I have been getting ready for my second go at intro physics by
- Re-designing the multiple-choice reading quizzes to be standards-based assessments
- Choosing whiteboard problems, in part, based on the kind of whole-class conversation that they will drive afterwards
- Tweaking labs so that they are more exploratory than confirmatory , and also so that we operate more like a community
Last Semester Reading Quizzes
Last semester, for example, students would have read a lecture about speed and velocity, and they would have come in, sat down, and taken a five question MC reading quiz. Questions would have been like, “In physics, the study of motion is referred to as _______ a) energetics b) dynamics c) kinematics d) kinesthetics e) mechanics” and “Which of the following is not a scalar quantity: a) distance b) average speed c) average velocity d) time” . My undergraduate TA would have graded the quizzes while I circulated around helping students answer some computer questions. Students would have gotten a score back.
Next Semester Standards-based Assessment
Now, I’ll have students come in and take an open-ended question targeting a particular standard. On this day, it will be: I can distinguish position, change in position, and distance. The question could be something like this, “Starting from the 4-m mark, Brian walks to the 10-m mark, then turns around and walks a distance of 7 meters. What distance did Brian travel? What is Brian’s final position? What is Brian’s change in position?” Students have to show some sketches, some work, or explanations in order for me to consider assessing it.
After the quizzes, students will then go to the back of room and answer to some computer questions. While I don’t think these computer questions are always great, I am deciding not to tweak these, for now. While they work on the computer questions, I will be writing feedback on what they did and wrote. I’ve piloted this, and it doesn’t take me long to give feedback. Now, during this time, I won’t be circulating around to help, but I will have a undergraduate TA in the room. While working on the computer questions, students and the TA will have the goal of keeping track of any questions/confusion that arise and to write them at the front board. Groups who finish early have the goal of checking out the questions at the front of the board, and trying to understand and address them for the whole class.
The second standard of the day “I understand the difference between average speed and average velocity” is not assessed until the end of the class, after we practiced and talked about those ideas with whiteboards.
White-boarding Last Semester
One of the difficulties with white-boarding and discussion has been that, while the problems that students are assigned are “on topic”, they were not necessarily designed for the purpose of driving a meaningful conversation or to make sure students make contact with an important skills, concept, or distinction. Rather, it seems the problems were designed to just give them practice solving problems similar to those they will be expected to solve on the exam. Many of the instructors in our end of semester meeting remarked on how unproductive the board meeting discussions had been. Many had given up on them at some point during the semester. Part of the blame certainly goes to the problems that were picked. A lot of the blame goes to lack of professional development about board meetings–discussing their purpose, learning about some skills on how to effectively manage them, and having a chance to observe a well-run one. Part of the blame also goes to not having specific learning goals in mind for the discussions–my sense is that students in most classes were just presenting what they did. The work student did wasn’t a jumping off point for anything intellectually worthwhile, but merely a routine to get through.
White-boarding Next Semester
To begin, I am picking problems and collections problems with much more deliberation. For example, on this day, I think there will be three different problems about back-and-forth motion. Each group will just do one, but they will all be related somehow. What I am leaning toward right now is having each problem end up having the same average speed but different average velocities–one negative, one positive, and one equal to zero.
Second, I am articulating goals for discussion and how they connect to the problems. See, with these problems, we have something to talk about during discussion. How can we all have same average speed but different average velocity? What is average speed telling us? What is average velocity telling us differently? What does it sign of average velocity tell us? Sure, maybe, other interesting issues or conversations will arise, and we can go in those directions. But I have goals and directions in mind that I can drive at, and I have set up the problems to drive at those discussion points.
I also have planned out challenge / extension problems*:
- For this day, one is for students to come up with a pair of problems that have the same average velocity but different average speed. This is opposite of the first set in two senses–what is now the same /different has swapped, and students have to create the problem not solve it.
- The second is for students to explain why the average speed is not simply the average of the speeds.
* In the future, I’d like to see these kinds of questions as mini-capstones… that students have to work out some number during the semester to get an A.
Another difference next semester is the instructions I am giving students. I’ve written about this before, but the instructions students are given are very equations-focused. Next semester, I will focus more on representations. Students will have to draw a motion map and a position vs. time graph before solving for summary information, including final position, change in position, total time, average speed and average velocity. During discussion, we’ll talk a lot about the representations, as well.
At the end of the day, I wrap back to the second standard of the day. Students take the assessment, and this time they self-assess instead of me assessing.
On this day of class, students are supposed to do a lab measuring diameter and circumference of various pipes to get an experimental value for pi. Previously, they would have been instructed on using the slope method, and students do this. But even with explicit instruction, students seemed to have no idea why finding slope would give Pi, and why it would be any better than just averaging all their data. My actual plan is to move this lab to the very first day of class, which was used to go over class syllabus and take the FCI.
So, my version next semester goes something like this:
- Every group gets the same one pipe to start, and 3 minutes to measure C and D to get a value for Pi, and fill in their data and value on the table at the front of the board.
- Now, we talk about our class’ data. Why is it so off? Why is there so much difference between our values?… Sure, I rushed you. Sorry about that. How would you do it better? At this point we’ll all try to agree to a more reliable procedure… perhaps wrap string around so many times and divide? Why is this better? Should we measure inner or outer diameter? Why? How can we be careful in wrapping the string, or finding the diameter and not just a chord? etc…
- OK, we all agree on how best to do this. Let’s, repeat experiment, and see if our data got any better. … It know it probably will, but not by as much as we’d like.
- OK, what else can we do? You probably noticed lots of different pipes at the front of the room. How can we use this to improve our data? Students will probably suggest taking an average, and I’m going to let them do it. But I’ll make sure to ask, why we think this will make the data better? What does averaging do? Now, every group takes data for every pipe, and instead of doing it at the board, we type their data into a spreadsheet at the front of the room.
- Once the groups are done, we again look at our data… I know our data should still tend be an overestimate of pi. I’ll ask again, what did we think averaging would do? Why isn’t our data very close to Pi? Hopefully they have some ideas based on the fact that we’re always overestimating, but if not, that’s OK. I know it’s because our systematic errors lead us to overestimate the circumference and underestimate the diameter…
- OK, so now what? Here’s where I shift away from inquiry and toward direct instruction. “I want to show you a new method for finding pi using our data”- one that hopefully won’t lead us to always overestimate pi. Here’s what I want you to do… go back to the computer and type in your data into excel. Find the best-fit line. Come back with ideas about what the slope and y-intercept tell us and why?
- Now, we talk about it. I do some explaining as to why this method works… Finally, a check out involves asking students what value we’d expect for the slope if we plotted circumference vs. radius… and/or diameter vs. circumference… Once they have answers, I won’t tell them if they are right or wrong, I’ll ask them to verify that using their data.
I’m interested in following along as you work on the whiteboard problems this next term. I’m terribly hit and miss with having specific learning goals in mind with my whiteboard problems or simply getting them to do an example that I would normally do for them in a pure lecture situation.
Also, I am going to be using challenge problems/questions a lot this coming term. And this will be for clicker questions, whiteboarding and even quizzes. At this point I don’t plan on making it so that they have any impact on student grades, but are simply there so that students that are done early have something productive and challenging to do while waiting for the other groups to finish up. I look forward to hearing how your challenge problems work for you.