Friday, September 12, 2014

Why AZ needs Fred DuVal and David Garcia


Educated Voting
American workers can’t compete with the cheapest overseas labor.  That is why we must create high value products and support educational innovation and the Common Core.

Your game host tells you that a box conceals two marbles, each of which could be colored red, blue, or yellow.  You must correctly guess the colors of marbles you will draw to get a prize.  An invisible demon makes certain that you cannot draw two marbles of the same color.

Common sense says that the colors are equally probable and that if you draw a marble from the box, there will be one chance in three of getting it right.  So you reach in and begin to draw a marble from the box, but before you have had a chance to look your host stops you and tells you that the marble you selected is not blue.  Then you are told to guess the color of the second marble to get the prize.  What color would you guess?  Are your odds of picking its color still one in three?  If the probability of the color is a property of the marbles, the second marble must still have a one in three chance.

Because you were given some information, the odds of the second marble being blue increases to one in two and the odds of it being red or yellow decreases to one in four.  If the first marble is not blue, then it could be red or yellow.  If the first marble is red, the second could be blue or yellow.  If the first marble is yellow, then the second could be blue or red.  There are four possibilities for the second ball, two of which are blue.  So, the odds  of blue increase to one in two and the odds of red or yellow decrease to one in four.

But how do we know that the marble’s colors are equally probable?  You could start by drawing marbles and counting to see if the colors come up equally, but they might not because of statistical fluctuation.  It is not scientific, unless you draw from the box an infinite number of times.  You could draw the marbles a large number of times and improve your estimate from that, but your result remains uncertain.  Statistics provides methods for deciding this.  However, there remains the philosophic possibility that you might develop telekinetic capabilities to cause a particular color.

All that is, is known by the mind.  Certainty is not just a property of the marbles.  It also involves you, the observer.  The marbles are at the root of how we learn.  We understand what we know, but we don’t know what we don’t know and we can’t know more than we do know.  The person cannot be removed from reality.  Understanding what does not work is as important as guessing at what does.  Experience, failure and persistence are as important as success.  Does teaching to the test measure this?

A teacher’s single comment, posed in unanswered question form, can change the world view of a student.  It is empathy and reciprocity that characterizes the real human exchange that cannot be provided by any computer and that won’t be found in multiple guess tests.  The key is to never tell a student that they are not made of the right cloth or close doors that could open to their future.  Life won’t always be fun, fair, or easy, but education should always be rewarding, relevant and interesting.

Big Data
Do we want our children to understand numbers, graphs, and probability?  Should they gamble at the casino?  The data collected by those who want to be our friends; government and business, is not meaning.  It is uncertain.  Only we bring meaning to data.

On recent television, a panel of noteworthy journalists debated global warming.  Citing a past data point that was cool; they agreed that there was little certainty that such a thing could be happening, and that consequently we should not worry.  I wished for the opportunity to teach them a lesson.

I would devise a computer simulation involving an unrevealed linear relationship.  The journalists would be asked to pick an input quantity, say dollars invested, and the computer would calculate the value at later times.  To obscure the linear relationship, I would program a noise generator so that the future investment value would often fall far off of any straight line making any pattern difficult to discern.

First they would see the  value of  their investment a month later, and  they would decide whether their investment  had been good or bad,  just like  they conclude that the economy is good  or bad based on a  single unemployment number or the stock market indicators on a  single day.  Then I would have the computer generate another data point and ask them to forecast a third.  To do that, with no other data, they might want to understand some things about a straight line, perhaps even its equation, and they would draw a line through the two data points and use that as a  predictor.  Then I would have the computer generate another data point that would be far removed from their straight line prediction.  What would they do then?  Suppose the computer generated more data points.  Would they connect each of the data points in a zigzag, or is there some way to pick a best line that simply represents the data, and how good does that line describe the data?  Could the data have happened merely by chance or is there a reason for it?  Is there more than one reason for the data?  Can the line really predict the future?

The point is that all the data matters.  Engineers, scientists, and mathematicians have tools to help with this problem that are commonplace, but these things are not introduced to the public.  As Fox news would say, we don’t want to get “wonky”.

Appreciating Math
In mathematics there is a thing called a derivative.   It is like a slope or tangent to a curve.  The derivative, how temperature is changing with time, is revealing.  The difference between magnitude, percent, and rate are important.  With global warming, temperature is changing much faster than ever before.  This coincides with the industrial age and the use of carbon-producing energy, measurements of carbon in the atmosphere, and a known chemistry of the greenhouse effect.  Mathematically, it is understood by a process called regression that calculates whether a correlation exists and whether what we observe could happen purely by chance.

In engineering sometimes we look at things like the derivative because we want to know if our process is dancing too close to the edge and in risk of falling.  In mathematics, there is a transfer function where we put something in and get a modified output.  Mathematical modeling locates the break points, where things fall off the cliff or run-away, and where the math trends toward zero or infinity.  They are the time constants that explain the rate of continuing change.  Financial bubbles, global warming, and electronic circuits can be modeled this way.

We don’t propose that students all become engineers, but they must not grow up to believe that scientists are greedy liberals and atheists.  They need better heroes than Christian anti-intellectuals, Duck Brothers, and swamp alligator people.

In industry, we had a problem with public innumeracy.  We found that, graphics, numbers, statistics, quality engineering, and process control can be taught to high school graduates.  We had a complete curriculum, books, teachers, and taught this in classrooms to everyone.  The result of this, along with the development of automation, made the production line worker more valuable to the company, increased salaries, provided advancement opportunities, and made work more satisfying to them because they knew that they made a difference and were an important part of the team.  These ideas are adaptable to K-12 education.

In high school, we thought that geometry was vocational, not philosophical.  But math is a fundamental part of how we understand the nature of reality.  It exists within politics, economics, health, religion, and spin doctoring.

Math has colorful personalities and an entertaining history.  It was controversial in the seventh century Church, as described in the April 2014 Scientific American article, The Secret Spiritual History of Calculus.  Calculus challenged the church’s belief in an ordered, rigid, logical, certain, and stable reality.  We don’t know if math was invented or discovered.  We do know that it works and helps seeing.

The ability to understand will increase when students are introduced to concepts in earlier grades.  Word problems, derivations, proofs, and real-life examples stimulate thought and are more important than inserting numbers into a formula and turning the crank to get an answer.

A computer program that uses the universal language and symbols of textbook math, MCAD, once offered special educational packages, but it was not adopted by schools and became targeted toward professionals instead.  Technical innovations that could leap-frog American students ahead of the rest of the world are plentiful but not cheap.

Comments made by a parent at the Arizona legislature hearing, supporting failed Republican bill SB1310 outlawing the Common Core, showed that he judged education for the future by his childhood experiences.  He complained about math with letters substituted for numbers and math education that was not arithmetic.

We must not retreat to the past.  We need the help of professional educators.  It will not come from business people. Technology is vastly different than ten years ago, and it isn’t stopping now, but it is not free.  Funding education is more important than business tax cuts that Republicans favor.
In the November election, we can pick a virgin, hoping that a new broom sweeps clean.  This is the option presented by Diane Douglas who claims that professional educators have, in fifty years of effort, proven that they can’t “fix the problem”.  She asks us to believe that her lack of qualifications is the solution, and that her endorsement by the extremist Michelle Malkin is a good thing.

If conservatives are confident about a solution to education’s problems, then the solutions must not be a new thing.  If they make a truly new proposal, then it is risky and they cannot be confident about it.  The Tea Party’s “grass roots” run deep, but no one has a crystal ball that can tell the future.  It must be crafted in small steps that are scientific instead of killing the horse in the middle of the stream.  The Common Core is not perfect and will need changes.  The best people to protect Arizona’s billion dollar education investment in time, effort, and good will are David Garcia and Fred DuVal.  Diane’s views seem to map into correspondence with Republican governor candidate Doug Ducey.  She casts herself as one of us, claiming that parents know what is best for their children, but that might not be true.

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