Modeling Instruction in Physics: I had no idea...

You know, when I started this workshop, I thought I had a good idea of what Modeling Instruction was. After all, I'd read teacher blogs, looked at the AMTA website, checked out suggested course info that had been posted online, and been to a couple of workshops on it.

What I thought I knew about Modeling was entirely superficial and nowhere near as powerful. You know - students do the labs first, develop the formulas from their data, and then are better prepared for problem solving. Instead of me working hard to make examples and demos and clear explanations to get them to understand, they'd be doing the work by experiencing the phenomena themselves and thinking about it. Oh, and it's fun, so they like it!

Oh, there's so much more to it! There's a focus on drawing out student preconceptions and creating discrepant events to get them to analyze their own ideas. There's repeated exposure to the same ideas but in different contexts. There's unobtrusively guiding discussions so that 1) there isn't an authority figure and 2) they fully discuss their reasoning and (eventually) determine if it is faulty or not. 

I'm so glad I'm in this workshop!

I'm so nervous for this next school year!

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.

Modeling Instruction in Physics: Buggy Practicum

I had the most fun of the week on Day 3, during the Buggy Practicum.

We had to create one of three car crash action sequences for a "movie", and tell our director where to put the camera to film it. (The Academy Award goes to Bryan for his role as the penny-pinching director.) The group I was assigned to had to create a car chase that results in a rear-end crash in front of the camera. (Scenario 2) 

Adding to the excitement was the short amount of time we had to figure out where to put the camera. 

We didn't have much argument about how to start our work. Everyone jumped right in, setting up a 2 meter distance for the cars to travel and pulling out phones to be stopwatches. There were 4 or 5 of us timing, so we took the average time to use in each calculation of the cars' speeds. We used those speeds to set up motion equations based on the generalized equation we'd come up with earlier. 

This is where our group split into two. Some of us graphed the equations to see where they intersected. Others did some math to find the solution for the simultaneous linear equations. Then we checked that our answers matched.

It's funny. You know these two methods will both work, but it's still really exciting to find out other people reached the same answer you did, but in a completely different way. It's confidence inspiring. As a math teacher, I always say that answers are strongest when there are many ways to reach them. But as a physics teacher, I haven't been focusing on the multiple representations (graphs, equations, verbal explanations) as ways to reach a numerical answer. The verbal and graphical representations are for conceptual (qualitative) questions, while the math is how you reach an actual numerical answer. My students have been missing out on that moment of "Yeah, I got that too, but I used the graph." (They do compare numerical answers with each other... but it's just not the same as using a completely different method. They're mostly checking that they can do algebra correctly.)

Anyway, the best part of the practicum was actually testing our solution. Everyone gathered around to watch, and we all rooted for the crash to happen in the right spot, cheering when they crashed. From my vantage point, that crash definitely happened where it was supposed to. 

Unfortunately, our "director's"  camera disagreed. So close!!

I can appreciate the point Bryan made about failure. It is important to fail sometimes, and have to deal with that failure. Our cars didn't crash on the point we'd marked. We failed. 

But... I do wish we'd had time to explore what went wrong. There is instantaneous feedback built into the practicum (did it, or did it not, work), but a failure doesn't mean I don't understand the concepts involved. I'm pretty sure our work was right, and that it was a problem with releasing the cars simultaneously. Releasing the chase car early would account for an early crash. So, as an instructor, I think I'd want to make sure I had time built in to have a conversation with the groups about where their errors happened. And maybe let them try it again to see if they're right about those errors. (Not, of course, to change their "grade" on the practicum.)

Modeling Instruction in Physics: Day 1

Today was the first day of the Modeling Instruction in Physics workshop (in Novi), and so far, there are 3 things standing out in my brain. 

1. We're getting a stipend for this! I'm having trouble comprehending the idea that I'm getting paid to get professional development I so very much want (and need, in my opinion). Honestly, I'd be comfortable paying for a 3-week intensive workshop like this.  

2. There's a big difference between thinking about Modeling Instruction and having a Modeling mindset. Ok, I know it's Day 1 of the workshop, but this is what struck me. I've been reading about and tinkering with Modeling in my classroom for a year now, so I have a lot of thoughts on how to implement it and how to adjust my teaching (you know, the "I talk too much and do more work than my students" sort of teaching). But I don't have a Modeling mindset. (It's the difference between thinking in English and translating to German, and thinking in German.) 

After class today, while I was waiting to ask Laura, one of our facilitators, a question, I jumped in on a discussion my group mate, Lindsay, was having with her. Lindsay was troubled by a statement made earlier that day, "Be less clear," because that's what her math students have always complemented her on - how clearly she breaks down whatever they're working on for them. What struck me most was the difference between my responses to her and Laura's responses to her. Mine consisted of, "Here's what you can do," and "Here's what I try to do." Laura's were along the lines of, "It's good that you're recognizing that in yourself," and "It's Day 1, what matters is Day 15 and how you've improved," and "Be thinking about how you can reframe those skills for Modeling." (All of those are paraphrases, not direct quotes - I can't remember the exact wording...) There I went with the telling, and there Laura went, letting the student figure it out. 

I hope I learn to think about the type of response I'm going to give to any question (teacher-to-teacher or student-to-teacher) before I talk.

3. Why couldn't my teachers have taught this way?! I wish my physics classes had been Modeling courses and not "story problems 101". 

This is going to be awesome!

How can I keep doing this?

(11/3/14) Today in Calculus, we were reviewing average rates of change. (You know, the slope equation you learned in your first algebra class.) Most of the problems had fractions (the horror!), and my students had a lot of trouble arriving at the correct slope value. As we check problem after problem, I ended up constantly repeating, "What are your y-values? How did you set up the average slope formula? What did your numerator and denominator simplify to?" Finally, the girl sitting nearest to me leaned way back in her chair and exclaimed, "How can you keep doing this, Mrs. Hamilton? If I had to keep asking these questions..."

It warms my heart that they recognize some of what this job takes and sympathize with me. That's how I can keep coming back to this school year after year.

My Year with Standards Based Grading (Part 2)

I'm really bad at blogging. I have lots of ideas scribbled down, and even a few drafts started, but I struggle with actually writing things up and publishing them. I'm trying to work on that. The result, however, is a large gap between my last post and what's happening now. There's so much that's happened in between that I don't have documented. This is my attempt at a "catch-up" post. After this, I'll use the ideas I jotted down in the context of my current classes.

So, here's a recap of what happened with my experiment in Standards Based Grading. Here's my idealistic, no-points system I started with in the fall of 2012.

There were a lot of problems with it. I had just started my graduate program, and combining the workload of redesigning how I teach and assess with the graduate workload was a bad idea. It took me a loooong time to write up meaningful feedback about what went wrong and what went right for each student. My students, despite the feedback I was writing up and the general rubric, had no idea what the difference between a "proficient" and an "advanced". They wanted me to spell it out for each topic, and I struggled to figure out a way to do that without just telling them the answers to everything. Adding the general, "I'm looking for you to pull together all of the ideas about this topic and use them and express them in a concise and mathematical way," was not an illuminating statement for them.

Most of my students were really unhappy about this grading system. They didn't want to be guinea pigs, they didn't want it to jeopardize their chances for college, they didn't think it was fair. Near the end of the semester, my director and our college counselor joined me in the classroom and ran a discussion with the students to let them say what they needed to say. I stayed (mostly) silent, and took notes on what they were saying. Here's a summary of the major points:

• Ease into it – start with younger students, not seniors!
• HW optional a bad idea… it won’t get done, despite the best intentions. Grade it.
• Need more help determining what each level of work looks like
• Are they being graded against a standard or other students’ work?
• Scaffold communicating what they understand
• Don’t like grade fluctuations, want some stability to count on.
• Different from previous courses – getting the answer isn't the focus anymore.
• Oral assessments are a great idea

The open discussion helped adjust the mood of the classroom, and I tried to implement some of those suggestions in our last few weeks of class, but they knew that I wouldn't change the whole system for just a few weeks.

But I certainly did for the next semester, Spring 2013 (we're on a 4x4 block schedule, so I had new classes). I was exhausted from trying to keep up with the workload of my system and looking to both ease up on how much work it was and how much complaining I got. So I gave up the "no points" idea and my 5 levels of achievement. Instead, I would take my assessments, figure out how many points there were for each skill in each problem and total them up. I didn't use a fixed 5 or 10 points for skills. It made it easier to grade, and for students to see what points they didn't earn. I was still writing comments for them, but they weren't quite as involved. The downside was that each time we reassessed a skill as a class, the base number of points changed. That made it a little harder to look at the scores as a quick reference for growth or decay over time.

I was going to say that another downside was a return to a fixation on getting points, but given how much trouble the previous class gave me over "Why isn't this advanced? See I had this thing that SHE wrote about..." I'm not sure there really was a change in mindset. Just a change in terminology.

I'm not really sure if what I'm doing counts as SBG anymore, since I'm using points again, but I kept the aspects that focused on growth over time and communicating what skills need to be worked on, so I'm going to call it an SBG-hybrid. I feel guilty from time to time when colleagues still refer to what I do as SBG, but this post by Frank Noschese eases that a bit.

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"?