We Teach Our Students to Misbehave...

… and then complain when they do exactly as we expect. A certain student came home from school reporting on a substitute teacher the class did not like. She began her report by asking me, “Doesn't a teacher have to let a student go to the bathroom if it is an emergency?” I did not answer; I asked what happened. The class in question took place after just after lunch. A girl came in, saw there was a sub, and began “dancing” near the classroom door. The teacher asked her to sit down. She continued to loudly make a scene. The teacher continued to ask her to sit down. The girl never did sit down, and continued to interrupt as the teacher tried to finish taking role. Then the teacher let her go.

After she left, several members of the class began asking the teacher out loud, “Why didn't you let her go? You have to let people go to the bathroom. What if it's an emergency?” The teacher explained that he would have let her go a lot sooner if she had just sat done when she was asked and allowed him to finish taking attendance.

Typical of many classes with a sub, there was a video which the teacher showed using the TV monitor. The students demanded out loud that the teacher put the video on the powerpoint projector instead of the TV monitor. The teacher refused. The students insisted their regular teacher always puts videos on the powerpoint projector. The teacher still refused. (an aside: students are really spoiled by all the technology available in classrooms these days. When I started teaching, we handed out purple, smelly mimeographs and showed filmstrips on a reel-to-reel. Some people reading this post may not have any idea what I am talking about. LOL)

My little friend came home complaining about what a mean teacher the substitute was. I guess she expected me to commiserate, and she was thoroughly astonished that I had an entirely different take on the incident. I told her the fault was with the students, not the the sub. First, the girl created a public scene when she could have walked respectfully to the teacher and quietly made her request. But no. She engaged in melodramatic, loud theatrics and essentially set a trap for the sub. She probably did not have to go to the bathroom at all.

Second, the students thought it was okay to question the teacher's response out loud, but worse, the teacher thought he had to answer their objections. Third, the students whined about the powerpoint projector. I told my young friend that no sub with a speck of common sense will do anything just because the students say the teacher does it. That is exactly the way to guarantee a whole period of one piece of nonsense after another. My little friend thought that perhaps her teacher forgot to write the part about the powerpoint projector in the lesson plans she left. Maybe so, I said, but the class will just have to do without, and they should never have been disrespectful to the sub about it.

She countered, “If we like the sub, we behave.” Wrong answer. Students behave because they are expected to behave whether they like the sub or not. Students have not the power, responsibility or authority to decide that they will behave “if we like the sub.” Liking the sub is irrelevant. Shame on our society for even giving such a wrong-headed notion any positive attention.

Then my little friend asked, “But what if the sub doesn't like kids?” What was she really saying, that kids have the right to punish a sub they decide does not like them? Wrong again. It is irrelevant whether “the sub likes kids” or not. Students are expected to behave, period. The problem in our society is that students did not get these wrong-headed ideas from nowhere. They have been socialized to them their whole lives. As a society, we do not really expect students to behave, the obligatory first day “expectations” lectures notwithstanding. In fact, I would suggest if we are still giving these first-day lectures to students older than about ten, both students and teachers have already conceded that students are expected to misbehave, regardless of our actual words. Furthermore, maybe we need to think a lot more deeply about what we mean by “student-centered.” In addition, there is tremendous pressure on teachers to avoid sending unruly students to the office.

As a junior high and high school teacher, I also gave the first-day lecture. I told the students I was doing so because I knew they were expecting one. I told them they had heard all the same expectations every first day since kindergarten, and now that they are secondary students, they get to hear the same expectations multiple times in one day. I listed the expectations anyway “on the off-chance there is even one person here who has not heard them,” and I explained the consequences of misbehavior. Faddish and wrong implementation of “democratic discipline” models leads to specious student “empowerment.” (Oh, I do hate buzzwords).

Up until this point, the students have basically tuned out what they have already judged to be merely a stricter sounding version of the usual first-day yadayada. But then, they all perk up when I say, “Here's the catch. There are no warnings. You guys are way too old for childish warnings. And I don't do second chances, and I do not negotiate.” About the third day, a student (usually a boy) will test me. I apply the consequence immediately and shut down the inevitable attempt to negotiate. Normally, I have no more problems during the year, because the thing is, students actually know how to behave. They just need teachers who genuinely expect them to. It is the Pygmalion Effect. When I had laryngitis while teaching in a school for "troubled" (read: disruptive) students, I learned that the students really do know how to behave. I learned to raise my expectations instead of my voice.

Japanese and Chinese students have a reputation for being well-behaved. I directly observed that overall, the expectation that students will behave is a Japanese societal given that does not require an annual review. Interestingly, a study found that “Chinese teachers appear less punitive and aggressive than do those in Israel or Australia and more inclusive and supportive of students’ voices,” and this in a country stereotyped to be just the opposite.

If you doubt that we encourage the very misbehavior we decry, check out this actual example from curriculum purporting to teach “critical thinking.” Really gotta watch for that “invisible curriculum.”

Do Not Use Baby Talk to Teach Math

Number sense is like a mighty oak rooted in the subconscious. Beginning in infancy, it is little more than a humble acorn. Misconceptions are weeds that also root in the subconscious and stunt the acorn's growth. The language we use to express number sense can nurture the acorn or plant the seeds of misconceptions. The resulting weeds are pulled only with great difficulty.

The baby talk some teachers use to teach addition can plant misconceptions that prevent students from properly developing the concept of mixed numbers. We should never, ever say, “2 and 3 makes 5.” Even a good quality text like Singapore Math talks baby talk, but that is because something was lost in the translation to English. We should say properly, “2 plus 3 equals 5.” Children are perfectly capable of learning correct language, and it saves them the trouble of unlearning it later. After all, we do not expect them to say “2 and 3 makes 5” forever. We expect them to transition to adult math expressions sooner or later.

So what is wrong with “and” anyway?

AND means something mathematically, and it is not “plus.” For example, 2½ does not mean 2 + ½. You do not believe me? How about -2½? Does that mean -2 + ½? Of course not, but that is not obvious to kids. The mixed number -2½ means “minus 2 and ½,” not “minus 2 plus ½.” more technically, it means “minus 2 and minus 1/2” or -(2 + ½). Subtracting a mixed number is often the child's first exposure to the distributive property, however I have never seen a textbook make it clear. Instead, we routinely plant misconceptions and then wonder why kids sometimes have so much difficulty with math.

It is not all that hard to teach either, especially if using money to illustrate. “If I have three dollars, and I spend two and a half dollars, how much do I left left?” I spent 2 dollars AND I spent ½ dollar. A seventh grade teacher mentioned in this blog the difficulty his own students were having.

I saw this post about a week after it appeared, and so I was prepared to prove MY 7th grade pre-algebra students would not make such mistakes. Equation-solving did them in, with this as a solution: -5¼ + 2½ = -3¾. I had previously showed them how illogical such a thing was, and how it didn't make "number sense", yet the method error persisted.

Break it out the way students do, and the thinking error emerges: -5 + ¼ + 2 + ½ = -3 + ¾ = -3¾. Our long custom of misrepresenting “plus” as “and” has led them to the idea that all you have to do is take out the plus sign and shove the fraction up against the whole number. If it is already shoved together, pull it apart, put the plus sign back in, and voila! The problem is solvable.

Because the root of the misconception is in the subconscious, even if they get some number sense training and even understand the training, they will fail to see the error of their thinking, and so the error persists. The teacher will probably have to name this misconception directly and explain to students how they were mis-taught in the past. They may then be able to pull it into their conscious mind and deal with it.

Decimal numbers might help. 37.2 is not “thirty-seven point two.” It is “thirty-seven AND two- tenths.” The function of the decimal point and the meaning of “and” is to differentiate the wholes from the part, whether in decimal numbers or mixed numbers (which brings me to another pet peeve. It is not that we are “converting” from decimal numbers to mixed numbers. Both forms are essentially the same: a whole number with a fraction). The decimal point does NOT mean “perform the operation of addition.”

AND is a mathematical operation called “union.” The performance of AND yields a result similar to addition only when the sets contain entirely discreet members. Otherwise, the result of the AND operation is a smaller number than the result of ADD. It used to be that AND (and OR) could be tough to teach. Nowadays, with Internet searches, lots of kids readily understand that search terms with OR between them will get you a bazillion, mostly useless hits, while search terms with AND between them will get you a smaller number of hits than each search term alone. Set theory using sets of hits makes sense, and a great way to exploit technology such that technology actually increases learning, instead of being the usual monumental distraction.

True, Authentic, Real Life Math Problem of an Eighth Grader

A certain student had recently missed much of the first quarter, so her band teacher did not count those weeks when figuring the credit for the weekly practice logs. Therefore, the student had only five weeks worth of practice log grades for the quarter whereas her classmates had ten weeks worth. She got 100% for each of the first three weeks she was back. When her report card came, she was shocked that she had a C. She thought she had an A in the bag.

Looking back at her practice log grades, she saw 100, 100, 100, 70, 0. “I forgot to turn in last week's practice log,” she explained. BUT, she knew how to figure averages, and when she did, she got 74%. “Ah, so there's the C,” she said.

Then she asked me, “How many minutes will I have to practice to bring my grade back to an A by next week?” True to form, I irritated her by telling her to figure it out. A real life math problem was staring her in the face. She had been wondering if there was such a thing as a real life math problem. “How do I do that?” she wailed. I told her to think about what she already knows and what she needs to know.

Her train of reasoning: One more week means I will have six total weeks of practice log grades. To average 100%, I will need 600 total minutes. I have 370 minutes. So I need 230 more minutes. I will need to practice 230 minutes this week. (An aside: I wonder if my teacher will give credit for so many minutes in one week). My practice log is due on Friday, so I have six days to practice 230 minutes.

So far, so good, but then her reasoning began to go awry. She divided 230 by 60, and got 5.5 on a calculator. She did not question the result. We need to teach students to determine the neighborhood of the result before doing any actual computation. I do not like to call this process “estimation,” because almost all kids have reduced estimation to mere rounding, and nothing more. Most kids tolerate estimation lessons at school, but basically tune them out because they have been socialized to value answer-getting techniques. Estimation does not, in their minds, yield “answers.”

(Now I have to explain that during this whole process, I was busy with my own work, so I was only seeing pieces intermittently, as she showed them to me. She showed me the calculator with the 5.5 in the display, which at this point was all I knew. I reconstructed her train of reasoning later from her comments).

I asked, “What does 5.5 mean?” She said, “5 hours and 50 minutes.” Remember, this student has all As in math, but as I have explained before, much of math in schools is misnamed. It is really non-math, but since schools call it math, students believe it is math, and if they get good grades in non-math, they believe they are good at math.

I probed, “How did you get that?” She looked at me like, well duh, isn't it obvious and said a little too loudly, “5.5 is 5 hours and 50 minutes.” Then turning away, she poked something into her calculator.

“How do I round this?” she asked. The display showed 0.9166666.

“You have asked the question wrong. No one can answer your question the way you asked it. You need to specify what place you want to round it to.”

“The thousandth's place. So 0.917.”

“That's right. But what are you counting?”

She pondered a moment and wrote 0.92.

“And what is that?” “Minutes,” she said, and wrote 92.

“How did you get that?”

“I need minutes, so I moved the decimal point.”

“'I moved the decimal point' is never a mathematical explanation for anything. You need to give a mathematical reason for the math you do. What did you do to get 0.92 in the first place?”

“I divided 5.5 by 6 to get the number of minutes I need to practice everyday. 0.92 minutes doesn't make sense so I need to move the decimal to get a number that makes sense.” (With this kind of reasoning, is it any wonder our students are so poor at math? And if they use the same faulty reasoning for any of life's other problems, no wonder decision-making ability is also poor. When they become adults, they are easily scammed by poor reasoning that sounds good to them).

She has three main problems:

1. Using disembodied numbers

Teachers have allowed her and her classmates to disembody numbers since first grade. What I mean is students have been trained to compute with only the numbers and attach the units to the result later. When students do that, they attach the unit they want, not the unit their computation produces. What she should have done is written 5.5 hours = 0.92 hours/day. Her unit was “hours/day.” However, since she was looking for minutes, she did the math the way so many students (and adults) do: 5.5/6 = 0.92 minutes.

2. Mixing bases

She did not realize that decimals numbers are base 10, and clock numbers are NOT base 10. I set up some place value columns for decimal numbers, and another set of columns for clock numbers. Then we did some counting so that she could see how numbers end up in the columns they do. First, we counted decimally, that is, in base ten. Then we counted time. As our paper time clock ticked over 59 in the minutes column to 1 in the hour column and 0 in the minutes column, she exclaimed, “Oh, base 60, like the Incas.” She could tell me that 0.5 = 50/100 = 50%, but still insisted that 5.5 hours = 5 hours and 50 minutes. She realized that she was looking for 50% of 60 minutes, but insisted she should divide 50% by 60. Eventually, understanding dawned. She realized that since 50% means half, then half of an hour is 30 minutes, so 5.5 hours means 5 hours 30 minutes. (My own work had come to a complete standstill long before). “So 'of' means multiply, right?”

3. Misunderstanding “Decimal Number”

She thinks, like so many kids do, that a decimal number is a number with a decimal point. Just take out the decimal point and presto, changeo, it is not a decimal number anymore. What else do we expect when we teach kids tricks,shortcuts and blind procedures,and call this strange conglomerate "math?"

In quite East Asian style, we had spent over an hour on this one problem. Eventually, she determined that (leaving aside the original calculator error), she actually had gotten her answer way back at 0.92 hours/day. She realized that the math had “spoken” to her if she had only thought about it correctly. What the math said was that she would need to practice a little less than an hour a day. She never noticed the calculator error, and I did not point it out.

Epilogue:

She practiced 60 minutes (in 30 minute increments) three days in a row. Then it occurred to her that if she practiced 60 minutes per day for 6 days, her total would be 360 minutes, not the 240 minutes she was expecting. She has not practiced for two days, but plans to practice 60 minutes on the sixth day. She got a real-life lesson in checking the math by plugging the solution back into the original problem, a step her teacher requires, but she resents as a time waster. We talked about that maybe her teacher really does have some wisdom in her requirements. She also admitted that her goal is to do the minimum necessary to secure an A. Excellence and doing one's best is just adult yadayada. At least her bar is set at A.

Tricks and Shortcuts vs. Mathematics

The issue is not whether algebra should be taught in the eighth grade or later. The issue is not whether local schools should be able to make their own textbook adoption decisions. The issue is about how easily states make big changes based on flimsy research which asks the wrong questions, only to backtrack later because solutions that solve the wrong problem do not work. California reverted to phonics in 1995 after abandoning it for a faulty implementation of whole language based on research that answered some questions, but not the questions that matter.

The emphasis on algebra in the eighth grade is misplaced when even students with good math grades enter algebra weak in math concepts. I am working with an A student now who is solving for x in problems involving mixed numbers. She wrote these "computations:" 2 + ¼ = 2¼, 3 + (- ¾) = 3-¾, and -2 + ½ = -2½. Do you see the pattern? In her mind, numbers are disembodied entities with no real meaning. She thinks all she has to do is take out the plus sign and push the fraction up against the whole number.

These silly errors happen in an education system where children have been taught tricks and shortcuts since first grade. The problem is teachers call tricks and shortcuts "math," and when children do well on a test of tricks and shortcuts, they learn their good grade is proof they understand math. Actually the grade proves only that they can reliably implement tricks and shortcuts.

I have worked with children who have terrible math anxiety because they do not do well with the tricks and shortcuts. Some part of their mind has rejected the tricks and shortcuts as not making sense, so "math" does not make sense. If they ever get a chance to acquire true number sense, then they find out they are good at math after all.

Sometimes we reward unthinking compliance (as when kids memorize the tricks and shortcuts) and punish the thinkers for whom the tricks and shortcuts do not make mathematical sense.

American Education is NOT Failing....

...In fact, it accomplishes its hidden curriculum perfectly, according to Danjo1987, who hits several out of the park his first day up to bat on EdWeek forums. hllnwlz wound up the pitch and effectively makes many of the same points.

If you have been following this blog, you know that last year I am the "parent" (from the school's point of view) for a particular child who is now an eighth grader. My kids are grown; still it has been instructive to observe her schoolwork and communicate with a school as a savvy teacher/parent. I have been reminded once again that schools really do not like interacting with savvy parents. When schools say they want parent involvement, what they usually mean is they want parents to bake cupcakes once in a while and make sure the student does the homework everyday. More than that, and you are stigmatized as a "helicopter parent."

Overall, the girl's teachers seem to be competent;a couple strike me as excellent. There is one teacher I simply cannot fathom. On the midterm progress report, this teacher gave this straight-A student a citizenship grade of "N" for "excessive absences" during a medical leave. Upon her return to class, she took a "diagnostic" test and got a "D." This is the student's only grade for the class, and the grade teacher put on the progress report. (The other teachers gave her "I" for incomplete).

For the past five weeks, apparently this teacher has done nothing gradable in class. At the close of the term last Friday, there was only one grade in the online system the school uses: that "D." The student's grade on the report card? C-. I am about to intervene.

Meanwhile, in her other classes, she often brings home homework that astound me with the easiness and triviality of it. I see the kind of homework I used to get as a second or third grader. For example, she has to write a little essay about a short story they read in English class. The first assignment is to analyze the writing prompt, write down the verbs that tell what the student is to do, etc. In eighth grade? And the requirements for the regular notebook checks are beyond ridiculous, but the school feels if they do not force the students to organize, none of them will. Apparently, they did not learn how to collect and organize their work in elementary school. The only reason she writes both her first and last name on papers is because I insisted she write a complete heading on each paper whether the teacher required it or not. "But I am the only one with my name," she complained. Does not matter.

What I see is a disjointed and inconsistent system characterized by low expectations, even as the adults give inordinate emphasis to test scores.

Wrong Questions About Spreadsheet Math

Spreadsheets are a ubiquitous and necessary tool these days. Students need to learn spreadsheet math.

"Our children still spend hundreds of hours perfecting their ability to add, subtract, multiply, and divide fractions. And the pinnacle of math for most of our K-12 students remains the ability to solve quadratic equations. When was the last time you used any of these skills? When did you last multiply two three-digit numbers together on paper, add two improper fractions with unlike denominators, or solve a quadratic equation?"

These are the questions people asked when it came to calculator use, and they are still the wrong questions. Spreadsheet math will not replace the ability to actually understand math any more than calculators did.

When the National Council of Teachers of Mathematics (NCTM) recommended calculators for even the youngest students, they rhapsodized about about how calculators would revolutionize math teaching, using the same sort of language that idealizes the potential of spreadsheet math.

"By teaching our children spreadsheet math we enable them to solve ...fascinating problems, problems without a single right answer, problems that can be explored, problems that get our children thinking "out of the box."

And that was exactly the wrong-headed pie-in-the-sky rationale for recommending calculators. It sounds great but does not work in practice. The problem with math instruction is not whether we should be using calculators or spreadsheets. The problem is the lack of skilled math teachers. The problem is the continued reliance on teaching tricks and shortcuts instead of math. Like calculators, spreadsheets have a similar tendency to replace thinking.

Beginning in 2001, I researched the calculator fallacy extensively culminating in a 78-page report in 2010. Briefly, I found that the research NCTM insisted supported the use of calculator in the early grades did not exist.

I agree that students need to learn spreadsheets, but not as a substitute for learning math. Since our elementary teachers lack an ability to teach math for understanding, abundant experience with mechanical processes, though far from ideal, is pretty much the only way kids learn to tell an unreasonable answer from a reasonable one, and even then they are not very good at it.

Just last week, a friend's eighth grade daughter (A+ in math per last progress report) was sure that if $27.50 could buy 10 lbs of hamburger, then $55.00 would buy over 150 lbs because "I followed all the steps correctly." When I told her that obviously she had not, she argued that even the calculator agreed with her, so I must be the wrong one. Just yesterday she insisted that -3 + ½ = -3½ (by analogy to 2 + ½ = 2½). In her mind, all you have to do is get rid of the plus sign and shove the fraction up against the whole number. When these kinds of misconceptions plague even good students, no wonder students who are not as “good” have math anxiety. Deep down, the anxiety is related to an unspoken and unspeakable suspicion that math makes no sense. They are right. When math is turned into a system of tricks and shortcuts, it makes no sense.

Surprise! Kids Value Rote Learning...

Surprise! Kids Value Rote Learning...

...just not when they are the one expected to memorize knowledge. Have you ever had a child ask you a question that require a memorized fact to answer? It happened to me recently. We were listening to a CD of classical music that had no printed table of contents. With nearly every piece, the (junior high) child asked, “Who wrote that?” Luckily, I can google the answer. She became exasperated with my lack of certainty and my need to look up so many of the composers. She asked impatiently, “Didn't you have to study music history when you were in school?”

Me: Yes, I did.

Her: Then how come you don't know who wrote all these songs?

Me: Do you like history class?

Her: NO, I hate it.

Me: Why?

Her: Because we have to memorize so many dates and other trivia.

Me: I guess you will start applying more gusto to your memorization.

Her: Why would I do that?

Me: Because clearly you think that memorizing facts is an important part of your education.

Her: Nooo. Whatever gave you that idea?

Me: Because you think it was an important part of my education.

Her: I never said that!

Me: But you clearly expect me to remember music composers off the top of my head better than I do. How would I have learned that information in the first place, except by memorizing it as facts? And you expect me to still remember it? Don't you think you should hold yourself to the same expectation?

Her: Well, of course.

Me: So I guess you won't groan anymore when teachers expect you to memorize stuff.

Her: Who said I minded memorizing stuff?

Me: Whatever.

Her: Hey, that's my line.

In Case of Nothing to Do, Break Glass...

...and then sweep up broken glass.

Americans have hopes and ideals for public education. As David Sirota explains,

Here in the industrialized world’s most economically unequal nation, public education is still held up as the great equalizer — if not of outcome, then of opportunity. Schools are expected to be machines that overcome poverty, low wages, urban decay and budget cuts while somehow singlehandedly leveling the playing field for the next generation. And if they don’t fully level the playing field, they are at least supposed to act as a counter-force against both racial and economic inequality.

The American ideal is that public education is supposed to be not only the engine of the American Dream, but also the primary mechanism for overcoming the social-economic obstacles of birth. Meanwhile, public educators consistently cite the poverty of their students as the number one reason public education fails to perform its promise. So, public education is supposed to give poor students the tools they need to overcome poverty, but public education cannot give them these tools because the students are poor. Teachers say education reform proposals that fail to address poverty are doomed to fail. We are trapped in a vicious circle. In such an environment, no wonder policy-makers, most of whom lack education experience, feel pressured to do something---anything. Education policies thus tend to be a perpetual cycle of creating and cleaning up messes.

And no wonder. Policy makers lack expertise themselves, so they turn to advice from those who seem to have proper credentials. Who do they ask? Education professors. Sounds reasonable, but guess what? Many education professors lack significant in-the-trenches experience in the very places teachers must implement policies handed down from on high. American society does not trust teachers. The main reason for the lack of trust is the double-mindedness of society. Sometimes we consider teachers to be professionals, and then undermine their professional judgment when we consider them hired laborers subject to dismissal for insubordination. We steadfastly refuse to put teachers at the head of the policy table even though, as Nancy Flanagan puts it, the teachers know where the carts are.

If we want to invest in a highly skilled teaching force, perhaps it's time to stop positioning teachers as drop-in observers who should be grateful for the chance to "represent" their peers in important decision-making bodies...Teachers should be at the head of the table, calling the meeting. The more professional responsibilities we take off teachers' plates, to standardize and homogenize, the more teachers' professional judgment is weakened.

Teachers should not be the target of reform, but the drivers. Right now, teachers are lucky if they can stand outside the door and listen at the keyhole.

At the start of the Obama presidency, when the Department of Education had lots of openings, the administration solicited applications. Many teachers applied. It turned that the administration was only interested in perpetuating more of the same, not ushering the change we all hoped for. Any PhD, especially a well-published PhD, whether they have actual significant experience or not, trumped highly effective, veteran teachers every time. Perhaps the number one disappointment educators have with the Obama administration is the refusal to listen to real teachers. They do not listen because they do not trust. They do not trust because our present policies prevent recruitment from among the most academically able students.

Teaching is not a top job choice, but a last resort. I routinely ask my education students why they want to be teachers. The answers are underwhelming. My top two favorite answers because they indicate the status of teachers in America: “I flunked out of hotel management,” and “It is either teaching or the Army.” In such an environment, it is difficult for the American public to accord teachers the respect and esteem they enjoy in other countries. Meanwhile, administrators break the glass and expect teachers to clean up the mess.

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.

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.

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.”

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.

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.

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.

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.