by ibrahima on 6/21/17, 5:25 PM with 82 comments
by forgotpwtomain on 6/21/17, 6:11 PM
I mean we didn't read a classic American author till 6th or 7th grade! And if I recall correctly there were still M&M's in math class in grade 4!
The US may have an education problem but somehow the Soviet Union and China did fine years ago with out all the ed-tech snake oil.
by closed on 6/21/17, 6:07 PM
This kind of data is commonly modeled using item response theory (IRT). I suspect that even in data generated by a unidimensional IRT model (which they are arguing against), you might get the results they report, depending on the level of measurement error in the model.
Measurement error is the key here, but is not considered in the article. That + setting an unjustified margin of 20% around the average is very strange. An analogous situation would be criticizing a simple regression, by looking at how many points fall X units above/below the fitted line, without explaining your choice of X.
by jjaredsimpson on 6/21/17, 6:25 PM
All the worst students will be very similar and all the best students will be very similar because the number of available states is low. Average students are all unique in their average-ness.
Am I missing some subtle statistical understanding that the toy example doesn't capture?
by tpeo on 6/21/17, 6:39 PM
I wondered about a very similar problem some weeks ago. I was bothered about the terms "ectomorph" and "mesomorph" because they seemed useless once you considered height: the vast majority of "ectomorphs" seemed to be taller than the average while the vast majority of "mesomophs" seemed to be of average height, so there's no point to these words. And so I wondered how would shoulder width would change given height (which seems to have some kind "decreasing returns"), and how the average measures would relate to actual average build. I mean, is the "average guy" really the guy with the average height and average shoulders? Because it's not as if the scale had just changed, like doubling the size of a cube, but there seems to be some deformation going on as well.
Anyway, didn't get past the wondering phase at the time. But I think it's too much of an important problem to be casually thrown as part of a pitch. I don't see an immediate reason why the average tuple should be the tuple of all averages, because some of the variables might be "dislocated" and thus not coincide with the averages of other variables. Some guy might be very close to average height yet still somewhere in the left-tail when it comes to body mass, shoulder width or any other measure. So there might be a typical student, but I don't think this is the way to find him.
by connoredel on 6/21/17, 6:38 PM
Take the simple case of 2 dimensions (each observation is plotted in 2D space) with possible values of 0-10. Let's say the extreme (far from average) space is within 5% of the border. The total extreme area is (10x10)-(9x9) = 19 (i.e. 19%). Now add a 3rd dimension. The extreme "volume" in 3d space is now (10x10x10)-(9x9x9) = 271 (i.e. 27%). You can see where this is trending. Add enough dimensions, and every observation is now "extreme." They become so far apart that each observation almost deserves its own cluster, and you lose any idea of similarity.
Back to this particular article: when you _add_ (or average) all of the dimensions -- like you do on an exam -- suddenly they are close again.
by fnovd on 6/21/17, 6:36 PM
According to the article, the average person doesn't exist, either. I don't know many people that are 13% fluent in Mandarin, 13% fluent in English, 9% fluent in Hindi... At the same time, having ~2 hands and ~10 fingers seems about right. Some metrics work with averages, some don't.
by PotatoEngineer on 6/21/17, 6:15 PM
The implementation varied between classes - in my World History class, there were a large number of objectives, and each objective was met by a small quiz that tested ~one skill. (There were a lot of retaken quizzes in that class.) In Biology, there were about 10 objectives for the entire semester, so you could still pass while missing a few small skills, as long as those missing skills were spread out among different units.
My high school used that "objectives" system less and less as I moved up the grades -I assume that most teachers got tired of it pretty quickly and just decided to make their usual teaching material "look like objectives" rather than rebuild their curriculum in later years.
by opportune on 6/21/17, 6:13 PM
by timemachiner on 6/21/17, 5:57 PM
by pacaro on 6/21/17, 6:28 PM
Questions are scored alpha for a completely correct solution, beta if the examinee demonstrated that they knew what they were doing by maybe made some small mistake, and gamma for a reasonable effort.
The bare minimum pass mark is one alpha.
by QML on 6/22/17, 1:55 AM
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I suspect that the distribution of the curve has to depend on: subjectiviness of the test and on the grading. Tests with questions where you know it or you don't. And how much partial credit graders are willing to give.
by bryanrasmussen on 6/21/17, 5:47 PM
by crimsonalucard on 6/21/17, 5:59 PM
by suyash on 6/21/17, 10:07 PM