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2014 April 11

Arthur Benjamin: Teach statistics before calculus!

I rarely have the patience to sit through a video of a TED talk—like advertisements, I rarely find them worth the time they consume. I can read a transcript of the talk in 1/4 the time, and not be distracted by the facial tics and awkward gestures of the speaker. I was pointed to one TED talk (with about 1.3 million views since Feb 2009) recently that has a message I agree with: Arthur Benjamin: Teach statistics before calculus!

The message is a simple one, though it takes him 3 minutes to make:calculus is the wrong summit for k–12 math to be aiming at.

Calculus is a great subject for scientists, engineers, and economists—one of the most fundamental branches of mathematics—but most people never use it. It would be far more valuable to have universal literacy in probability and statistics, and leave calculus to the 20% of the population who might actually use it someday.  I agree with Arthur Benjamin completely—and this is spoken as someone who was a math major and who learned calculus about 30 years before learning statistics.

Of course, to do probability and statistics well at an advanced level, one does need integral calculus, even measure theory, but the basics of probability and statistics can be taught with counting and summing in discrete spaces, and that is the level at which statistics should be taught in high schools.  (Arthur Benjamin alludes to this continuous vs. discrete math distinction in his talk, but he misleadingly implies that probability and statistics is a branch of discrete math, rather than that it can be learned in either discrete or continuous contexts.)

If I could overhaul math education at the high school level, I would make it go something like

  1. algebra
  2. logic, proofs, and combinatorics (as in applied discrete math)
  3. statistics
  4. geometry, trigonometry, and complex numbers
  5. calculus

The STEM students would get all 5 subjects, at least by the freshman year of college, and the non-STEM students would top with statistics or trigonometry, depending on their level of interest in math.  I could even see an argument for putting statistics before logic and proof, though I think it is easier to reason about uncertainty after you have a firm foundation in reasoning without uncertainty.

I made a comment along these lines in response to the blog post by Jason Dyer that pointed me to the TED talk. In response, Robert Hansen suggested a different, more conventional order:

  1. algebra
  2. combinatorics and statistics
  3. logic, proofs and geometry
  4. advanced algebra, trigonometry
  5. calculus

It is common to put combinatorics and statistics together, but that results in confusion on students’ part, because too many of the probability examples are then uniform distribution counting problems. It is useful to have some combinatorics before statistics (so that counting problems are possible examples), but mixing the two makes it less likely that non-uniform probability (which is what the real world mainly has) will be properly developed. We don’t need more people thinking that if there are only two possibilities that they must be equally likely!

I’ve also always felt that putting proofs together with geometry does damage to both. Analytic geometry is much more useful nowadays than Euclidean-style proofs, so I’d rather put geometry with trigonometry and complex numbers, and leave proof techniques and logic to an algebraic domain.

2014 January 1

Technical entitlement—is it a thing?

Filed under: Uncategorized — gasstationwithoutpumps @ 18:49
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I learned a new buzzword yesterday: “technical entitlement”.  I encountered the phrase on  the blog On Technical Entitlement | Soshitech.com, though apparently Tess Rinearson originally wrote it in June 2012 and also published it on medium.com.

I’m the granddaughter of a software engineer and the daughter of a entrepreneur. I could use a computer just about as soon as I could sit up. When I was 11, I made my first website and within a year I was selling code. I took six semesters of computer science in high school, and I had two internships behind me when I started my freshman year of college.

Despite what it may seem, I’m not trying to brag—seriously. I’m just trying to prove a point: I should not be intimidated by technical entitlement.

And yet I am. I am very intimidated by the technically entitled.

You know the type. The one who was soldering when she was 6. The one who raises his hand to answer every question—and occasionally tries to correct the professor. The one who scoffs at anyone who had a score below the median on that data structures exam (“idiots!”). The one who introduces himself by sharing his StackOverflow score.

That’s technical entitlement.

“Technical entitlement” seems to be the flip side of “imposter syndrome”. In imposter syndrome, competent people question their own competence—sometimes giving up when things get a little difficult, even though an outside observer sees no reason for quitting.  “Technical entitlement” seems to be blaming those who have both competence and confidence—as if it were somehow deeply unfair that some people learned things before others did.

Certainly some things are unfair—as an engineering professor I’ve been able to provide opportunities for my son to  learn computer science and computer engineering that would not be available to a parent who knew nothing about those fields.  And some of the characteristics she lists would apply to my son—I can see him correcting his professors, and although he’d never introduce himself by sharing his StackOverflow score, he did include it in some of his college essays, as evidence that he was knowledgeable and interested in sharing what he had learned.

But Tess Renearson goes on to say

It starts with a strong background in tech, often at a very young age. With some extreme confidence and perhaps a bit of obliviousness, this blooms into technical entitlement, an attitude characterized by showmanship and competitiveness.

While my son has confidence in his abilities and “perhaps a bit of obliviousness”, neither showmanship nor competitiveness are big factors in his behavior.  I think that Ms. Renearson has confused a personality trait and stereotypical US male behavior (showmanship) with early technical education. I see the arrogance as a bad thing, but the early technical education (which she herself had) as a good thing.

The rest of her post goes on to talk about ways that Amy Quispe and Jessica Lawrence managed to increase participation (particularly by women) in tech events.  But the analysis there really addresses imposter syndrome more than it does “technical entitlement”.  She quotes Jessica Lawrence: ‘“There is,” she said, “an under-confidence problem.” But Ms. Renearson then says

Sound familiar? Yep, it’s exactly the kind of self-doubt that can arise when there are so many technically entitled people around.

Somehow blaming “technically entitled people” for the under-confidence of others seems to be imposing blame where none is warranted.

Now imagine someone starting out as a college student taking their first CS course. Imagine how the technical elite make them feel.

I can understand someone being intimidated when entering a new field if they are surrounded by people more skilled in the field—but that is hardly the fault of the those who are skilled.  Newcomers anywhere are going to feel out of place, even when people are trying to welcome them. The “technical elite” are not making the newcomers feel intimidated.

If Ms. Renearson’s point is that some of the tech communities are not sufficiently welcoming of newcomers, I agree.  I’ve seen snarky comments in places like Stack Overflow that offered gratuitous insults rather than assistance.

But Ms. Renearson seems to assume that anyone who is more experienced than her is automatically trying to put her down, and that this is the way that everyone should be expected to feel.  When one starts with that assumption, there is no remedy—no matter what those more experienced or more skilled do, they will be seen as threatening.

Perhaps she has not identified those who should be getting blamed precisely enough.  I don’t think that it is “The one who was soldering when she was 6″ who is a problem, but those who refuse to give children an opportunity to learn (no public school in my county teaches computer science, except one lottery-entry charter) or who force students who’ve been programming for 6 years into the same classes as those who have never programmed, as many college CS programs do, providing no way for more advanced students to skip prerequisites.

Unfortunately, identifying the problem as being “technical entitlement” makes the problem worse not better, as it encourages public schools to suppress the teaching of technical subjects, rather than expanding them.

If she means to attack the arrogant culture of “brogrammers”, mean-spirited pranks, and other unpleasant culture that has emerged, then I support her, as I’m not happy with some of the culture I see either.  But don’t blame it on the kids who learned tech early, nor on the parents who taught them—the late-comers are more likely to be the arrogant bastards, since that arrogance is mainly a defense mechanism for incompetents.  The competent tech people are much more likely to be eager to share their enthusiasm with newcomers and help them join in the fun.

2013 December 5

Unconcern at Berkeley about math education

Filed under: Uncategorized — gasstationwithoutpumps @ 09:08
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On Tuesdays I buy the New York Times (in hard copy) to get the Science Times section, but I often read other parts as well, since they are sitting around on the breakfast room table as I eat.  I was struck by one quote I saw this morning:

Richard Rothstein, a research associate at the liberal Economic Policy Institute and a fellow at the University of California, Berkeley School of Law, said he put little stock in the PISA results. He said educators and academics should “stop hyperventilating” about international test rankings, particularly given that students are already graduating from college at higher rates than can be absorbed by the labor market.

(online as  American 15-Year-Olds Lag, Mainly in Math, on International Standardized Tests).

I don’t know Rothstein, but I’m not surprised at a law school “fellow” being worried about over-production of  graduates—law schools have been producing many more lawyers than any sane society could absorb for decades. (And generally making their students take on far more debt than honest work would allow them to repay—perhaps he is in favor of students not having enough math to understand compound interest.)

He also has not been trying to teach engineering majors who can barely do algebra—”graduating from college” is no longer a sign of competence in math, if it ever was.  Unlike many, I’m not overly concerned with the standing of the average students relative to their counterparts in other countries.  The average American has never been noted for intelligence or wisdom.  I believe it was H.L. Mencken who said “Nobody ever went broke underestimating the intelligence of the American public.”

What I am more worried about is the shrinking number of students at the top levels.  Again from the New York Times article:

In the United States, just 9 percent of 15-year-olds scored in the top two levels of proficiency in math, compared with an average of 13 percent among industrialized nations and as high as 55 percent in Shanghai, 40 percent in Singapore, and 17 percent in Germany and Poland.

We may not need huge numbers of scientists and engineers (probably not as many as the NSF and STEM educators would like to have people believe), but we do need for them to be good at their jobs.  The American education system is not succeeding in producing sufficient numbers of highly capable people in STEM fields (though more than enough marginally competent ones).

Getting a few more, or even a lot more, students to be “college-ready” or to “graduate from college” is not going to help much—particularly if it comes at the expense of cutting standards so that the colleges are flooded with marginally competent students and honors courses are eliminated in favor of remedial course (which seems to be the trend at state-supported schools).

I don’t have a simple solution to offer—perhaps there is no solution in a culture that despises math and worships athletes.  As long as basketball and football coaches are the most highly paid employees in academia, I have no hope for improvement.

What could be done, by those colleges who have not indebted the next two generations to pay for unneeded football stadiums? Maybe having admissions officers who cared more about academic strength and less about extracurriculars, sports, and diversity would help a little.  Having competitive scholarships that were tied to high performance, rather than just need-based grants? Having endowment funds that could only be spent on teaching honors courses or undergraduate research? Reversing grade inflation, so that the average grade was once again a C, rather than an A (so that the students at the top were distinguishable by  their records from the run-of-the-mill students)?

High schools could help by making honors courses and AP courses really challenging, and not just playgrounds for students whose parents think they ought to be there.  Eliminating social promotion, so that a high school diploma means that a student can take college courses without remedial classes and not just that they managed to keep a seat warm for 4 years without being expelled.

I guess I’m just dreaming here—I see no indication that anyone except a few curmudgeons like me has any interest in raising standards.  The rallying cry is “college for everyone”, which requires putting a lot of educational resources into getting those who aren’t really capable of the work up to a level where they can appear marginally competent.  The US gave up years ago on providing training for those who could benefit the most from it (except in sports, of course, the real religion of the US).

2013 December 1

Low-cost Arduino-compatible electronics kit

Filed under: Uncategorized — gasstationwithoutpumps @ 10:14
Tags: , , , , ,

There is an Indiegogo campaign to sell a kit for learning electronics that seems to have better pricing than most of the similar kits I’ve seen: BE MAKER! KIT plus FREE lessons on electronics, from Zero to Internet of Things | Indiegogo.

The most popular product they are selling seems to be a $69 kit with a microprocessor board (a clone of the Arduino Leonardo); a “shield” with an LCD display driver, pushbuttons, microSD card reader, 2 servo connections, RGB LED strip driver, and Ethernet adapter; a bunch of useful electronics parts (including an LCD display for the shield and an RGB LED strip); “lessons” (which are probably just assembly instructions for different projects, but may be more tutorial) and a box to keep all the tiny parts in.

As Arduino and Arduino-compatible kits go, this one looks pretty good.  Forget about it for holiday gift-giving though, as they don’t expect to deliver until February 2014.  If you want something similar for this year, look at the somewhat more expensive kits from AdaFruit or SparkFun.

2013 November 15

Udacity moving into corporate training

Filed under: Uncategorized — gasstationwithoutpumps @ 10:21
Tags: ,

I just read a good article, Udacity’s Sebastian Thrun, Godfather Of Free Online Education, in which the author claims that Udacity is abandoning the MOOC vision of free university-level education in favor of the more lucrative field of corporate training:

It is a good story, as well manicured as a college quad during homecoming weekend. But there’s a problem: The man who started this revolution no longer believes the hype.

I can’t say I’m surprised.  I’ve always regarded the MOOC as more of a PR gesture than an enduring way to provide college education, and I predicted that the companies doing MOOCs would drift into corporate training after burning through their initial corporate capital (if they didn’t simply fold or downsize to the level sustainable as a purely public-relations game).

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