I am seriously trying not to use the word “conceptual” anymore– not to describe the kind of understanding I want my student to have and not to describe the kinds of questions I often like to use to assess student understanding. It is not a very useful word. It’s not a useful word, in part, because it’s a word that my colleagues use to mean various thing that I don’t. When they hear the word “conceptual”, I think some hear something like, “the easy physics” or the “basic physics”, or “mathless physics”. For others, I think it means something like “deep understanding.” For others it’s just a word to describe those tough questions that physics education researchers have come up with to stump students. For others, it means a multiple choice question, where students don’t actually solve a problem.
In fact, I’ll say I don’t actually use the word very often. It turns out that my colleagues do. I mention some question I asked my students and they say, “Oh yeah, those conceptual questions.” They smile and nod. I wasn’t thinking it was a conceptual question. I was thinking of it as a question that illuminated some aspect of my students’ understanding, or a perplexing question that inspired my students to think, talk, and argue. I was thinking of it as a question that demanded that they pull together more than one tool from their toolbox, or to pull out tools that they rarely get a chance to use (and so are clumsy with). I wasn’t thinking of it as a conceptual question. I was thinking of it as a useful question for teaching and learning— useful for me to find out what my students know or don’t know, or useful for my students because it provoked meaningful engagement with disciplinary ideas and skills.
There are, of course, other alternatives to the word. Skemp, for example, uses “relational” understanding and contrasts that with “instrumental” understandings. And I think this gets at something closer. But I don’t think a new word is the issue. I’m not sure what the issue is exactly… For some, it seems to be a difference in what we think is important for students to know and be able to do. That’s an issue of values. For others, it’s a difference in what we take as evidence of understanding. That’s an issue of assessment. For others, it’s a difference in what understanding is. That’s an issue of epistemology. I don’t mean epistemology in the abstract philosophical notion. I mean one’s personal sense of what it means to understand something. Like when my student told me last week that they knew how to solve every problem but still didn’t feel like they understood anything. By the way, this student did ace the exam. Epistemology is a feeling you develop, a personal sense of what understanding feels like when you have it and what it feels like when you don’t.
Of course, our values concerning learning, the ways in which we assess, and our personal epistemologies are not separate… but neither are they build together coherently. Developing them and working to make them consistent is tough work. For me, myself, I suppose it’s a lot of what I am trying to work out with this blog
Teach. Brian. Teach. 
Brian,
I totally agree. I think your questions get at understanding—with no modifier in front of it, and I’ld like someone to make an argument to me as to how the problem:
Bill drops a ball from height of 20 m, how many seconds does it take to reach the ground?
assess any form of understanding. At this point, if we can type the problem into Wolfram Alpha and get a solution, I think I there is at least a case to be made that it doesn’t assess understanding at all.
Thank you for explaining one of my greatest pet peeves much more eloquently than I usually do. I hear phrases like “conceptual understanding,” “conceptual teaching,” “problem-solving,” and “critical thinking” thrown around ALL the time in my work, and usually it takes quite a bit of in-depth conversation for the participants to realize they’re not actually talking about the same thing. Or, in the case of “conceptual teaching,” not really talking about anything (definable or concrete) at all.
That said, I do wish there were some way to concisely articulate “the type of understanding that goes beyond how to do the steps and how to do the standard textbook application word problem” so that I could explain why it’s valuable without talking myself into circles. I’m not fully convinced by instrumental/relational, concept/generalization/procedure/fact, or any of the models that use various levels of verbs (even though I see the value in each of them, I’m not sure any of them actually answer the question).
Or maybe this reflects a desire to simplify and define something that simply can’t be nailed down, as I think you’re starting to ponder in the second-to-last paragraph. Because maybe we have no way of knowing what’s really going on in someone’s mind (I sympathize with your student: I scored a 5 on my AP Calc BC exam as a junior without the slightest clue what a derivative or a function was), and even if we did, our language isn’t precise enough to articulate it.
Sometimes, when I get trapped in this circle, I think Dewey is only way out. It’s not just ideas for ideas sake, but ideas for how they transform us as human beings and the ways in which we experience ourselves, the world, and our relationship to the world. I don’t know.
Glad you referenced Skemp. Your dilemma is rather Skempian, I would say. Your concern with conceptual parallels his with understanding. It’s not a useful word if we cannot agree on its meaning.
I see two big reasons you cannot agree with your colleagues on the meaning of conceptual. First, at its root is concept. What is a concept? How is it different from a skill or an idea? If the noun is fuzzy and ill-defined, the adjective deriving from it is going to be problematic too. Second, this is a common ailment in teaching. We don’t define our terms in operative ways very often (where operative means that we have defined a term in such a way that two different people will nearly always agree on its application). We tend to use words without serious examination of what we mean by them.
Which is why I love Skemp so dearly.
Can you guys put up a reference to Skemp?
link in blog now.
I love the word “Skempian” …I suppose, most (if not all) of our metaphors for thinking and talking about knowledge and knowing are problematic.