Wednesday, December 09, 2009


Thinking About Undergraduate Research (for Grant Writing) ...

I think I may have mis-underestimated the challenges involved in both teaching of and doing research with undergrads.

First there is the general issue of training vs. doing research. One of my frustrations with getting any research done is that my research students take so long to get even the most basic tasks accomplished. But thinking of what is involved in research from their point of view, I realize that part of the difficulty is that they are not just writing the simple sub-routine I've assigned to them ... they are students and what they are doing is learning. While it would serve my research goals if they just got the work done, it's important for them to understand what they are doing (would that the majority of my general and bio-chem students were this diligent about actually understanding the material). Yes, it's frustrating that, in order to get a student to write a few lines of code to convert between ppm and increments, they need to finish working through an upper-division math text on Fourier analysis, but part of the research experience for them is learning useful concepts they don't have a chance to learn in their regular coursework (e.g. as chem/bio-tech majors).

More fundamentally though is the challenge of working with students who have difficulties with abstract thought. When you think about it, there are really three levels of abstract thought: (1) thinking abstractly about abstract things, (2) thinking abstractly about concrete things and (3) thinking concretely about abstract things.

Most smart students are actually decent at level (1): they wouldn't have gotten 'A's in there general education courses if they were not able to analyze abstract literary concepts in a conceptually rigorous way. But (2) really is a challenge. For students to even take abstract thoughts and come up with concrete examples of those concepts really is difficult. Hence so many student complaints about "well I understand the concepts but I have problems applying them in solving problems on a test". But (2) goes even beyond Bloom's taxonomy of cognitive learning outcomes and most students can't go beyond that. For me, this was not a challenge: which is why I was able to find upper-division math courses so easy. Once you are able to think abstractly about numbers, upper-division math, for example is a breeze. But most students just can't get there.

Of course the real challenge is thinking concretely about abstract things. I am starting to realize that you just can't expect most undergrads to do this, even though it is necessary to get actual results in quantitative research. I was spoiled dealing with the best of the best undergrads in research settings both at Rutgers and at FSU. But as I think back to where I was as an undergrad, I certainly wasn't capable of taking abstract concepts and really thinking through them to get concrete results.

Indeed, when you think about it, it (literally) takes an Einstein to reach level (3) in some cases. E.g., the abstract concept of relativity is very old: Kant had conceptually figured out special relativity and Poe figured out general relativity. But to take those abstract concepts and translate them into a concrete language from which the applied mathematicians could generate models, thus turning (abstract) philosophical thinking into (concrete) science (e.g. testable hypotheses), took the genius of Einstein. I certainly never even mastered level (3) enough to make any progress in applied math (although my Ph.D. should be evidence that I could do such a thing well enough to have a career in scientific research).

So I guess I should be more patient that my undergrads, even my best and brightest research students, cannot make this leap?

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