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.