What does conceptual understanding mean to researchers?

In yesterday’s post, I implied that research demonstrating that certain practices are associated with improvements in ‘conceptual knowledge’ should be read cautiously. I suggested:

“If you have the time, try reading some of the ‘productive failure’ literature. This often assesses ‘conceptual knowledge’ and yet the questions that are used to assess it will probably surprise you – they often look for all the world like recall of relatively simple declarative knowledge. This is why I am more impressed with evidence of transfer…”

Productive failure is on my radar as part of my PhD research and so I have been reading the relevant papers.

What I didn’t know at the time of writing is that this issue has already been investigated in a far more comprehensive way by Crooks and Alibali. Their article is not paywalled and is worth a read. Thanks to the helper elves who alerted me.

Crooks and Alibali note that the questions researchers use to assess ‘conceptual knowledge’ are not exactly what we might expect. For instance, they have noticed the prevalence of questions that ask students for a definition of the equals sign (i.e. what does “=” mean?).

I doubt anyone really thinks that conceptual understanding is equivalent to being able to trot out definitions. It might be a good proxy, provided test subjects have sufficient language skills and provided nobody has explicitly taught them the definition which they could, presumably, just parrot (see Willingham’s ‘menagerie lion‘). But that’s the problem: Why wouldn’t a teacher explain what it means to their students? Any student who then gives an accurate definition could either be showing conceptual understanding or could simply be remembering what their teacher said. The difference between these two possibilities rapidly becomes a philosophical question, particularly since it would be so difficult to detect.

Given the oddness of the research questions, I am more inclined than ever to think that conceptual understanding isn’t the thing we think it is. The more you stare at it, the more it disappears from view. Is it a subjective sense of realisation? Is it knowledge of certain underlying principles? Is it, as in the examples provided by Dan Meyer, just the difference between novices and experts, perhaps related to the development and connectedness of their schema? I think it may be all of these.

What I doubt is that there are ways of assessing it that are not highly intertwined with other skills and knowledge.


4 thoughts on “What does conceptual understanding mean to researchers?

  1. Conceptual understanding is the last resort of the incompetent: “sure I’ve got a conceptual understanding of mathematical equalities, I know there are mathematical equalities, and I know when I’ve got to employ someone to deliver a mathematical equality, but I don’t feel the need to have the detail on it”

  2. I just dipped into Willilngham’s linked article. He mentioned that we want to produce ‘problem solvers’. Now I’m not having a go at him for this objective, but I come across this in business alot. “We need problem solvers”. I don’t think that this is so. Generally, problem solving is pretty easy…it requires knowledge and the ability grows with experience and curiosity, but in my business I want ‘problem finders’. I want to know where we can improve, what we can do that will surprise and attract customers. When I was studying architecture the lecturers liked to call a design program a ‘problem’. I always rankled at this, the problem was either retrospectively trivialised, e.g. the ‘problem’ of not having an opera house on an old tram depot on Bennelong Point in Sydney, or empty, recalling one of my design programs; the ‘problem of not having an art gallery in a disused underground reservoir. There are many incidently problems to be solved, compromises to be resolved in architecture, but fundamentally there are opportunities to be explored, taken, indeed, exploited and inventions to be tested. This is what I need in business. Not ‘problem solvers’.

    1. Thank you! And yet, so many people in leadership roles (note I didn’t say “leaders”) say, “Give me solutions, nor problems”. Those are often different skillsets. Plus, a correct diagnosis is 80% of the solution.

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