Post festum analogies

In recent work I have been looking into analogies that arise in authoritative and dialogic discourse-- the former being those analogies generated, primarily, by teachers and curricula for the acquisition of scientific concepts, the latter being generated by participants in a discussion trying to make meaning and share their ideas to understand phenomena. This arose from a dissatisfaction with Structure Mapping models of analogy -- it struck me as too propositional, too wedded to language-as-unambiguous, and depicting thinking as information processing-- and yet too correct (its implications verified experimentally) to be out-and-out wrong. So rather than providing an alternative to Structure Mapping (my first stab at understanding analogy), I'm carving out a space (dialogic discourse) that might better be served by looking at analogies through another lens.

Today I came across a paper that notes a similar distinction-- "post festum" analogies (analogies that arise after one understands the target concept) and heuristic analogies (the analogies that guide and shape understanding of a topic). From Wilbers and Duit, 2006:

Currently employed theoretical approaches emphasize the role of propositionally based knowledge in analogical reasoning. The above considerations suggest that propositionally based knowledge is solely employed in the construction of post-festum analogies. The rule-based inferences of the post-festum analogy operate on propositional structures. In accordance with various other authors we expect non-propositional knowledge based on visual imagery to be of the essence in the heuristic use of analogies. Zeitoun (1984) underlines the significance of visual imagery for analogical reasoning and mental images, so mental models seem to be of the essence. Clement (1993) takes regard of abstract imagery that he calls intuitive schemata. Sfard (1994) shares the view that image schemata are crucial for analogy use while Lakoff and Johnson (1980) and Johnson (1987) arrive at equivalent terms with respect to metaphors using the notion of embodied schemata. Taking a cognitive point of view, analogy hinges on pictorial rather than on propositional elements of cognition, such as intuitive schemata, mental images, mental models, etc.

While I wouldn't characterize dialogic analogies as necessarily heuristic (they may even be post-festum, or "after the fact"), their attention to, and critique of, the propositional nature of structure mapping is useful, as is the recognition that a post-hoc analogy serves different conceptual goals and may arise from a different cognitive mechanism than analogies that students use to guide their thinking.

Mentioned on listserv.

A recent post on several listservs[1] mentioned 32 education blogs. Listed was this blog, which hasn't been updated in a while. In the past year I've begun a position as an assistant professor in physics & science education at CSU, Chico. Over the next weeks I hope to update with topics related to recent readings and current research interests.

Current research interests:
- designing open-ended curriculum
- understanding the genesis and development of scientific representations
- analogies as representations (generated analogies as models)
- scientific argument

Underlying all of these topics is the distinction between logic and understanding-- both the cognitive/brain side of things (why it is that proofs are not convincing? what kinds of narratives are convincing?) and the socially-mediated side of things (what counts as a proof? to what communities? how does that reflect what it means to 'understand' in science?).

Particulary intriguing (& related to the research interests) right now is Zimbardo's Stanford Prison Experiment, Giere's work on representation, and studies from conversation analysis & discourse analysis on how to extract meaning from utterances.

[1] Hake, R.R. 2008. "Thirty-two Education Blogs," AERA-L post of 7 Nov 2008 16:38:18-080; online on the OPEN! AERA-L archives; abstract only to AERA-A, AERA-B, AERA-C, AERA-D, AERA-GS, AERA-H, AERA-J, AERA-K, AERA-L, AP-Physics, ASSESS, Biopi-L, Chemed-L, DrEd, EdResMeth, EvalTalk, IFETS, Math-Learn, Math-Teach, Net-Gold, Physhare, Phys-L, PhysLrnR, POD, PsychTeacher (rejected), RUME, STLHE-L, TeachEdPsych, TIPS, & WBTOLL-L.

Situated Language and Learning

I really enjoyed Gee's Introduction to Discourse Analysis and picked up his book, Situated Language and Learning.

One implication that I hope this book has is this: if you want to design a learning environment, don't start with content, start with the following sorts of quesitons: "What experiences do I want the learners to have? What simulations do I want them to be able to build in their heads? What do I want them to be able to do? What information, tools, and technologies do they need?" Another way to put these questions is: "What games do I want the learners to be able to play?" The first decision, then, ought to be about what are good and useful and powerful experiences for people to have, and what are good and useful and powerful games for them to be able to play.

-from James Paul Gee's Situated Language and Learning: A critique of traditional schooling.


He talks about how kids learn to read in the context of playing video games:

Computer and video games often contain lots of print and they come with manuals. it is notorious that young people don't read the manuals, but just play the game. While older people bemoan this fact as just one more indication that young people today don't read, these young people are making a very wise decision when they start by playing and not reading. The texts that come with games are very hard to undersand unless and until one has some experience of playing the game-- experience which, then, will give specific situated meanings to the language in the text.

--- he pulls out examples of passages in video game manuals that make absolutely no sense, but presumably would if you'd tried to play the game and run into some snags. then he compares that to a science textbook (a passage on erosion) and how difficult it would be to make meaning out of that without first "playing the game" of science.

This reminds me of spending weeks having conversations with high school students about "Why is the sky blue?"-- by the end of the discussion we read pop-literature (a NYTimes article) that addressed why the sky was blue and they could critique it and underatnd it in a really sophisticated way.

So far (by p. 46) the message of the book is that what's difficult about reading isn't phonics and decoding words, per se, but instead putting those in context, matching them up with some kind of embodied meaning. I like the way he uses "embodied." (as opposed to the very strict embodiment that I usually think of when I hear the word.)

Another nice example...

these two sentences [from the paragraph on erosion] are meant to be definitions, though not of the words 'erosion' and 'weathering' in everyday temrs, but in specialist terms. And , of course, I do need to know that they are definitions and I may not even know that if I have had little experience of specialists trying to define terms in explicit and operations ways so as to lessen the sort of ambiguiity and vagueness that is more typical of everyday talk.

So the message to me is that kids need to have participated in scientific ways of knowing, talking, thinking to be able to make any kind of sense of these kinds of texts.

The Cognitive Science of Math v. the Mathematics of Math

One of my favorite books about links between math and mind is "Where Mathematics Comes From" by Lakoff and Nunez. A mathematician who reviewed the book critiqued it for its mathematical claims, rather than the cognitive science claims-- something I see in physics (and science) education quite frequently.

Lakoff and Nunez, in their reply to her criticisms, note:

"We have to keep in mind, however, that our goal is to characterize mathematics in terms of cognitive mechanisms, not in terms of mathematics itself, e.g., formal definitions, axioms, and so on. Indeed, part of our job is to characterize how such formal definitions and axioms are themselves understood in embodied cognitive terms.

We simply have a different job than professional mathematicians have. We have to answer such questions as: How can a number express a concept? How can mathematical formulas and equations express general ideas that occur outside of mathematics, ideas like recurrence, change, proportions, self-regulating processes, and so on? How do ideas within mathematics differ from similar (but not identical) ideas outside mathematics (e.g., the idea of "space" or "continuity")? How can "abstract" mathematics be understood? What cognitive mechanisms are used in mathematical understanding?"

This is a great way of understanding some of the difficulties in math or science education-- on the one hand you have the logic of math (and science)- not contextualized, impersonal, precise; on the other hand you have the language the mind uses - embodied, contextual, analogical. Understanding each is side is crucial to understanding how to teach.

"Nutritionism" and Sciencification of Everything

The NYTimes Magazine ran an article, Unhappy Meals, from which this quote comes:

"In the case of nutritionism, the widely shared but unexamined assumption is that the key to understanding food is indeed the nutrient. From this basic premise flow several others. Since nutrients, as compared with foods, are invisible and therefore slightly mysterious, it falls to the scientists (and to the journalists through whom the scientists speak) to explain the hidden reality of foods to us. To enter a world in which you dine on unseen nutrients, you need lots of expert help."

Which makes me think of all the other -isms out there-- all the places we need experts where folk wisdom used to do pretty well. -- nutrition, sleep, gardening, drinking water, teeth cleaning (are teeth cleaner today as a result of all those new toothbrushes?).

I'm down on science education lately. And not the science part of it, but the standards and textbooks and tests and what we think it means to know something and what we think is worth knowing.-- I think a lot of science education works to create this -ism divide between experts and non-experts. It happens when we focus on the things- like the Krebs cycle- that students cannot understand deeply and must rely on experts to tell them about.

I remember David Hammer relating a story about how when he says he's a physics professor people ooh and aah; when he says he's an education professor people start in on their ideas about what's wrong and right in education. But people have far far more experience with the physical world than they do the educational world-- somehow they've learned that their ideas and thoughts about physics are not valid or relevant, while their ideas about education are.

Why teach science.

From Schank's blog:

"Do we really believe that the reason that there so many foreign applicants to US graduate programs is that they teach math and science better in other countries? China and India provide most of the applicants. They also have most of the people. And many of those people will do anything to live in the U.S. So they cram math down their own throats knowing that it is a ticket to America. Very few of these applicants are coming from Germany, Sweden, France or Italy. Is this because they teach math badly there or is it because those people aren’t desperate to move to the U.S.?

In the U.S., students are not desperate to move to the US, so when you suggest to them that they numb themselves with formulas and equations they refuse to do so. The right answer would be to make math and science actually interesting, but with those awful tests as the ultimate arbiter of success this is very difficult to do...

You can live a happy life without ever having taken a physics course or knowing what a logarithm is.

On the other hand, being able to reason on the basis of evidence actually is important. Thinking rationally and logically is important. Knowing how to function in a world that includes new technology and all kinds of health issues is important. Knowing how things work and being able to fix them and perhaps design them is important.

Lets get serious. We don’t need more math and science. We need more people who can think."

-- I would argue "We need more people who can think mathematically and scientifically"-- which is all too often not taught in math and science courses.

Other interesting blogs:

• Susan Ohanian
• Alfie Kohn

Understanding the Math Wars, Implications for Science

In the American Journal of Physics-- a journal for which most of the publications are physics professors sharing interesting problems/labs/ideas, but also some interesting physics education research-- the following editorial was published this month:

School math books, nonsense, and the National Science Foundation


The editorial itself isn't too surprising; it's the kind of editorial that shows up in newspapers and websites when mathematics education reform curriculum is introduced. And it's from a vocal critic of those reforms. What is surprising is that the AJP decided to publish it, with all of its ranting rhetoric.

Some history on the Math Wars is necessary for understanding how to interpret Klein's editorial.

I think science education has different concerns: for one, most parents have less expectations about what students should learn in science than they do for math, are less likely to think they use traditional science content every day, and so are less likely to be vocal opponents to reform curricula. Also, people have an image of scientist as a doer of experiments; a mathematician (perhaps?) they think of as a knower of math. (Actually, I wonder what most people think that mathematics professors do all day?) So science-as-activity is easier to pull off.

But it is concerning that this shows up in the AJP. I composed an editorial in response. (Tried attaching it to no avail. I'll try again later.) We'll see if it gets published.