Units in Calculations? Not a chance…

OK, I have to weigh in the units thing:

First, I don’t carry around units in calculations. I think it creates clutter and distracts me from the important thinking I need to be doing. That clutter makes it MORE difficult to diagnose mistakes I’ve made, both during and after the fact. Sure, there are a small number of mistakes I could make which would be easier to spot carrying out units, but that benefit is far outweighed by the increase in mistakes I would make because I am bothering to work out the units along the way AND by the difficulty it will be later to gander at my work at spot more meaningful mistakes.

Second, most of the physicists I know don’t carry around units their calculations either. I don’t want to pretend that making students carrying units around is some important scientific skill. Sure, thinking about quantity and how units figure into the notion of quantity is important, but carrying around units is not a stand in for understanding notions of quantity and rate. In fact, many physicists do all they can to get rid of units, so that they don’t have to carry them around in calculations. One way they do this is setting as many units as they can equal to one.  Then, they go about carrying out their calculations with all units and constants all hidden in dimensionless ratios. Then, only at the end, do they  introduce units back into their work. I’m not saying, we should make students do this.

I don’t know where the idea that students should carry units around came from. Does anybody know?

Last thing, I am all for teaching students to do dimensional analysis, but that’s different than carrying around units in a calculation.

There, I’m done. I said it.

Anticipating and Developing the Question List

Yesterday, I had student groups think again about the questions we have about light and the puzzles that we have uncovered. We didn’t have time to talk about them as a whole class. On Wednesday, Id’d like to aggregate all our questions. I’m doing my best to anticipate the range of questions that will arise, and also trying to add in some questions of my own that stem from what they have wondered about or have made contact with:

Why did some of us see a “dark spot” in the middle of the the bullseye but others saw a bright spot in the middle of the bullseye?

Why does the circle of light on the wall get bigger and dimmer the further we hold it from the wall?

Is it a circle on the wall because of something the mirror is doing or because of the circular shape of the flashlight end?

When objects are visible, is it because they soak in the light or because light bounces off them? What could we do to help us decide?

If we concentrate bright light enough (in a really dark space) will we see the light going by or does it have to hit something like dust, moisture, smoke?

Is “reflected” light always dimmer than direct light? Does it depend on material?

Does light “reflect” off mirrors differently than a white piece of paper or a black piece of paper? [Can we come up with rules that describe what the light might be doing in each case?]

What are the mirrors really doing inside the flashlight? What would the light look like from the flashlight without the mirror?

What happens when you adjust the adjustor piece on the maglite?

Can we come up with rules for drawing the paths taken by light to predict what shape will appear when light goes through different shape or sized holes?

Does light really travel in straight lines? Or does it expand to fill space? Or does it leak and spill? What could we do to help us decide?

How (and why) is the pattern of light different from a flashlight vs. a candle, bulb, or latern?

Is the path(s) taken by light distinct or is it fuzzy?

What happens when light hit moistures, dust, or smoke that allows you to see the beam? Does this “enhance” the beam or do you not see the “beam” just see the objects illuminated?

The cool idea about light that I’m going to brag about today

In my class, we were talking about what happens when some dust floats across the path of our flashlight.  We had mostly agreed that, while we can’t usually see the path, there must be some path because the light gets to the end of hallway where we see it on the wall. I had them now white-boarding in groups, trying to show what the light might be doing when there’s not dust in the path and what happens differently when there is a piece of dust in the path.

One group, in particular, said that the light was both absorbed and reflected when the path of light got the dust particle. I asked them to say more about what they meant by absorb and reflect, and here’s what came up:

First they elaborated on the absorb idea by saying that the dust particle soaks up the light. Later, I asked them if they meant like a sponge–like how a sponge can soak up water and then it’d be wet. By their idea, the dust particle soaks up light and by virtue of having the light, the dust particle is lit. This idea makes sense to me. Without light, things are not visible. With light, they are visible. Their idea very much connects with the light is a substance metaphor. The word soak is, in fact, very similar to words students had used before, like spill and leak when talking about how light got from the hallway to the room.

The group had a much harder time talking about what they mean by reflection (and later decided to drop the word in favor of just absorb). They mostly just kept repeating the word reflecting, so I suggested that it might be easier for them to draw what they meant then to say it. They ended up drawing some lines around the dust particle going every which way, using a different colored marker than the color they had used to show the light coming from the flashlight. I asked them if those lines that had just drawn were light. They were very adamant that these lines were not light and pretty darne certain that light did not go out from the dust particle. I think they mean those lines to indicate that the object was lit or visible. Their reasoning was also very sensible to me. They argued to me that when we look directly at a lightbulb, it is bright. They seemed to be saying, “It is that brightness that lets you know it is a source of light”. Later in a whole class discussion, their argument was more precise: The dust particle was not glowing–not in the same way a the bulb does–and thus light couldn’t be going out in all directions from it. They argued that you simply see the dust because it has absorbed light; but that the dust itself was not a source of light.

At this point, the idea that objects “soak in” light to become visible is completely sensible. In fact, it is a giant step in the right direction. Previously, our thinking had been that you can see light going by you in the shape of a beam. We’ve found since then that you can’t see the beam of light, at least in most circumstances. This group’s idea explains a lot of what we have observed and come to understand: It’s consistent with the notion that we can’t see light going by and that we can see objects. It is also consistent with the idea that you can only see objects if light shines on them.  The same group even earlier had the idea that when you look directly at a flashlight that you aren’t actually seeing light, but that you are  seeing the glass (an object) full of light. They are fairly committed to the idea that we can’t see light, and they are trying hard to tell coherent story of only being able to see objects. So much so, that they don’t want to say you see light when you look at the flashlight, but that you see glowing glass. This is progress along several dimension: thinking that is increasingly accountable to evidence and thinking that increasingly internally consistent.

On Wednesday, I think we’ll spend some time doing observations and experiments to see if we can tell whether any light comes off objects that are lit from a flashlight. Based on this, we’ll have some more evidence to ponder and some more thinking to do.

We’ll also be trying to come to some class consensus about how to we’d like to draw and represent paths taken by light. Right now every group’s diagrams are so idiosyncratic that’s it’s difficult to disagree with anyone. There’s definitely a movement in my class of “We’re all saying the same thing,” and “We all agree with each other.”  I keep having to convince them that we can’t be all saying the same thing if we are all predicting we’ll see different things. This was also true today, I had to make the case that “absorbing” light like a sponge was a different idea that light “bouncing” like a tennis ball. This subject about the tendency to want to politely agree, I suppose, is for another post.

Scaffolding my students’ Capstone projects with blogging

In my inquiry class, students have to do a capstone project to be get an A. I am scaffolding this work through required blogging about things they are wondering about. My hope is that writing these three blog posts will help students be in a position to go a little further with their independent investigations. To get credit, they will have to write a paper that I accept. In the spirit of growth, they can turn in the paper as many times as they want before the end of the semester, but I need one week to have to time to read and give feedback if they want a chance at a resubmit.

Blog Post #1:

You need to describe something you saw that made you wonder about it. Describe that thing in enough detail to help others wonder about it, too. Take pictures or movies if you feel it will help. Next describe specifically what you are wondering about it and why? Do your best to help your readers wonder with you.

Blog Post #2:

For this post, you will need to discuss another observation or experience that you think relates to the first observation. Discuss why you think these two observations are related. Explain to your readers how you are making sense of what’s happening with those observations. What ideas do you have that help you make sense of it?  How is the new observation helping you to make sense of the first observation? What parts of it are you still struggling to explain? Do your best to help your readers understand your thinking about the two situations.

Blog Post #3

For this post, you will need go out and do some experiments to help you sort through your ideas and explanations. Explain what you did and why you did it. Be sure to explain why you thought the experiment would help you sort of your ideas. What were you hoping to learn by doing it? Second, explain what you observed as clearly as possible. Take pictures or include video if need be. Finally, you will need to explain what this observation tells you about your thinking. Does it lend support for your ideas? Is it making you think something new?  Do your best to help your readers understand how you’re thinking has changed as a result of what you did.

Note: You are free to change your mind about what you are wondering about at any time. For example, let’s say you are no longer interested in what you wrote about in Blog Post #1. If that happens, you will need to describe two new situations in Blog Post #2, and explain what you are wondering in addition to explaining your thinking.


Any way, what do you all think?

Why I’m going to brag about my students’ misconceptions

In the past, I’ve talked a lot about why I love certain kinds of misconceptions. In this particular post, I talked about why I love the misconception that the earth gets closer to the sun in the summer. Two recurring claim of mine have been that (1) student ideas should be evaluated with respect to the evidence and reasoning they currently have available, and that (2) sensible, explanatory, and well-articulated misconceptions are to be cherished over impoverished but accurate scientific statements.

In this vein, If you have never read Philip Sadler’s 1998 article, “Psychometric Models of Student Conceptions in Science: Reconciling Qualitative Studies and Distractor-Driven Assessment Instruments” in the Journal of Research in Science Teaching, you might want to.

To steal a quote from its abstract:

…instruction appears to strengthen support for alternative conceptions before this preference eventually declines. This lends support to the view that such ideas may actually be markers of progress toward scientific understanding and are not impediments to learning.

Misconceptions are markers of progress. Yes, he said it.

To give you yet another reason to read the paper. Here’s Figure 2 from page 276, showing the popularity of different ideas to explain the seasons at different “ability levels” collapsed along single dimension. What patterns do you see?

It is true that often times when we see misconceptions in class, we gasp. But here we have yet another reason to think about misconceptions as important for learning and possibly necessary to make progress. This year, I’m going to brag a lot more about all the misconceptions that come up in and because of my class. I’m going to brag because it might mean that my students are making more progress by developing misconceptions than by either idly sitting around not thinking about the world or by trying to memorize correct scientific statements. Be a good teacher this year: go out and cause some misconceptions.

A must read about the dilemmas of teaching

This is a must read about one of the dilemmas of teaching– in this case, the dilemma of when to switch gears in a classroom because you have a responsibility to cover a certain amount of material.

Chazan, D. & M. Schnepp, (2002). Methods, goals, beliefs, commitments, and manner in teaching: Dialogue against a Calculus backdrop. In J. Brophy (Ed.), Advances in Research on Teaching, Vol. 9: Social Constructivist teaching (pp. 171-195). JAI Press.

This will be the third time this year that I’ve returned to read it. I keep coming back to it. It talks about why “methods” of teaching can’t be judged in the abstract. It argues that that methods must be evaluated against the backdrop of context, goals, beliefs, and commitments. This article is fun, engaging, and ends with a nice interview between the two authors. Lots to think about.

How listening transforms my feedback

I keep trying to write blog posts to help articulate for myself a kind of teaching I aim for. I don’t have it down quite yet (not even close), but someday I hope to. For now, I hope by articulating what I do and why, I’ll get better at it. So here goes another attempt:

I work hard at listening and trying to understand my students. I try my best to remember and document what the ideas were, who had those ideas, and when and where those ideas came up. Doing so, allows me to give feedback like this on student blogs:

I’m noticing that you have a bunch of ideas to begin explaining what you saw: One idea seems to be that the bright spot in the center of the circle (on the ground) is the direct light from the bulb, and the dimmer areas are the reflected light off the mirror. This makes sense with your idea from class two Wednesday’s ago that reflected light should be dimmer than direct light. To me, this sounds like a more specific theory about what the mirror is doing than we’ve heard before. Maybe in your notebook you could draw a sketch of how you think this works?

It makes me wonder what Jane Doe would think, because she wrote in her paper that she didn’t think that reflected light would always dimmer, especially off a mirror. Jane, you around to weigh in?

Think about how that feedback would be different I didn’t remember past ideas and I didn’t remember who had what ideas and couldn’t pinpoint when those ideas surfaced.

  • I wouldn’t be able to help draw connections between ideas (ideas that occurred over 10 days)
  • I wouldn’t be able to pit two different ideas against each other
  • I wouldn’t be able to give appropriate authorship and be  reliable source of cited information (ideas that came from different persons in different venues)
  • I wouldn’t be able to invite a critic and dissenter to the conversation.
  • I wouldn’t be able to comment about how this idea is progress from previous attempt to explain

Collateral Damage

One of the worst things we do to students is try to convince them (through any means necessary) that objects fall at the same rate. I think we do this to them in the name of stamping out misconceptions, but I believe it is high up on the damaging things we do to introductory physics students. I believe some of us do it because we think it really is cool, but mostly in doing so, we steal the possibility of it ever being cool for students.

I think it is damaging for a couple of reasons:

We mascarade around with one or perhaps a few demonstrations, and propagate the myth that single (or few) experimental outcomes determine truth.

We attach this observation or decree to the value of “g”, long before students have a chance to even understand what acceleration means.

We tell the lie that mass doesn’t matter for falling objects, when it fact it does, doubly so. It influences both the gravitational force and the intertial response of the mass to net force. It is the interesting intersection of these two truths (along with certain approximations) that something like mass doesn’t matter emerges. [Aside: The canceling of m’s across an equal sign is an injustice to the grounding and coordination of ideas that’s really involved.]

We fail to let them in on the interesting and perplexing conundrum of how it might even be possible for objects of different masses to always move the same way. The conundrum of “Man, I know it’s harder to get the more massive objects moving. So how does the gravitational force “know” to pull harder on the more massive one and to pull less hard on the lighter one? Or I know that the more massive object is being pulled down harder, shouldn’t it fall harder too?” That is where I want my students to be… in it. In the conundrum, misconception or not.

We rig contraptions to prove our point about freefall in a vacuum, long before our students are even poised to understand how that contraption could possibly work and before they’ve had a chance to think about why one would even care to do physics in vacuum. Isn’t there enough physics around us without vacuums?

I believe we kill the patient to cure them of an ailment they never knew they had.

An attempt to articulate what I (try to) do…

One of the hardest things is describing how I teach (and make instructional decisions) in my inquiry course for future elementary teachers. It’s something like this:

I offer some situation that will hopefully create a diversity of ideas and invested persons. I listen to what my students have to say, and encourage them to say more. I help them to listen and to try to understand each other. I model what it means to listen, understand, and empathize. I also model what it means to ask questions as a honest listener and to probe people to say more because you are interested. I model what it means to be interested and help shed light on why they should be interested, too. I point out distinctions I am hearing, and similarities and differences between ideas, in order to model what it means to not to just listen to ideas but across ideas. I ask them if they think the ideas they are hearing are similar or different than their own, and in what way.

I ask students to write about those ideas–both their own and others’ ideas. I make them read each others’ writings. This is both to learn about others’ ideas and to learn about how to write and respond to others’ ideas. I respond to their ideas and to their responses to others’ ideas. Sometimes I summarize their ideas. Sometimes I ask if they mean ABC or XYZ. Sometimes I ask for elaboration. Sometimes I press for specificity or examples. Sometimes, I tell them that it’s clear to me they didn’t really put in any effort toward expressing their ideas. Sometimes I ask questions. Sometimes, usually later, I start offering critical questions, critiques, or counter examples, or ideas of my own.

Based on their ideas, both in discussion and in their writing, I think long and hard about their relationships to disciplinary understanding and practices. Sometimes those relationships are simple, and other times they are complex. I then ponder over where and how to next press upon those ideas: It might be offering another situation. It might be by pitting one or more ideas against each other. I may ask students to think about what questions they have, and let those questions be the guide. I might completely let students decide what to do. I might, but usually not until later, offer up ideas myself. Sometimes I press them in directions of normative scientific conceptions. Sometimes I press them in directions of mature scientific practice. Sometimes I press them in directions that are epistemologically authentic. Sometimes I press them in directions that are about aesthetic experience. Sometimes I press them in directions of enhanced personal agency, and others in the direction of external accountability. Sometimes these different aims are in conflict with each other, and sometimes they are reinforcing of one another.

I usually have in mind the horizon we are aiming for, but not the exact heading along that horizon. I don’t mind taking detours. I don’t mind if we head a little farther north or a little farther south. I know that there will always be horizons to move toward, no matter how far get or which way we head. It is the pursuit that matters in the end.

Brian weighs in on the flipped classroom

In my intro physics class today, I chose to send students back to do their computer exercises. I don’t always send them back, but today I did. For these problems, students had to pick out various x vs. t ; v vs. t; and a vs. t graphs for a free-falling object. They also had to answer some questions about the direction of acceleration of an object on the way up, down, and at the top of the motion. Having students do such things is really the “do problems in class” part of the flipped class model.

In my flipped class, I tell students all the time that’s it’s their job after computer exercises to bring what’s confusing back to the whole class. Not surprising, pretty much everything was confusing, because all they had to go on was a reading and some practice problems. Having students do these readings is the “do lecture at home” part of the flipped class model.

To me, it’s not really about the flipped class. To me, it’s about something entirely different. See, interesting thing happens in my class when students know (1) that I care about what they think, (2) that it’s OK to be wrong, and (3) that class is the place to sort out confusion. The interesting thing isn’t surprising. They start telling you what they think. They start being ok with being wrong. They start demanding that we sort out their confusions in class. They won’t even let me “wash them over” with curriculum. I might try, but they won’t let me.

This has some really amazing benefits. I spend class time talking about and working on problems where students are actually struggling. Today we spent most of our time talking about acceleration–what it means, how it could possibly be the same direction the whole time in free fall, and when and why you would call it positive or negative, and how to solve problems. I also get to rely on students to do a lot of the teaching–they come to insights that they want to share with the whole class. Today, after having drawn some motion maps, a student says: “This must mean that the speed that it leaves your hand is the same speed it has when it comes back down and hits your hand”. Bingo!  They also come up with alternative ways of explaining the same thing. Today, they had three different explanations for why the acceleration of a tossed ball can’t be zero at the top. They discussed conceptual questions. They worked on problems. And we talked as a class about the big ideas and these problems fit within them.

This I think is what the “flipped classroom” is supposed to be about. But I will tell you, the flipped classroom is not what makes this happen. It requires that I make adjustments constantly. It requires that I be constantly assessing students. It requires that I constantly make decisions about whether something a student brings up is a interesting tangent to hold off on, a worthwhile insight to share, a confusion we need to address now, or a confusion that can wait. It requires that I decide whether the questions students are supposed to work through are worth it, now or ever. It requires that I anticipate the difficulties students will most likely have, so that I am not completely improvising. It requires that I constantly probe the “affect-meter”, both for the class as a whole, and for individual students.

Although I am in the habit of mind to do these things, I am not a veteran teacher with years of experience. Somedays, it happens more naturally than others: I may do a good job of anticipating where the struggles will be; my choices to include or abandon problems are good ones; my “in-the-moment” listening and decision-making is both effortless and productive. But other moments, it is a struggle. Things are a little less smooth than they should be. Maybe I didn’t engineer the right variation of the activity or question. Maybe I let the emotion of the room fall flat. Perhaps I didn’t anticipate enough of the difficulties they’d have, and I’m struggling to know what to do next. Those times, it makes class exhausting. For the most part, those days aren’t bad; they are just more exhausting.

I can understand why people are big advocates of flipped classrooms. I am certainly a big fan of using class time to sort out confusion. But that doesn’t happen because students are reading at home. It doesn’t happen because you decide to do problems in your class. It happens when you are constantly doing your own inquiry into your students at the same time they are constantly doing inquiry into the content. It is at the intersection of those two inquiries that something resembling the dreams of the “flipped classroom” are possible.

Flipping your class is not a structural change, where you invert homework and lecture. Flipping the class is a process change where two usually independent inquiries converge into the same space and time.

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