In elementary classes we consider it a good thing to be able to move from the abstract to the concrete. We ask students to count and perform arithmetic on objects, even contrived ones. We ask students to group socks, slice pizzas, and describe snowballs. A critical person might suggest these are all examples of pseudo-context, … Continue reading Is bad context worse than no context?
Criticism of the Common Core State Standards (CCSS) has sadly devolved into theater, when it and schools would benefit from critical analysis. CCSS criticism is all-too-often hyperbolic while CCSS defense delves in dismissal of concerns or even ridicule. That’s a shame because CCSS could use a critical eye: one that understands the standards as an … Continue reading Critiquing the Common Core on its Merits and Demerits
I can get better at almost everything. You can get better at your practice, regardless of your teaching style. I know I often come across as dogmatic with regards to Problem-Based Learning (see Fig. 1), but really, it's all about steady improvement, irregardless of your teaching style. My personal preference is inquiry and complex task oriented groupwork 100% … Continue reading Getting Better: I can improve anything for students, but I can’t improve that
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
Baseball Prospectus I never liked baseball as a kid. Maybe it's because I wasn't any good at it. Maybe it's cause I never went to a professional game. Maybe it's because it is quite boring when you watch it on TV. Then in the late 90's the sabermetric revolution upended the stuck-in-the-50's baseball establishment by … Continue reading Inheriting the wind; these are two of my favorite books about math
This NPR radio spot confirms much of what we already know about struggle. There's so much good stuff in this report, I'd encourage you to go listen to it or read it. Here are a couple nuggets I found particularly illuminating (emphasis mine). ================= For example, Stigler says, in the Japanese classrooms that he's studied, … Continue reading The Struggle for Productive Struggle
I had a great twitter conversation tonight with a bunch of people about the topic of "authenticity." That is, what's the relationship between pure mathematical investigations (like, say, this one - a problem I absolutely love), versus a more concrete, applicable problem (like, say, this one - a problem that I also love). It's a … Continue reading The Problems have become self-aware: Introducing the Skynet line.
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”)
Two Thousand Eleven was a whirlwind of a year. A year ago at this time I thought I was headed to CU-Boulder to begin a PhD. A couple weeks later, a friend let me know about a job as a Math Coach for New Tech Network of schools. Soon after, I was hired and waved … Continue reading What I learned in 2011
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.