Stand still when giving directions. Try your hardest not to shush anyone during directions — it makes it harder to hear.

Feedback comments should connect to something. And they should be very brief, like slogans. (Or, at least, that’s one way that comments can work.)

Don’t introduce two similar things at the same time. Pi-r-squared and 2-pi-r should happen on different days, different weeks. One at a time.

I want to make little flashcards for myself, to get better at solving tough geometry problems. On one side is a diagram, on the other is all the auxiliary lines you need to find the answer.

Oh shoot, there were a few other things knocking around in my head lately. Uhhh.

Writing a few bits of directions for later on the board is a decent use of class. Obviously, it’s better to do that before the bell, if possible. But having a visual of instructions is beneficial. (I bet there’s a benefit to having these instructions in physically different parts of a board, rather than on a slide. That’s just a guess.)

Sometimes what’s fun about teaching is the big things, but the last few weeks have been about the little stuff for me.

In this instance, as in others we observed in this group, the conversational routine involved the following: (a) normalizing a problem of practice, (b) further specifying the problem, (c) revising the account of the problem (its nature and possible causes), and (d) generalizing to principles of teaching. Through a routine of normalizing, specifying, revising, and generalizing, they created an interactional space rich with opportunities to learn about teaching practice.

From: Horn and Little, Attending to Problems of Practice: Routines and Resources for Professional Learning in Teachers’ Workplace Interactions

The biggest takeaway for me was how exceedingly careful they are with people talking to the whole room. First of all, in classes that are 2 hours a day, full group discussions are always 10 minutes or less. Secondly, when students are talking to the room it is always students that Bowen and Darryl have preselected to present a specific idea they have already thought about. They never ask for hands, and they never cold-call. This means they already know more or less what the students are going to say. Thirdly, they have a distinction between students who try to burn through the work (“speed demons”) and students who work slowly enough to receive the gifts each question has to offer (“katamari,” because they pick things up as they roll along) – and the students who are asked to present an idea to the class are only katamari! Fourthly, a group discussion is only ever about a problem that everybody has already had a chance to think about – and even then, never about a problem for which everybody has come to the same conclusion the same way. Fifthly, in terms of selecting which ideas to have students present to the class, they concentrate on ideas that are nonstandard, or particularly visual, or both (rather than standard and/or algebraic).

From Ben Blum-Smith. Some of these standards, I think, break down in the face of a full-year k-12 classroom. (Less planning time, fewer students so less control over group dynamics, etc.) Still, I’m pretty enthusiastic about a lot of these ideas and the whole post has more goodies.

The MTBoS blogbot has trapped me it says that it’s hungry, so hungry, and that I need to write it more blog posts please someone help me before it’s too l234q[875uakaaahhhhhhhhhhhhhhhha[;

1. I am an amateur reader of research, and that’s not the same as being a bad expert. These days, I think being an amateur presents its own special set of challenges. I’m not heir to any sort of research tradition, and there’s a lot of training that I lack. So there are distinctive challenges, but I like these challenges. I might be an amateur, but I hope someday to be expert at my amateurism. And this expertise, for what it’s worth, is entirely personal. Any “rules” are just patterns that I’ve noticed in my own inclinations. I’m sure there are better ways to go about all this.
2. Never tell other people they should read more research. I love reading research, because I learn a lot from it. (I also have this sort of unhealthy need to not leave things that I don’t understand on the table.) I see reading research as a kind of conversation with thoughtful people, who are trying to really nail down an aspect of teaching. It’s a blast. But I don’t spend enough time thinking of awesome review games for my kids to play in class. There are lots of things that can make one’s classroom teaching better, and I can’t think of any good reason to privilege reading research above anything else.
3. Usually, there’s a way to get past paywalls. This is an art unto itself. Searching the title of the paper with “.pdf” in the search often works. Besides, a paper rarely comes from nowhere. If I can’t find what I want, there’s often a dissertation, presentation or related article that I can find. Plus, the public library. And there’s always begging people to send you stuff. So paywalls aren’t really an issue, I find.
4. Don’t worry about “keeping up.” I can’t, it’s not like things change that fast, I don’t need to be on top of things, and there’s an inexhaustible amount of material from the past for me to catch up on.
5. I currently lack the capacity to critically evaluate the methods used in a study. This is an important thing for me to keep in mind. It’s one of these humility/chutzpah double-combos that this amateurism is all about, for me. Since I can’t really dismiss anyone’s work on the merits, I end up giving the methodological benefit of the doubt to pretty much everyone. I have a very hard time closing the door on any sort of study — I don’t feel competent to. This feeds into some of my natural inclinations to try to find common-ground between seemingly conflicting positions.
6. I want to better understand methodological issues. Ever so slowly, I’m making progress. Sloooooooooooowly.
7. Don’t read research looking for evidence, read it for perspectives. I find it helpful to read a research paper as the work of a single individual colleague. (Even when there are joint authors or whatever.) This is a single individual who had certain experiences, has a certain view of the world, and wants to tell me something that they think is true, and why. This often keeps me from dismissing papers that seem off-base to me. It also keeps me from feeling bludgeoned by research that doesn’t fit what I know. Humility/Chutzpah.
8. Don’t read single, isolated studies unless it’s part of a larger research project.  I don’t trust myself to understand what’s going on in a single study. I completely lack the context to critically evaluate a piece of research unless I make an effort to get to know the neighborhood. Practically, this means that I don’t read a ton of research, but I read in fairly focused ways. Read a lot about feedback, and eventually you get to know a few of the major results, the history, highly-cited papers, some of the constraints, the interpretive issues, etc. It’s so much fun for me to build this network. This is always more meaningful for me than just diving into whatever link someone happens to be trumpeting. Once I started diving deeply into little sub-literatures of educational research, everything got better for me.
9. “Is teaching an art or a science?” is a very confused question. There is a body of knowledge called “Physics.” It is a science. There is a profession called “Physicists” who “do Physics.” Being a scientist is an art — there is no recipe for coming up with wildly inventive theories or experiments. Teaching, then, is obviously an art. The only relevant question is whether the body of knowledge surrounding teaching should be considered a science or not. I don’t think this is an interesting question, but there is obviously a mix of contestable and incontestable facts that make up this body of knowledge.
10. Never cite research as evidence to another teacher. Since teaching is an art, educational research has an awful reputation, and since I mostly read research to change my perspective (rather than collating evidence), there seems to me little point in trying to use a citation to support my views. It’s not like anything I could cite would be anything like the final word, as far as teaching goes. When I know that a body of research disagrees with someone, I find it a helpful exercise to think of ways to get at this disagreement through only discussing our teaching experiences.

I think there’s something here for everybody to hate, and every time I’ve talked about research in the past I’ve embarrassed myself. Still, I think this is a fairly accurate picture of how I go about things these days. I’m eager to know how the other amateurs out there think about this.

I was trying to get R to put some stuff on his page.

I stared off past R into the wall. I realized that it wasn’t for my sake that I wanted him to show his work. My point, to R, was that he was doing all these calculations in his head and dropping numbers and slipping up along the way. He had good ideas, but if he kept track of each sub-calculation on his page he would be far more accurate.

“What I’m saying isn’t that you need to go back and show me how you did it. I’m saying just barf your thoughts onto the page, as you’re having them.”

That line worked for him, and for a few others kids in Algebra 1 later.

Maybe there’s even a developmental path we can trace for how kids can see the value of showing more than just an answer.

1. At first, kids show work that’s useful for their own calculations. At this stage, revision would seem like a useless exercise unless the answer was wrong.
2. Then, kids can see how how showing their work might represent how they thought about the question. Revision might seem more sensible to kids at this stage.
3. Finally, kids might show work that does more than represent their thinking, but also is structured so as to justify it against potential skepticism.

All that is just speculation, though. What I know is that I’ve found a new way to ask kids to show their work.

I often find myself at a desk, agonizing over whether or not it’s worth it to give comments on student work. I have a similar worry that arises when kids are working in class. Should I say something? What should I say? Will it help?

Clearly, sometimes comments don’t work. Sometimes hints help. Sometimes they don’t. True, there’s always going to be some guesswork involved in teaching. Nothing works, at least not all the time. But come on! There has got to be some trends, some patterns that I can lean on.

A few weeks ago, I was talking to a kid about whether 3x^2 or (3x)^2 is equal to 9x^2. She wasn’t sure, and I found myself in that agonizing moment: what do I say? should I give a hint? let her flail?

I decided to speak up, and I found myself offering the following hints:

• “For this sort of problem, you’re probably looking to either use number testing or an area model.”
• “Why don’t you try number testing?”
• “Can you find a shortcut using the area model?”

These hints worked for this kid, and I’m left wondering why?

I wasn’t trying to do a whole lot of conceptual development during this one-on-one discussion. These were comments that were just asking this kid to connect strategies she had thought about in a whole-group setting to her personal work. I was using my hints/comments to draw a connection, not to develop an idea.

I was hoping that this idea would help me make decisions about when to give feedback in other situations. Today, I was trying to figure out whether to give comments on the work of my 4th Graders, who are working on multiplication. As I stared at the pile, I felt my gut say “AVOID!” Were my instincts right, or was I just being lazy?

I realized that I had no special language with which to give comments to my 4th Graders. I wanted to do for them what I did for my algebra student: refer them back to models or strategies that they had some understanding of already. Otherwise comment-writing gets insanely laborious and tricky. (How do you teach a kid to use a new strategy in two lines?) I wanted to leave them comments like “try doubling!” or “what if you broke apart this number by 10s?” or “put this multiplication in a word problem.”

I couldn’t do any of this, though, because we hadn’t focused on these strategies and we hadn’t named them, yet. So I didn’t write comments.

Instead, I ran a opening mental-math lesson. I asked this series of questions:

• 8 x 3
• 20 x 3
• 28 x 3

We named the strategy that many of them used: it’s splitting up the numbers, or breaking then numbers apart. Then I asked them to practice it with a new problem:

• 13 x 12

And we collected a few different ways of doing this, and talked about why it works.

And then, when they were working alone on practice with multiplication, I went up to A. She was using laborious doubling methods for her multiplication. I said to her, “Could you try breaking these numbers apart?” She said, “I prefer to use doubling and adding.” I said, “Well, that’s good too, but if you were going to break them apart, how would you?”

And she said 37 x 4 is the same as 30 x 4 and 7 x 4, and she solved it, and now we’re in business.

So, in short, one thing that works for me is giving hints that refer back to strategies we’ve already talked about.

You want to know my methodology, right? Well, first I went back in twitter time and looked for pieces that I shared. Of those, I picked a favorite for each month, or two if it was a good month. I tried to vary up the people whose posts are in this list, so there aren’t any repeat appearances.

January:  Grace Chen, “Teacher Moves for Cultural Competence”

Bonus: Shanker Institute, “Update on Teacher Turnover”

February: Andrew Gael, “There’s More Than One Way To Skin a Task”

Bonus: Adam Lefstein, “Against Boldness in Teaching”

March: Fawn Nguyen, “Reversing the Question”

Bonus: Dan Willingham, “Computational Competence Doesn’t Guarantee Conceptual Understanding in Math”

April: Raymond Johnson, “A Few Thoughts from NCTM 2015”

Bonus: NCES Blog, Free and Reduced Lunch, a Proxy for Poverty?

Aside: Lots of good blogging about hints from Anna, Henri, Mike, Annie, Umussahar, Joe, Dylan and others too. Also, Max and I talked about complex numbers. I also talked to Justin’s undergrads about math mistakes.

May: Anna Weltman, “There Are No Kids Here”

Dan Goldner, “Anticipatory Set”

Bonus: Fallace and Fantozzi, “Was There Really a Social Efficiency Doctrine?”

June: Nada, I took June off from blogs/twitter. (New year’s resolution: less time on twitter?)

July: Dylan Kane, “Standards-Based Grading: Skepticisms”

Bonus: Eric Schwitzgebel, “Cheeseburger Ethics”

August: Carl Oliver, “What Would a Teacher’s ‘Off-Season Workout’ Look Like?”

Bonus: Joe Posnanski, “The Age of Tiger”

September: Daniel Schneider, “ELL Math – 3 Weeks In”

Bonus: Larry Cuban, “Research Influence on Classroom Practice”

October: Kent Haines, “Open Number Sentences: Is this _____ actually useful?”

Bonus: Melinda D. Anderson, “The Misplaced Fear of Religion in Classrooms”

November: Chris Lusto, “From Fallujah to Pennsylvania, My Life as a Marine and a Math Teacher”

Tina Cardone, “Expressions With Absolute Value”

Bonus: 

https://twitter.com/rohmansoldier/status/668885496286834688

December: Tracy Zager, “Counting Circle Variant: Tens and Ones”

Joe Schwartz, “22? 30? 50? 100?”

Bonus: Alan Jacobs, “My Year in Tech”

Bonus: Stephen Burt, “Overrated Writers”