seamless (w)holes

from instructivist:

[Carolyn once said that math was "a seamless whole" inside her head,...]

I don't know if this ties in with the idea of a seamless whole, but it has occurred to me that discrete skills are needed first before one can appreciate the connectedness of math. Without these concrete skills, math is more like a seamless black hole.

This became apparent to me again when teaching a group of seventh and eighth graders brought up on EM and currently using CMP who are a tabula rasa when it comes to the simplest bits of math knowledge. They can't do any operations with fractions (e.g. change mixed numbers to improper fractions let alone addition and division), can't divide decimals, don't have knowledge of even rudimentary geometry... One wonders what they have been doing for seven and eight years.

The seventh graders are currently in the CMP stretching and shrinking stage. Their homework consisted of finding the scale factor of two rectangles the width of which goes from 1.5 cm to 3 cm. So the idea was to divide 3 by 1.5 (they can't do it because they can't divide decimals). When I tried to show an alternative way of division using fractions to demonstrate the connectedness of math (seamless whole), I ran into trouble, too. They don't have the discrete skills of seeing 1.5 as 1 1/2, then changing this mixed number to 3/2 and dividing 3 by 3/2 (they absolutely can't divide fractions and moreover don't see 3 as 3/1. It would have been spectacular to make them experience with understanding that the more complicated decimal division problem 3/1.5 virtually solves itself when you divide the respective fractions (3 divided by 3/2). Invert and multiply but they have never heard of reciprocals and how they work. The 3 cancels and 2 is left standing without much ado!

So the upshot is: they use Connected Mathematics but can't see the connectedness of math because they don't have discrete skills (skills they could have learned through drill and kill but haven't). So to them, math is a seamless black hole from which not even light can escape.

This one's going in the Greatest Hits file. (on the sidebar)


wholes, not parts
top down teaching
whole math taught wholly

book club

We may need to form a book club for interested folks. I say this selfishly because I need people to help me brainstorm my way through Karen Pryor's Don't Shoot the Dog, especially now that I'm hyper-aware of how difficult it is to generalize newly-acquired knowledge.

Pryor's book is brilliant. Reading it I see that I've been barking up the wrong tree thinking cognitive science has the answers. (barking?) Cognitive science does have answers; it's a valuable and riveting field. But when it comes to education the behaviorists are way out in front. Direct Instruction, Precision Teaching, Don't Shoot the Dog -- they're so far out in front they're disappeared from view.

No wonder their work is no longer taught in ed schools. (scroll down)


life-altering factoid number 1

Chickens procrastinate.

Using either fixed or variable schedules, extremely long sequences of behavior can be trained. A baby chick can be induced to peck a button a hundred times or more for each grain of corn. For humans there are many examples of delayed gratification. One psychologist jokes that the longest schedule of unreinforced behavior in human existence is graduate school. [ed.: followed closely by middle school]

[snip]

Another phenomenon occurs on very long schedules: slow starts. The chick pecks away at a steady rate once it gets started, because each peck brings it nearer to reinforcement, but researchers have noted that a chick tends to "put off" starting for longer periods as the schedule of reinforcement gets longer.

This is sometimes called delayed start of long-duration behavior, and it's a very familiar aspect of human life. On any long task, from doing the income taxes to cleaning out the garage, one can think of endless reasons for not starting now. Writing, even sometimes just the writing of a letter, is a long-duration behavior. Once it gets started, things usually roll along fairly well, but, oh! it's so hard to make oneself sit down and begin, James Thurber found it so difficult to start an article that he sometimes fooled his wife (who was understandably anxious for him to write articles since that was how the rent got paid) by lying on a couch in his study all morning reading a book in one hand while tapping the typewriter keys at random with the other.

Don't Shoot the Dog, Revised Edition, p. 25

palisdesk on change in ed school curriculum
The Misbehavior of Organisms
Marian Breland Bailey: many lives (pdf file)
book club
a heroine I didn't know I had

Rote Learning in Core Knowledge, An Example

Last week, my son came home from school with a study sheet for the last big test for the year. The test covered some basic US geography, including the names of the Great Lakes, some facts about the Mississippi River, some facts about the US Flag, and locating some major geographical features. In addition, the students were supposed to be able to name at least 25 of the states, given a list showing only the first letter of each state.

Over the next one-and-a-half weeks, A. and I studied for his test about 15 minutes each night. This studying was the exactly the sort of studying that ed. schools teach as being the most harmful: pure rote memorization.

Early in this process, A. objected to the continued practice of the entire list on the basis that, "I only have to know 25 states, not all the states." My sympathy was notably limited; we studied the whole list. 8-)

By a couple of days before the test, A. was pretty reliably naming all the states starting with a given letter when prompted with that letter. (BTW, "M" is particularly annoying.) By this point, he was starting to think that getting the entire list right was pretty cool.

The day before the test, the teacher announced to the class that any child who could name all the states would get extra credit and a small prize.

Of the 26 kids in the class, 8 named all the states on the test the next day. None of those kids needed to have his or her self-confidence artificially boosted after the test, and they all now have a much better understanding of the value of hard work.

fight the power

Math is hard.

Didn't Barbie say that?

Mr. Percent

I'm having way too much fun.

how to pronounce ISEE

I - see

Now you know.

On the other hand, if you go around calling the ISEE the I-S-E-E, people do know what you're talking about.

personal narrative

from Tracy W:

Okay, I love my calculator. Sharp EL-5120. It's on my desk at the moment. It's not much to look at, but its functionality means that it rocks my world. In terms of calculator-adoration I am probably in the top 1% of the world's population. My calculator has literally travelled around the world with me (there's no way I'd trust it to any removal company). I'm not a poet, but if I was I would write love poems to my calculator. The only reason I do not sleep with my calculator is that I fear it will disappear down the end of the bed and I will never see it again. When it comes to using calculators, I strongly suspect I am not normal. However, despite my deep and undying affection for my calculator I am sometimes without it, and on those occasions it is useful to be able to do basic arithmetic such as long division with pencil and paper or in my head. This may not be normal, but why should we educate kids merely to be normal people anyway?

Priceless!

SAT problem

YouTube rules.

I love this guy

But I still need a percent chart.

help desk - percent chart

Is there an all-around mode of charting the values in percent problems similar to the charting taught for distance problems?

this one's fun

During a sale, a bookstore sold 1/2 of all its books in stock. On the following day, the bookstore sold 4,000 more books. Now, only 1/10 of the books in stock before the sale are remaining in the store. How many books were in stock before the sale?

source:
SSAT & ISEE 2007 Edition Kaplan
p. 161

C. came pretty close to doing this one on his own.

Of course, close doesn't cut it on a standardized test.

I realize that.

This problem can't be done.

Right?

Not enough information

Or way too much information, as the case may be.

Two trains are loaded with equal amounts of rock salt and ball bearings. Train A leaves Frogboro at 10:00 A.M. carrying 62 passengers. Train B leaves Toadville at 11:30 A.M. carrying 104 passengers. If Train A is raveling at a speed of 5 mph and makes four stops, and Train B is traveling at an average speed of 86 mph and makes three stops, and the trains both arrive at Lizard Hollow at 4:30 P.M., what is the average weight of the passengers on Train B?

source:
Kaplan SSAT & ISEE 2007 edition
p. 155

Center for Environmental Therapeutics

A psychiatrist friend of mine recommends this web site. She says it has a self-administered diagnostic test for seasonal affective disorder that tells you exactly when to use light therapy.

We have enormous, aging light boxes all over the basement, but we've never known when to use them. We got them because John (Ratey) told me he'd visited the NIMH and all the shrink researchers there had light boxes on their desks. That was enough for me. We used to train one on Jimmy every day.

Today's Times has an article. (sorry - this is a paid subscription link, I believe - can't get the Times link generator pages to open.)

In 2001, Dr. Thomas A. Wehr and Dr. Norman E. Rosenthal, psychiatrists at the National Institute of Mental Health, ran an intriguing experiment. They studied two patient groups for 24 hours in winter and summer, one group with seasonal depression and one without.

A major biological signal tracking seasonal sunlight changes is melatonin, a brain chemical turned on by darkness and off by light. Dr. Wehr and Dr. Rosenthal found that the patients with seasonal depression had a longer duration of nocturnal melatonin secretion in the winter than in the summer, just as with other mammals with seasonal behavior.

Why did the normal patients show no seasonal change in melatonin secretion? One possibility is exposure to industrial light, which can suppress melatonin. Perhaps by keeping artificial light constant during the year, we can suppress the “natural” variation in melatonin experienced by SAD patients.

There might have been a survival advantage, a few hundred thousand years back, to slowing down and conserving energy — sleeping and eating more — in winter. Could people with seasonal depression be the unlucky descendants of those well-adapted hominids?

Regardless, no one with SAD has to wait for spring and summer to feel better. “Bright light in the early morning is a powerful, fast and effective treatment for seasonal depression,” said Dr. Rosenthal, now a professor of clinical psychiatry at the Georgetown Medical School and author of “Winter Blues” (Guilford, 1998). “Light is a nutrient of sorts for these patients.”

The timing of phototherapy is critical. “To determine the best time for light therapy, you need to know about a person’s individual circadian rhythm,” said Michael Terman, director of the Center for Light Treatment and Biological Rhythms at the Columbia University Medical Center.

People are most responsive to light therapy early in the morning, just when melatonin secretion begins to wane, about eight to nine hours after the nighttime surge begins.

How can the average person figure that out without a blood test? By a simple questionnaire that assesses “morningness” or “eveningness” and that strongly correlates with plasma melatonin levels, according to Dr. Terman.

The nonprofit Center for Environmental Therapeutics has a questionnaire on its Web site (www.cet.org).

Once you know the optimal time, the standard course is 30 minutes of fluorescent soft-white light at 10,000 lux a day.

and....

It may sound suspiciously close to snake oil, but the newest promising therapy for SAD is negative air ionization. Dr. Terman found it serendipitously when he used a negative ion generator as a placebo control for bright light, only to discover that high-flow negative ions had positive effects on mood.

Now that is exciting. I've been interested in negative ions forever. Negatives ions probably explain why it's impossible to be depressed on the beach.

Santa may be bringing me a negative ionizer for Christmas.


source:
Brought on by Darkness, Disorder Needs Light
December 18, 2007
Brought on by Darkness, Disorder Needs Light
By RICHARD A. FRIEDMAN, M.D.

Shadow Syndromes

Enhancing Academic Motivation

I've just ordered Enhancing Academic Motivation from Research Press thanks to a friend of mine whose child is seeing Dr. Brier. Every word out of Dr. Brier's mouth so far has rung true.

When I discovered that Dr. Brier had published with Research Press, I was sold. Research Press published the two books that shepherded Ed and me through our first years with Jimmy: Gerald Patterson's Living with Children and Wesley Becker's Parents Are Teachers. Both are classics.

Wes Becker worked with Engelmann on Project Follow-Through:

During the Project’s third year, we found out that Carl was leaving to go to Canada and become an investigator for the Ontario Institute for Studies and Education and a professor at the University of Toronto. He invited Valerie and me to join him. Valerie accepted; I tentatively declined.

Carl’s impending departure presented serious problems to the preschool project. The reason was that I was not qualified to head the project. The only degree I had was a BA in philosophy, and the position I held then was Senior Educational Specialist, which did not allow me to administer projects. Neither Jean nor Cookie could assume directorship of the project because they also lacked formal credentials.

The rumors were that the Institute for Research on Exceptional Children would take over the project and change it as soon as Carl left. I later found out that Jean and Carl met with Wesley Becker, a gifted professor in the Department of Psychology. Their goal was to seek his help in preserving the project. I had heard a lot about Wes Becker from my sister-in-law, Geraldine Piorkowski, who earned her PhD at the University of Illinois. Wes was her advisor; from her descriptions of him I assumed he could even run on water. Among other achievements, he had set the all-time track record at Stanford for attaining a PhD, entering as a freshman and taking only six years to earn a PhD in clinical psychology and statistics.

At the time he advised Geraldine, Wes was a cognitivist, but shortly after she received her PhD, he became an energetic exponent of Skinner’s behaviorism, which is based on evidence that behavior may be changed by manipulating positive or negative consequences that follow responses. Wes abandoned his earlier orientation because it lacked data of effectiveness, a signature characteristic of Wes. The professional articles that Wes wrote in the '60s show his change in orientation from 1961 to '67: “Measurement of Severity of Disorder in Schizophrenia by Means of the Holtzman Inkblot Test” (1961); “A Circumflex Model for Social Behavior in Children” (1964); “The Parent Attitude Research Instrument” (1965); “How We Encourage Cheating” (1966); and “The Contingent Use of Teacher Attention and Praise in Reducing Classroom Behavior Problems” (1967).

I had met Becker only once. He had presented to our project staff and graduate students. He summarized his current research, which involved working with teachers in failed classrooms and teaching them techniques for using positive reinforcement with their students. His data showed that even though most teachers had to be instructed in how to give praise, and even though the praise some of them issued sounded contrived and unnatural, it changed students’ behavior. The basic thrust of Wes’s training was, “Catch kids in the act of being good.” His studies were among the first applications of Skinner’s version of behaviorism to humans and school settings.

After the meeting I told him about some of the observations we had made in the preschools. He listened, then asked, “Where’s the data?”

I told him I didn’t have any formal data related to the observations. He smiled and shrugged. The message this gesture conveyed was that if I wanted to demonstrate the validity of my assertions, I needed data.

Jean and Carl had set up their meeting to ask Wes if he would assume the role of director of our project. They didn’t have a chance to ask him, however. As they entered his office, he greeted them, and said, “I know why you’re here, and the answer is yes.”

I count this as one of the more amazing commitments a person could make. The project was embroiled in controversy. The work was demanding. By saying “yes,” Wes made an official break with the fortress of higher learning and moved to the trenches, the gritty realities of working with teachers and kids.

Wes brought some of his graduate and undergraduate students with him. Thirty years later, I still work with three of them: Doug Carnine, a shy undergraduate who had already authored articles that appeared in professional journals; Linda McRoberts, an adventurous and outspoken graduate student who later would become Linda Carnine; and Susan Stearns (now Susan Hanner), only nineteen years old but very smart and industrious.

[snip]

Wes devoted some of his “free time” to writing the book, Applied Psychology for Teachers, a very ambitious work that covered everything related to effective practices and background information—from behavioral principles to the theoretical underpinnings of effective instruction and how to interpret data on student performance. I believe that Wes considered this book his ultimate achievement, an opus that positioned effective teaching and the analysis of learning in a framework that could be comprehended by undergraduates and that would establish DI as at least a contender in the field of education. The work, positioned as a textbook for undergraduates, was published by SRA in 1986. It was a colossal work—472 pages, in 8 1/2” x 11” format, with 275 references (over 11 pages).

It was another false hope. The book did not sell, was not adopted by more
than a handful of the faithful, and after only a few years, was discontinued by SRA. No other publisher was interested in it. I recently bought a copy of it online. It was in very good condition and cost $4.50.

[snip]

Goodbye to a Good Guy

Wes and Julie were divorced in1980. Wes continued in his role as associate
dean until 1992, when he became involved in political wars with the College of Education and quit the University. After retiring, he refused to talk about education. On three or four occasions, I tried to discuss the book we had started. I got the same response each time. He said that he would talk about golf or other sports and the stock market, but that was all. He declined to talk about the Association for Direct Instruction, or about anything else related to education. He told me, “That is something from a past life. It’s dead and I have no interest in it.”

In 1993, Wes sold his shares in Engelmann-Becker Corp. and moved from
Eugene to Sedona, Arizona. There was no going-away party or celebration
because he didn’t want one. Just before he left, I asked if there was anything I could do for him. He asked if I would give him a painting I had done of a lion. Yes.

I called him several times in Arizona to see how things were going. Not well. I called him once around noon and he sounded as if he’d been drinking. His leg had gone bad so he couldn’t play golf, and the stock market had not been kind to him. His son David lived with him for a while but left. Wes never remarried and lived alone. A couple of times I asked him when he was coming back to visit us in Eugene. He seemed to entertain the idea but it apparently didn’t make the seriousplanning list. I never saw Wes again after he moved to Arizona.

[snip]

Wes’ death came as a great shock. I hadn’t been in touch with him for months.
I knew he was getting frequent tests, but I had no idea that he would die at 73. We felt we should do something to honor him and decided to hold a memorial service for him in Eugene. We put a notice in the paper, made many calls, and arranged to hold the service in the church that Wes had attended (the Unitarian Church). A lot of people showed up for the service, including Don Bushell, Wes’ daughter Jill (who is a professor of biopsychology at the University of Michigan), his son David, and his ex wife, Julie (who lived in Florida). We took turns telling Wes stories and feeling sad.

I said, “Those who worked with him were routinely amazed, not only by his
skill, but the speed with which he could do things. Perhaps his most impressive quality, however, was the strength of his will. In the face of terrible setbacks and impossible deadlines, Wes prevailed. If he promised to get something done by a particular time, it was not only done on schedule, but done very well.”

Several others echoed this observation. One researcher who studied under
Wes said something that I had observed many times, the amazing speed at which Wes could identify glitches in raw data or elaborate calculations. About the time I was looking at the first few numbers on a spreadsheet of data, Wes would point to a set of scores in the middle of the display and say something like, “It’s impossible for them to have a correlation of point 9 with these data. These scores account for no more than 5 percent of the variance.” Possibly a minute later, I would see what he meant, but if I’d figured it out on my own, it would probably have taken closer to an hour.

I pointed out that even with the incredible number of things he had to do,
Wes was a good dad (a lot better than I was during the Follow Through years). Wes’ daughter Jill expanded on this theme. She told about some of the nice things he had done and indicated that the only time he lied to her was a couple of months before he died. She had visited him in a hospital in California. The last thing she said before leaving was, “Now, you take care of yourself. I’ll be back in three months.”

He said, “I’ll be fine.”

The clinical causes of Wes’ death had to do with his liver, kidneys and blood
pressure. One of the contributing causes was that he probably drank too much. These may have been the measurable causes, but the psychological cause was that he killed himself. When the establishment rejected Wes and his beliefs in data, he rejected education. To do that, he had to reject a huge part of himself. The image of himself that he had to maintain afterwards was one with many amputated parts, the hollow core that could survive on what had been peripheral interests. When his physical health failed, he had nothing.

The sad part of this equation was that Wes had to reject himself not because
he did anything reprehensible but because the establishment made a mockery of his beliefs and accomplishments. Jill believes that someday he will be recognized for his singular contribution to Follow Through. I hope she’s right, but I can sympathize with Wes. It is not very comforting to know that you can help thousands of kids and teachers, but you lack credibility and have no access to these victims. It hurts to see your professional beliefs trampled by educators who cling desperately to myth and folklore.

A colleague recently showed me a picture from the ‘70s, taken at a “Zignic” (a
picnic at the Veneta property for all our trainers and friends). Six people, including Wes, Bob, and I, were wearing t-shirts with the motto, “Show me the data.” For Wes, it was a way of life.

How is Wes remembered? In 2003, the College of Education at the University of Oregon launched a fund-raising campaign to support construction of a mega-building to house the College. Part of what the planners did was to make up a price list for “dedications.” If you want an office named after somebody, donate $25,000, and the plaque goes up. For a decent-sized classroom, the ticket is about $100,000.

Shortly after the list came out, Doug called me about raising enough money to have a classroom named after Wes. I told him that we shouldn’t have to pay anything. My feeling was that the College should have dedicated an entire wing to Wes, with no donation required. The College didn’t see it that way. Doug is currently trying to negotiate the price of a plaque for both Wes and Bob at the entrance to the Clinical Services Building, which was one of Bob’s projects.

Siegfried Engelmann 2007

Parents Are Teachers table of contents
Living with Children table of contents

Rye Country Day

wow----

School says that since 1996, 97% of kids taking the Advanced Placement BC Calculus course received perfect scores on the AP exam.

How the Schools Stack Up (pdf file)
WSJ

still can't do fractions?

Tom Loveless is back:

The 2007 NAEP test results showed small but statistically significant gains in both math and reading. Mathematics scores at fourth and eighth grade continued the steady progress registered since the main NAEP test was first administered in 1990. Both grade levels notched 2 point gains in scale scores. Table 1-1 reports the magnitude of the math gains in scale score points and years of learning. Figure 1-1 illustrates the upward trajectory of the scores. The gains indicate that fourth and eighth graders in 2007 knew more than two additional years of mathematics compared to fourth and eighth graders in 1990. On the face of it, this is an amazing accomplishment. Previous Brown Center Reports have raised questions about such gains. The primary question concerns the content of the NAEP math tests. Students are clearly making progress, but at learning what kind of mathematics? Suffice it to say that students are making tremendous progress on the mathematics that NAEP assesses, in particular, problem solving with whole numbers, elementary data analysis and statistics, basic geometry, and recognizing patterns. NAEP pays scant attention to computation skills, knowledge and use of fractions, decimals, and percents, or algebra beyond the rudimentary topics that are found in the first chapter of a good algebra text. In sum, we know that students are getting better at some aspects of math. But we do not know how American students are doing on other critical topics, including topics that mathematicians and others believe lay the foundation for the study of advanced mathematics. Thus, the years of learning gain must be taken with a grain of salt.

The 2007 Brown Center Report on American Education:
How Well Are American Students Learning

plus ça change (scroll down)

Spellbound

wonderful

perfect

especially for Christmas

or the Fourth of July!

Spellbound

daily lit for Christmas

My siblings don't know it, but they're about to receive free novels via email for Christmas.

I think.

I'm getting one for me, too. Maybe I'll finally be able to finish The Prince.

middle school math teacher preparation

William Schmidt is working on an international report. I like Schmidt. He's the coherent curriculum guy.

snippets:

• The mathematics knowledge of US future middle school mathematics teachers generally is very weak compared to future teachers in Taiwan and Korea. It is also weak compared to German future teachers in all areas except statistics.
  

• Taiwanese and Korean future teachers were the top performers in all five areas of mathematics knowledge – including algebra, functions, number, geometry and statistics.

• School algebra (which includes functions) is the topic that, across almost fifty countries studied in TIMSS, was the major focus of instruction at seventh and eighth grade.
  

• On the algebra and functions tests, US future teachers performed at or near the bottom among the six countries—over a full standard deviation below the performance of future Taiwanesse teachers.
  

• The results for the statistics test were the only bright spot in future US teachers’ performance. The US future teachers scored enar the mean of the six countries.
  

• Future middle school teachers prepared by a secondary program performed somewhere between one-half to three-fourths of a standard deviation higher in algebra, functions, geometry and number compared to those prepared in either of the other two programs. The difference was slightly less in statistics.

COURSE TAKING

• On average, the Taiwanese and Korean future teachers reported taking courses that covered around eighty percent or more of the advanced mathematics topics typically covered in undergraduate mathematics programs.
  

• For analysis (the study of functions) Taiwanese future teachers covered virtually all of the topics (ninety-six percent) while, in Korea, the coverage was seventy-nine percent.
  

• In the algebra and analysis courses which provide the mathematical background for middle school algebra, the Taiwanese, Korean and Bulgarian future teachers all covered around eighty percent or more of the possible topics while Germany covered around 60 to 70 percent.
  

• Mexican and US future teachers covered less than half of the analysis topics. The same was true for Mexico on the algebra topics, but US future teachers covered on average 56 percent of those topics.

etc.

Bill would ban military slot machines - CNN.com

Bill would ban military slot machines - CNN.com

Why not, everything else is banned in the Military.

The perfect military troop: Non-smoking, non-drinking, church going, Habitat for Humanity voluteering, non-extreme sporting, anti-gambling, feminish supporting, college educated, safety oriented killer.

why is there 1?

Cleared away one of my floor stacks today. I'm glad I did because one of the objects in the stack was the Algebra 2 notebook in which I'd written an anecdote about C. & math. The notebook went missing a few months ago and now I've found it.

This is C. last summer at the picnic table outside our kitchen. We were probably working on percent (scroll down).

I don’t like math.

Why is there 1!?

1 + 1 equals 2!

Why is that?

I don't like math.

Words make sense. If I read “the dog,” I know what “the” means.

Math doesn't make sense.

- CHB summer 2007, 12 years old

I know you will all be impressed by the fact that I did not say, "You know what 'the' means?"

Myrtle on procedural and conceptual knowledge

Maybe I can make a convincing argument that a student who only thinks of multiplication as iterative addition and can't multiply 24X86 has neither procedural nor conceptual knowledge.

There is more to the "concept" of multiplication than iterative addition. (Try applying iterative addition to 1/8 x 2/5.) Perhaps iterative addition is appropriate for 2nd and 3rd graders learning their multiplication tables (or is it 3 and 4th graders these days?) But "the" concept of multiplication includes the fact that it distributes over addition (and that it's associative as well). The multiplication algorithm invisibly makes use of the distributive "concept," and does not employ an iterative "concept." Perhaps I'm overdoing the disdain quotes but I've been lied to too many times by people telling me that something is the "concept" of a procedure or rule and it turns out not to be.

A child with a conceptual knowledge of multiplication, and a lot of time on his hands, could successfully multiply two digits numbers without the multiplication algorithm:

24 X 86 means that
(20 + 4)(80 + 6) which means/implies that...

Etc. You see where I am going with this. One of the benefits of Singapore is that the kid does end up with a conceptual understanding of multiplication, and can apply his knowledge of concepts to come up with correct answers.

Notwithstanding operations on super hairy numbers, he is capable of doing the algorithm on paper when he needs to and can resort to "concepts" when he needs to do mental calculations.


the multiplication algorithm invisibly makes use of the distributive "concept"

I love that!

I love the whole Comment, in fact. People like me -- people who value liberal arts education in general and mathematics education in particular but who aren't expert in mathematics and probably never will be, have no way to get at these things.

I intuitively grasp the notion that there is some kind of "starter understanding" a person can have without being fluent in procedures. Seeing that 6x4 is the repeated addition of 6 4s or 4 6s as the case may be (I've spent quite a bit of time muddled over that one!) strikes me as superior to not seeing it. (I had no idea multiplication could be called repeated addition until I started reteaching myself math, and then I noticed it on my own.)

But at the same time I am gripped -- and gripped is the correct word -- by the conviction that a starter understanding is not a real understanding.

And yet because I lack a real understanding I have no way to express this and thus no means of combating the forces of reform math when they threaten to overrun my son's education.

I'm logging this post under Greatest Hits so I'll know where it is when I need it.

compare and contrast

presidential primary candidate:






professor of psychology and education:

WHAT DO WE WANT CHILDREN TO LEARN?

Beyond basic literacy and numeracy, it has become next to impossible to predict what kinds of knowledge people will need to thrive in the mid-21st century....[T]he only defensible answer to the question of what we want schools to accomplish is that they should teach students to use their minds well, in school and beyond (Kuhn, 2005). The two broad sets of skills I identify as best serving this purpose are the skills of inquiry and the skills of argument. These skills are education for life, not simply for more school (Anderson et al., 2000). They are essential preparation to equip a new generation to address the problems of the day.

Deanna Kuhn, Professor of Psychology and Education Teachers College
Is Direct Instruction an Answer to the Right Question?
a response to Why Minimally Guided Instruction Does Not Work (pdf file)
EDUCATIONAL PSYCHOLOGIST, 42(2), 109–113



Apparently Mike Huckabee has not set foot inside an ed school any time within recent memory.

bonus observation: I might actually be willing to pay more taxes to stop the extraordinary professional development and ongoing education teachers "require."

Starting with the workshops on writing to learn in math and science. I would pay to have my district's science and math teachers not attend another one of these things.

Blind Father Needs Help

This question was just posted on another list I follow.

Hello all. I am totally blind, but my wife and children are sighted.

My son is nine years old and in the fourth grade, and he is having a little bit of difficulty with long division--Especially when dividing a double-digit number into another number (e.g. 5128 divided by 47).

Can any one give me some pointers on how I might explain and illustrate the concepts of how to perform these types of problems, with emphasis on how to explain how to estimate?

I hope that this question is clear enough and that someone may have some ideas that will help me.

Thank you for your assistance.

This request was posted on a list where most of the members are adult blind mathematicians who are unlikely to know what is currently going on with grade school math and to what extent the son's problem is likely to be related to the educational environment.

I don't think this Blogger interface is very accessible to persons who use screenreaders. However, if anyone has any advice or suggestions, I'm happy forward them to this father.

hyperspecificity in Math A

Another classic example of hyperspecificity:

C. did not recognize this expression as a case of the distributive property:

2x(x+1) + 3(x+1)

Can't say I blame him.


update

from Barry:

This isn't real obvious when you first come across it. So do this. Let's let x + 1 = T.

Now substitute T in the expression and you get:

2x(T) + 3(T)

Can you factor out the T?

Yes. You get T(2x + 3)

Now substitute the x + 1 back in. You get:

(x+1)(2x+3)

I think it was Ron Aharoni who referred to seeing expressions such as (x+1) as single entities as "chunking". To help students do such "chunking" it helps to do what I did above so they can see that x + 1 represents a number, and as such it can be factored.

I'm amazed by how difficult it is to see that "expression X" is the same as "expression Y." This is an ongoing source of pain in my mental life these days (not to put too fine a point on it), because I came to feel, shortly after Animals in Translation was completed, that Temple's & my thesis concerning hyperspecificity in animals and autistic people is wrong in some important way -- either wrong or perhaps right for the wrong reasons.

We argued that autistic people, children, and animals are hyperspecific compared to typical adults. Autistic people, children, and animals are splitters; nonautistic adults are lumpers; etc. (I know I've said all this before, but feel I must repeat in case newcomers stop by.)

The classic hyperspecificity story re: autistic children is the little boy who was painstakingly taught to spread butter on bread and then had no clue how to spread peanut butter on bread.

Until I began to reteach myself math, this kind of thing seemed to me incontrovertible evidence of the otherness of the autistic brain. But now that I'm factoring trinomials I've discovered I have something in common with that little boy. That's probably why God or the universe decided I should take up math. I needed an object lesson.

Still, the observations Temple has spent a lifetime making of animals' (and autistic people's) hyperspecificity aren't wrong. Normal adult humans aren't hyperspecific in the same way animals and autistic people are hyperspecific.

Sometimes I wonder whether the issue is simply that non-autistic adults pass through the hyperspecific stage of knowledge more quickly or more frequently than autistic people do. When a "typical" adult (typical being the preferred term these days) encounters brand-new material he, too, is hyperspecific, as I am with math. Everyone starts out a splitter.

But I don't think that's quite it, either.

I'm getting the feeling that animals may not be hyperspecific across the board, but perhaps only in certain realms. Maybe animals are more hyperspecific than adult humans when it comes to sensory data? e.g.: To a horse a saddle feels completely different at a walk, a trot, and a canter -- so different that he will buck his rider off when he moves from a trot to a canter if he hasn't been carefully trained to tolerate the saddle at all 3 gates individually.

Better story: Temple's black hat horse.

This was a horse who was terrified of people wearing black hats. He wasn't terrified of people wearing white hats or red hats. Just black hats.

I'm thinking, this morning, that humans may be relatively oblivious to "sensory data," that we're lost in words -- so perhaps words are the place where you'll see us being hyperspecific ? (There's evidence that language masks sensory data, but I don't know it/remember it well enough to summarize.)

Temple complains about this all the time. She'll give a talk and her audience will take away a too-specific meaning from her words; then they'll go out and apply her advice all wrong & bollocks things up. "People get hung up on the specific words," she'll say. (I'll write down the next example of this that crops up - can't think of one offhand.) These conversations have gotten to be quite funny because, after years of reading countless articles on autistic people being literal-minded and "concrete," I am now spending my time listening to an autistic person complain that normal people are literal-minded.

Well, she's right. Looking at an expression like 2x(x+1) + 3(x+1), I'm like the horse with the saddle and so is my 13-year old son.

"x+1" next to 2x is completely different from "x+1" next to 3.

Different enough to make us start pitching our riders into the haystack.


percent troubles
Robert Slavin on transfer of knowledge
rightwingprof on what students don't know
Inflexible Knowledge: The First Step to Expertise

what understanding without procedural knowledge looks like

Extremely useful comment left by palisdesk:


on the 5th grade students she assessed:

I assessed a whole [5th grade] cohort in math (only one was a special education student, and he was no worse than the rest), with similar results.

They scored well in understanding "concepts." Whoop-de-doo. But none could reliably do computation with regrouping, do mental computation of any sort, measure accurately, use a number line, name fractions, or do any operations with fractions or decimals. Surprisingly they could not even count money correctly!! They could not figure out elapsed time, nor read non-digital clocks.

What good is all this great "conceptual understanding" if you can't count coins under $3.00, measure the length of a board, find the perimeter of a triangle or determine whether to add or subtract to compare two numbers? The one thing most were good at was reading graphs -- pictographs, bar graphs and simple tables.

Some of these students were quite bright and had good reasoning ability but what they ALL lacked was knowledge of number facts, facility with algorithms, precise vocabulary (perpendicular, acute angle, numerator, range), an organized approach (if guessing didn't work they were stuck), in short MASTERY at any level. Like [instructivist's] students, all have had nothing but fuzzy blah-blah since entering school. Few to none can afford Kumon and most don't have computers at home or access to them, so even that kind of practice is not available to them.

A recent study of teacher competence in our district found that most teachers in 5-8 grade mathematics did not themselves show mastery of the subject at that level. I think we may have come full circle. The system is now being run by people who are its products, and many are quasi-literate and numerate, however bright and caring they may be. Also, the lack of any kind of intellectual rigor or scientific and statistical training in their preparation has left them vulnerable to every fad that comes down the pipeline.

conceptual understanding w/o procedural knowledge:

The best way to illuminate my point would be to contrast my findings with what might have occurred in "the old days." Time was -- the 50's? 60's? when you might often find students who could proficiently, or at least adequately, perform basic operations -- including, in many cases, operations with fractions and decimals -- but would have been at a loss to explain what they were doing, or why they were (for instance) regrouping in subtraction, or inverting fractions to divide them. It was not considered necessary for students to have a "deep" understanding of the number system per se. Most of us (I remember this myself) "got it" in the process of learning the algorithms and how to apply them, and did (eventually) understand why you had to regroup, what you were doing when inverting fractions (I would have wanted to show how it works, even now it would be hard to explain succinctly in words, but it's easy enough to demonstrate).

The children I was assessing -- with a detailed, widely-used norm-referenced diagnostic math test and also with a locally developed "performance assessment" -- showed the opposite pattern. They understood about place value (haven't played with Base 10 blocks for years for nothing), knew that multiplication is repeated addition, that fractions can name parts of an object, or members of a group, and so on. They could show you (with the ever-present manipulatives), or draw a diagram and explain. They could tell you why you have to rename the ones as tens, why you have to keep the decimal points lined up, what the value of various coins etc. is, what the "big hand" and the "little hand" on a clock indicate, and so forth.

What they could NOT do was reliably apply a procedure to come up with an answer. Given a problem like 24X86, they knew this means you make 24 groups of 86 (or 86 groups of 24), but would get lost trying to build them with blocks or count out the tally marks. If they tried to use the algorithm, typically they got directionality, order of steps, etc. all mixed up, and they didn't know the number facts. The brighter ones would figure out the answer had to be something around 2000, but many did not even get that far. When counting coins, they lacked a strategy such as, counting the quarters first, then the dimes, then the nickels, etc. They randomly counted each one separately and continually lost count. They didn't know how to "count up" to find a difference (or an interval between numbers or clock times).

This is so helpful. It makes sense to me that a student could have some degree of conceptual understanding without procedural knowledge, and yet when I try to think of how that would work I come up with a blank. It's clear to me, for instance, that my "conceptual understanding" of unfamiliar subjects -- economics, say -- is thin at best. God is in the details.



hyperspecificity for conceptual knowledge -- ?

One thing I think I see happening with palisdesk's 5th graders is "hyperspecificity" for conceptual understanding. I'm used to seeing hyperspecificity for concrete knowledge. I hadn't really thought about hyperspecificity for concepts such as the meaning of multiplication. It makes sense, though. I'm pretty sure it happens to me all the time, teaching myself algebra 2. I'll have a basic conceptual understanding of a concept -- logarithms, say -- that doesn't immediately transfer to a problem type I haven't done before. I'll try to come up with an example to post.

As usual, I'm hamstrung by a lack of terminology. Our sturdy workhorse words -- procedural, conceptual -- are failing to give me the distinctions I need within the category of "conceptual understanding."

These 5th graders have for arithmetic what I have for logarithms: some kind of start-up understanding of the concept that won't take them very far when confronted with an actual logarithm problem in the flesh.



thank you palisdesk, pissed-off teacher, instructivist, redkudu, dy/dan, nyc educator, exo, smartest tractor (I'm sure I'm leaving others off ....)

For parents and the broader public schools are a black box. Mike Schmoker says that's by design; the official term for management in schools is "loose-coupling," which means, I gather, that the goal of management is to protect the core functions of the organization from outside scrutiny. (more later...much, much later)

Teachers who share their experiences with outsiders are functioning as the education reporters our country needs but does not have.


Robert Slavin on transfer of knowledge
hyperspecificity posts
loose coupling & instrutional leadership

tales from the front, part 2

from pissed off teacher --

A zillion years ago when my son was in first grade and computers were still a novelty, he decided to write his spelling words on the computer. The little twerp was using copy and paste to write them the required ten times. When I made him stop, he told me "but my teacher said it was okay". As I said, computers were new and she did not know how he was using it.

Kids have always cheated. We just have to be smarter than them to stop them in their tracks.

The middle school's Civil War Museum exhibit last spring put the kids' papers on display. Ed looked at every paper & saw a huge amount of internet text. Same thing the year before at the Jason Project exhibit. Many papers included downloaded text. A couple of papers were the same paper.

Of course most people didn't notice because they were looking at the crafts projects, not the papers.

Crafts projects are to a middle school what misdirection is to a magician.

Possibly.

tales from the front

from Cheryl T in Singapore:

I once had a 9th grade student who turned in an essay on Greek mythology that was totally plagiarized. When confronted with the computer screen shots of the essay's genesis, he denied it up one side and down the other.

Finally, he broke down, blurting out, "But I didn't even write the essay -- my MOM did!" I spoke that night with the mom, who freely admitted ghost-writing her son's essay. She claimed not to know that cut-and-pasting huge swaths of someone else's writing was wrong. Where to begin?!?

(This happened at a GREAT public high school north of Chicago...)

My favorite cheating story happened at Iowa, where I was teaching the freshman rhetoric course. One of my students plagiarized her entire essay, word for word, from the textbook. She denied having done so and then, when I opened up the textbook and did a side-by-side comparison, said, "I remembered."

Of course, now that I have two autistic kids, it strikes me that she could have remembered....

cut and paste

from a comment left by NYC Educator:

I'm amazed at the number of kids who simply copy things off the net, with the labels still there, and expect me not to notice it was written by some professional hack writer instead of an ESL student.

True!

They all do this! Not just the ESL students, everyone.

Ed was talking to a French journalist this week who told him kids in France do the same thing. They think writing means downloading from the internet. The less sophisticated kids cut and paste things whole; the more sophisticated kids cut and paste individual sentences, piecing them together as they go along.

It's as if the basic unit of composition is no longer words but sentences, and you look up the sentences you need on the internet not in the dictionary.

National Survey of Algebra Teachers

How have we missed this?

Research Question #2: To the degree that the teachers believe students need to be better prepared, what are the major shortcomings?

The teachers were asked to rate the importance of a “solid foundation” in the each the 15 skill/knowledge areas asked about with respect to their target class students’ background preparation. Since the same background skills and knowledge for which the teachers rated student background as inadequate were also rated as important, the following areas emerge as the major shortcomings: rational numbers, word problems, and study habits.

Final Report on the National Survey of Algebra Teachers for the National Math Panel (pdf file)
National Mathematics Advisory Panel

They're not too keen on parents:

Research Question #12: Do they find more parents helpful in encouraging students in their mathematics studies, or do too many parents make excuses for their children’s lack of accomplishment?

Questionnaire item II.1i asked teachers to rate the extent to which they see “too little parent/family support” as a problem in their school. The responses indicate that about 28% of the algebra teachers feel family participation is a serious problem and another 32% believe lack of family participation is a moderate problem (Figure 13).

It's a bit difficult to cess out what this means exactly. The question itself seems off-base; the handful of direct quotations from teachers have nothing to do with parents "encouraging" their kids versus "making excuses" when their kids do badly:

The written-in “verbatim” responses most often mentioned included handling different skill levels in a single classroom, motivation issues, and student study skills. Some notable responses were:

Walking into a class of 30 students in which 1/3 of them don't have the prerequisite skills necessary to be in the class. Many of whom don't know their basic arithmetic facts and know they aren't going to be successful from day one no matter how hard they try.

Students come to me without a basic understanding of math. I am constantly re-teaching concepts that should have been mastered in the earlier grades.

Parents not letting me do my job as I see fit. (Autonomy in the classroom.)

Getting students and parents to believe that education is important. Students don't do their homework...you call the parents...they say that the student will start doing the work (and coming to tutorials). The students still don't do the h.w. -and still don't come to tutorials.

Engaging students who have come to believe that they are stupid because they are struggling with my state's cognitively inappropriate standards.

Report's conclusions:

The Algebra I teachers generally reported that students were not adequately prepared for their courses. The teachers rated as especially problematic students’ preparation in rational numbers, solving word problems, and basic study skills. A lack of student motivation was by far the most commonly-cited biggest challenge reported by the teachers. The problems the teachers identified with the pre-Algebra I mathematics curriculum and instruction and with the lack of parental support for mathematics were likely to be contributing factors to the lack of adequate student preparation and motivation.

[snip]

In light of the generally favorable views the teachers report with respect to curriculum and instruction, the issue of unmotivated students implicitly is something the teachers view as more of an “algebra-student problem” than an “algebra-teacher problem”. The generally-negative views expressed by the teachers of parental support for mathematics reinforce that attribution. Taken together with the generally negative ratings of background preparation, the lack of student motivation suggests that careful attention to pre-algebra curriculum and instruction in the elementary grades is needed, both to remedy the specific skill deficiencies as well as to identify ways in which negative attitudes toward mathematics are developed.

Our schools need a paradigm shift. If you've got an "algebra-student problem" then you also have an "algebra-teacher problem" by definition and you need to take action. Institute supervised homework study halls, formal reteaching of foundational skills, whatever.

Motivation as the Magic Key to All Learning is overrated in any case, I think. How motivated were Siegfried Engelmann's students in Project Follow-through? How motivated are the KIPP kids?

My own 8th grade child is not exactly gripped by a coursing desire to learn algebra. However, he is learning algebra, and he's learning it pretty well. That has to do with the teacher.

And, yes, it has to do with "parental support for mathematics," which in our case means that I do every homework assignment so I can check C's work and have him re-do the problems he missed.

You can't leave algebra up to student motivation.

Mathcounts Help Needed

Okay, my math kid has been working on his practice sheets for the upcoming Mathcounts competition next year. He seems to be doing great with the practice problems, but the warm-ups sometimes seem harder.

I'd love to help, but as many of you know, I am the resident Math Phobe of KTM. With the husband out of town, you are my only hope to helping him with this one particular problem. I have a feeling it is something really obvious.

Here it is:

"The sum of two numbers is 32, and the product of these two numbers is 48. What is the sum of the reciprocals of the two numbers? Express your answer as a common fraction."

I have the answer sheet, but no explanation on the best way to approach this.

Any and all help would be appreciated. Speak slowly, though....although the kid will probably understand what you're saying.

SusanS

2 teachers out of 50

This is exactly what I'm seeing:

Of a staff of more than 50, only one other teacher and I have more than 10 years experience, and I'm the only one with much expertise in instructional issues. There is definitely a generation gap in knowledge and skills, no fault of the newer folks. Most had no preparation at all in curriculum, behavior management, instructional design, teaching skills etc. Lots of philosophy instead. I don't dare contemplate what things will look like in another 10-15 years.

My district is hemorrhaging experienced teachers.

In their place we hire novices. More than half of our new hires have never taught; the rest have fewer than 5 years' experience. The administration's stated intention, with all new hires, is to grant tenure. A great deal of time and energy are devoted to mentoring and supporting new teachers who are struggling.

My district has, in the past, refused even to interview experienced math teachers. One person denied an interview was qualified to teach math and physics. He had glowing recommendations. Another experienced NY teacher was told that if he taught here he would have to take a pay cut to the salary of a 5th year teacher. He has retired from the public schools and is now teaching in a private school.

I wonder whether this qualifies as a form of age discrimination? Someone asked the Board about the average age of new hires; the answer was, "We're not allowed to ask age." Wouldn't a policy of interviewing only novices be a problem in terms of age discrimination?

I suppose not. We do interview and hire career changers.


10-year rule

I should add that we've had some terrific young teachers. It's not the case that a young teacher can't be good. She can. (Mostly, these days, it's "she.")

It is the case that he or she isn't as good today as he or she is going to be.


The Why Chromosome
Practice Makes Perfect (the 10-year rule)

palisadesk on guerilla instructivism

This WAS an interesting article. However, there must be tremendous variability -- ours is considered an excellent plan, but I did the math and if I retired now I would have to live on 46% of my current income (doable if I moved to a trailer park or seniors' home -- but I'm not attracted to the former nor eligible for the latter). Even at max pension is 60% of previous income. The coup de grace is that one has to purchase one's own medical and dental plan, and there are no comparable ones available from any providers at any price. This isn't so much a consideration for actual seniors but it is if you're in your 50's. Correspondents from other large districts in the east and Midwest have similar stories.

Fighting the system is something that does definitely lose its appeal over time. Guerrilla instructivism is energy-draining. Can't agree more about the frustration of being confronted with one obstacle after another every time you want to actually teach or help a kid. However I do still get an iconoclastic rush out of defying authority and successfully teaching basic skills: the pedagogical equivalent to manning the lifeboats. One consolation is that if I get REALLY p.o.'d I only have to give 10 days' notice. I could get a pleasant job in a bookstore or something to stay afloat. Of a staff of more than 50, only one other teacher and I have more than 10 years experience, and I'm the only one with much expertise in instructional issues. There is definitely a generation gap in knowledge and skills, no fault of the newer folks. Most had no preparation at all in curriculum, behavior management, instructional design, teaching skills etc. Lots of philosophy instead. I don't dare contemplate what things will look like in another 10-15 years.

pissed-off teacher on why we are losing experienced teachers

That article hits it on the nose--if I retired today I would be bringing home more money than I am working full time.

I don't work for the money, or for the few extra dollars I will make by staying longer, I am working because I really love what I am doing. Most of us 55 year olds are staying for that same reason. We are leaving, not to get more money but to get away from a system that is abusing us and abusing children. Kids are being forced to learn things they don't understand, and will never understand or need. Classrooms are over crowded. There are no meaningful tutoring programs and the system keeps piling on more and more tests. Older teachers are being harrassed. The schools only want the young ones who are earning a much lower salary and will jump as high as any admin tells them too.

We are just tired of the BS. WE are tired of being fought every time we want to do something to help a kid. We might as well take the money and enjoy our lives.

farewell to the baby boomers

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.

Two Million Minutes

Two Million Minutes

THE DOCUMENTARY
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.

source:
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

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!)

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.]

source:
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!

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.