Modeling Instruction in Physics: End of Week 1

This week has been one of the most intellectually stimulating weeks of my career. I've had so many thoughts going through my brain this week about the teaching I've done and the teaching I want to be doing.

First, it's well known that students come into class with preconceptions, based on their observations of the world, that don't match Newtonian physics. This was a theme in both my preparatory work and my graduate work. So I have some questions built into the beginning of some of my units to get an idea of what misconceptions my students have. But not all of my units. And I don't really use the questions I do have all that well. I try to remember to point out when something we just learned is contradictory to answers they gave on those preconception questions, and that's about it.

Those preconceptions students have are tenacious. Just pointing out and talking about them doesn't do much of anything. Students might modify those ideas slightly, but even that is unlikely. My students learn what to say on the tests and how to do the calculations they need to, but none that shows that they've changed their minds about how the world works. What I need are better questions and problems to introduce the contradictions between their thinking and what we observe, and my students to recognize that those contradictions exist and then work to find what the correct idea is.

Enter everything we've done this week. All of the labs and discussions are designed to bring different students' ideas out into the open and compare them with the physical data from the lab. Not just once, but over and over again.

Students will struggle with this. They will have trouble understanding each other's points and interpreting the data and graphs, and they will be confused. But nothing worthwhile is easy, and only ideas that more worthwhile and meaningful will replace what students already think. And what's more meaningful than an idea you came up with?

I love physics. I love watching the world around me and knowing why it works like it does. There's something awe-inspiring about how it all fits together. And I want my students to have that understanding. But I'm learning it has to be their work that gets them to that point, not mine. I can't take what I've learned from my efforts and distill it into simple phrases to tell them, and expect it to have any meaning for them. Instead, physics becomes nothing but empty phrases to parrot back and story problems to solve. There's no joy in that.

Struggles and Frustration

Today was a hard day. 

First, I was hoping we could develop the definition of a tangent line in our shortened class period. It's a discussion I've done every year, and it can go very quickly. I give the girls these 6 pictures of tangent lines, carefully chosen so their previous definition of "touches a function at only one point" will not hold, and tell them that they are all pictures of tangent lines. Their job is to come up with a definition of what a tangent line is. 

Graph A

Graph B

                                                      

Graph C

Graph D

Graph E

Graph F

 The first problem is that none of them had even taken the time to look at these pictures ahead of time, like I asked them to. They came in cold to the discussion. Of course, I didn't realize it until I started moving around the room, noticing that there was nothing written in their notebooks. No wonder it was like pulling teeth to get them to list anything. 

The second problem is that when a student offered up "It touches at only one spot, it doesn't go through..." and trailed off, I jumped in with, "What about graph C? Or E and F?" Centering myself in the conversation seems to be the fastest way to kill it. 

I tried asking a question and just waiting. And waiting. And waiting. Then, I'd cave, and ask another question (or a variation on the last one). I still got blank stares. Thank God for the three girls who were willing to eventually speak up.

On the bright side, one student asked if I could give them a definition of a secant line, so they could work from there. Here's what I gave them: "A line that cuts through two points on a curve and whose slope equals the average rate of change of the curve between those two points."

Eventually, I told them to think about these bullet points we'd developed and come up with a statement about what makes a tangent line different from just a secant line:

• Touches the curve at at least one point
• Touches but doesn't go through (what about E & F?)
• Some tangent lines can also be secant lines (B, C and E, but not F)
• Slope?
• Terminology: point of tangency (See D)

I had to end the discussion a little early, because they have a take-home assessment on proving functions are continuous that is due tomorrow, and they asked for time to ask questions on it.

Enter frustration #2. On both sides.

They're somewhat upset that they don't have any examples just like these problems to refer to in their notes or practice problems. No, they don't. Instead, they have lots of examples and practices problems about different aspects of continuity that they can pull together to develop an understanding of the functions they have to prove are continuous. They get frustrated because I'm not pointing them to an exact template to follow. Instead, I'm suggesting that they think about what they know about what continuity and think about how it can be applied to these unusual functions. 

Who said take-home tests were supposed to be easy?

Here's what I want to say to them. I have the email written, but I'm not sure yet I'm going to send it.

Struggle is good. Embrace it. Work through it.
You have all the pieces you need. Now you have to put them together. Think about what you know about these functions. Think about what you know about continuity. Think about what you know about how properties and theorems work: conditions to be met, results you get when they are.

So the question of my day is, how do I teach them how to think and synthesize information? How do I get them to engage in the activities that will allow them to practice those skills instead of begging to be told "the answer" or "the method"?