Cross-postEducationPedagogyPrimary Education

A Meditation on Ratio

What do you think a ratio is? I emphasize “think” because I’d like you to be interested only in the fragmentary pictures conjured by the question—you want to be aware of what you think a ratio is, not what you think you know about ratios, which are two different thinks. …


Teachers Should Be “Poised and Articulate”

At the end of what seems like a long chain of events back in 2007, I asked, and answered yes to, this question about professionalizing teacher practice: Is there one or more cultural “teaching scripts” that might tend to stymie the practice of collecting and critically analyzing specific best-practice knowledge …

Critical ThinkingCross-post

Intuition and Domain Knowledge

Can you guess what the graphs at the right show? I’ll give you a couple of hints: (1) each graph measures performance on a different task, (2) one pair of bars in each graph—left or right—represents participants who used their intuition on the task, while the other pair of bars …

Critical ThinkingCross-postEducation

Letting Go of Free Will

The most popular conception of free will—a notion that lies mostly unexamined until it becomes necessary to defend it—is that there is something inside our minds (a “ghost in the machine“) that, as Steven Pinker says, “reads the TV screen of the senses and pushes buttons and pulls levers of …

Critical ThinkingCross-postEducationPedagogy

Telling Vs. No Telling

So, with that in mind, let’s move on to just one of the dichotomies in education, that of “telling” vs. “no telling,” and I hope the reader will forgive my leaving Clarke’s paper behind. I recommend it to you for its international perspective on what we discuss below. “Reports of …

Critical ThinkingCross-postEducationUncategorized

Sophisticated Educators, Please Stand Up

People have been talking about false dichotomies in math education forever, it seems. And so have I (as long as you think of seven years ago as “forever”). And so has Professor David Clarke! His paper, titled Using International Research to Contest Prevalent Oppositional Dichotomies, was published in 2006, and …

Woman in front of mirror with towel on her head.
Critical ThinkingEducationPedagogy

Teaching Topless

I’d like to share a really nice presentation below by Valerie Otero, professor of science education, and Edd Taylor, assistant professor of math education, both with the University of Colorado at Boulder. And then I’ll bother you with some thoughts about it.   The unifying theme here is the pyramid …

A row of cups that look like faces.
Critical ThinkingEducationPedagogy

You Cannot Not Have Conceptual Understanding

In education, we seem to take some delight in shoveling a confused mix of folksy connotations into sciencey-shelled words and phrases. Some of my colleagues would call the result edujargon, though I think that word allows us to feel too smug about our own obtuseness—as though the problem is that …