Friday, June 22, 2012

Smart People (You and Me) are Stupid

A recent provocative article from the New Yorker begins:

Here’s a simple arithmetic question: A bat and ball cost a dollar and ten cents. The bat costs a dollar more than the ball. How much does the ball cost? The vast majority of people respond quickly and confidently, insisting the ball costs ten cents. This answer is both obvious and wrong. (The correct answer is five cents for the ball and a dollar and five cents for the bat.)
Or try this one:
West and his colleagues began by giving four hundred and eighty-two undergraduates a questionnaire featuring a variety of classic bias problems. Here’s a example: In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake? Your first response is probably to take a shortcut, and to divide the final answer by half. That leads you to twenty-four days. But that’s wrong. The correct solution is forty-seven days.
Our first mistake is to assume the human beings are rational. We should start from the premise that human beings are lazy (Yes, I am talking about you, and I am talking about me).
When people face an uncertain situation, they don’t carefully evaluate the information or look up relevant statistics. Instead, their decisions depend on a long list of mental shortcuts, which often lead them to make foolish decisions. These shortcuts aren’t a faster way of doing the math; they’re a way of skipping the math altogether. Asked about the bat and the ball, we forget our arithmetic lessons and instead default to the answer that requires the least mental effort.
My son calls it the “slacker syndrome.” The first step to learning to make good decisions is to humbly acknowledge that deep down we are all slackers. The smarter we are, the more stupidly we decide, like the super-smart guy who thinks everyone else is an idiot, but HE can time the stock market.
...smarter people are more vulnerable to these thinking errors...intelligence seems to make things worse. The scientists gave the students four measures of “cognitive sophistication.” As they report in the paper, all four of the measures showed positive correlations, “indicating that more cognitively sophisticated participants showed larger bias blind spots.”....
Okay, now that I know I am prone to this weakness (maybe the next time a job interviewer asks me about my number one weakness, I should admit that I am stupid....hmmm...maybe not), I can use this new-found self awareness to avoid it in the future. Think again.
...“people who were aware of their own biases were not better able to overcome them.”...
Even worse, we all tend to think of ourselves more highly than we ought.
Perhaps our most dangerous bias is that we naturally assume that everyone else is more susceptible to thinking errors, a tendency known as the “bias blind spot.” This “meta-bias” is rooted in our ability to spot systematic mistakes in the decisions of others—we excel at noticing the flaws of friends—and inability to spot those same mistakes in ourselves.
Wow, that sounds like a modern version of old advise from Jesus.
"Why do you look at the speck of sawdust in your brother's eye and pay no attention to the plank in your own eye?” (Matthew 7:4)
Education and self-awareness do not work because the meta-cognition is not available.
The problem with this introspective approach is that the driving forces behind biases—the root causes of our irrationality—are largely unconscious, which means they remain invisible to self-analysis and impermeable to intelligence.
Therefore we are doomed to live in a Zen paradox.
The more we attempt to know ourselves, the less we actually understand.
Nevertheless, I cannot help but feel education and self-awareness of our biases must be better than ignorance. At least, we can learn to be more tolerant and forgiving of others.

Tuesday, April 24, 2012

Parents In Contempt

As long as schools hold the public (who pays their bills, by the way) and parents in utter contempt, I seriously doubt that they will be able to build the relational trust necessary to academic achievement. Even worse is the contempt demonstrated toward those parents and members of the public who are education colleagues who might actually have a message worth listening to. I am just going to tell the story. A friend's child brought home a math assignment on perimeter and area. One of the problems was unsolvable as presented. It looked something like this (I do not have the actual diagram since child already turned her homework in):

The problem is unsolvable because there is not enough information. There is no way to know whether the angles that “look” 90 degrees are in fact 90 degrees. There is also no way to know whether the vertical segment that “looks” like it bisects the base in fact does so. The child made these points in class, but the teacher shot her down. So thinking I was being helpful to a young teacher, I sent her an email. After some brief introductory remarks, I wrote,
... the last problem of a recent homework assignment on perimeter and area had insufficient data to solve the problem.  One of the principles of geometric diagrams is that we never go by appearance.  We solve using givens and proven facts.  Since that particular diagram gave no indicators of equivalent length, bisection, 90-degree angles, etc, no conclusions could be drawn regarding the length of the side opposite the one measuring 15 units, or any other non-given length, without making unsubstantiated assumptions.  We are miseducating children if we teach them, even indirectly, bad thinking habits.  One of the purposes of math instruction is the logical and critical thinking skills it cultivates. And if we are as worried about high-stakes tests as we say we are, we will teach students to think properly.  A favorite trick of bubble tests is to lead the students down a primrose path of faulty assumptions. If you would like discuss ways to help students learn to think, please let me know.  I spent a lifetime teaching math, first to junior high and high school, and later, college students.
The teacher sent a reply that seemed quite understanding, but showed that she somehow missed the point. She replied,
I completely understand what you are saying in the email. I also concur with what you said, however, I did verbally tell the students that angles that appear to be right are. ..However, if the student drew it out on the grid paper, then that student could find an area for the figure they drew. We are at an entry level with these problems, and so I looked at how the student drew the problem out, and determined if their area and perimeter matched that drawing.
Am I the only one who found the reply disturbing? So I wrote back,
Thank you for your reply. "I did verbally tell the students that angles that appear to be right are."  Angles that appear to be right are most decidedly not right just because of appearance.  I really think that if the student's math level is lower, then it is all the more critical to precisely teach thinking skills.  Drawing on grid paper does not really help, because it only pushes students harder to make unwarranted assumptions.
I closed by repeating my offer to help. Then I got this curt dismissal:
Hi again, Thank you for your response, it seems that on this particular problem I did not satisfy your criterion and I am sorry to have let you down. Have a nice day.
Okay, so she really does not want any help, I guess. And apparently she is happy to miseducate kids. I figured I would just move on, until....the school's guidance counselor contacted me, and let me know that she considers my communication with the teacher inappropriate and unprofessional. Seriously? She even challenged my right to have any conversation with the teacher by pretending that I was discussing a student, not a math problem. Now when I was teaching, the only time I passed communications on to administration was if it contained a personal insult of some kind, of course, a very rare occasion. Maybe it is unfair to extrapolate from one experience, but I assure you, schools routinely show contempt for parents, the public, and even the education-savvy members of the public. We must be careful that we as teachers refrain from thinking we get to define the terms of parental involvement. I know plenty of teachers who actually resent fully involved parents if those parents dare to challenge the teacher or the school. Then teachers vilify the parent as a "helicopter parent" in an ad hominem attempt to dismiss with contempt the parent's concerns. A lot of schools want to limit parent involvement to conferences and making cupcakes.

Wednesday, April 18, 2012

Unresolvable “Science” Debate?

Will the controversy between evolution and creationism ever end? Is it destined to swing forever on the pendulum of public opinion? The entire controversy is sustained on both sides by too much emotional investment in unexamined assumptions. The latest pretext for acrimony is a Tennessee bill intended to permit teachers “to help students understand, analyze, critique, and review in an objective manner the scientific strengths and scientific weaknesses of existing scientific theories covered in the course being taught.” In case that wasn't clear enough, the bill repeats its intention from the other way round. No teacher shall be prohibited from “helping students understand, analyze, critique, and review in an objective manner the scientific strengths and scientific weaknesses of existing scientific theories covered in the course being taught.”

I read the bill. It is only two pages of plainly-worded text. It mentions creationism not at all. It does refer to scientific theories, of which there are many, each with its own strengths and weaknesses. However, creationism is not one of those theories because it is not science.

You see, science is all about collecting only evidence that can be perceived with just the five senses. The sense may be amplified as when we use a telescope or other instrument. Science is concerned with explaining data collected only with the five senses. Other data is not considered.

An explanation that tries to account for extra-sensual data is, by definition, not a scientific theory. Nevertheless, due to public confusion and the desire of some that creationism be recognized as a scientific theory, it will be in science class that students ask their questions. Teachers need to be prepared to answer them while respecting deeply held religious beliefs.

The bitter acrimony is really unnecessary. It is easy and reasonable for students to accept that science attempts to explain only sense-based data. Most of the problem stems from a widespread misunderstanding of what science is.

As far as evolution goes, it suffers from historical bar-lowering, as it has weaknesses that do not adequately account for the scientific facts. Even within my lifetime, scientists have weakened the definition so much as to create a near tautology: evolution is change over time. Many science texts state it just like that. Others pretty it up a little, “evolution can be precisely defined as any change in the frequency of alleles within a gene pool from one generation to the next.” However, such a definition in non-controversial. Organisms do change over time. The biblical Jacob realized it thousands of years ago when he made a deal to work for Laban, receiving only the spotted sheep as his wage. Laban promptly removed all the spotted sheep from the herd. Nevertheless, by careful breeding, Jacob was able to create a herd of mostly spotted sheep from a herd of un-spotted sheep.

Years ago the National Association of Biology Teachers (NABT) used a fairly stringent definition: "The diversity of life on earth is the outcome of evolution: an unsupervised, impersonal, unpredictable and natural process of temporal descent with genetic modification that is affected by natural selection, chance, historical contingencies and changing environments." Unwritten, but understood and unquestioned, was the additional idea that mechanisms of descent were robust enough to account for the change from say, sponge to zebra.

In fact, this unstated implication is the root of the controversy. Pro-evolutionists (as distinguished from scientists) believe the implication; Anti-evolutionists (again, as distinguished from scientists) do not. For many, the implication goes directly to deeply-held belief systems. Later, the NABT deleted the words “unsupervised” and “impersonal.” Today, there is no definition on the website at all. One of the reasons that the definition of evolution has gotten weaker and weaker is that the data, especially as regards speciation, is inconclusive, and fails to support the more robust definition. There are lots of instances where it is not at all clear whether two organisms are members of different species. A high-quality university level biology book addresses the speciation continuum and other issues, but it can be a tough read.

As inconceivable as it may be to some, it is possible to discuss the weaknesses of evolutionary theory without smuggling in creationism. Only ideologues would consider the mere mention of evolution's weaknesses as an attack upon evolution. For critical thinkers, it is the grist of intelligence-making. As F. Scott Fitzgerald said, “The test of a first-rate intelligence is the ability to hold two opposing ideas in mind at the same time and still retain the ability to function.”

Friday, March 2, 2012

How Rigor Empowers Academic Achievement

Maybe we do need another word besides “rigor”, but “challenging” and “rich” are weak alternatives.

Rigor in my teaching practice means conscientious excellence. For example, rigor requires students to differentiate solution from answer. Suppose the question is, “What are the best dimensions for a particular garden?” The student will algebraically calculate two perfectly legitimate solutions. One solution will show two negative numbers; the other will show two positive numbers. Students must choose the solution which answers the question. Since the question is about a garden, that would be the solution with the two positive numbers,because a garden cannot have negative measurements. A different question might require the negative solutions to be the answer.

Or perhaps the question is, How many cars do we need for the field trip. The solution might be 7.2, and it can be the correct solution, but the wrong answer. The correct answer is, "We need 8 cars." Mindless rounding also yields a correct solution,but a wrong answer. I require answers written in complete sentences that also include the unit. I would mark all three of these so-called answers wrong: "x=8", "8," and "We need 8."

I also require students to keep units attached to numbers when they calculate. So the area of a room is not 9X12, with the ft^2 attached later. When students show their work, I want to see 9 ft x 12 ft = 9 x 12 x ft x ft = 108 ft^2. Please do not dismiss my simple example as trivial. This sort of training, call it rigor if you like, pays off big when students must do chemistry or physics calculations with lots of units running around. My physics students learned that if the resulting unit is not what they expected, they probably also made a more serious mathematical error somewhere. That self check is lost when units are divorced from numbers and remarried at the end of the calculation.

In the earliest grades, rigor may imply making sure students understand the role of an equal sign, and knowing that the horizontal line separating a column of numbers from the result of a calculation is not a substitute equal sign. Many adults graduate from high without a proper appreciation of an equal sign.

Every field has similar examples of the value of conscientious excellence. Most people prefer the two syllables of “rigor” over the seven syllables of “conscientious excellence.” Just because three of the definitions seem negative and harsh does not invalidate the value of the fourth definition. Rigor, properly used, is not a blockade to academic achievement or educational accessibility, but its open door.

Thursday, February 23, 2012

What Happened to the Geezer Teachers?

A self-identified geezer teacher asks what happened to all the other geezer teachers. Why is the modal experience one year, not the historical 14 years anymore?

Here is what happened. A lot of proven expert teachers move (for whatever reason) to a new district or a new state. Or maybe they move back to the US after a decade or two teaching overseas in our Department of Defense schools maintained on military bases for the children of military members. When they come back to America, they are "out-of-district" for every district in America. These expert geezers discover to their dismay that they are unemployable. Most schools choose a novice over an experienced teacher any day of the week. "It's the budget, doncha know."

If budgets were really the problem, schools would jump at the chance to get a geezer at a steep discount. Remember, most districts give only five-years credit for experience on the salary scale. A geezer with 25 years experience is willing to take a 20-year pay cut, but no dice. Schools reject expert teaching applicants every day while simultaneous complaining about looming teacher shortages, especially in math and science.

Those highly experienced education experts even have difficulty getting jobs training the next generation of teachers. Schools of education overwhelmingly prefer a newly-minted PhD over an expert geezer-teacher. Education students suspect their education professor have no substantial experience, and now with so many curricula vitae online, it is easy to confirm the validity of their suspicions.

Meanwhile, California wants to help laid-off teachers get new credentials in math and science. Problem is, like most teacher recruitment programs, it targets novice teachers. California schools could start by credentialing the out-of-state math and science teachers they already have. Fact is, a teaching credential will not help. It is only a third strike. The first strike is experience; the second is post-graduate education. Teachers with all three strikes are rejected with apologies. Teachers lacking only the credential do not even rate the apology. Districts airily dismiss them as unqualified even though they are probably more qualified than most teachers in the school.

States and schools could start by eschewing the check-box method of evaluating qualifications, and actually look at what the applicant brings top the table. A top teacher with a fat stellar portfolio should be able to walk into any state credentialing office and walk out with the credential. Instead, the evaluator will likely say something like, “We can't accept your NTE scores, or your scores from the other state's teacher competency tests. Our state has it own more rigorous standards.” (Arizona actually said that to me about my umpteen NTE and California tests, all with scores in the 90+ percentiles. The California credentialer had tears in his eyes when he told me that because of bureaucratic rules, a world-class teacher like me would never get a California credential).

Schools boards are waking up to discover that their schools are staffed with novices. There are few mid-career teachers because experienced teachers cannot get hired, and if they do manage to get hired, they are the first laid off again in the next budget panic (last in, first out), destroying resume continuity. The late-career teachers are retiring. A lot of those mid-career teachers love teaching and would love to secure a stable teaching position, but most of them have moved on. They can be found filing medical records, selling insurance, doing taxes, pouring coffee. Sad. Truly sad. In spite of all the noise, America appears to have the education system it wants.

Tuesday, February 21, 2012

Kindergarten Academics Is Not Academic Achievement...

...no matter what anyone says otherwise.

Robert Slavin, creator of the reading program Success For All, and before that, creator of the reading program CIRC (Cooperative Integrated Reading and Composition), says we know how to make sure every first grader can read.

Imagine that your job were to ensure the reading success of every child in a Title I school by the end of first grade, and you had flexible resources to do it. You'd make sure kids had language-rich preschool and kindergarten experiences,

So far so good, but then he blows it by endorsing the current fad of pushing first grade academics into kindergarten.
learned phonemic awareness and letter sounds in kindergarten, and were taught using proven kindergarten- and first-grade reading programs that emphasized systematic phonics, comprehension, fluency, and vocabulary.


Kindergarten is not the place for academics. Gesell Institute of Human Development Executive Director Marcy Guddemi agrees.

Guddemi said quality early education programs for ages 3 to third grade, the years defined as early education, are essential in providing proper experiences and exploration, rather than to learn more letters earlier.

The extra time in kindergarten spent on so-called academics has come at the expense of schema-building, the foundation for reading comprehension beyond mere decoding. Kindergartners should cut and paste. They should also visit a bakery, the newspaper, the fire station etc., etc. They should plant sunflowers and morning glories, raise butterflies, and experience a whole host of other activities. They should go on field trips every week. When it rains, they should play in the mud.

In Japan, kindergarten teachers are likely to take the kids out into a rain shower and let them model creeks merging into rivulets, and rivulets merging into rivers, flowing into a lake (puddle), as well as the powerful effects of water erosion. On a windy day, the kids will run around with makeshift plastic bag kites, learning how the wind inflates the bag. All these experiences and many more form the treasury of reading comprehension. Children create and refine schemata as they assimilate each new experience.

In other words, schema provides the context for comprehending what we read. Even adults who are excellent readers may decode perfectly but still perceive the result as gibberish if they lack the appropriate schema, as illustrated by the following little piece of actual prose.
The increased flexibility to adopt a divisional basis other than a territorial or field of use basis entails the need for provisions to prevent abuse and facilitate compliance. Capability fluctuations, whether market-driven or strategic, that materially alter the controlled participants’ RAB shares as compared with their respective divisional interests create the equivalent of a controlled transfer of interests and should therefore equally occasion arm’s length compensation. Accordingly, the temporary regulations modify the change of participation provision to classify such a material capability variation, in addition to a controlled transfer of interest, as a change in participation that requires arm’s length consideration by the controlled participant whose RAB share increases, to the controlled participant whose RAB share decreases, as the result of the capability variation.

Young children, more so than adults, need time to build schema. Pushing first grade into kindergarten is a quick and dirty route leading only to the facade of increased academic achievement.

As Guddemi said, “Unfortunately, in an effort to close achievement gaps,” parents and schools have embraced a philosophy that earlier is better. Kindergartens these days burden children not only with “reading,” but also math. More and more schools require kindergarten teachers to teach them to calculate according to algorithms as if they do not know that children can learn an awful lot of math without ever putting pencil to paper. All kinds of activities effectively teach mathematics and number sense, like puzzles.

Furthermore, technology is not the answer. So-called ed tech is not simply a tool like pencils or pens. Ed tech is pointedly very different from a pencil or a pen. First, Pre-K should be doing almost nothing with pencils or pens. For example, they should not be writing numerals and letters. Instead, they should be doing real math with real objects. Math on a technology device is not real; it often strikes the students as magical. For example, they really do not understand how the animation is supposed to convey a idea such as carrying even when they are as old as second or third grade.

Too much modern animation is far too lifelike. Children have enough trouble learning to tell the difference between what is real and not real without having to contend with squirrels who give high fives or dogs doing hip hop. Kids were better off when dancing rabbits were (and looked like) cardboard figures on a stick.

Let the children play. Of course, the best kindergarten teachers plan and guide children's play activities. The worst thing we can do is push first-grade academics into kindergarten and call it advanced academic achievement.

Wednesday, January 11, 2012

The Measly Educator Expense Deduction

A Heritage Foundation study of teacher salaries has provoked quite an outpouring of response.

I would like to address the $250 educator expense tax deduction and some typical hiring practices.

The first $250 a teacher spends on qualifying expenses is an "above the line" deduction, meaning it occurs on the Form 1040 before the line containing either the standard deduction or the itemized deduction. This first $250 deduction is easy for any teacher to take, at least until Congress takes it away. If a teacher spends more than $250 in any calendar year, or the above-the-line deduction disappear, there are two hurdles teachers must surmount in order to claim education expenses.

Any amount exceeding $250 becomes part of the calculation of itemized deductions. The first hurdle is that teachers can itemize only the amount of educator expenses that exceeds 2% of adjusted gross income. For example, suppose the adjusted gross income(AGI) is $25,000. The first $500 is on the teacher. If the educator's deduction is in force, this teacher would need to spend more than $750 before it is even worthwhile to start a Form 2106. If the AGI is $50,000, another $500 would have to be spent before the next dollar can be itemized.

Overcoming the 2% obstacle is just the first step. The itemized deduction hurdle is the second step. Unless itemized deductions exceed standard deductions, teachers get no tax benefit for expenditures greater than $250 (or any expenditure should Congress repeal the educator's deduction). A single teacher's 2012 Schedule A would have to total more than $5,900 in order to deduct even $1 of classroom expenses. Married teachers need more than $11,900 of allowable Schedule A expenses. Unless there is a mortgage, more than likely a teacher will eat their classroom expenses. Contrary to the cited article, the IRS would have no idea how much teachers are spending by looking at tax returns, in part because they have no way of knowing how much educator expense the standard deduction swallowed.

On the other hand, when a teacher purchases their own equipment, they are free to take it with them to the next school. I purchased several sets of Algebra Gear with my own money, and took them with me. If I had to leave them behind because the school had bought them, I would have to ask the new principal to buy them. The answer would likely be NO. I was very glad the Algebra Gear belonged to ME.

Before 2003, most educators got no tax break because the standard deduction swallowed their expenses. The above-the-line deduction was enacted to remedy the situation a little, but it is a far cry from being a reimbursement. The $250 deduction reduces taxable income by $250. A teacher in the 10% tax bracket would save $25 of income tax. A teacher is the 25% tax bracket (they do exist) would save $62.50. In both cases, the savings is peanuts, but the higher-paid teacher get 2.5 times the benefit. Remember too, that the educator expense deduction is perennially on the chopping block, and Congress could eliminate it any year now. Then the 10%-bracket teacher loses even the measly $25 savings.

Private sector workers also have out-of-pocket costs. As an aside, one of my pet peeves are bosses who hire go-fers and expect them to use their own car for the boss's errands without reimbursement. Those expenses are not likely to take the go-fer into Schedule A territory, so the low-paid go-fer eats it. The boss effectively pays an even smaller wage by foisting business expenses onto a low-paid employee.

As far as teacher salaries go, since tax prep was my moonlighting job, I have seen lots of teacher W-2s. Some seemed really low, especially private and charter school teachers. Some seemed really high like the third grade teacher making $70,000 per year and claiming thousands of dollars of furniture purchase every year. Really?

I have linked to the salary schedule of what is probably a median school district. Typically, you put one finger on your education level and one on your years of experience. Your pay should be where your fingers intersect. However, expert out-of-district teaching applicants are virtually unemployable, ostensibly because they are too expensive. Suppose an expert teacher with “Class IV” education and 15 years experience moves into the district and applies for a teaching position. If you think the pay would be $68,985, you would be wrong. See the typical note at the bottom of the schedule, “experience outside Ventura Unified School District is limited to five years.” That expert teacher's salary would be no more than $51,432. The school district would get the expert teacher for a discount of more than 25%. In some districts the pay cut is far larger.

Nevertheless, many expert teachers who change districts for whatever the reason are willing to take the cut. Teaching is their livelihood, their calling. Shortsightedly, school administrators would rather pay a novice an even lower salary than hire a proven expert. As baby boomers begin to retire, some schools have realized the hole they have created in their teaching cadre. They have a lot of novices. They have turned away mid-career teachers. Their veterans are retiring. American society has the education system we are willing to pay for.