Teacher-as-alchemist, turning silence into gold

I teach a course about teaching and learning in #highered to a dedicated and enthusiastic group of graduate students and postdocs. One of our sessions is about “teaching-as-research,” something the Center for the Integration of Research, Teaching and Learning (CIRTL) Network describes like this:

The improvement of teaching and learning is a dynamic and ongoing process, just as is research in any STEM* discipline. At the core of improving teaching and learning is the need to accurately determine what students have learned as a result of teaching practices. This is a research problem, to which STEM instructors can effectively apply their research skills and ways of knowing. In so doing, STEM instructors themselves become the agents for change in STEM teaching and learning.

Teaching-as-Research involves the deliberate, systematic, and reflective use of research methods to develop and implement teaching practices that advance the learning experiences and outcomes of students and teachers.

* CIRTL focuses on STEM but this description of scholarly teaching applies to every discipline, from Anthropology to Zoology


In my class, students begin outlining a teaching-as-research project they could execute in their next teaching opportunity. When we get to the part about the design of the experiment, I show them this  fantastic video by Derek Muller.


Go ahead and watch. Play along with Derek and try to solve the puzzle.

The point is to be wary of confirmation bias. If you do some kind of intervention in your class and then students get good course marks, well, you don’t really know why. It could be just another white swan.


Mine is a teaching and learning course so I work hard to model the practices we discuss. When using video in class, I recommend the instructor prompt the students to watch the video like an expert in the field would watch it. That way, students can anticipate and recognize when key events occur, so they’ll be prepared to contribute to the discussion after the video.

So, please watch the video again. This time, watch for the golden moments when people got it, those light-bulbs-going-off, “A-ha!” moments when you know learning occurred.

When I watch the video, there are a couple of times when I sit up, point at my screen and exclaim, “There! Right there! Something just clicked in that guy’s head!”

Three times…

Those golden moments are rare and precious. If there’s potential for one to happen, you don’t want to get in the way. So, please watch Derek’s video again. This time, now that you know something magical happens a couple of times, watch carefully for what happens just before the light bulbs go off. I noticed something and I want to see if you notice it, too.

Did you notice?

Here’s what happens starting at 2:05 in the video

Derek: Hit me with three numbers.
Woman: 3, 6, 9
Derek: Follows my rule.
Man: Oh, that didn’t follow my rule.

Screen capture at 2:14 from Derek Muller's "Can You Solve This?" Text added by Peter Newbury.

Screen capture at 2:14 from Derek Muller’s “Can You Solve This?” Text added by Peter Newbury.

That’s the golden moment. And what happened just before something clicked  in the man’s head?

A pause.

An eternity-long, 5-second pause.

No prompt from Derek.


Just silence.

Our students need time to think! So quit yapping at them, filling every silence with information and helpful(?) hints. Learning is hard. It takes time. Time to think. Telling them what to think, how to think, when to think — that’s not helping them learn. They need to experience what to think, how to think, when to think for themselves.

Silence is golden. Go create some in your class.

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Losing control

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Chalkboard tips

[Update Jan 19, 2015: Within hours of posting these chalkboard tips, Andy Rundquist left a comment that immediately made me stop and think (Thanks, Andy! You should follow him on Twitter at @arundquist). I’m making the assumption below that what students should get from class is an accurate, written record of the material presented. That’s very short-sighted of me, considering the amount of energy I put into promoting active classrooms. Here’s the question that’s now got me stumped: what artifact do I want students to take from a class that’s driven by peer instruction? Should students be taking notes to capture their own thinking, the conversations they have with their neighbors, and the class-wide discussion? No, i don’t think so – I want them present and engaging, not writing in their notebooks. Unless note-taking enhances their engagement? Definitely need to think more about this. ]

I work with a lot of instructors, many of them teaching for the first time. We talk about the design of the course, what active learning techniques to use, things like that. I often forget about the basics, though, like how to use the lav mic, managing the classroom, and (the subject of this post) how to write on the chalkboard. (I’ll use “chalkboard” – some people call it the “blackboard.” These tips apply to using whiteboards, too.) The sobering part is, the best-laid plans of the instructor are irrelevant if students can’t read the chalkboard.

What do suppose the students have in their notebooks? (Image: The University of Waterloo School of Architecture by Jason Paris on flickr CC-BY.)

What do suppose the students have in their notebooks? (Image: The University of Waterloo School of Architecture by Jason Paris on flickr CC-BY.)

Many of the points below are directed at instructors who use the chalkboard to derive formulas or solve math problems but many apply equally to instructors who write names, concepts, theories, dates, etc. on the chalkboard while lecturing.

Disclaimer: Some of these points may seem obvious and there are legitimate reasons to ignore any one them.  And c’mon, writing on the chalkboard — how hard can it be, right? Well, I’ve witnessed instructors “break” every one of these tips. Not because they’re malicious or lazy but  because it’s how they learned when they were students.

Practice writing
Writing on a chalkboard  is different than writing on paper – it takes your whole arm moving from your shoulder rather than just your hand resting on the page. It can be tiring. And it’s a skill that takes practice.  The first time you write a complete sentence or a derivation on the board should not be your first class. If you haven’t done it before (or haven’t done it in a while), find an empty classroom and practice.
Write large enough
Write larger than you think you should, especially if there are (matrix) subscripts. I know, it looks huge to you. That’s because you’re standing right there, mere inches from the board!  Students don’t have the expertise to know matrix entries are always xij, for example, so they’re struggling to accurately copy exactly what’s on the board. The smallest characters need to be visible to the students sitting farthest away.
They have to be able to read your writing
The writing has to be legible – you can’t count on students listening to you as you scribble an expression or someone’s name on the board: they have to be able to read it.
Write in horizontal lines
Be careful to write in roughly horizontal lines. It’s not uncommon to see instructors start writing at their eye-level and then the text drops down to the right along the “arc” of their arm. (Maybe this is true only for right-handed instructors?) Instead of reaching, shuffle your feet along as you write.
Don’t write and talk
There’s often a delay between when you write something on the chalkboard and when students copy it into their notebooks. For one thing, they have to wait for you to get out of the way. They might also be thinking about the material and get a little behind on the notes. If you say the words you’re writing as you write them


your students probably aren’t listening. They’re half a board behind you and all you’re doing is distracting them or splitting their attention (Should I be copying the notes or listening to him speak?) When you write something on the chalkboard, finish writing, step out of the way, and give the students time to copy it into their notes. You’ll see their heads bobbing up and down from the board to their notes as they draw/copy. When the bobbing stops, they’re ready to listen to you and follow as you talk them through it.

Work from notes
Don’t hesitate to stand at the board with notes you carefully wrote on paper, and copy them out. You don’t need to re-derive the results or solve problems in real time on the board. You should be concentrating on making it legible rather than using your brain to actually do the derivation. The students won’t think less of you because you’re not doing it “live” but they will get frustrated if you regularly get stuck. Don’t be that prof with chalk in one hand, the eraser in the other, who goes back and corrects mistakes.

Wait, what?! Why isn’t the answer negative? [stands back, looks at chalkboard for a minute] Oh, here’s the problem, I used -2 instead of +2 over here. Okay, let me just change this [erase, re-write] and this [erase, re-write] and…this [erase, re-write] Yes, that’s better. Now, as I was saying…

Write connecting phrases
Especially in classes with math, you need to include English words on the board between the steps of the derivations/solutions. It’s not enough that you say them out loud because 1) students only write what’s on the board 2) they’re likely a board behind copying the notes you’re no longer blocking. Adding the extra words takes longer but it’s critical that the students have a record of the reasons why this step follows that step or what this result means.  For example, you should write words, “Therefore, by the conservation of energy,” or “Because matrices are invertible if and only if the determinant is non-zero,”
Chalkboard + PowerPoint
There are a hundred questions about how to use PowerPoint and/or the chalkboard but I’m only going to address one here: instructors who present the majority of their content through PPT slides and add snippets of content on the chalkboard. You should imagine a math instructor who does worked examples on the chalkboard or a philosophy instructor who write key names or phrases on the board. Let me use the math example to describe what I’ve seen:The instructor flips through PPT slides, flip, flip, flip, walk to the chalkboard for a quick calculation/derivation, flip, flip, flip, draws a graph, flip, flip,… What do the students end up with in their notebooks? A series of context-free, unrelated bits of math. Later, when they’re studying from the PPT slides, they don’t know to look in their notes for the supplemental info. When they look through their notebooks, they don’t know where any of these snippets come from. Students don’t have a chronological record of what happened in class.What to do about it? Instructors could abandon PPT and do the whole class on the chalkboard. Or they could abandon the chalkboard and only use PPT. There are pros and cons to both of these. If you insist on using a mixture, how about this: Each time you write something on the board, start by writing a label or tag that marks where the snippet goes. Nothing huge and energy-sapping, just write “(Slide 24)” on the board before you proceed. Coach the students to have their notebooks open next to their computers when they study so when they flip, flip, flip to slide 24, they see the matching supplemental content in their notebooks.
Record your “sense-making”
Experts often talk about equations and results, with “testing” (“Wait, let’s check the units here…yep, m/s^2. Okay, so…”) and “sense-making” (“Notice if Mass 1 is much, much larger than Mass 2, this reduces to the simpler case from last time – good.”) This is where you share your expertise with the class! It’s the rationale for why this follows that, why you use this approach instead of that one, how you know this result is correct (well, not wrong, at least). Instead of only saying it aloud, write it down. When the students are reviewing and studying later, they’ll see those flashes of expertise in context in their notes.
No using things again!
You’ve probably seen it: the instructor solves a long problem or does a long derivation that takes a chalkboard panel or two. The next part of the lesson is solving a similar problem, this time with mass m=50kg, with 4x instead of 2x, or with amino acid A instead of T. The instructor works his way through the chalkboards with chalk in one hand, an eraser in the other, making all the little changes, and eventually, reaching a new conclusion. Students can only record notes by working down the page, not jumping back and changing, updating, or re-using things.If you draw a diagram or write an expression like a big matrix and then come back to that panel of the chalkboard later, if you need to use it again, you have to write it out again, giving students the time to write out it out, too. That’s the only way students will have the correct sequence of notes. Yes, this takes longer but you have to let the students keep up.
Portrait, not landscape
The board is “landscape” but students notebooks are “portrait”. Don’t write long expressions by working farther and farther across the chalkboard because students cannot reproduce that in their note books. Consider drawing a line vertically down the middle of the chalkboards, creating  “pages” on the board. Work your way down each page and then to the right. If you’re writing a long calculation or derivation, you should already have it on paper.  Your sheet of notes is “portrait” so it will automatically set the width of the work on the board.
Erase deliberately and fully
When you re-use a chalkboard, fully and deliberately erase it completely. All the way to the top and all the way to the tray on the bottom.  If there are marks, lines, ticks left behind, students may think those marks part of the new material. We know that little chalk line is left over from before but to a student, it might look like a prime or an accent. Remember, they’re not always copying notes “in real time” – they’re often a  board behind (because they have to wait for you to move out of the way) and they won’t notice the tick marks are NOT part of the new material.
Two colors, max
I’ve had math profs who come to class with a box of colored chalk and create glorious, multi-colored graphs where white means one thing, blue means another, red…, green,… And I’m sitting there with a pencil and a pen – two colors. Unless you’ve asked your students to bring colored pens and pencils to class, you should stick to two colors, max.
Describe how to draw it
I’m forever grateful to my first graduate-level quantum prof, Luis de Sobrino, for teaching us how to write complicated matrices in our notebooks and on the board so that the entries are centered down each column. The problem is, when you write entry a11, how do you know where to write it so it ends up centered on the column (especially when entry a31 is a longer expression)? The trick, de Sobrino told us, is write the longest entry first. You can easily estimate where the row should be so go down that far and write the longest entry. This sets the width of the first column. Then add the other entries in the column above and below, centered in the first column. Now move to column 2, and so on. The thing is, de Sobrino made sure to tell us this trick because no one noticed what he was doing (we were still copying the expressions on the previous board and didn’t witness the creation of this work of art.) So, if writing expressions, sketching certain kinds of graphs (like trying to draw in 3D in math class), or drawing a map of France is a skill you want your students to learn, teach them how to do it.

What tips do you have?

What did I miss? What do you do that’s different from the suggestions here? Which of these tips do you think is completely wrong? Feel free to leave a comment!

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