. When we’ve carefully, slowly pushed it all the way in, how much water is in the smaller jar?
Stop, think about that for a bit.
Yeah, so did we learn some specific math fact, function, or technique we’d never seen before? I guess perhaps not. Did we apply what we knew in a way I’d never thought of before? Sure did. Did it reinforce our understanding and make it more resilient to future challenges? I’d bet yes.
So, yes, Peter did teach us mathematics, because he created a situation and an environment in which we learned something.
He also taught us something about math education. The evidence is above.
Comment on your experiences in doing a problem from Tuesday’s class with one of your classes using vertical surfaces and random groups.
So this isn’t the first time I’ve had students work on a problem using random groups at the whiteboards, but one of the many reasons I’m grateful for this course is that it’s forcing me to stick to it. I could talk about my excuses I made back in Sept, but the truth is, I’ve caved for nonsense reasons because for some reason I’ve believed that making students stand up and work with someone outside of their usual cluster is somehow a burden on them.
This week’s experiment is helping put that idea to rest. My class that was “too small to work in shuffled groups” loved it. My class that’s “too noisy to work at the whiteboards” was more on-task with both this problem and with just straight-up review questions at the whiteboards than a usual day. Honestly, the only problem with the entire endeavor was that I didn’t have a full 1.5-hrs worth of good problems lined up and ready to go as part of their end of course review.
Which I could fix. Starting with tomorrow.
Dang it. Okay, that’s enough journaling, now I’ve got work to do.