A teacher's thanks

April 25, 2004 Sometimes it seems like teaching is a thankless job, especially when (as with all professions) folks are far more likely to complain than say a positive word. Having said that, here's a interesting incident that happened recently.

I was in the middle of an activity with my students when the school's guidance counselor approached me. With a very serious face, said he had a parent who wanted to speak with me, and would I be willing to spend a few minutes with her while he watched my class?

Not a problem. I went to his office, and found a glowing parent, who profusely thanked me for all that I'd done for her daughter, who would be graduating at the end of this school year.

She was especially grateful for one little thing I did.

Take a guess as to what that one thing was.

See, I'd given her daughter an F for the third quarter, and her mother couldn't be more tickled.

What this failing grade had done was give her daughter a well-needed kick in the pants. She'd done a mediocre performance the first two quarters, but this failing third quarter grade gave her the sobering thought that she might fail the entire course.

As a senior, she most certainly didn't want that.

What had happened is she'd stopped showing up to school for a good portion of the quarter, and thus was unable to catch up when she was present. As a result, she failed most of her quizzes and tests.

But what is nice about this story was that the student had already approached me a week before her mother's visit, and sat down with me to discuss exactly what she needed to do to pass my course, which I felt showed a certain maturity on her part.

Better yet, she'd already started acting on the plan we created that day.

She showed up every day, on time, and did her homework conscientiously, paid attention and participated in class, and asked questions when she needed clarification.

Thus when I met her mother, I begged off when she attributed her daughter's turnaround to my actions. I insisted that her daughter get full credit for the change.

After all, what did the teacher do?

I simply gave her the grade she earned.

Calculators are like Bicycles

April 21, 2004 We could go on for days about what we really think of calculators in K-12 math classes (we think they're great for science classes, especially stochiometry in Chemistry), but suffice to say it just might be one of the signs of the Apocalypse.

A recent entry by Joanne Jacobs quoted a study demonstrating that students who use calculators do poorly in arithmetic when forced to do without. While School of Education wonks insist that students be "exposed to technology" at every level of K-12 education, we know that putting calculators in the hands of students learning arithmetic is incredibly shortsighted and harmful.

Our analogy relates to a child learning to walk.

Imagine taking a child who's pretty good at crawling, and starting to pull himself up on things, and placing him in a modified tricycle, one with a supportive cradle for a seat so he can't fall out. Soon he'd learn to push the pedals, randomly at first, then with purpose, as with steering the handle bars.

In no time he'd be zooming around on his little three-wheeler, after which he can be moves up to a real tricycle with a bicycle-style seat. From this he could evolve to a bicycle with training wheels, which can be raised incrementally so that more and more of the time he's on two wheels, after which they can be removed completely.

Now, if the child were placed in these three- and two-wheelers, each and every time he was attempting to stand or walk, there's little doubt that he'd quickly be far more skillful in pedaling himself around than two-footing it. Sure, the kid might learn to walk (probably looking like Frankenstein's monster), but he'd probably never learn to run.

Why bother when it's faster (and easier) to bike?

And so it is with calculators.

Personally, we think calculators (and just about any other technology made possible by the transistor) are great, and they sure do save a lot of time.

But that's not the point behind teaching children arithmetic in school.

The point of doing paper-and-pencil arithmetic (for example, finding the product of 47 and 9) isn't to actually find the product (like we didn't know what the answer was, and that's why we have kids do these problems). The whole purpose of this exercise is to practice a skill accurately to the point of automaticity.

Memorizing the times tables (for example, up to 12x12) is a gateway to so much more. Once a child has memorized every single fact contained in this grid of 144 products, then simple division (where both divisor and quotient are numbers between 1 and 12) is only a matter of backwards thinking.

For example, in picturing the number 24 one might think of 4x6, 3x8, or 2x12 (and of course the commutative versions of those three). Thus 24 divided by 8 is a fairly simple matter.

But doing longer division, especially when it involves remainders, is harder, because the dividend often is not a number found in the times tables. And very quickly, if the lesser skills of simple addition, subtraction, multiplication, and division are not mastered to automaticity, it quickly becomes a chore.

One reason why paper-and-pencil long division is going the way of the dodo bird is because it involves too much computation, 100% of which has to be done accurately, or the whole answer is wrong.

Take a simple problem of dividing a three-digit number by a one-digit number, for example dividing 301 by 7.

7 into 3? No.
7 into 30? Yes, 4 times.
7x4 = 28
Subtract 8 from 0? No.
Borrow a 1 from 3 (make it 2), write it next to 0 to make 10.
10-8 = 2
2-2 = 0
Bring down the 1.
7 into 21? Yes, 3 times.
7x3 = 21
21-21 = 0

Depending on how you count, it takes about ten steps, most of which are calculations, but even so this problem should be done in under 15 seconds.

Truth be told, it should take fewer steps the more fluent one is with numbers, for example the step of subtracting 28 from 30 can be done as a quick mental math step without all the borrowing. And of course there's no real need to actually subract 21 from 21 at the end.

But the point is that this fluency cannot come if students aren't asked to solve a great many paper-and-pencil problems (yes, this means worksheets and flashcards) over a number of years of studying mathematics.

Unfortunately in a great many places, the handheld calculator is seen as a way of relieving this drudgery. Students may still be given worksheets, but are permitted to use calculators; a pointless exercise.

We mentioned the shortsightedness of this strategy earlier. Many fresh math teachers (especially in our inner cities where calculator use seems to be at pandemic levels) see nothing wrong with the use of calculators to do simple basic arithmetic, for the simple reason that the calculator is fast and accurate. So much time is freed up for higher-order thinking skills!

Unfortunately, middle and high school math desperately requires a certain fluency with numbers which dependence on a calculator simply cannot permit.

In late elementary school and middle school, students learn things like manipulating fractions (where finding the lowest common denominator is a key skill, one that requires being able to instantly look at several numbers and mentally seeing the greatest common factor or least common multiple) and using square roots (also requiring the ability to instantly factor numbers).

And in late middle school or early high school there's algebra, one place where the calculator isn't much help.

While we're sure a calculator exists which can factor the binomial 49x² - 25 such a beast is not in wide circulation, and if it were, most kids wouldn't know how to tell it to solve such a problem. But if a student has some number sense the answer of (7x + 5)(7x - 5) should be completely obvious just by inspection.

Unfortunately most of the folks advocating rampant calculator usage in the early grades probably can't do algebra, let alone trig or calculus.

In having a child master the calculator, that child just might become its hobbled slave.

Some thoughts on standardized testing

April 19, 2004 While trolling through our archives, we noticed (a bit late) that Liz over at I Speak of Dreams had responded to our "least worst" posting on standardized testing.

While she agreed that there is a place for testing, she wrote:

I also loathe the idea that a standardized test (say the SATs) capture the value of what an individual student will add to the classroom.

While we agree with her wholeheartedly, we can't help but feel she's invoking a straw man.

Just who exactly has ever said that standardized tests "capture the value of what an individual student will add to the classroom?" We know that our friend Kimberly Swygert has never said such a thing, so who is the guilty party?

Well, the short answer is no one.

Standardized tests aren't magic, and they certainly aren't designed to be omniscient. They aren't meant to crawl inside a child's brain and have a look-see, or to predict the future. They are simply designed to measure a sampling of knowledge and skills, as deemed important by the authors.

Now, one can argue that there exists poorly-written standardized tests. You'll get no argument here, for we've seen some tests which we can fairly guarantee were either: a) never field-tested, b) written by committee, and/or c) never came within 50 yards of a psychometrician.

One could also argue about the content on which some tests focus, such as the Maryland math exam that "took the algebra out of Algebra."

Or one could ask if the big push for mandated high-stakes testing is a good way to improve K-12 education.

The point is that there are criticisms of standardized tests which experts in the field will admit are valid concerns.

The idea that they are designed to capture the value of an individual student simply isn't one of them.

The Ladder: One idea for serious school discipline problems

April 17, 2004 Endless second chances don't exist in the real world, therefore students are not well served in a school environment which gives them endless second chances for serious disruptions.

A recent posting over at Number 2 Pencil got our attention:

Elizabeth Anne Moore, a reading teacher at Trevor G. Browne High School (AZ), claims in a court petition that the 15-year-old student daily tells her in front of other students "to go (expletive) myself." [ . . . ] Tom Horne, state schools superintendent, said Friday that legal action is rare for a teacher, if not unprecedented. "If the facts alleged are true, the student should have been expelled," Horne said.

One classic mistake made by public schools is the lack of consideration to quantity. Sure quality is important, such as if a student sets fire to his desk or injures a teacher we'd advocate immediate expulsion. However, many schools don't tally the lesser suspendable offenses.

As a result, there is no limit on how many times a student can be suspended.

Since many students regard suspension as a "get out of school free" card, if that's the only punishment for serious infractions, then there's little incentive for the student to change his behavior. Remember, insanity is doing the same thing over and over and expecting different results.

We propose a ladder for serious offenses.

The first principle is that classroom discipline is first and foremost the domain of the classroom teacher, with all petty infractions being handled by the teacher.

Having said that, serious disruptions to the learning environment must be forwarded to a higher level. A five-step ladder can go a long way to eliminating chronic disruption from a school, as the students responsible for such behavior either quickly change their behavior or are expelled. Most students choose to change their behavior.

Here's how the ladder works. For serious offenses, a staff member writes up a discipline referral for the student, including a description of the incident(s) and any steps that were taken before the referral for discipline, such as contact with the parent and discipline measures taken in the classroom.

Each referral will move the student up one step on the ladder, regardless of the staff member writing the referral.

1. Student is given a one- to three-day suspension, depending on the seriousness of the offense.
2. Repeat step one, but the student must be reinstated by a parent, during which the staff member who wrote up the student can have a brief conference with the parent and the student, to try to stem future incidents.
3. Repeat step two, and the student is additionally placed on probation, for one more incident will result in an expulsion hearing.
4. Repeat step two. After serving the suspension, the parent and student will attend an expulsion hearing (presided over by board members, administrators, and disciplinary staff). The purpose of this hearing will be again to try to stem future incidents, and to give the student one final chance to change his or her behavior, for the next step will result in expulsion.
5. Expulsion. Any questions?

If a student cleans up and goes incident-free for three months, he or she is moved to the next lower step on the ladder, as a reward for good behavior.

One teacher, who works in an urban public school that uses a very similar ladder, relates a recent incident:

I'd had a lot of difficulty with one 16-year old boy, with him having disruptive outbursts in the classroom, and with him calling me inappropriate names like "boo," "child," "honey," "dear", and "sweetheart" which I most certainly did not appreciate. I'd counseled him privately on his behavior, and spoken with his mother, and he'd insisted each time that he was going to behave.

One day, he started yelling in my classroom, and walked out into the hallway to be with his friends loitering there, but when I followed and asked him politely to return, he yelled at me, putting his hand in my face, and called me an inappropriate name. He then returned to conversing with his pals.

Though I'd never written him up for any of his previous behavior, this was unacceptable, so I wrote up a referral for discipline. Later that day, he approached me and asked me to rescind my referral (teachers are given this option, at their discretion), because he didn't want to get expelled, as this was his fifth referral. I said no.

Before the end of the day, he again approached me and handed me a very nicely written letter of apology, in which he profusely promised to never misbehave for me again, and would I please rescind his referral, because he didn't want to be expelled.

I told him, "Good luck in your next school."

At first glance this may seem a bit cruel, expelling a kid for a bit of yelling and putting his hand in his teacher's face.

But the reason why the teacher stood fast and refused to rescind the referral was that this young man had been written up four previous times by other teachers, and still he did not change his behavior.

At some point, we must teach our students that they are responsible for their actions, especially after they've been given fair warnings and second chances.

To do otherwise is the real cruelty.

Not In My Back Yard!

April 15, 2004 Residents in one big American city are up in arms over a proposal to build a certain facility in their neighborhood:

"This will be a total nightmare for all of us," resident Gary Grisafi wrote in a letter protesting the [...] proposal to build on a 21-acre site . . . Grisafi said the [facility] would bring myriad problems including "fights, violence, drug activity, litter, noise, vandalism, loitering on our streets and steps, car and bus traffic, sex acts, no parking for residents."

Pop Quiz: The facility under consideration is:

A) A shopping mall

B) An amusement park

C) A minimum-security prison

D) A casino

E) A combination strip club / bar / adult bookstore

F) A public high school

The answer (of course) is F.

A new public high school is proposed for the Crescentville neighborhood in the "great northeast" of the city of brotherly love, Philadelphia.

But doesn't it say something about Philly high schools that they prompt fears of sex acts, drug activity and vandalism?

Not in my backyard, indeed.

Placing the blame for school failure

April 15, 2004 While in a philosophical mood recently, we tried to get a "big picture" of school failure here in the United States.

What inspired this reverie was our frustration at trying to teach tenth graders the Pythagorean theorem. After meeting much resistance and failure, we did quite a bit of probing, and the problem turns out to have nothing to do with tenth grade Geometry.

The problem is in these kids' preparation, more specifically, with the body of math skills which they've gained from nine or more previous years of schooling. In other words, what their previous teachers have taught them.

If it sounds like we're blaming their previous teachers, you're correct, but please don't take this as a case of "teacher bashing." While it has become painfully obvious that their teachers have not taught them what they should have been taught, we're not going to take this opportunity to lash out at teachers as a group, but rather at the folks who hired and trained these incompetent individuals to be teachers.

This would mean principals and school boards.

Quite simply, the failure of schools is a failure of leadership. While principals, school board members, and other administrators don't actually do any teaching, they sure are responsible for teaching to occur on their watch.

In the case of too many inner-city schools, teachers are hired who have no business being in a classroom, and folks who have the potential to be decent teachers are given little or no supervision, and few incentives to do the hard work of teaching our youngsters knowledge and skills.

One way to turn around our schools is to hire better leaders. We've quoted Jack Welch's "Four E's" in a previous entry, in which he outlined several necessary characteristics a leader should have: Energy, Energize, Edge, Execution, and Passion. Basically, a leader should have positive energy, the ability to motivate others, the courage to make decisions, the will to get the job done, plus a passion for the task at hand.

Hiring better leaders isn't a panacea (we still need to address some of the bureaucratic nonsense at the state and federal level), but it would go a long way to improving our schools.