"Math class is tough!" a few thoughts on a problematic metaphor for learning

Academics, and especially academics who think about culture (which is to say, more or less, all academics), seem to really like metaphors and similes. Here's one that made me mad this week.


Jim Greeno: Learning how to participate is like being in a kitchen.
Situativity theorist Jim Greeno, in "Number Sense as Situated Knowing in a Conceptual Domain," considers how people develop conceptual models for participating in disciplinary communities (what he calls "conceptual environments"). He explains that

knowing how to construct models in a domain is like knowing how to work in an environment that has resources for a kind of constructive activity, such as a woodworking shop or a kitchen.

A shop or a kitchen has objects, materials, and tools that can be used to make things. Knowing how to work in such an environment includes knowing what objects and materials are needed for various constructive activities, knowing where to find those objects and materials in the environment, knowing what implements and processes are useful for constructing various things, knowing how to find the implements, and knowing how to use the implements and operate the processes in making the things that can be made.

In constructing conceptual models, the ingredients are representations of specific examples of concepts.... We can think of the conceptual domain as an environment that has representations of concept-examples stored in various places. Knowing where to find these, knowing how to combine them into patterns that form models, and knowing how to operate on the patterns constitute knowledge of the conceptual domain. The representations of concept-examples have to be understood in a special way. They are not only objects that are drawn on paper or represented in the mind. They are objects in the stronger sense that their properties and relations interact in ways that are consistent with the constraints of the domain.

This example would be fine if everybody agreed on a.) where everything belongs in a kitchen; b.) what everything in the kitchen should be used for; c.) what activities afforded by the kitchen are most appropriate; and d.) whether the kitchen is appropriately and effectively designed.

Let's say, just for kicks, that the cabinets are made for glass and have been installed at just the right height for someone who is, say, at least 5 feet 9.2 inches tall. I'm 5'3". If I want to get to the materials I need to, I'm going to need to find something to stand on.

If there's nothing to stand on (and if most people who use the kitchen stand around 5 feet 9 inches, there would be no reason to keep stepstools or the like around), I might try to climb up onto the counters. I might try to find some sort of utensil--a spatula, maybe, or a wooden spoon--to help me access the ingredients I need. If I'm really desperate, I might try to throw things in an effort to shatter the glass cabinet.

To an outside observor, none of the above activities would appear appropriate in the kitchen setting. The spatula is made for cooking, not for prying open cabinets. And shattering glass cabinets--that's just destructive.

You see my point, I hope.

Then there's the unavoidable issue of choice of metaphor. Greeno offers a kitchen or a woodworking shop, which we might say is a nice way to offer one example for each gender! But though it's true that Greeno doesn't take it a step farther to prescribe who gets to enter which type of space, the gendered nature of the examples is undeniable. These examples are not neutral, just as the practices that occur in the examples are not benign, at least not always, and not for everybody.

Metaphors do lots of good work for us; indeed, it may be that our entire culture rests on a bed of shared metaphors. As Bonnie Nardi and Vicki O'Day write in their 2000 book Information ecologies: using technology with heart,

Metaphors are a useful form of shorthand.... But it is important to recognize that all metaphors channel and limit our thinking, as well as bring in useful associations from other contexts. That is the purpose of a metaphor, after all--to steer us to think about the topic this way rather than some other way.

What are you doing? Stop--stop throwing soup cans at the cabinets! You're liable to break something!

To which you respond: I never liked tomato soup much anyway. And I sure as hell hate glass cabinets. Good riddance, you say, even as you're being hustled out of the kitchen. Good--

And that's when you realize they've shut the door behind you. Maybe even locked it. See what kind of trouble metaphors get us into?