kitchen table math, the sequel: 12/2/07 - 12/9/07

Saturday, December 8, 2007

fresh horses

It is a profoundly erroneous truism, repeated by all copy-books and by eminent people making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle—they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.

A.N. Whitehead, An introduction to mathematics, 1911 New York: Holt, p. 41

He makes this observation while discussing mathematical symbolism:

One very important property for symbolism to possess is that it should be concise, so as to be visible at one glance of the eye and to be rapidly written.

Friday, December 7, 2007

Two Million Minutes

Two Million Minutes

Regardless of nationality, as soon as a student completes the 8th grade, the clock starts ticking. From that very moment the child has approximately

…Two Million Minutes until high school graduation…

Two Million Minutes to build their intellectual foundation…Two Million Minutes to prepare for college and ultimately career…Two Million Minutes to go from a teenager to an adult.

How a student spends their Two Million Minutes - in class, at home studying, playing sports, working, sleeping, socializing or just goofing off -- will effect their economic prospects for the rest of their lives.

How do most American high school students spend this time? What about students in the rest of the world? How do family, friends and society influence a student's choices for time allocation? What implications do their choices have on their future and on a country's economic future?

school for horses

Working on the horse chapter has been unnerving.

Arguably the number one animal welfare problem where horses are concerned is poor teaching. Horses are in the same predicament as U.S. children; many trainers use ineffective techniques while ignoring the techniques that actually work. Not surprisingly, the techniques that work for horses are the same techniques that work for children. Direct instruction based in learning theory.

For horses, success in school is a matter of life and death, as a horse who can't be ridden will likely be euthanized. One study in France found close to 2/3 of all domestic horses being euthanized for reasons other than ill health. (source: Equine Behaviour by Paul McGreevy A terrific book.) "Reasons other than ill health" means one of two things or both:

  • horse can't be ridden
  • horse has behavior problems

These outcomes are, in most cases, training failures although they are blamed on the horse. The parallel to children, who can also fail in two ways (failure to learn; failure to behave) is haunting.

brain melt

My brain is officially fried.

Dogs, cats, horses.....and on to cows:

It is now well established that domestic animals construct responses to their environment that depend on experience and on integration of several features of the environment, including social partners.

Ontogeny of social awareness in domestic herbivores
I. Veissier a,), A. Boissy a, R. Nowak b, P. Orgeur b,
P. Poindron
Applied Animal Behaviour Science 57 1998.233–245

Tuesday, December 4, 2007

Why I Don't Assign Homework

Liz Ditz left a link to Dy/Dan's blog.

I love this guy!

the homework problem

Here's what I love about Dy/Dan's post on not assigning homework.

First and foremost, not only has he thought out his position, he's researched it for a Master's thesis. The research is icing on the cake; the fact that he is so closely scrutinizing and adapting his "practice"* in response to his students' achievement is what makes me long to have a kid in his class.

Ed and I have been talking about the homework issue lately, mostly because C's social studies teacher told Ed he has students who never do their homework. We were both surprised to hear this though we shouldn't have been.** Kids not doing homework is a chronic issue for teachers everywhere.

Here's a Phi Delta Kappan article on the subject:

I tried to figure out why promising students in my own geometry classes persistently failed. Every year students entered my classes not fully prepared for the large body of new concepts, vocabulary, skills, and logical principles that are central to a college-prep geometry course. With rare exceptions, the deficiencies were surmountable, provided that these students accepted the need to study and work on sample problems outside of class. But, despite a claimed orientation toward college, many of them failed geometry, in large part because of "homework resistance" that seemed rooted in early elementary school and shaped by adolescent identity pressures.

Occasional missed geometry assignments weren't a big deal in my classes. After all, an unknowable but surely substantial portion of completed homework involved copying from classmates. An additional portion consisted of "homework simulations" with correct answers to odd-numbered problems (which have answers in the back of the book) embellished with jottings that gave the appearance of work. So, like most of my colleagues, I gave credit for homework but based most of a student's grade on tests, quizzes, and in-class projects. Class time was an intense geometry experience for all but the most tuned-out. But since test questions looked remarkably similar to those covered in homework, students who didn't do the homework had trouble passing tests or participating fully in class.

At year's end, out of 90 geometry students in three sections, 38 had completed less than 60% of the assignments. Of these 38, two quite talented students managed to earn a semester grade of C, another three earned D's, and the remaining 33 all earned F's. In contrast, all but a handful of the students who had completed 80% or more of the assignments passed with grades of C or better.

The puzzle. Why would so many students willingly waste a year sitting through geometry class and earn zero credits toward graduation? All had managed to pass algebra, and many even had good attendance in my class. Most had the requisite mathematical ability and would have passed had they spent 40 to 50 minutes daily outside of class on the homework. Free tutoring and homework help were available at lunch and after school, but no one showed up more than once or twice; most never came at all. What were they thinking? Countless frustrating conversations convinced me that most students in this situation can't tell you the teal reasons for their behavior, because they themselves don't know. They offer a charming variety of excuses, evasions, defensive maneuvers, mea culpas, and doleful expressions, many well practiced from prior confrontations with parents or counselors. Almost all say that to succeed they would need to start doing all their homework. They further insist that they want to be successful. So what's going on that students can't explain to us - or to themselves?

Homework Inoculation and the Limits of Research
Bruce Jackson
Phi Delta Kappan Sep 2007 Vol. 87, Iss. 1 pg. 55

Jackson's idea is that the practice of having kids do largely pointless homework assignments in K-5 in order to build "good homework habits" leads instead to homework refusal when kids reach middle school age and begin to assert themselves. Homework inoculation.

So....the cure for h.s. kids not doing homework is to get rid of homework K-5.

I'm sure that will work.

This is the kind of thing that makes me want to send this fellow a link to Karen Pryor's web site. Pryor makes short shrift of such motive mongering. She doesn't care to learn why a dog is behaving badly; she doesn't want to hear his history:

Karen helped me learn to read Ben's canine signals accurately, unhindered by my own emotion....She was the one, who during one of Ben's fits in class, came over, gently put her hand on my arm and calmly said, "Emma, it is only behavior."

"Only behavior?" I gasped. Could it be so simple? This "behavior" had caused me so much grief in my life, both personally and professionally. It had become a source of tension in my marriage and almost caused me to lose several friendships....I had allowed Ben's aggression to balloon into a problem that took over our lives. I found hope that night in class, with Karen's calm words: "It's only behavior." After all, through positive reinforcement, behavior--any behavior--can be changed.

Click to Calm Healing the Aggressive Dog
by Emma Parsons

Animal behaviorists make a useful distinction between ethology and psychology.

You do need to know ethology (how does this species act & think?)

You don't need to know much about psychology (how does this particular animal act and think, and why?)

When it comes to students not doing their homework, all you really need to know is that procrastination is a core human behavior that is not going to be conquered any time soon and certainly not by high school students. Asking students what they are thinking when they fail to spend 50 minutes a night doing geometry homework is absurd. They're not thinking about geometry one way or the other. That's the point.

This teacher needs to forget about what students are thinking and ask the school to send a behavior analyst to his class to change the incentives. A mere amateur like myself can spot some major de-motivators in his data.

If he can't round up a professional, he should read a book on behavior analysis and figure it out himself. ***

The "homework situation" appears to be an unholy mess. Setting aside the question of homework quality, I would like to see schools adopt policies of supervised homework like the one in place at La Salle High School. If a student is not getting homework done at home, I would assign him to a supervised homework study hall where he would get it done because a responsible adult would see to it. And I would make this a positive experience, not negative.

If I had my druthers, our schools would drop-kick the many state-mandated character-ed implementations over the stadium wall and replace them with school-wide positive behavior plans devised by the Bob and Lynn Koegels of this world.

Or else just hire a whole lot of teachers like Dy/Dan.

* hate that word, but it's correct in this context
** I have no business being surprised by any failure to complete assigned work...
*** I'm starting with Karen Pryor's Don't Shoot the Dog, which I will be using for my kids and for me.

US Students Do Worse in Science and Math

This just in.

U.S. students are lagging behind their peers in other countries in science and math, test results out Tuesday show.
The test, the Program for International Student Assessment, was given to 15-year-olds in 30 industrialized countries last year. It focused on science but also included a math portion.
The 30 countries, including the United States, make up the Organization for Economic Cooperation and Development, which runs the international test.
U.S. students ranked 24th in math.

I hate projects

My fifth grader came home recently with a “Global Warming” handout that included these proclamations:

Do your share, show you care. . . .
If you don’t do your part:
- everyone will die
- the Earth will burn
- there will not be any community in the world
It turned out this was prepared by a fellow student as part of her project on the topic of global warming. All students have been assigned similar projects, and the theme seems to be environmental causes. I think we all know the drill. Take a huge topic. Assign an elementary student to research the Internet. Make a poster along with dioramas, poems, songs or puzzles. Present to class. Yuck!!

Having watched my kids progress through the public school system being assigned numerous time-wasting projects that teach very little practical academic content or skills, I have developed an abhorrence for most of these. Additionally, I’ve observed the alarmist, unscientific message about global warming that seems to pervade much of the curriculum.

However, this particular example sent me over the edge a bit.

(Of course, I don’t fault the child or even the teacher in this case. In fact, my observation is that this student is unusually bright and probably completed this project without much parental help. Good for her!)

Monday, December 3, 2007

farewell to the baby boomers

pension plans and the 55-year old retiree

it's going to get worse before it gets better

from the May 2007 issue of Phi Delta Kappan, international world headquarters of constructivist fuzzery (subscription required):

THE MATH classroom is, and probably always will be, a center of controversy. Teachers, mathematicians, and researchers may never come to agreement on exactly how their beloved subject is to be represented in school. That said, aren't we all making some obvious mistakes? I contend that there are some practices, common to nearly all math classrooms, that we can all agree simply must be done away with. Here are my four prime candidates.

1. Forty problems a night. Most of my mathematician friends and I are only able to solve about two problems a year - if we're lucky! Tell a mathematician you've solved even five problems in a single day, and the first thing she will think is, "They must not have been very interesting problems." Outside of mathematics, does anyone you know ever get 40 things done in a day? [ed.: Everyone I know gets 40 things done in a day.]
2. The third-person czars of math problems. A strange, anonymous set of people are constantly referred to in math classrooms. We frequently hear teachers and students ask such questions as "What do you think they mean in problem number 4?"...Who are these people?...If we decide, as we often do, that our classrooms are going to be guided by the mathematics of the past, then let's at least talk about real people - not mythical ones. [ed.: Perhaps math textbooks could include a photograph of Skip Fennell.]

3. Teachers give problems; students give answers. If only mathematics were that easy! A mathematician would arrive at her desk to find that her problems were all there, waiting for her in a list. The reality is that the largest challenge in mathematics is finding a good problem to solve or theorem to prove - a single conjecture that is both interesting and approachable...[Y]ou would be hard pressed to find a classroom where the students regularly face the challenge of finding a good problem.

4. Suppose a student still "doesn't get it" by the end of a math class, and the teacher decides not to set him straight for the time being. Many people would label such a decision as "immoral," fearing that it would endanger the student's academic future. Because of the high stakes we attach to learning math in school, we seem to lose our perspective on these matters. Do we really think that mathematical learning is that simple and straightforward? Might a student have a richer mathematical experience if he is allowed to fumble around with a misconception for a few days than if he is steered promptly to the "truth"? [answer: Having now watched my own child fumble around with a misconception concerning the distributive property for the last 2 1/2 years, I would prefer America's math teachers stick to the business of clearing up misconceptions not fostering them. Alternatively, if fumbling around is to be the goal, let's knock off giving students grades of C, D, and F on tests due to fumbled answers, shall we?]

We must deemphasize answers and correctness as the only worthy goals in mathematics. Sure, "right answers" are an important part of math, but they aren't always the bottom line. Instead of always asking, "What's the right answer?" we should also wonder, "What's the right question?" and "What's the most interesting way to the answer?" Mathematics is about bold, adventuresome ideas, and the history of the subject is therefore fraught with mistakes, contusion, and invalid convictions. Let's make the classroom a bit more like the discipline and allow our students to revel in the "wrong" while they pursue the "right." [ed.: Reveling in the wrong is incompatible with being graded on a curve. You'd think a person majoring in math education would know this.]

Four Practices That Math Classrooms Could Do Without
Nick Fiori
Phi Delta Kappan May 2007 Vol. 88, Issue 9, p. 695
author bio: NICK FIORI is a doctoral candidate in mathematics education at Stanford University, Stanford, Calif.

Here is our situation, demographically speaking. Ed schools stopped teaching the methods of direct instruction in the second half of the 1980s. Teachers who earned Masters degrees in education in 1980 are now in their mid-50s which is retirement age in my district (and, I gather elsewhere, too). They are leaving the profession in droves.

Nearly all certified teachers under the age of, say, 45 have been taught constructivism and constructivism alone. And while Robert Slavin claims that a new back-to-basics movement is brewing inside ed schools, I'm skeptical. (If others have seen a shift, let me know.) The fact that a doctoral candidate in Stanford's school of education would assume that "we can all agree" on these four propositions tells me that as yet there has been no challenge to the orthodoxy.

This means that ed schools are still producing constructivist teachers who will teach for 25 years before retirement benefits kick in. Many if not most of these new teachers will not be mentored and overseen by baby-boom era teachers trained in direct instruction as earlier cohorts of constructivist-trained teachers were.

They will be mentored and overseen by 40-year old constructivists.

Suncast Powerblade

best snow shovel on the planet

You can use it as a hand snowplough. Amazing!

Sunday, December 2, 2007

My latest rant

Chi-square in high school?

What we are up against

Math isn't what it used to be

This isn't an article it's an advertisement for Everyday Mathematics. There isn't even a single mention in the article of the possibility that some parents, teachers, and schools might not like it.

Some selected quotes:
The curriculum is designed to integrate strategies such as algebra, probability, geometry and statistics into the lessons for students as young as kindergarten and first grade. Also through the lessons, students are taught several different techniques to solve problems, while traditionally, students were only taught one way.
Fremgen said another benefit is that most of the math ideas spiral through the curriculum throughout the year, so if students don't understand a method or concept the first time, it will come around several other times for them to try again.
The program's success also may be because of the curriculum's real-life applications that allow students to use what they learn in everyday experiences, Fremgen said.
This reporter didn't even need to get out of bed to write this article. All she had to do was have the textbook creators fax in the article to her editor.