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On Sunday we had our yearly student conference. Almost everybody spoke about their research. Vince, however, gave a talk about teaching, and I am very glad that he did. His focus was on our introductory courses, which he renamed as follows:
1211: "Statistics with calculus"
1111: "Statistics with algebra"
1001: "Statistics with words"
His main point was that most students in the latter two courses don't think the way that we do, and that constructivism was a better teaching philosophy than the mere "information transfer" approach (which is very tempting, especially given the ubiquity of the illusion of transparency, but this mode of communication is unusual in the general population and it takes time to develop). There is a bit of a false dichotomy here, since information transfer does not exist without some degree of interpreting words in terms of pre-existing concepts, but I think the general idea is clear: the more you tie it to things they understand, the better they will understand it.
The hard reality is that many students don't understand if-statements, and somehow they still hang in there. When I see students who can do MLE derivations but who don't understand what a parameter is, I am disillusioned but I'm also impressed at their level of dedication... and I am more than happy to teach them. In particular, I like to illustrate the concept of a parametric family with the metaphor of an oscilloscope with a number of knobs: "first knob is location, second knob is scale. "Which settings best fit this data?". "The likelihood is a product of densities, and to maximize that you don't want any points to get a density close to 0."
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Last semester I TA'd 1001, which was basically a course on critical thinking about statistics. Their first project consisted of taking a news article involving statistics and critiquing it from a methodological perspective, ultimately trying to answer "Does the study support the conclusions presented by the news article?". They had a rough outline of points to address (including: author biases, experiment vs observational study, randomization, control groups, sample representativeness / self-selection biases, causal confounding, etc).
I really enjoyed the experience of grading this project, because there is a large number of concepts that go into it, and it forced me to organize my thoughts, e.g. to explicitly see that the question "is there selection bias?" is one failure mode of another item: "is the sample representative?" which is equivalent to "do the conclusions generalize to the wider population?" (i.e. what population does the sample come from / can tell us about, without resorting to common-sense assumptions?).
Other basic but cool insights:
* proper randomization controls for unobserved (and unimagined!) confounders.
* common-sense assumptions are ubiquitous; after we hammered "correlation is not causation" into their skulls, I was amused when a student hinted that maybe such-and-such disease causes changes in DNA.
* students often said that experimental data pertaining to certain questions would be impossible to get for ethical reasons, because they only imagined intervening in one direction. But it was often the case that you could ethically intervene in the other direction, e.g. by asking people not to smoke.
* causal language can be slippery
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In case anyone is interested, here is the grading scheme that I came up with: ( Read more... )
1211: "Statistics with calculus"
1111: "Statistics with algebra"
1001: "Statistics with words"
His main point was that most students in the latter two courses don't think the way that we do, and that constructivism was a better teaching philosophy than the mere "information transfer" approach (which is very tempting, especially given the ubiquity of the illusion of transparency, but this mode of communication is unusual in the general population and it takes time to develop). There is a bit of a false dichotomy here, since information transfer does not exist without some degree of interpreting words in terms of pre-existing concepts, but I think the general idea is clear: the more you tie it to things they understand, the better they will understand it.
The hard reality is that many students don't understand if-statements, and somehow they still hang in there. When I see students who can do MLE derivations but who don't understand what a parameter is, I am disillusioned but I'm also impressed at their level of dedication... and I am more than happy to teach them. In particular, I like to illustrate the concept of a parametric family with the metaphor of an oscilloscope with a number of knobs: "first knob is location, second knob is scale. "Which settings best fit this data?". "The likelihood is a product of densities, and to maximize that you don't want any points to get a density close to 0."
---
Last semester I TA'd 1001, which was basically a course on critical thinking about statistics. Their first project consisted of taking a news article involving statistics and critiquing it from a methodological perspective, ultimately trying to answer "Does the study support the conclusions presented by the news article?". They had a rough outline of points to address (including: author biases, experiment vs observational study, randomization, control groups, sample representativeness / self-selection biases, causal confounding, etc).
I really enjoyed the experience of grading this project, because there is a large number of concepts that go into it, and it forced me to organize my thoughts, e.g. to explicitly see that the question "is there selection bias?" is one failure mode of another item: "is the sample representative?" which is equivalent to "do the conclusions generalize to the wider population?" (i.e. what population does the sample come from / can tell us about, without resorting to common-sense assumptions?).
Other basic but cool insights:
* proper randomization controls for unobserved (and unimagined!) confounders.
* common-sense assumptions are ubiquitous; after we hammered "correlation is not causation" into their skulls, I was amused when a student hinted that maybe such-and-such disease causes changes in DNA.
* students often said that experimental data pertaining to certain questions would be impossible to get for ethical reasons, because they only imagined intervening in one direction. But it was often the case that you could ethically intervene in the other direction, e.g. by asking people not to smoke.
* causal language can be slippery
---
In case anyone is interested, here is the grading scheme that I came up with: ( Read more... )
