So, we are ending the year in inquiry by studying the seasons. We started by talking about the following situations:

(1) You are at a concert. What could you do to increase or reduce the impact of the sound on your ears?

(2) You are by a fire. What could you do to get hotter or colder?

After they muddled with those situations, I introduced a third test case.

(3) A person in the room has a smelly perfume? What could you that would make your experience of the smell more or less intense?

The goal was to generalize a set of general patterns on what affects the intensity of “emanating stuff”. Our initial list was the following:

Volume (how strong the actual source of smell, sound, or heat is)

Proximity (how near are far you are from the source of smell, sound, or heat)

Duration (how much time you spend around the smell, sound, or heat)

Protection (how many barriers, blockers, or filters are between you and the source of heat, sound, smell)

We went into the detail explaining how these might work in each case, but that’s the gist.

An Experiment to Foster Thinking about A New Mechanism

Two identical heat lamps were set 10 inches away from a sheet of paper. Under the sheet of paper was a thermometer. The identical lamps fixed the volume. The 10 inches set the proximity. We set the duration time to 1 minute. The identical paper fixed the level of protection.  One lamp was set to shined directly down on the paper, and the other was set to shine at a very shallow angle (being careful to keep the 10 inch separation from the thermometer).

Students were asked to discuss what would happen to the temperature when I turned on the lamps.

Most groups believed correctly that the lamp shining straight down would make it hotter. Here is how we eventually built pieces of an explanation for why angle matters:

• You are more likely to be burned by the sun from in the middle of the day, than the morning or evening, the sun’s rays must in some way be stronger when overhead than we angled low in the sky.
• Direction also matters for our previous example. With fire, you can turn your cheeks toward fire to give it more direct access to fire’s heat. With a sound you can turn your ears away. With sound, you can turn your nose away.
• With angled light, the rays of light hit the paper at a shallow angled creating a “glancing blow“, like skipping a stone on water, or a car hitting a wall at angle (vs. throwing a pebble straight into the water or driving you car head-on into a wall). The shallow angle creates only a glancing blow, which has less impact than a “head-on” collision.
• With angled lamp, the light rays end up hitting a large area on the paper; where as the angled down rays hit the paper in a small area. This changes the concentration of the heat. It’s like heating up a large room or a small room with the same space heater. The large room will take longer to warm up, and may not even get up to same heat, because the heat gets spread out more.

We did the experiment, and in one minute the overhead lamp heated the thermometer to 130 degrees, while the angled lamp only heated up the thermometer to 78 degrees. Huge difference. I even rigged the deck in opposite way so that the angled lamp was actually closer than 10 inches and it got the thermometer that read a little higher. It was no contest. We added a new factor to our list, so that we now have:  Volume, proximity, duration, protection, and now direction.

Our goal over the next 3 days will be to figure out which of our 5 factors are most significant for explaining the seasonal changes to temperature–that is to collect evidence and arguments for the relative importance of each and to refine our sense of mechanism about how they work in the case of earth.

Why I’m liking this approach?

#1 We are drawing on knowledge from everyday experience : sitting by a fire to keep warm, smelling something rotten, being around loud music, etc. Had I asked what causes the seasons, it would have been about orbits and tilts. That would lead us down a frustrated track of sterile and unproductive school knowledge.

#2 We were generalizing quickly from a set of particulars, and naming them to help support generalization. We were not not just swimming in a vast sea of specific situations, and hoping that abstraction and connections were made. I specifically asked them to connect case specific mechanisms and to come up with general names.

#3 We are making sense of contrived situations in terms of everyday mechanism, such as getting burned, car crashes, skipping stones, and heating rooms. While I suggested the situations early on, students quickly extended to and built on other everyday sources of knowledge. This suggests that I helped “frame” the conversation as building on everyday knowledge. Going to the contrived could have tipped us out of, but it didn’t.

#4 Keeping the initial conversation away from the learning target (i.e., the seasons) and toward other phenomena (i.e., fire, sound, smell), keeps my “misconceptions” ears from perking up. Instead, I’m listening for useful ideas, analogies, observations, mechanism, insights, etc.  My listening patterns in turn influence my interactions with students, which in turn influences the nature of the discourse that emerges. My commitment and ability to focus on the good students say rather than the wrong stuff depends on the context I set up. I’m setting up a context, not only in which students will hopefully draw on everyday ideas productively, but I’m setting up a context in which I will be more likely to hear and draw on their ideas productively.

#5 I hope this will get us to “tilt” last, which is the empty vacuous understanding that many students have. Instead, I hope we will initially focus our explanations on locally observable changes, such as changing amounts of daylight and changing altitude of the sun in the sky. Tilt will be, hopefully, for the purpose of explaining the changing daylight and changing altitude. Thus, changing daylight and changing altitude will be the explanation for the seasonal variation in temperature.

In spring, I’m teaching “Teaching of Physics” again.  Here is my stab at trying to organize my thinking about that course around 3 big questions:

Understanding Physics: What does it mean to understand physics content in deep and meaningful ways? What do such understandings look like in general? What does this look like in particular with respect to the specific domains of physics content that I will likely teach?

Learning Physics: How does meaningful physics learning develop? What do my students need to be engaged in for this to happen? In what ways are exemplary physics curricula / instructional practices organized to engage students in these ways?

Teaching Physics: What do I as a teachers need to know and to be able to do to effectively orchestrate exemplary instruction that supports students in meaningful learning? What practices and habits of mind should I consider high-leverage and generative for me in developing as a teacher?

I’ve tried lots of other ways of organizing it, but this is where I’m at now.

Next steps:

(i) What specific learning outcomes do I think are most important?

(ii) What would count as evidence that students have learned those things?

….

Today, I didn’t have time to revise the sample problem I’m supposed to do in physics. So I worked the sample problem as given. We were doing standing waves. In the particular problem, there was a string with both ends fixed and we were told it was vibrating in the second harmonic. In this case, the wavelength is equal to the length of the string.

After my sample problem, students were given a problem where the string was vibrating in its fifth harmonic. A fourth of the class did it correctly, drawing it out and concluding that the wavelength must be 2/5 the string length. Half the class did it wrong saying that the wavelength was equal to the string length. And a third of the class said the wavelength was 5/2 of the string length. As I was walking around, I asked a student why they thought so many people were making these mistakes.

She responded without hesitation, “The sample problem was poorly designed. You shouldn’t have given us an example in which the wavelength and the string length were equal. That makes it easy for everyone to think that’s what you are supposed to do every time. Plus dividing by 1 or multiplying 1 gives you the same result, so it’s easy for people to mix it up. Next year, you should use a different harmonic to set up the problem.”

I wish my future physics teachers knew had to unpack a sample problem like that, and see how it might lead to over-generalizations and misinterpretations.

For class, I was searching google images for drawings depicting impossible moons. I’m pretty sure this one wins because of its irony with the title. Note that I haven’t read the book.

My thinking:

#1  You can’t see a crescent moon with this orientation at night time, because the sun would have to be in the sky (i.e., above and to the right), thus making it day time.

#2 The star to the bottom left of the crescent shouldn’t be there due to occultation–the dark side of the moon is still there, blocking our view of that star.

Today in Inquiry was more much better than Monday. Here are some reasons why:

• A very clear goal was given to students for the day
• A product was required to meet that goal and it was tied to public performance
• Expectations for public performance were clearly established
• Expectations that everyone had to contribute and be involved were clearly established
• I reminded them of what tools we’ve developed that they have at their disposal to get started
• I acknowledged and set aside interesting ideas and questions that were tangential to activity

Today wasn’t great, but it was a step in the right direction.

What wasn’t soooo great, was we were a little rushed toward the end, and so being engaged in listening and making sense of what others had done wasn’t fantastic. Or, maybe I didn’t set expectations for what they should be doing while the others were listening…

Today was very challenging day in inquiry. I could easily mark this one as the worst day of the year, but I think that’s just how I feel at the moment.

Here are some reasons why I think things culminated in such ickiness today:

• It turns out that I have very little experience and knowledge concerning the difficulties and resources that students have to think in 3D dimensions and about rotations in three dimensions, but especially concerning how they might think about 2D representations of 3D things. This is an issue, because we are learning about the moon. For example, I am capable of noticing that students are really struggling “in-the-moment” of class and I can get some sense of what they might be struggling with, but I’m not good at anticipating any of it ahead of time. Thus, I’m improvising way too much in class, and my plans don’t go so well because they are not designed with knowledge of those difficulties or resources. In many cases (like today), I have chosen to abandon plans, but realize in hindsight that it would have been better to stick with plan. My improvising becomes too geared toward putting out fires, rather than pursuing meaningful activity in which fires arise and become resolved more graciously. Not being aware of what resources students are likely to benefit from, there are certain linge-pin ideas that I didn’t build up earlier when I should have, and then it can feel like (today) the whole bottom of our understanding falls apart. Like, on Wednesday, it felt like we all understood the moon, and today, everything we built about the moon was a house of cards. It wasn’t really, but it certainly felt like it.
• Somewhere along this semester, I have cultivated a very a “needy” classroom. If they can’t figure something out immediately, many just disengage and/or wait for me to come around and give them hints. I’ll have to think hard about how this happened, because this is not the norm for my classes. This facet of my class is of course exacerbated by the fact that I’m not doing a good job anticipating their difficulties in this unit. So, of course, they have more problems than I expect and I also provide them with less scaffolds than they need. Therefore I’m running around more, putting out fires table by table, while actually just flaming the fires of neediness.
• A few students I’ve let engage in a kind of classroom talk that is really unproductive–not talking about the science, but about the classroom itself. Those few feel like should let us know if we are doing something they don’t find personally meaningful or worthwhile. They have a strong voice that either pulls others in, or makes others roll their eyes. I’m generally OK with students have input and say, but it’s gotten unproductive. This is also exacerbated because of the two things list above.
• This unit has become (unintentionally) very focused on the ways in which our prior ways of understanding of the moon have been impoverished, rather than focusing on ways in which our new understandings are becoming rich. We have been talking a lot of the idea that the phases are caused by Earth’s shadow, but I think in talking about it in certain ways, some students have walked away feeling stupid for having ever thought it, and that’s not my intention.

Things to remind myself before I go home and have a glass of wine:

• I can learn from mistakes in my teaching. In fact, we learn much of the time by making mistakes.
• I can have bad days teaching and I can recover from them, both emotionally and practically.
• A class can have bad days and it can recover from them, both emotionally and practically.
• Although not always true, sometimes sticking with a plan is a good idea, even if you know it’ll be bumpy. A bumpy road is better than driving off the road into a ditch. And boy some ditches are painful.

Some possible changes on the horizon for algebra-based physics here:

#1 The adoption of PER-informed textbook

#2 Use of established research-based curricular materials / activities

This is a big changes for our department in terms of how to think about reform. Most of the reforms in our department have been made without close attention to the subject matter. We have collaborative group work, whiteboards, and clickers. Those are all good things, but none of that has anything to do specifically with physics or how students learn physics. Don’t get me wrong: I’m all for interactive engagement and technologies that support that engagement. But at the end of the day, what students are engaged with matters.

U-shaped Development:

Sometimes, as we learn new skills, our performance drops before it rises again. Intuitively, this makes sense of sense, especially in the context of sports. Let’s say you intuitively learned how to shoot free-throws a certain way, and over time you were able to get up to 70% of them in. Unfortunately, you end up stuck at 70% accuracy for years. A friend comes along and shows you a better technique. At first, when you try his method, you can barely get in 25%. Your tempted to give up, because it seems like this method is never going to work. Your friend encourages you to keep trying. After a few weeks of putting in the practice, you end up getting in close to 90% in.

This kind of development shows up in children as well. Children’s performance balancing blocks declines as they start to develop theories of how objects balance. Children’s use of language declines as they start to develop generalizations about the structure of language. Sure enough, even through their performance dips in the short run, it comes back better than before as they develop more general, more powerful strategies for understanding the world and the languages they are immersed in.

Physics Makes You Worse at Physics?

The same kind of thing might be said about students’ performance in physics. Learning formal physics concepts and problem solving strategies can make students’ performance decline, at least in the short run. One example of this comes from Andrew Heckler’s work that I’ve written about before. Students who are prompted to use force diagrams do worse than students’ who aren’t. This can be accounted for because students who draw force diagram are more likely to use formal strategies (which they are novice in carrying out), whereas students who aren’t prompted are more likely to use intuitive strategies (in which they are more experienced). Another account is that students who are prompted to use force diagrams stop actively monitoring for whether what they are doing makes sense, because the method itself doesn’t really make sense to them. That is, force diagrams, are not a sense-making tool. They are just something your physics teacher asks you to do. Doing problems without trying to make sense of what your doing is a recipe for not being successful.

Some Recent Work by an Undergrad

Recently, an undergraduate student working with me asked physics students and non-physics students the following question:

Two cars are located 200 miles apart from each other on a long straight road. Both cars start driving toward each other. One car drives at 50 mph, while the other car drives at 30 mph. How long will it take for the cars to meet along the road?

The results: About 57% of the physics students we surveyed get the answer correct, while about 90% of non-physics majors surveyed get it right. Our numbers are small (about 25 per group), but that difference is quite large, and statistically significant enough for exploratory work (p < .05).

Why do Students do Worse?

Roughly, there are three categories of physics students who get the question wrong.

Category #1:  Students pursue an equations-based approach, and somewhere along the way they either give up or do something erroneous.

Category #2: Students explicitly state that the problem cannot be solved without kinematics equations, which they don’t have memorized.

Category #3:  Students take an intuitive approach that gives the wrong answer.

So what about non-physics students? THey almost always take an intuitive approach. 90% of the time they get the answer correct, and 10% they get answer incorrect. So, what are the intuitive approaches:

Intuitive Approaches that lead to high level of Success

Draw a sketch and use to figure out where the cars are hour by hour.

Consider the combined speed they have as 80 mph covered.

Set up an “algebra” problem (30x + 50x = 200)

Intuitive Approaches that lead to low levels of Success:

Calculate how long it would take each to travel 200 miles and then do “something”–sometimes average the times, but more often subtract the times,

Try to construct a ratio where the ratio of speeds equal some other ratio

Now, one might be tempted to think that non-physics majors do better because they use intuitive approaches, and that most of them use intuitive approaches that lead to high levels of success. But that isn’t entirely true. Many of the non-physics majors begin with an intuitive approach that doesn’t get them the right answer. But then something leads them to solve the problem another way, or to cross out that answer and try again. Some students explicitly write about how their first method was invalid and how it didn’t make sense. They end up with the right answer, because they are actively checking for whether their answer and their approach makes sense. They try some new way. Others students solve the problem multiples ways to check and see if they get the same answer. Almost none of the physics students try to solve the problem multiple ways, or check the reasonableness of their answer. Due to this, physics students who do take an intuitive approach are more likely to stop with that wrong answer.

Why would physics students be less likely to check for reasonableness of an approach or an answer?

We ask students to engage in problem-solving methods and techniques that don’t make sense to them. They get so used to things not making sense, that they begin to stop trying to make sense of the things they do and the answers they get. In other words, learning physics teaches them not to check for sensibility.

So What?

And and all, I want to say that there are two reasons why physics students do worse. First, they are less likely to draw on informal methods for solving problems, which are often successful. Second, when they draw on informal methods for solving the problem, they are less likely to monitor their approach and their answers for whether or not it makes sense.

Sp? Is this a case of “Normal” U-shaped Development? One argument would say, “Yes. Don’t worry that students are doing worse. In the long run, student performance will rebound. Their intuitive approaches won’t get them much farther than easy problems. As they get better at these more powerful and generalizable methods, the benefits will be seen.” There is a part of me that thinks this argument makes sense.

One counter-argument to this is the following, expressed by my friend Sam McKagan. Normal U-shaped development might be fine if students went on to take more physics courses, but it looks like we are dropping students off at the bottom of the curve.

A second counter-argument is the following. It would be OK for students to do worse if they were just making mistakes in implementing expert strategies. That would be like the basketball player getting worse when learning the new free-throw technique. But imagine if the basketball player started trying to the new technique with no regard for whether or not the ball went in. What if they thought the goal was to do the method, and not even check if the ball went in, or adapting the new method to improve their game. That would seem bad, right? And that’s what it looks like students are doing–they stopped aiming for the basket.

All and all, a decline in performance isn’t necessarily a bad thing. We have to look the causes of that performance decline. My hypothesis is that this particular decline in performance is less about healthy/normal U-shaped development than it is about the effect that instruction has on students’ sense of the game they are trying to play. In grand picture, I’d like to collect more data and to continue the arguments going.