Friday, March 14, 2014

Teachers most important, least powerful


By George Templeton
Gazette Columnist
Uncommon Core

The self-proclaimed, “intellectually honest” host on the fair and balanced channel explained that he was living evidence of the results of a proper education.  We must eliminate unions! They just raise salaries, taxes, and prevent firing bad teachers.  It has been shown that money does not improve education and proven by teachers in parochial schools that are paid less.  Education can be fixed by requiring students to wear uniforms and by forcing strict discipline in the classroom.

Contrary to that view, students are not motivated because they are not receiving the special attention that came from Sputnik and federal government education programs.  They don’t believe “our day will come” because they don’t see the young man who bought a new Corvette with earnings from his good paying manufacturing job.

Meanwhile, conservative Arizona Republicans have loaded their cannon with their broken wine bottles, rusted chains, nuts, bolts, ball bearings, and whatever rocks they could come up with to blaze away at the Common Core.  We had SB1310, SB1388, SB1395, and SB1396 that would change horses in the middle of the stream.  SB1236, SB1237, HB2150, and HB2291 would extend school privatization, giving up on failing public schools instead of strengthening them.

The proponents of free enterprise in education would like to provide public funding in the form of vouchers to Arizona’s one million students including “non-religious” parochial education.  Our State Superintendent of Public Instruction seems to agree, having gone so far as to record phone calls to parents promoting private schools.  So far, the courts have sided with him.

When does public education become “religious”?  HB2563 and HB2473 show our Tea Party legislators authorizing a non-secular sociology course, exclusively using the Christian Bible, while maintaining “religious neutrality”, to teach literature, art, music, history, public policy, morals, and values.   It’s reminiscent of the TV preacher who advocated the use of the Holy Trinity to introduce reading and Bible verses to teach the alphabet.  Should public funding go to schools teaching pseudo-science that starts and never deviates from the Biblical truth of Genesis and the 6000 year age of the earth?


The uncommon core has different classes of truth.  We can claim that no bachelor is married without examining all bachelors.  That’s logical, but factual elements contributing to truth cannot be separated from logical elements.  The bumper sticker reads:  “guns save lives”.   The logical identity is that the lack of guns kills.  But what are guns for?

Does logic play any role in thinking?  It concerns constructing sound arguments and evaluating the arguments of others.  It focuses on inconsistencies between statements.  It is a defense against prejudice, uncivilized ideas, and ill-conceived politics.  We reach conclusions in two different ways.

Deduction reasons from the general to the specific.  It is impossible for the premise of the argument to be true and the conclusion false.  The opposite is induction.  It has the problem that its “more of the same” inferences could be illegitimate because they are unobserved.  Anecdotal stories fall into this box.  The paradox of the ravens helps to simplify and present this problem in a simple way that is free of emotional bias.

The philosopher, Carl Hempel, tried to test the hypothesis that “All ravens are black”, finding that it was not feasible to examine all ravens.  The hypothesis can be logically restated as “All nonblack things are not ravens”.  It is easier to find a white shirt that is not black and not a raven, thus confirming the statement, than it is to examine all ravens.  But a blue jay, being nonwhite and not a raven, also acts to confirm that “All ravens are white”.

All ravens are simultaneously black or white!

You can see how the politicians can make use of this way of thinking.  It’s logical, but it is a psychological illusion that the statement is only about ravens.  Of course, you can argue that observations of things that are not ravens can’t tell us much about ravens.  But that never stopped a politician.  Likewise, the voucher bills, called “Empowerment Scholarships”, are not just about individual choice.  They are about giving up on “government” schools.

The search for truth is difficult.  The more black ravens you see, the more likely it is that they are all black.  But the number of black ravens seen is irrelevant to the truth of the proposition.  The ravens at the polar ice caps might be white so the polar bears could not so easily see them!  Hemple’s hypothesis is wrong only if there is a raven somewhere that is not black, and right only if there is no such raven.  There are a lot of ravens in the world to examine, and even more non-ravens.  A small number of possibilities would make our determination easy, but we often don’t know the dimensions and cannot tell when to stop looking.


Our thinking needs categories.  The philosopher, William James, explained that words are powerful.  The TV preacher explained that the Bible is not about meanings.  It has words, every one of which is true.  Like the Biblical naming in Genesis 2:19, words give us dominion.  Like ravens which are all black, we expect uniformity in nature, but this lends support to too many inferences.

In 1953, the philosopher Nelson Goodman presented a deliberately paradoxical problem in a story where an English-speaking jeweler hypothesizes that all emeralds are green and will remain green.  Another jeweler, speaking the Gruebleen language, uses the term “grue” to refer to the same color because there is no green in his language.  But grue, in English, is defined so that something which is green before January 1, 3000 and blue thereafter is “grue”.  Grue depends on time, green, and blue.

Neither jeweler perceives that emeralds can change color.  Both never knew them to be any color different from what they are now.  The English-speaking jeweler says in the distant future they will be green, and the Gruebleen-speaking jeweler says they will be blue.  We cannot observe that either jeweler is wrong, because “thereafter” never comes.  The quandary here is that both jewelers have used the same inductive reasoning, but they have reached mutually exclusive predictions.  At least one jeweler must be wrong!

We are inclined to think that green is the correct definition because it is simpler and does not contain time, but the Gruebleen-speaking jeweler has another color word, “bleen”.  An emerald is bleen if it is blue until January 1, 3000 and green thereafter.  Bleen depends on time, blue, and green.  We could argue with the Gruebleen-speaking jeweler, but we would have to explain in his language that something is green if it is grue before January 1, 3000 and bleen thereafter.  To him, green depends on time, grue, and bleen.  Green is the complicated gerrymandering color.

We must put ourselves in the shoes of the jewelers who are trying to understand each other, and not claim that emeralds can never change and that blue, green, grue, and bleen are all the same color.  The situation has a circular “which came first, the chicken or the egg” symmetry, characteristic of cross-definition.  It illustrates the problem of projecting qualities into the unknown.

We really cannot say which jeweler is right, because it is equally true that every emerald that has been observed is grue. Why should we mix time with color?  The time in Indiana depends on which county you are in.  Like daylight savings time, it was also an arbitrary decision.  It seems ridiculous that color would change, but yellow bananas turn brown eventually.  When we say a banana is yellow, we do not mean to imply that it will remain that color forever.

With suitable choices of terms and zero hour, anything confirms anything else at any later time!

Things besides time can be used to confuse and change meaning.  Severe conservatives perceive standards, curriculum, and tests in peculiar ways.   They gerrymander these terms when they do not make clear distinctions among them.

Standards become curriculum.  Our governor changed the name of the Common Core to the “Arizona’s College and Career Ready Standards”.  Educational vouchers are also “scholarships”.  Parents are also members of the school district, community, state, and nation.  It’s we, not us versus them.

The video of the Arizona Senate education committee hearing on the anti-common core bills did not reveal much mutual understanding, refinement of viewpoint, or clarifying debate.  Thinking in circles was infused with confusion, anecdotal stories, and conspiracy.

Teachers, the most important but least powerful link in the educational chain, are threatened by new requirements.  They have an uncertain future.  We ponder how probability fundamentally relates to testing, learning, and the uncommon core.


Statements involving probabilities are not falsifiable.  The argument for the objectivity of probability comes from the law of large numbers, claiming that they will better approximate truth.  We rightly believe that confidence improves with sample size, but the key word here is belief.

Geometry and God’s predestination did not allow probability.  It was not taken seriously until Blaise Pascal wagered about God’s existence in the seventeenth century.  A’ priori or counting probability is a truth not grounded in observed experience, and it makes the assumption that the dice are not loaded.  It is a circular proposition, an uncertainty grounded in uncertainty, but it seems intuitive.  It was not extended to more complex situations until the early twentieth century when logic, set theory, diagrams, and symbolic algebra were introduced.

Quantified probability, a number between zero and never, and one for sure, is like the glass of water that is half-full and half-empty.  It adds to one.  It can be deceptive because we assume that probability is out there, a constant that is independent of belief.

Without us, probability does not exist.  Our perception changes when the world changes and when we acquire new evidence.  We have to take risks.  We must not be like the gambler who simultaneously wagers six dollars on a sixty percent chance that it will rain, hoping for a ten dollar payback, and six dollars on a sixty percent chance that it won’t, hoping for a ten dollar payback in that event.

We cannot predict any single outcome from the toss of a fair and balanced coin, but with an infinite number of tosses it falls heads or tails an equal number of times.  This is not scientific because we cannot observe and verify what happens in the infinite limit.  That would take forever.  We cannot prove that statistics provides the same truth that comes from counting.  Sometimes we cannot see to count.  Then we use statistics to describe what has happened, what is, not what will be.

The search for truth goes back to the eighteenth century Reverend Thomas Bayes who formulated an equation describing how to calculate probability given pre-existing beliefs.  It has the personality of formal logic.  His theorem applies if you agree that intensity of conviction does not make truth.  It is about beliefs, evidence, and learning.  It is the uncommon core.

Suppose you have a rare disease.  Intuition suggests that a 99 percent accurate test would correctly predict that you have the disease.  But the 99 percent is the test confidence and does not give the probability that you have the rare disease.  Ten people will test false positive even when only one in 1000 has the disease, so the chance you don’t have the disease, given a positive test, is slightly more than 90 percent.  That is the problem with any less than perfect test that claims it knows the details about a minority.

In the nineteenth century, craniometry, the measurement of the size of one’s head was the standard for intelligence.  Modern tests are better, but they infer too much.  Learning involves generalizations, problem solutions, facts, values, and broad categories, but assessment has to deal with the true or false nature of unambiguous measurable objectives.  Can the student’s answer to multiple guess questions really be sufficient evidence to hold students behind, fire teachers, close schools, and privatize education?  Anybody can make a test, but will it be reliable, valid, and predictive?


Bayes’ theorem hopes that factual evidence will win over mere intuition, but there is no proof that humanity makes progress.  The web of truth can always be distorted around its edges to make any wrong seem right.

No comments: