Category: commentary
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A Premature Address to the Teaching Class of 2024 and 2025
I’ll be teaching a course for future elementary teachers this Fall (2021) at the University of Wyoming. It’s a freshman course, so most students will be coming off of their high school experience from the past two years. As such, I’d like to give an address to them and all college students, current and future,…
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Is bad context worse than no context?
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,…
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Critiquing the Common Core on its Merits and Demerits
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…
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Getting Better: I can improve anything for students, but I can’t improve that
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%…
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When to scaffold, if at all
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?…
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Inheriting the wind; these are two of my favorite books about math
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…
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The Struggle for Productive Struggle
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,…
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The Problems have become self-aware: Introducing the Skynet line.
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…
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“Isn’t Problem Based Learning easier than Project Based Learning?” and 10 other myths about PrBL. (“Real or not real”)
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…
emergent math 