Month: October 2015

Total 8 Posts

Redefining Inquiry-Based Learning

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.

Interesting Teachers Are Interested

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.

Classkick Defeats The Mind-Reading Math Robots


Classkick allows you to give your students written feedback on work you assign on iPads. Crucially, that student work can be handwritten, which is (potentially) more valuable for feedback than multiple choice work. I thought it looked promising and I wrote about some of its promise last September.

Ruth Eichholtz didn’t find it as useful in class (where it’s hard to focus on a dashboard) as she did out of class, when she took a personal day:

I had my iPad at home and had iPads brought to the students at the beginning of the lesson. They were monitored at the start by a substitute teacher, who made sure they were present and that they received my email instructions. And then they joined my lesson on Classkick and worked, for 75 minutes, with me. As the students worked through each review problem, I could see their progress. I could make comments on their solution methods, correct their mistakes, and praise their successes. A few times, I tried to tell them they could use pencil & paper and just resort to Classkick when they needed help, but every single one chose to work on the iPad for the entire lesson!

I’m pessimistic about any vision of math education that has a robot grading the work of millions of students. These robots just aren’t good enough yet.

I’m intrigued, however, by this vision of math education that has one expert human analyzing and responding to the handwritten mathematical thinking of many more students than could fit in the same room at the same time. Let’s push ahead a little farther on that path.

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The first thing I thought about after seeing the tutorial was that I could start a mini Saturday school lesson for those students that need or want the help. Also, some of my students have a lot of after school activities, I have meetings and trainings, so I could see setting a time where we could review some work.

Great Moments In Classroom Culture


This goes beyond “great classroom action.” These are great moments that go great lengths towards defining the culture of a classroom.

Nathaniel Highstein offers a full week of activities:

The start of the school year is one of the most important moments for my classes. Setting the right tone and attitude right from the beginning can mean buy-in from students right away — and conversely, a bad start can be really tough to recover from. I had a pretty good start this year in my Algebra 1 and Algebra 2 classes. I wanted to share some things that worked for me in case someone else might benefit, and to document the week, as I may repeat much of this work next year.

You can find lots of posters that describe the practices of a mathematician, the elements of a growth mindset, etc. Sam Shinde went a different direction, turning student work into a poster, and annotating it with mathematical practices.

Nora Oswald uses a viral YouTube video to illustrate the mathematical practice of perseverance:

After we watch this, I like to make the connection to the classroom.
“Do you ever feel like you’re driving around in circles?”
“Do YOU ever feel like you look like a fool and others are laughing at you?”
“Did this woman give up even though she may have looked foolish and stupid?”
“At what point do you ask for help?”

As best as I can tell, Jonathan Claydon has constructed a positive and productive classroom culture entirely out of gags like this.

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Mr. Corey Math:

I use my document camera for students to come up and “sacrifice their mistakes to the math gods”. The class usually makes eating sounds and says “yum”.

Falcon Radar

The speedometer in this video is broken.

Can you (or your students!?) fix it? Be careful: there are a couple of interesting ways to get this one wrong.

Also: what would the graph of speed v. time and position v. time look like here?

Let us know how you’re thinking about it in the comments.

2015 Oct 17. Updated to include the answer video and answer graph. You can also download these files at 101questions.