One question I asked a lot of the future physics teachers during their oral assessments was to discuss the following expression in terms of what it could mean (i.e., the story it tells) and if it seems to be a valid statement or not.
Δx = vf Δt – 1/2 a (Δt)²
Follow up question were targeted at asking students to identify correspondences between various terms and features of graphs.
With some students, this led to a conversation about all three of equations below–how they were similar and different etc, and how they corresponded to features of graphs.
Δx = vi Δt + 1/2 a (Δt)²
Δx = vavg Δt
Δx = vf Δt – 1/2 a (Δt)²
The growth that I’ve seen in many of the students is this. At the beginning of the semester, most students would have either said that the equation was wrong by pointing out that the wrong velocity and the minus sign, or for some, their only way of determining its validity would have been to substitute another equation into that equation until it looked like an equation from a textbook that they already knew. Thus, by the authority of the textbook, the statement must be true as well.
Most students by the end of the semester were able to look at this brand new equation–one they have never seen or considered before–and tell both a verbal story and a graphical story that explains and validates the equation without need for algebraic substitutions. I am impressed.
In other areas, growth has come in fits and starts, and there were many relapses. Many students during oral assessments this last week exhibited one of more of the following difficulties:
- Confusing instantaneous velocity with constant or average velocity (e.g., claiming that an object thrown upward with a speed of 20 m/s goes 20 meter in the first second)
- Confusing change in velocity for average velocity–the two are subtly related in constant acceleration case. Interestingly, this mistake came up both mathematically and conceptually for the same student in the same assessment.
- Confusing acceleration, velocity, and displacement–claiming that when an object falls 10m, it will take 1s to do so, and be up to 10 m/s of speed.
- Confusing change in speed with change in velocity–claiming that a bouncy ball experiences no change in velocity upon rebounding off the floor.
To be fair, these relapses often came up within much more complex physical situations and tasks that were more cognitively demanding–bouncing balls, oral assessments, deriving a result, etc. It’s good to know that, distinguishing these concepts, is not stable and automatic for them. It requires specific cognitive attention to maintaining the distinctions. They can do it, but are prone to making these mistakes when there are many balls to juggle all at once. I discussed with students how the mistakes they are prone to making here are similar to the mistakes we encountered all semester in looking at student work and how they are similar to the ones they are going to encounter in the classroom, so it is best to understand these mistakes well by making them yourself in as many different situations as possible, and doing the hard work of finding your way out of them.
Doing oral assessments for standards makes the assessments spontaneously grow into interesting conversations. Sometimes, what I thought I was initially assessing became something else entirely. Sometimes during assessments, I would respond to wrong things student said by saying, “OK. Tell me about that again, and then tell me why what you just said can’t be right.” Some students would be able to recover, and others would need more time, and I’d give it to them. Other times, I would send a student off, saying, “There’s a mistake in here. I want you to go figure out what the mistake is. When you come back, I don’t just want to know what the right answer is, I want to know why you made that mistake and why it’s a big deal.”
It’s been interesting to watch the varied resiliency of students in the face of my refusal to accept their work as proficient. The only times I know I was doing a less-than-good job was when they would come back and say, “Is this what you want?” Fortunately, it wasn’t often, but it did happen a few times. Most of the times they would come back saying, “OK. I got it now,” or, “I still don’t get this, can we talk about it some more?”
Next year, I’m putting a 2-week rule on my standards, so that students have to turn in an initial draft within 2 weeks. I had many students flying in last minute trying to work through all the standards.