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2012 April 18

Distance learning for gifted kids

Suki Wessling, a local writer who is home-schooling her kids, recently wrote an article about distance-learning oppoturnites for gifted kids: Boutique distance learning offers variety for gifted kids – National gifted children | Examiner.com. We have not used any of the “boutique” services she mentioned, nor, for that matter the large services like Johns Hopkins University’s Center for Talented Youth or Stanford’s Education Program for Gifted Youth.

There are several reasons we’ve been reluctant to use many on-line courses:

  • Many are quite expensive. EPGY courses are around $500 to $750, plus $50 registration and shipping fees, JHU-CTY courses are $500–$1280.  I’d want to know that the course would be a very good fit and of higher quality than a corresponding community college class (about $300) before committing to an online course.
  • Too much screen time.  My son already spends more time in front of a screen than is healthy (as do I, so I can’t chide him too much). At least with community college classes he gets the exercise of bicycling to the class (in fact, this provides so much exercise that it counts as his PE class: about 4 hours a week).
  • Difficulty in finding courses that fit his educational needs and interests.  There are undoubtedly a number of courses that would be an excellent fit for him, but it is very difficult to distinguish them from other courses that have similar descriptions but would be at the wrong pace, wrong level, or have too much busy work.

So far we have only used one on-line course provider: Art of Problem Solving.  A year ago, I posted about our experience with with their precalculus course: Good online math classes.  My son did their calculus class this year with the same instructor, and we had similarly good results.  The AoPS calculus classes are not cheap ($500 with books), but they were an excellent fit for my son. If I could be assured of as good a fit in other online courses, I would be more willing to use online providers.

This year my son has been keeping time logs for his consultant teacher in the home-school umbrella.  For the AoPS calculus class that just ended, he did almost all the weekly and challenge problems, but not quite all. We added up the total hours (class and homework) for February and March, and got 56 hours—just under 7 hours a week.  His total workload for all courses (including the cycling that counts as PE) averaged 40.75 hours a week in February, which I regard as about the right amount of time for a high school student to be spending on school.  It is certainly much larger than the 2–3 hours a day that some home schoolers regard as adequate.  The main advantage for us of home schooling is not a reduction in workload, but a spending the time on appropriate work, rather than busy work or dead time.

I think that the calculus class was a good deal higher workload than the Precalculus class last year, but we did not keep time logs then, so I may be mistaken.  My son did not take any of their lower-level classes, so I can’t comment on the workload of any of them (though we did use the intro algebra and intro geometry books some earlier, and were happy with them, which is why I was willing to give AoPS online courses a chance).

My understanding is that by the end of the AoPS calculus course well over half the students had dropped, possibly because they could not keep up with the pace or the workload.  You only get your money refunded if you drop in the first 3 weeks, so a lot of families ended up wasting the tuition money.  I’m afraid of a similar thing happening if we pick an online course that is not a good fit for our son.

He will probably do one AP practice test before taking the AP Calculus BC test next month, but that should only take about 3.5 hours.  The AP test should be a good review of the essential material of the course, but so far as I can tell, the AoPS Calculus class covers more material in greater depth than the usual AP calculus BC course or the usual first-year college calculus class.  It is definitely a calculus-for-mathematicians course, with a lot of emphasis on problem solving and rigorous foundations (like using Darboux integrals, a somewhat cleaner equivalent to Riemann integrals).  Some of the differential and integral equations they had in the last challenge set seemed difficult even for me (though I must admit that ODE was never my favorite subject, and it has been over 30 years since I last did any differential equation other than a trivial exponential decay).

The AoPS courses also cover complex numbers fairly well, something that is not always done in other precalculus and calculus classes. Another gifted high school student I know has taken calculus through multi-variable calculus at the local community college.  I was amazed to find out that he’d had almost nothing about complex numbers: not even such fundamental things as Euler’s formula: e^{i\theta} = \cos \theta + i \sin \theta.  This lack came to light during physics class, when I was deriving acceleration for something moving in a circle by taking the second derivative of R e^{i \omega t} with respect to t.  It is so much easier to work with exponential functions than trig functions that it didn’t occur to me that the community college calculus classes would not have covered it.

2010 November 23

Few taking AP CS A exam

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I recently looked at the statistics on number of students taking AP exams, by state. This was prompted by a post on Mark Guzdial’s blog, which provided a summary of the state-by-state statistics for the AP Computer Science A exam.

The discussion on Mark’s blog indicates the difficulty in interpreting statistics:  the post started out congratulating Georgia high-school teachers for the increase in the number of students taking the AP CS A exam and improvement in scores, but commenters on the blog pointed out that the demise of the CS AB exam meant that the total number of students taking AP CS exams had dropped and that the rise in scores probably reflected the students who in the past would have taken the more difficult CA AB exam taking the CS A exam instead.  The bottom line seems to be that there has been no improvement in Georgia high-school teaching of CS, and probably some loss of quantity or quality.

Of course, I’m not in Georgia, so I was more interested in California, and how it was doing. In the state-by-state figures, California had the second highest number of AP CS A test takers in 2010 (after Texas).  Of course, both are big states, so per capita rates are more interesting. Texas drops to number 4 and California to number 9.  One state stands out as having had a high number of AP CS A test takers: Maryland at 241 test takers per million population.  The next highest was Virginia at  150.  California had 76 test takers per million.  The lowest state (as in most measures of educational attainment) was Mississippi at 1.7 test takers per million.  I am a bit worried about how California plans to retain anything in Silicon Valley if so few Californians are learning to program.  Somehow I’m having trouble imagining Baltimore taking over as the center of the computer industry, but stranger things have happened. Maryland’s average score on the AP CS A exam was 3.03,  somewhat lower than California’s 3.34 and the national 3.14, but not so low that Maryland can be accused of packing the exam with unprepared test takers. Maryland, California, and the nation as a whole have bimodal distributions, with scores of 5 and 1 being the most common.

I looked over the national statistics for 2010, and saw that many of the exams that require math had this sort of bimodal distribution.  Fields with multiple exams (like Calculus or Physics) tended not to have the bimodal distribution on the harder exams, with scores peaking at the high end on the hard exams.  This is not too surprising, as students who fail the easy exam are unlike to go on and fail the hard one as well.  The humanities fields tend to have unimodal distributions centered around 3, rather than with peaks at the ends like the math-based exams.  Looking over all fields, the lowest mean scores were on Human Geography (2.46) and the highest on Chinese Language and Culture (4.56, but only taken by 4832 students, probably mostly native speakers).  The test with the most 5s is Calculus AB (48752), and the test with the most 1s is also Calculus AB (79457).  That’s not because it is the most common test—that would be US History, with 384566 test takers, but the most frequent score there is a 2, rather than a 1 or 5.

The Computer Science AP A exam had only 19390 test takers (versus 236502 for Calculus AB and 75132 for Calculus BC), so there are about 16 times as many high school students getting college-level calculus classes as college-level computer programming classes.  This ratio looks wrong to me, as there are far more jobs that require programming than there are that require calculus.  (OK, job preparation is not main purpose of high school education, but I could argue for the greater improvement in cognitive skills that comes from programming rather than calculus also.) My own son’s high school doesn’t offer any computer programming, though they do have Calculus AB and BC.  Perhaps the problem is that there are not enough unemployed programmers retraining to be underemployed teachers.  It may be easier to convince math teachers to learn programming than to convince programmers to become teachers (of course, one the math teachers have learned enough programming to teach it competently, many will drift off to industry to get the higher pay).

 

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