## Friday, March 11, 2011

### Chains of Reasoning: Sand and SW

I'm trying to directly, explicitly work on students in physics reasoning well.  By "well," I mean that they can construct a linear path of inference from known information to the conclusion.

They think that this is easy, and that they're just "not showing" some steps that they did in their heads, but... about two-thirds of their initial answers are wrong!

Here was the prompt:

This is the best of the student work; I was surprised at the amount of difficulty that many of the groups had here.  Many thought that they were just not writing down some steps, but when I made them do it, there were gaps in their logic.  Filling in the gaps led to the correct answer!

My main message:

Science isn't about 'knowing;' it's about being able to figure out something that you don't know!  If you can't reason, then you're not doing science.

The biggest resistance is from the 'memorizers,' and why not?  It has worked for most of them before.

Here's about what I'm looking for - the student group above did a pretty good job of it, but many groups weren't quite able to get to here:

One thing that made it trickier for them was that this isn't really the totality of the situation.  If I really went through everything, it might look more like this:
The reasoning process isn't linear - there are branches, dead-ends, parallel tracks, islands that don't connect, etc.  It's a central skill to be able to prune that tree - to figure out what inferences and facts are relevant, and how they connect to form a complete argument.

How do we teach that?  Well, that's the trick, isn't it?  I think that being forced to explicitly write it out can help model the processes will push them in the direction of logical progression of thought when they don't write it down, but I'm open to suggestions!

1. I really like the idea of giving activities that force them to make the steps in their reasoning explicit. I'm sure for many of them, that was the first time that they had to sit down and consider each step that led from the given information to the conclusion.

Is this something that you are thinking of making a Standard in the future?

2. This is great. Thanks to your earlier prompt, I've written previously about trying to teach long chains of reasoning, and I've heard from at least one college professor, thatit is a most essential skill for future science success. When I tried this with momentum, we actually made chains from paper, and students asked to later use them on the assessment, which I thought was great. I like your idea of mapping them out perhaps even better, since it is easier to visualize, and you can see unlinked items.

3. @Joss: I'm sure that it was the first time - shame on me! I'm going to start earlier next year, when the material and the connections aren't as complex. Hopefully, it'll translate forward!

I originally had a "Synthesis" standard, but I dropped it for want of a way to reliably assess it. Maybe I'll come back to it. I do use a "logic" standard, though. The score is set high if they can find and identify a couple of logical fallacies in the media, and lowered if/when they make an illogical argument (after which they can find some more to pump it up again).

4. @QP: Maybe that's a good way to bill it: college teachers say that students that can't reason have huge problems?

5. It's funny that the first thing I thought when I saw the prompt was that the standing wave would collapse. I really liked how you talk about the logic "boxes" not necessarily all connecting to each other.

I think getting students to be specific about their process is awesome. I think finding a way to have it be a standard is a great idea.

6. @TP I (heart) your "logic" standard with finding logical fallacies in the media. Does it get lowered for illogical arguments that come at any time (classroom discussions, when assessing another standard, etc)?

7. @Joss :) I have just been doing it for lab reports, quizzes, tests, etc. There's a fine line there between real-time assessment and making the kids nervous about everything they say being 'graded'! I haven't exactly determined where that line is. :)

8. @TP I think it might be reasonable to do it for things that they say as well as long as you always gave them a chance to identify their own logical fallacies. If they could do that they could get a no change or even bumped up logic score even if they didn't try to fix their argument. They could step back and say "I guess that I wasn't making a good argument because of X" and that would still be a good demonstration of the standard.

9. I usually try to model this by putting pictures up on the board and asking students to describe what they see before they try to explain or predict. It started as a way to keep the fastest students from blurting out before the slower students had a chance to process what they were seeing, but it's also helped all the students understand how to gather and check facts before they make inferences.

10. @Elizabeth: great point. It's obvious to us that there's a difference between guessing and predicting, but not really to them!

11. Although I love the idea of explicitly mapping out students' reasoning, this seems like a confusing example to give them. "The waveform will collapse" is not really clear to me. What will happen is the waveform will become a superposition of standing waves. The amplitude at a fixed location will be time-dependent, and it takes Fourier analysis to see what happens next. This seems like an unreasonably difficult problem for beginning students.

12. @arc: Keep in mind that this was at the end of over a month on waves, followed by over a month on sound, so SW are familiar to them. The concept that SW can only exist in a medium at certain frequencies is one that they're very familiar with. We don't need to get into the details about how to predict the amplitude as a function of time: it suffices for us that the superposition won't be regular and that the amplitude won't be consistent, nor as large as at some places with the SW. That's all we're getting at.

The idea that taking (most of) the math out of a course often requires substitution with reasoning that's _more_ complicated than what an 'honors' class might be doing is a good one, though. I choose to respond by making the reasoning more difficult in the honors class. It's not 'conceptual' vs. 'math' for me; it's 'conceptual' vs. 'conceptual and math'.

13. @Tatnall I see - your students have more preparation than I realized! Did any groups accurately predict what happens?

14. @arc: Well, now I'm all proud. :) I'd say that maybe 4/8 did it correctly the first time, with everyone getting it when I gave a bit of a hint about the frequency being controlled by the machine. When I gave this on the final last term, I included some scaffolding questions: What happens to the tension?, ...wavespeed?, ...frequency?, ...wavelength? Most students got 2/4 correct, and maybe a quarter got them all.