It's been a while since I've revisited the Taxonomy of Problems I threw together a while back, but I think it'll be helpful to spend some time there when considering the following Most-Wanted question around Problem-Based Learning: At what point after allowing the students to work on a problem do I scaffold the content knowledge? … Continue reading When to scaffold, if at all
You've seen the tasks. You've read the research. You're basically bought in. But how do you begin? More importantly, how do you introduce students to inquiry driven learning? Or maybe you're not convinced. Perhaps you maintain that the teacher is the primary knowledge constructor. Perhaps you've been burned in the past by inquiry driven instruction. … Continue reading A Problem Based Learning Starter Kit
I often hear teachers and parents talk about how math skills build on each other in a way that other subjects do not: you have to know how to add before you can subtract, you have to know how to multiply before you use exponents. This is certainly true to an extent, however, I'm wondering … Continue reading A non-linear approach to curriculum mapping
So you've decided to undertake inquiry-based learning. That's great. I'm really glad you see the inherent value in having students swim through a challenging problem on their own a bit before the teacher jumps in with instruction. I'm also glad you've been creative at creating new mathematical tasks with cool entry videos, perplexing pictures, and … Continue reading Kicking things off: How do I start the facilitation of a problem?
In my last post, I tossed out a loose taxonomy to name four different types of problems: Content Learning Problems Exploratory Problems Conceptual Understanding Problems Assessment Problems I felt it necessary for myself. Up until now, I'd been labeling all problem equally: they're problems! They're tasks that are supposed to get students to learn stuff! … Continue reading Taxonomy of Problems (Part 2): Ways and what to assess
Why would we design all problems and facilitation in a similar way without having the type of problem identified? It's possible I've been a bit too broad-brush when describing Problem Based Learning (PrBL) in terms of task design and facilitation. I'm beginning to wonder if we need a taxonomy of problems. After all, every problem … Continue reading Developing a Taxonomy of Problems: Not all problems are implemented equally
About a year ago, I started advocating and pushing towards a Problem Based approach in mathematics, as opposed to a solely Project Based approach, which many/most of my peers currently employ. But before we go any further, let's better parse the differences between Project- (PBL) and Problem-Based Learning (PrBL). I realize that different people define and … Continue reading “Isn’t Problem Based Learning easier than Project Based Learning?” and 10 other myths about PrBL. (“Real or not real”)
Want to learn more about Problem Based Learning but don't have time to read several posts with graphics? Want to see what a student-centered math unit looks like from start to finish, but would prefer to see it visually and hear it in a nasally voice? Well, look no further, my friends! I recorded a … Continue reading Problem Based Learning, start-to-finish, in Ten Minutes
We've been exploring some of the steps to an inquiry-based lesson in mathematics recently. In the last post, I tossed out a few .png images and laid out a few general steps in preparation for actually getting into the meat of inquiry-based mathematics instruction. Which we'll do so starting today. Step 1: Posing a problem … Continue reading Inquiry-based mathematics: the posing of a problem is only the beginning of the problem-posing process.
Last week, I mentioned that, having begun to attempt to slay one of the two giants of inquiry-based math instruction, I’d be steering into a potentially trickier aspect of inquiry based instruction: namely that of instruction and facilitation. Most of us learned math like this. We have decades of evidence suggesting that this method of … Continue reading An oversimplified model of an inquiry-based lesson, with visual aids