On the first day of our inquiry into light, students predicted what they would see standing in a room, looking into the hallway where a friend was shining a flashlight. There were many ideas. A big surprise for many students was that they didn’t see a beam.

So on the next day, I asked each research group to answer to following question

(A) Why didn’t we see a beam? What is happening that would explain why we didn’t see a beam?

(B) Is there a different situation in which you think you would see a beam? What’s going on differently in this situation that would explain why you would see a beam?

The main ideas that arose out this discussion were the following:

Idea #1 The light was too dim. A brighter light would allow us to see the path of light. Some said that maybe this is because humans eyes are only good enough to see the path for really bright beams. One group talked about how maybe a cat or a camera could see the beam. Others thought that maybe it’s not just the brightness of the like, but the kind of light–laser light, flood light, LED, etc.

Idea #2 The hallway (or box) wasn’t dark enough to allow us to see the beam. Some said that a darker room would allow us to see the path of light, because there would be more contrast between the darkness and the beam.

Idea #3 The hallway (or box) was too much of a closed space. A more open space would allow us to see the path of light, because there wouldn’t be any reflections (off walls) to interfere with the beam. The ideas about how and why reflected light interferes with the beam were unspecified, although the word destroy and mask came up

Idea #4 We couldn’t see the beam because we weren’t actually in the hallway (or box) where the beam was. Some said that whether you see the path of light, the source of light, or just lit areas depends on where you are standing and looking. There was a lot of discussion about whether there is a distinct boundary of the beam or whether it’s a “fuzzy” boundary or of it’s just a gradual dimming as you get farther from the center of the beam. They also discussed that a laser might have a distinct boundary while a flashlight probably would not.

Idea #5: The path of light is only visible when it hits something in the air (like moisture, smoke, or dust). What happens when light hits water droplets was unspecified, although the words scatter, reflect, and absorb came up.

They’ve been sent home to make observations that will help us to sort out these ideas.

I wrote in their homework the following:

“Your homework is to make some observations that will help us to sort out these different ideas and possibilities. You might experiment using brighter and dimmer flashlights. You might experiment shining flashlight in somewhat dark and very dark rooms. You might shine flashlights in small closets, in large rooms, and outside. You might shine a flashlight and stand in different areas to see if and when you see the beam. You might try shining some light through some smoke, dust, or fog. It doesn’t matter what you choose to do, but your job is to write a clear explanation of what you did and what you observed in a blog post. You will also need to read and comment on at least one other post. “

Today, my students turned in their first homework. So today, I asked my students to look over three examples of mock student homework that I had made up. I asked them to look at each and discuss in groups the following questions:

What do you notice about each one?

What is similar and different?

Are the ideas clear and understandable? What did they do to make those ideas clear (or unclear)?

What was done well? What made it that way?

What was not done well? What made it that way?

Is there enough detail? Is there too little detail? Is it vague? Is it repetitive?

Each group reported out what they noticed, and what they are taking away from the activity. During this time, I often asked groups to point to specific places in the text and to explain why it was either vague or unclear or whatever. I took notes during the discussion with the purpose of writing up some advice that we’d give others for improving their writing. Here’s the advice they came up with:

Ideas to Improve your Writing

Organize your writing in some way:

• Use descriptive titles for sections
• Break down ideas into paragraphs
• Summarize big points

Include pictures, sketches, or diagrams that strengthen the writing

Use examples from real life experience, perhaps to

• Help clarify an idea or the experience it comes from
• Provide evidence to support (or refute) an idea
• To draw an analogy between two things

Talk about things you don’t (yet) understand. For example,

• When something doesn’t make sense, attempt to articulate why it is hard to understand or what specifically you don’t understand

• Include some of the questions you are still wondering about and why you are still wondering about those questions

• Talk about problems you are still thinking about and what makes them problematic.

Be concise when you can, rather than being repetitive

At same time, use enough description and detail in your explanation to be understandable. You might try

• Breaking down information or ideas into parts
• Explaining “the why” not just “the what”
• Telling the story of your thinking and its process
• Including the steps of your reasoning
• Using everyday examples or analogies
• Elaborating when necessary

Cite other people’s ideas when appropriate–try to understand & explain them from their perspective

Some things to Avoid 

Being overly repetitive

Only describing without explaining

Including irrelevant detail

Rambling on in a distracting way

Using terms or vocabulary that aren’t defined

Being accusatory or mean

Making claims that aren’t supported in anyway

In many traditional classes, students are shown a demonstration either during, before, or after the teacher explains what is to be demonstrated. The idea is that seeing and hearing is believing, and that it’s better than just hearing. I think it’s also implied here that actual “real-world” examples (ones you can see and touch) help students relate to the concepts and that demonstrations get students paying attention better.

In many reform-oriented classes, students discuss predictions before observing the demonstration, and only then the teacher explains. The idea here might be that asking for predictions helps students commit to an answer, perhaps causing some cognitive conflict when they observe something discrepant, and that now they are ready to hear the explanation. There’s also the idea that students might hear alternative explanations during discussion, some of which will be close to the right explanation.

In fewer reform-oriented classes, students go back and discuss the observation; and only then after having discussed it again, the teacher uses the ideas that arise during discussion as the basis for explaining. The ideas here are (1)  students need time to process what they’ve observed and to begin to put some of the pieces together before they hear an explanation from the instructor and (2) discussion allows a teacher to tailor the explanation in a way that helps students make connections between their ideas and the explanation.

In far fewer reform-oriented, students will then have to make a new predictions about some new situation in light of the new ideas that have been discussed and explained. The idea here is that the understanding can be fleeting and that knowledge can be very context-bound. By letting students try to apply the same idea to a new situation, some nuances will arise about what it actually means to understand that concept or what it means to be able to apply that knowledge in a new context. The teacher also gets some additional evidence about how well the students understand the concept, in terms of its “span” not just “depth”.

We did all of this in my class, except that I never gave my explanation. I only tried to help us all better understand all the explanations we’d heard. Lots of ideas came up about “Why we didn’t see a beam in the hallway”.  Instead of me telling them what situation they are supposed to make a prediction for, students came up with the new observations they’d like to make. They each made their own predictions and explanations for why we would or wouldn’t see a beam of light. Now, they are being sent home with express purpose of making those observations and reporting back to class.

This week I learned of some new possible misunderstandings that I had never considered or observed before. I received several emails this week from students asking about what is meant by the “x-component of velocity”. If you haven’t been following, my class is somewhat of “flipped” class, where students read lecture materials online and come to class to think through conceptual problems, work on solving quantitative problems, and carryout some investigations.

So far, we’ve only been talking about one-dimensional motion, but the reading material has been using “x-component” of velocity rather than just “velocity”. I can sympathize with why someone might choose to write it this way, but I think, in reality, its cumbersome, wordy, and confusing.

So I began yesterday, by asking students to talk with their neighbors about what they think “x-component of velocity” means. After some discussion, I asked to hear idea about what it could be.

Here are the two answers we heard that I had never heard before

(1) Velocity is made up of two parts (or components), the magnitude (speed) and the direction. The x-component must be either the speed or the direction.

(2) Velocity is made up of two parts (components), the Δx part and the Δt part. The x-component of velocity means you only look at the Δx.

What this shows me is that students were trying to make sense of this vocabulary as best they could. They were thinking, “component?” well that’s like a part. What parts does velocity have? It had magnitude and direction parts. It’s also calculated using distance and time parts. The x-component must be one of those parts. To me, this is completely reasonable thing to do. It’s also a good sign to me, that at least students are reading and trying to make sense of strange terminology.

I had a brief activity ready, one involving the directions given by google maps to get various places. I gave them a few examples of paths moving along North-South streets and East-West streets, some moving along both, and some moving along a diagonal street.

At the end of the day, someone asked, “Why would I ever care to describe just the x-component of velocity (as – 30 mph) when I could just describe the whole velocity as 42 mph Northwest?” I said, that’s a really good question.

I want to be clear that vectors or finding components of vectors has not been covered in this class, and that there are difficulties in students’ understanding them. I also want to be clear that the two misunderstandings are likely the result of the format of flipped class and the choice to introduce the terminology of “components” before (I believe) it made sense to do so. I don’t think these two are deep-seated confusions; rather they are the result of asking students to read something before we’ve helped them to carve out some distinctions which would have helped them to read that text.

If you are interested in how to make readings or lectures more effective, you should read this paper, called “A time for telling” by Daniel Schwartz and John Bransford. In this article, they talk about three experiments they carried out to better understand what kinds of pre-lecture or pre-reading assignments help prepare students to learn from text or lectures.

In my intro physics class, I have an undergraduate TA who is both a physics major and a future math and physics teacher. My advice to him for how he could be most helpful in class was the following:

I told him that his main job was to listen carefully to students and to scout out interesting ideas that students have. I told him that I wanted him to walk around, listen, and ask questions to see if he notices anything interesting students are talking about or using. I asked him to report back to me about interesting things he notices students are doing or thinking–it could be right or wrong ideas or procedures; it could be interesting but different solutions to problems; it could be peculiar or ordinary ideas; it could be novice or advanced ideas. I told him that it was his job to help me scout out ideas, so I that I could decide if any of those ideas needed to be elevated to the level of the entire course.

I gave him several examples of what I thought were interesting ideas that occurred over the past couple of days, which I had decided to bring to the level of the whole class. Those ideas included,

Many students not knowing where the x =0  on a x vs. t graph;

Stan’s theory about why we couldn’t see any acceleration in our data for the falling coffee filter (even though it must have accelerated at some point);

That one group got an acceleration of 6,000 mph per hour; while another group got 1.67 mph per second;

One group’s idea to “half the range” for the uncertainty in time measurements vs. the TA’s own idea about using “reaction time”;

He had already been asking students questions and helping to explain things to students. I told him that he should certainly continue doing this, but that he might ask students questions in order to find out what they are thinking, rather than to just find out if they have they right answer.

If you had an undergraduate helper in your class, what would you want them to see as their job?

A lot of hard work and good ideas have gone into creating the flipped class I’m teaching. I do think there’s a good base to work from, but yet still I’m finding it hard to be at ease with it. So here’s where I’m at with the flipped class curriculum I’ve been asked to teach after week one.

First, a list of wants:

(1) I want the computer exercises that students are asked to work on to

(a) be at an appropriate level for what the students know and are able to do, taking into the account that they are working in groups and there is a diversity of knowledge, experiences, and backgrounds.

(b) match what the students have been asked read to before coming to class

(c) be understandable (at level of writing) and not filled with unnecessary wordiness

This week, they failed at a, b, and c. Many of the exercises were not within students grasp. Sometimes because they were outside what I would expect them to be able to do. Sometimes because they really couldn’t have been expected to take such things from the reading. Sometimes becomes the writing of problems was cumbersome, wordy, or confusing. Sometimes all of it.

(2) I want the problems I am asked to model to be an example that touches upon key concepts, not just be an example of how they might approach their problems to come.

This week, the problem failed to do this. I know that merely going through a problem, even as clearly as possible, would do nothing to help students understand the concepts of average speed and average velocity, and the difference between the two. In the class I observed, the example problem didn’t seem to help anyone on their problems anyway (and it was presented nicely, clearly and was also well broken down), so I’m left wondering why we do them.  In my class, we did a little more work to build an intuition around the concepts, but I felt strangled by the example problem.

(3) I want the concepts and skills that are touched upon in the computer exercises to be somewhat  relatable to the example problem I model.

This week failed at this as well. The computer problems had students interpreting strobe diagrams, x vs t graphs, velocity vs. time graphs, and connecting those to written descriptions. The example problem was pretty much straight plug and chug to calculate average speed and average velocity. While all were in the topic of kinematics, they neither called upon the same concepts nor the same representations. It felt to me and students we were just being pulled along to do widely different thing, much of which we didn’t understand or understand their relationship.

(4) I want the problems students work on their whiteboards to be the jumping board for a good board meeting.

This week failed this criteria as well. All the problems were mostly just random variations. There are basically 4 questions randomly assigned  across eight groups. The problems, as far as I can see, have random numbers that lead students to have to do slightly varied procedural moves (perhaps calculating t from x and v or x from t and v in order to calculate an average velocity for a whole trip). Students have no reason to be interested in each others’ problems, because the problems are not built to do so. I’d prefer that every group either do same problem (for which there might be different approaches we can compare and contrast); or that there be 2 carefully picked problems that draw out some important skill, distinction, or concept between them.

I made the best I could from the se of questions, helping students to note certain subtleties within or across problems. But I want the problems and the problem set to drive interesting puzzles and conversations from the student end, and not need me to swoop in to notice interesting things. I believe that careful choices can make this more likely to happen (although I know there are no guarantees).

Second, What’s missing?

I know I’m picky. I know I have high expectations. But I’m trying to articulate what’s missing. I mean everything sounds good, right? Students working on conceptual problems with feedback from a computer. Students working on problems collaboratively on a whiteboard. Students discussing solutions with each other. Yet, there’s something missing. I think it’s

(1) An understanding of where students are at coming into the course (maybe the demographics have changed). Whatever the reason, the curriculum fails to meet them where they are, on day one.

(2) An understanding of how pick problems and sets of problems that help build both important procedural skills and conceptual, and that are likely to squeeze some learning out of problem solving (not just be problem solving).

(3) A coherence across the class activities that are an the appropriate grain size.

Last, what I might do

I’m somewhat torn about what to do. At some level, I’m responsible for doing much of the same things as other sections; but I have a hard time doing things that I know are just washing over students. I’m wondering how much tweeking I can do around the edges without undermining the course structure and without driving myself crazy prepping each week.

I do think that I might be able to (1) tweek the example problems so that they are more connected to exercises, (2) get students interactively engaged with my example problem so it isn’t just a lecture washing over them, and (3) be more selective about which problems I will allow student groups to work on, so that more connections can be made during discussion.

Anyway, that’s my plan as of today: Connect the pieces, engage the students, trim the fat.

Today, I tried my best not to let some bad (untimely? unfortunate?) curricular elements harm the well-being of my class and the students who come to it. The way I see it is this: It is a high priority of my job to protect my students from any undue or unnecessary harm to their sense of self-worth and ability, especially those that will function as serious liabilities for their learning in this course and beyond.

Today, in my flipped class, students were sent back to a computer, which then proceeded to blast away at their self-worth by asking questions that never should have been asked. For example, groups were asked by a computer how to find x-component of displacement from an x-component of velocity vs. time graph. Out of the 16 groups that I observed (8 in my class and 8 in another class), only 1 group  was even in the ballpark of understanding what the question was asking. In the class I observed, I only knew this because I visited each group and listened and watched. When the instructor asked, “Did everything make sense? Does anybody have any questions?”, not a single student spoke up. In my class, I knew this because every group of students knew it was their job to share with the class what was confusing. They raised their hands and called me over. I had already set the tone that we are here to learn and that confusion is where learning lies. I was and am proud of them for having the courage to stick up for their right to learn and not to just click through some computer problems that were completely incomprehensible to them. I had to explicitly tell them afterward that they could not have been expected to understand everything, rather that those exercises are merely fore-shadowing the things you will need to come to understand.

Let’s back track, a little bit. Before class, several students asked me to meet with them before class to discuss some  problems they were working on. I think the problem was about a person running 3 m/s for 30 minutes, and they were supposed to find the distance.

This is what the students had done:

3 m/s / (30 minutes / 60 seconds) =

I asked them what they did and why. And they said, “we divided because we saw that the seconds was in the denominator [pointing to the s in the m/s], and we figured we had to convert to seconds somehow. But we weren’t sure exactly how to do it.”

OK. So I decided to ask a simple question, “How far does it go in one second?” Someone answered 3 meters. OK, well, how far does it go in 2 seconds? Someone said 6 meters. Now I asked, why? Someone said, its 3 times 2. I said, “Yeah, and it’s also 3 + 3. He traveled 3 meters in the first second and  another 3 meters in the second second”. Then, I asked how far it would go in 10 seconds. It was certainly not automatic for them to say 30 meters, suggesting to me multiplication by 10s was not at their finger tips. So, then I asked them how far would it go in a whole minute, and they were able to eventually figure out that it must go 60 * 3 m/s. And then it wasn’t easy (but neither hard) for them to realize that is must be 3 * 60 * 30.

This. this stuff is ground zero for these students–quantities, rates, and ratios. Jumping to finding the area under a curve is absurd (a bit too quick to the gun?)

Let’s talk again about computer problems. Students had another question where there was written description of a motion–on object moving toward the origin, then going slower in the same direction, then stopping, then going faster in the same direction and moving through the origin. They had to pick out the right graph. Many students were struggling with this as can be expected, so I asked the following question to several groups, “Can you show me where x = 0 is?” Some students pointed to the center at (0,0), while most pointed to vertical axis.

Once again, interpreting graphs and reasoning across written and graphical representations is tough stuff, but no one had even invited them to the playground. These students were confused about why the “x” was on the y-axis and were (understandably) confusing the origin of coordinate systems with the (0 second, 0 meter) location on our position vs time graph. Total stuff I expect to see, depending on the population.

So afterwards, I took a poll. I asked them to talk with their group about, “Where x=0 is?”. After they talked, I asked for ideas, and four ideas came up. It is the vertical line (axis). It is the point (0,0). It is the horizontal axis line. It is arbitrary and could be any horizontal line. Someone brought up the fact that when you zoom in a graphing calculator, the horizontal line shown isn’t always zero. I simply just wrote up their suggestions as they gave them and I asked for why someone might think this. I then sent them back to their groups to discuss what they thought it should be after hearing all the ideas. All the groups came back saying it should either be the horizontal line of the axis or it could be any horizontal line if it isn’t labeled.  We ended up deciding that you should always label your axes, but if you find one that isn’t labeled, it’s a safe bet that the axis represents the zero value.

I was already “waaaay behind”. Note here that I didn’t say, my students were waaay behind. I think my students were probably now a little less behind than students in the other class, but the my INSTRUCTIONAL timing was behind. I refuse to leave my students behind, and that’s why I shouldn’t be allowed to teach certain courses.