Category Archives: commentary

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 … Continue reading

Posted in commentary, problem based learning, Uncategorized | 7 Comments

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 … Continue reading

Posted in commentary | 11 Comments

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 … Continue reading

Posted in commentary | 5 Comments

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 … Continue reading

Posted in commentary, problem based learning, spectrum of struggle | 3 Comments

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 … Continue reading

Posted in commentary, Uncategorized | 2 Comments

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 … Continue reading

Posted in commentary, spectrum of struggle | 13 Comments

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, … Continue reading

Posted in commentary | 7 Comments

We must get rid of Algebra because Roger C. Schank can’t behave at parties, knows weird mathematicians.

When Andrew Hacker wrote his “Is Algebra Necessary” article I was basically like But at least it was well written and brought up some good points about math instruction, many of which math instructors actually agree with. Hacker had a fresh … Continue reading

Posted in commentary, Uncategorized | 13 Comments

“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 … Continue reading

Posted in commentary, inquiry based instruction, problem based learning | 7 Comments

What I learned in 2011

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 … Continue reading

Posted in commentary | 2 Comments