Confidence in Reasoning

My inquiry-based experiments forced me to face something I hadn’t considered: my lack of confidence in the power of reasoning.*  I spent a lot of time worrying that my students would build some elaborately misconstrued model that would hobble them forever. But you know what?  If you measure carefully, and read carefully, and evaluate your sources carefully, while attending to clarity, precision, causality and coherence, you come up with a decent model.  One that makes decent predictions for the circumstances under test, and points to significant questions.

Did I really believe that rigorous, good quality thinking would lead to hopelessly jumbled conclusions?  Apparently I did, because this realization felt surprising and unfamiliar.  Which surprised the heck out of me.  If I did believe that good quality thinking led to poor-quality conclusions (in other words, conclusions with no predictive or generative power), where exactly did I think good-quality conclusions came from?  Luck?  Delivered by a stork?  I mean, honestly.

If I was my student, I would challenge me to explain my “before-thinking” and “after-thinking.”  Like my students, I find myself unable to explain my “before-thinking.”  The best I can do is to say that my ideas about reasoning were unclear, unexamined, and jumbled up with my ideas about “talent” or “instinct” or something like that.  Yup — because if two people use equally well-reasoned thinking but one draws strong conclusions and the other draws weak conclusions, the difference must be an inherent “ability to be right” that one person has and the other person doesn’t.  *sigh* My inner “voice of Carol Dweck” is giving me some stern formative feedback as we speak.

Jason Buell breaks it down for me in a comment:

Eventually…I expect that they’ll get to the “right” answer. At least at my level, they don’t get into anything subtle enough that a mountain of evidence can be explained equally well by different models.

If they don’t get there eventually, either I haven’t done my job asking the right questions or they’re fitting their evidence to their conclusion.

Last year, I worried a lot that my teaching wasn’t strong enough to pull this off — by which I mean, I worried that my content knowledge of electronics and my process knowledge of ed theory wasn’t strong enough.  And you know?  They’re not — there’s a lot I don’t know.

But for this purpose, that’s not what I need.  I have a more than strong enough grasp of the content to notice when someone is being clear and precise, whether they are using magical thinking or causal thinking, begging the question, or being self-contradictory. And I have the group facilitation skills to keep the conversation focussed on those ideas.  Noticing that helped me sleep a lot better.

A slight difference from Jason’s note above: I don’t expect my students to get to the “right” (i.e. canonical) answer.  The textbook we use teaches the Bohr model, not quantum physics. If they go beyond that, great.  If they don’t, but come up with something that allows them to make predictions within 5-10% of their measurements, draw logical inferences about what’s wrong with a broken machine, and it’s clear, precise, and internally consistent, they’ll be great at their jobs.  And, it turns out, there is a limited number of possible models that satisfy those criteria, most of which have probably been canonical sometime during the last 90 years.  I don’t care if they settle on Bohr or Pauli.  I care that they develop some confidence in reasoning.  I care that they strengthen their thinking enough to justifiably have confidence in their reasoning, specifically.

* For the concept of “confidence in reasoning,” I’m indebted to the Foundation for Critical Thinking, which writes about it as one of their Valuable Intellectual Traits.

7 comments

  1. I agree. It’s really hard sometimes to sit back and “know” that they will get to a good answer without being directed on what to think. An important aspect of this, I’ve found, is to keep the small groups separate from each other while they are working. If every group comes up with a different wrong solution to a problem, the discussion will lead them all to a pretty good solution. If they all have the same wrong solution, though, they’ll just agree. If they see and hear what other groups are doing while they are forming their own ideas, then they will all basically come to a consensus without discussion before the whiteboard presentations, and (especially at the beginning of the year) they will usually have nervously adopted pretty wrong thinking. At the start of the year, when they are still programmed to think that being a good student means being right the first time every time, it takes a lot of meta-talk to make sure they don’t copy other boards or thinking before presentations happen.

    Amazingly, when they do their own thinking instead of cribbing ahead of time, this whole discussion thing seems to always work out (so far). I’m still a little surprised each time (most especially when it starts with no one having a good solution), so I guess I’m with you on not 100% having internalized the belief yet.

    • …keep the small groups separate from each other while they are working…

      I think you’re on to something here. I haven’t fully fleshed out my thoughts, but this was part of my thinking about why I did my best to make sure they all had different questions to analyze.

      Also, I mostly had them working in groups of two, or ideally, individually. When I tried bigger groups, I saw a lot of “pseudoteaching” within the groups: one person would declare that it was thus, and the rest would unthinkingly agree. Even if the declarer was making a well-founded judgement and clearly explaining their reasoning, I found it no better than if I made a well-founded judgement and clearly explained my reasoning. In other words, left to their own devices, they recreated standard lecture-based classroom dynamics. (Depressing.) Have you seen this type of thing? If so, I’d be curious to know how you handled it.

      As for the conversation leading to good reasoning, I definitely found that true, but not automatically. I spent a fair amount of time coaching them on how to discuss — how to ask for clarification or precision, how to figure out which questions are likely to be significant, how to disagree respectfully, how to mine a failed experiment for why it went wrong (not just “that” it went wrong), how to point out a contradiction without being an ass. I definitely need to spend some time gathering those thoughts. Do you find that your students come to class with those skills already? Where do they learn them?

      • You are giving me a lot of good things to think about and analyze about what is happening in my classes. I’ll try my best at a first pass here:

        I think there are two separate situations: (1) when the students are all working on the same problem and we do a big “whiteboard face-off” or a big board meeting and (2) when the groups are all presenting different problems to each other.

        Situation (1) doesn’t actually happen very often in my classes. There are very specific times when we do problems that way. The first worksheet in the balanced forces unit, which is 4 or 5 pages of the same problem 4 or 5 times, but with slight changes from time to time—that’s one of the few times that immediately comes to mind for me. I let them work in our little balance of “individually together” group work where they are basically thinking on their own, then thinking together, but always writing on their own papers. That sort of thing is the majority of our class time all year. But on these problems, I let them do that work until they’ve gotten through a couple of pages at least, then I have every group whiteboard the first version of the problem. I give them the talk about needing to stay away from the thinking of other groups until the presentations happen. Then we circle up, and their job is to come to a consensus about how the board should look. Since this unit happens really early in the year, I intervene a little here and there to focus them on what parts of the board are most important (like the changes in slope, not the slope itself, since the graphs are qualitative).

        Situation (2) happens very routinely. Every student works on every problem in that individually together pattern at their tables (I have about 10 to 14 students, usually sitting at 5 to 6 tables). If they ask me to help them with a problem, I nudge them along, but I try to resist confirming right/wrong answers, etc. I try to just help the groups that get totally stuck. I always tell them, “We’re whiteboarding this,” and once we’re far enough into the year for them to understand that, almost all of them are totally fine with me not confirming answers then. When I’ve seen that everyone is far enough (everyone has done 5 or 6 chunks of work—problems or maybe halves of problems, if applicable), then I assign each table one of those chunks to whiteboard. We always play the mistake game (there are a very few exceptions for activities that aren’t really worksheet problems and where intentional mistakes might just make it confusing and long instead of helpful). I think the nature of the mistake game helps teach them the kinds of things you mention above (asking for clarification, correcting, knowing what is important, etc).

        Since they know that there is at least one mistake on the board, it prompts an immediate need for a discussion. Since they know at least one of the mistakes is intentional, they don’t immediately turn to me to confirm or deny the validity of the work on the board. They already know it’s wrong! They are only allowed to ask questions of the group presenting about the work that the group did. They can’t make statements or ask about their own work. This kind of questioning is really really really hard. Almost immediately, a poorly thought out question (or “question”) will be posed. It might be just blurting out “That’s wrong!”, or it might be something like, “Isn’t that wrong?” If it’s not a question, I always intervene (a lot at the start of the year, but it becomes mostly a nonissue later) and ask them to take a moment to think and come up with a question that helps expose their disagreement. If it is a poor question, I often pause them and we talk about how the skill of posing questions is really difficult.

        There’s definitely a lot more depth to the mistake game than I realized before. It helps set up the right kind of discussion during whiteboarding in a way that doesn’t feel forced or uncomfortable for the kids. When I used to just do normal whiteboarding, it took a really long time at the start of each year to get each class to even understand what I wanted them to do, much less to buy into doing that every time instead of just turning around a board, everyone asking questions of me instead of their peers (if they asked any questions at all—many would just copy down the work without even knowing whether it was correct), then sitting back down. I don’t think I’d ever go back to trying not to make mistakes with whiteboarding. 🙂

        Okay, and back to the larger groups question. I rarely let them work in groups larger than 2 or 3 (not counting the whole-class discussions during whiteboarding). In my best classes, they are capable of having whole-class discussions any time (by the end of the year). They don’t look at me or even invite me into the conversation. And if I add something, they tend not to take it as any better or worse than anything else being said. I had one class this past year that was unbelievable about that. I’m not really sure how that happened. I did try to help the other Honors Physics section get closer to that kind of work, and I think I succeeded in moving them in the right direction by having brief time-out talks during class about what the best physics classes do (like one about talking to each other instead of sequentially making statements). They really grabbed on to what I said to them in those talks, and they saw big improvements in short amounts of time. One task for this summer is to try to figure out how to get every class there. I’ve been thinking about the forming, norming, storming, performing ideas (http://en.wikipedia.org/wiki/Tuckman's_stages_of_group_development) and how to get classes to the performing stage. If you read the norming stage description, it reads like what I think many people would describe as a “good” class[room]. Not a very efficient stage, but I guess it looks good. In fact, many students really ache for the class to be in that kind of state. The teacher directs everything, everyone is polite to everyone else, and everyone is very focused on themselves. But I think that if a student had the chance to be part of a class that reached the performing stage (like one of my classes this year certainly did), I don’t know how they could ever be satisfied with anything else. It’s just so much fun. And also so much more efficient.

        Sorry, this got really long. It also has some fragments of at least 2 in-progress post drafts that I’ve been thinking about for a while. I’m hoping to round that all out soon (or at least during the summer).

      • Wow. Looking forward to the blog posts this becomes.

        I like the term “individually together.” I think you’re right to draw a distinction between when there is a single record of the group’s work, and when there are multiple records — I’d like to take a closer look at how it affects the kinds of “talk moves” students use.

        I love what you’ve written about the “mistake game.” I need to go back and reread some of your posts about whiteboard techniques. I haven’t found a good way to incorporate it, since we spend an entire year trying to learn to measure well and research well, which doesn’t lend itself (I don’t think). I need to look more closely at the distinction between worksheet problems and others — one thing I want to improve for next year is to provide more procedural practice for those who need it, and the mistake game might be a good way to continue our theme of justifying reasoning. I can see how could reduce cognitive load, by taking away the need to worry about whether the solution is “right,” and by making it more obvious exactly what everyone is supposed to do.

        I’m hoping you’ll write more about your thoughts on why “the skill of asking questions is really difficult,” the kinds of meta-talk you use, and how the students respond.

        if I add something, they tend not to take it as any better or worse than anything else being said.

        Congrats!! I have a funny story about my failure to accomplish this — coming soon to a blog near you. 😉 Hope you’ll keep us posted if you discover any clues about how to make this more likely…

        like one about talking to each other instead of sequentially making statements). They really grabbed on to what I said to them in those talks…

        Good point about the sequential statements. My students grabbed on to this stuff too, and started proposing their own group-dynamics improvements (I was shocked). We did an exercise on “rights and responsibilities” at the beginning of the year, and I used it as the basis of the evaluations we did about every three weeks. Sharing (anonymously) students’ comments seemed to make them notice group dynamics more.

        As for why students would put up with mediocre levels of mutual support, I really don’t know. But one thing has definitely happened this year: as I’ve seen how well my students can do, I have become impatient with inefficient, compliant teams.

    • That’s an interesting point. It’s especially interesting because I spent a lot of the last 10 months feeling depressed as I discovered metacognitive skills that my students didn’t have. So this idea seems hopeful. I will have to think about it some more.

      I was definitely doubting the power of reasoning though. I watched them consistently improve their thinking and demonstrate some downright impressive reasoning. And even while I was gloating inwardly about how well that was going, I was gripped with fear that good-quality reasoning about good-quality sources might not be enough. When I suddenly realized that good-quality reasoning is, by definition, what leads to good-quality conclusions, it was a relief. Weirdly, of course, if you had asked me about it in so many words, I would insisted that I already knew that. I need to hang on to this experience of “not-internalizing,” because my students do it all the time and it’s hard for me to relate to it when it happens to someone else.

      So I’m trying to identify exactly what else I thought we would need. I guess besides “talent,” I was also worried that we wouldn’t have enough time for them to strengthen their thinking enough to be ready for the next course, and that they wouldn’t have enough patience or energy to stick with the process. I expected mutiny, I think, yet it never came. That seems like more evidence that I underestimated them.

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