Definitions of “inquiry” typically focus on the student’s inquiry. Fine, but I also appreciate Mylène at Shifting Phases’ shifted focus to teacher inquiry:

My definition of “inquiry” as an educational method: it’s the students’ job to inquire into the material, and while they do that, it’s my job to inquire into their thinking.

So she measures the quality of her tasks and instruction by how how much access they grant into her students’ learning. She also shares an organizational strategy that helps her understand which of her tasks grant her the most access. All great.

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Tracy Zager writes in response to several commenters who think this is all obvious and everybody already does it:

I disagree in a big way. My own children come home from school with endless folders of completely useless products. Useless in that they give the teachers no actionable information, no insight into the children’s thinking.

Imagine you had a single piece of student work and were going to talk about it with colleagues for an hour or two. Which pieces of work would lead to rich discussions about students’ thinking and mathematics, and which wouldn’t? If you’d run out of things to talk about in 5 minutes—if the assignment wouldn’t lead to a productive, insightful discussion among teachers—why are we assigning it?

Yeah, practice. Why else? That can’t be the answer for everything.

Most of what I see assigned in schools yields no insight into students’ thinking for teachers.

So I think this is a big, important idea that goes far beyond common sense.

2015 Oct 31. Mylène posts a follow-up, “Who’s Inquiring About What?” and the the last paragraph is a stick of dynamite:

Want to help me improve? Here’s the help I could really use. If you were one of the people whose first reaction to my original post was “I already know that” – either I already know that to be true, or I already know that to be false… what would have helped you respond with curiosity and perplexity, adding your idea as a valuable one of many? If that was your response, what made it work?

2015 Nov 11. Also make sure you read (at least) the intro to a paper linked by Brian Frank that coins the term Discovery Teaching.

Russell Davies, all the way back in 2006, in a post called How to Be Interesting:

The way to be interesting is to be interested. You’ve got to find what’s interesting in everything, you’ve got to be good at noticing things, you’ve got to be good at listening. If you find people (and things) interesting, they’ll find you interesting.

A teacher emailed me after my workshop at the Alaska State Math & Science Conference:

As I mentioned after your session, I watched your CUE talk and have since worked to cultivate my Feedly account to provide more perplexing math content, inspiration, and lesson ideas. I have followed ed-tech and blended learning resources on Twitter for years, but am looking to expand my resources for engaging and interesting math content.

So I’m going to share a certain set of blogs. I follow these blogs with so much devotion, I’d be surprised if I’ve missed more than a handful of their posts since I first started following. And I’ve been following some of them for close to ten years. Some are written by math teachers but most aren’t. They share two features in common:

1. They link. Much of their content isn’t original, and little of it relates directly to math or pedagogy, but they share links that reliably light up the cluster of my neurons that loves to design lessons for kids. (A tech blogger inspired my Joulies lesson, for instance.)
2. They’re interested. Even more than they’re interesting, they are self-evidently interested people who have cultivated a way of looking at the world and being in the world that I want for myself. They are voracious, omnivorous consumers of their surroundings.

I started to share this set of blogs in an email reply to the teacher, but I’d rather share them with all of you, and then I’d rather all of you share your own set of links in the comments, links that fit the bill I’ve described.

• Best of Metafilter
• Colossal
• Daring Fireball
• Devour
• Futility Closet
• Kottke
• Lonely Sandwich
• Marco.org
• Math Munch
• (Mathhombre) Miscellanea
• Sine of the TImes
• Visualizing Math
• Waxy Links