Why push math education onto students?

Math education is important for many reasons, but I will focus on offering an answer from a societal economic policy level that stresses employment and the labour market.  I will refrain from mentioning all the other great reasons for having a great math education for children in this post.

This all came to my mind after reading Ramanathan's article in The Washington Post.  Ramanathan is a professor emeritus of math, statistics, and computer science, at the University of Illinois.  He contends that although a lot of effort and money has been put into making math seem essential to every child's and adult's daily life, it is not, as compared to history, politics, or music. Further, the article contends that no one should feel obligated to love math, any more than anyone is obligated to love grammar, or composition.  He contends that there is no evidence that all the money spent has actually helped student math achievement.

There really are a number of different issues that Ramanathan is attacking.  They include:
  1. Should every person love math any more than grammar or whatever else that is perhaps boring and pedantic to some?
  2. Has the money spent on improving math education been spent effectively?
  3. Is math really as essential to every child's and adult's daily life as politics or history?
  4. Given the answers to the previous questions, should extra effort or money be spent into improving math education and to improve students' math achievement?

The last question is, insofar as education is publicly funded (it is, more of less, in Canada. I am aware the writer is talking about the USA), a matter of public policy.  So we have to put our public policy hat on before continuing, because it makes a difference in how the question is answered.

The difference is this: when it comes to public policy, the answer to the first three questions are irrelevant to the fourth.

Here's why.


Suppose you're wrong. How would you know?

I'm asking this question in the scenario where you do not go out of your way to find out whether you're right or wrong. That is, based only on the regular experience and data that you would collect while doing nothing out of the ordinary, how would you know if you were wrong about what you ordinarily believe.

The point of the question is to highlight cases where you can't trust a belief.  I have, ordinarily, too many beliefs to be skeptical about and to prove, if I truly want certainty.  Fortunately, the world provides us with plenty of data through our ordinary experience, and it allows us to form pretty trustworthy beliefs, most of the time.

It's good to question at least some of our beliefs, though, especially in cases where you maybe shouldn't trust a belief, without first having gone out of your way to gather data to refute or verify it.

A simple example: suppose I believe I can walk through walls.  Well, how would I know I was wrong?  Without going out of my way, I can recall all the times I've accidentally backed into, or bumped into, a wall.  The ordinary course of experience provides me data to the contrary of that belief.  It's easy to be disabused of beliefs like being able to walk through walls or being able to fly.

Case 1

You may have heard of the "statistic" that 99 Out Of 100 Programmers Can’t Program. Maybe you believe it. Maybe you don't.  But now, just suppose it's wrong.  How would you know without going out of your way to gather data?

I would know because based on my experience, I can recall all the times I've met or talked to programmers who can program.  In fact, I might recall that the vast majority of programmers I know of can program just fine.  That's how I would know if the statistic is wrong.

Well, in fact, based on my experience, that is true of all the people I consider programmers of interest (so I'll exclude programmers who are just starting to learn, for example).  So without going out of my way, I would believe that statistic is wrong.

Notice that this is basically gathering data through a convenience sampling.  It's convenient because the sample has already been gathered through the course of ordinary experience!

Now that doesn't mean the statistic is wrong on the whole.  Perhaps a random sample would prove the statistic.  But I'll be lazy for a moment, and instead, try to understand the context where that original "statistic" was proposed.  That statistic was proposed by people doing hiring, but I have never had the experience of hiring someone.  So what might be a better explanation for both my experience-created convenience sample, and the proposed "statistic"?


Unintended consequences in education and teaching

Case 1
In a paper published recently [1], Job, Dweck, and Walton provide evidence that contradicts the theory that willpower is a limited resource.  They show that willpower is correlated with a person's underlying belief about whether willpower is a limited resource, so that one's belief about willpower is kind of like a self-fulfilling prophecy.  If you believe willpower is not limited, then your willpower will not be limited.

I don't know if that's true, since it goes against other research showing that willpower is a limited resource that can be depleted.  For all we know, the belief that willpower is unlimited may simply increase one's amount of limited willpower.  Whatever the case, the true nature of willpower has a big impact on how students should be taught in the classroom, and how they should be taught to study on their own.

If willpower is truly a limited resource, then teachers should take that into account in their lesson plans, and also teach students to take breaks to recover their willpower store.  The latter is dangerous advice, of course, since the unintended consequence is that it licenses students to take frequent breaks in the name of recovering willpower and attention-span, even when such breaks are unneeded.  Perhaps the trend of college students studying less and less is a one of the unintended consequences.

On the other hand, if it is true that believing willpower is an unlimited resource will enlarge one's willpower store either to some larger limit or to become truly unlimited, then of course this should be taken into account in teaching as well.  Students would have to be influenced into believing that willpower is an unlimited resource, and that the apparent diminishing of willpower is merely a symptom of a limiting belief.

We know willpower is important to academic achievement, as shown in studies described by Lehrer, so these contradictory studies really puts teachers in a bind.  What is a teacher to do in practice?


Getting Apple's Exposé feature on Windows 7

You need Switcher for Windows 7.  It can also be downloaded from CNET.

The computer power user, and especially a software developer, might have half a dozen windows open at times...per running application.  A few dozen tabs in Firefox, spread over a few windows.  Half a dozen Windows Explorer windows.  A Skype window.  A few Emacs windows.  Maybe a Pidgin window or two.  A few Visual Studio windows.  A Git GUI window or two.  You get the idea.

When things get messy, I want organization.  But when things just get over-whelming, I want a bird's eye view of everything.  And I mean everything.

Apple's Exposé is just ingenious for that.  It shows you all the windows you have open, laid out all for you to see all at once, on your giant 17'' LCD monitor.  That's the whole reason for getting a 17''+ size monitor, so you can see everything!

Ubuntu gives you the same feature, arguably with less polish, through Compiz's Scale Plugin.

What does Windows 7 have?  Nothing built-in.  You might think Aero Peek is the comparable feature, but nope, says another blogger, who I'll agree with.  How about Win7's Flip 3D feature?  If Flip 3D is an attempt to copy Exposé, it's a horrible attempt.  Why would anyone cascade the windows in 3D, showing me just the top of that stack of windows, using the entire screen?  When I have 30 windows open, I don't want to win-tab 15 times to get to the window I want!  Absolutely frustrating.

But there's Switcher, which is a fantastic clone of Exposé.  And it can also be downloaded from CNET.

I can finally be productive on Windows again.  Now if only there was a good multiple-copy-paste clipboard program for Windows...


What Good is Higher Education?

On the one hand, the conventional and traditional position of the good of higher education is defended against the current wave of anti-higher-education chatter.

On the other hand, there are two pretty persuasive types of arguments against higher education as it is done today:

(1) Economics: it costs too much, and the money is used only to increase the university's prestige rather than better education.

(2) Useless research: instead of citing mainstream media on this, see instead this researcher's commentary (pdf) on systems software research, and this on Realtime Linux: academia v. reality as prime examples.

But actually, what bothers me more is the job prospects in higher education.  Here's a professor wanting to convince students to not become a scientist.  Here's noting that science doesn't pay. The chatter on what it's like to work in academia doesn't sound all too pleasing either.

It's a legitimate question: what good is higher education?

(Edit: and I answer it in Higher Education is like Traveling!)