kitchen table math, the sequel: 8/12/07 - 8/19/07

Wednesday, August 15, 2007

birthday & a vacation

Christopher & Andrew turned 13 today.

And tomorrow is vacation.

Tonight, after C. blew out the one candle that was still lit after our wait for Christian to get Andrew (back) to the table, I said that my birthday present would be having Christopher tell me what 10% off twenty-five dollars was.

Christopher started to say, "Irvington," the perseverative in-joke he and Christian swap back and forth 50 or 60 times a night. (The joke is: Jimmy, asked a question, will often answer, "Irvington." What'd you do this weekend, Jimmy? "Irvington!" What day is it, Jimmy? "Irvington! Irvington!" Hence Christopher, when asked What is 10% off twenty-five bucks also answers "Irvington!" which is just as hilarious the 10,000th time he's said it was the it was the first couple thousand.)

Anyway, he started to say, "Irvington," then stopped mid-word. Which is not easy to do. I know this because Georgia Mason's Stereotypic Animal Behaviour: Fundamentals and Applications to Animal Welfare 2nd Edition says so.

Then he said, "It's $2.50, and the price is..... $22.50."

Back on the 25th!

hyperspecificity in autism
hyperspecificity in autism and animals
hyperspecificty in the rest of my life
hyperspecificity redux: Robert Slavin on transfer of knowledge

Inflexible Knowledge: The First Step to Expertise
Devlin on Lave
rightwingprof on what college students don't know
percent troubles
what is 10 percent?
birthday and a vacation

an otter on a box

wonderful story

From Jaak Panksepp, perhaps my favorite of the neuroscientists whose work I've read:

We find ourselves at the tall-tale end of an intellectual era when the animal mind was deemed nonexistent or impenetrable. Gentle Darwin was prescient when he coaxed us to see our own emotional nature as continuous with that of our fellow animals.
Beyond a Joke: From Animal Laughter to Human Joy?
April 1, 2005 Vol. 308 no. 5718 pp. 62-63

Animal Passions--Fido Loves You (on Panksepp and his work)

Doug on French TV

[hmmm... just noticed that headling is a bit misleading - Now appearing on French TV!]

oh, well

I suspect that a part of the advantage of listening to television is that actors and talking heads speak more clearly than the average person on the street but less clearly than a language teacher. IME, language teachers teach platonic forms of a language's phonemes -- forms that are very seldom used in precisely those forms in speech by normal people.

In addition, television uses common idioms from the language, not the artificial phrases used by teachers.

I suspect the combination is quite useful to a language learner.


I find this whole area pretty fascinating.

Here's another research factoid:

Kuhl's earlier research found that 9-month-old American babies who played games with and were read to by Mandarin speakers could still hear Mandarin phonemes at 14 months after only a dozen 25-minute Mandarin sessions. A control group could not. Babies who were exposed to videotaped Mandarin could not.

So why does human connection make a difference?

"The hypothesis is that interaction is what sets the brain up to acquire learning," Kuhl says. "It's an opening of the cellular floodgates . . . There's this arousal thing . . . that might do something biochemically that allows cells to acquire information in a more memorable way. We know that hormones play a role. We know that when children are apprehensive, under stress, they don't learn."
Infant Science

That tends to argue against the "French TV" hypothesis, unless adults have a different set of "social arousal" needs than infants, which is not only possible but, I would imagine, likely.

Still, I think this does speak to the Eternal Quest for learning technology in our schools. I've always had the strongest feeling -- it's an intuition, nothing more -- that the physical presence of the teacher is an "irreducible." You don't have school without a living, breathing teacher in the same room with the kids.

Clifford Stoll has a chapter on the utter failure of "distance learning" that suggests 20 year olds need human teachers, too.

Space Teacher is Spacey

From the NYT:

Barbara R. Morgan got back to teaching yesterday. The students were in Idaho; she was in space, orbiting aboard the International Space Station.


The event yesterday was the culmination of a summer of space-related activities at the Discovery Center of Idaho, in Boise. Ms. Morgan, who is now what the space agency calls an educator astronaut, told the students that being an astronaut was not so different from being a teacher, at least in some ways.

“We explore, we discover and we share,” she said. And both “are absolutely wonderful jobs.”

What the hell is she talking about?

Tuesday, August 14, 2007

Coming to a kitchen table near me...

the Liberal Arts and Singapore math too!

I will be educating my fifth grader at home as of this fall for more reasons than I could ever begin to list here. So much of this decision has been inspired by KTM-2 discussions and I thought it appropriate to thank you for sharing your ideas, resources and thoughts in this forum. We're looking forward to a rigorous, comprehensive curriculum that continually raises the bar.

You keep blogging and commenting, I'll keep reading and learning ....

evil parent moment


I'm wondering whether C. will flip out if I tell him he has to start watching Spanish TV 15 minutes a day?

Martine usually watches the French news along with Jimmy & sometimes Andrew.

Probably everyone in the house can understand spoken French now except me.

Back when Andrew was around 2 my in-laws came to visit. Andrew, who was very out of it - couldn't speak, couldn't understand, didn't interact - was in the back bedroom with my mother-in-law when Martine sang out, "Andrew. Viens manger." [sp?]

Andrew looked towards the door, stood up, and trotted out to the kitchen to eat.

My mother-in-law just about plotzed.

case study of an autistic child, birth to age 2

Patricia Kuhl also studies autism.

I don't think I can bear to read this, but the link is here:

Case Study of the Development of an Infant with Autism from Birth to Two Years of Age (pdf file)
Geraldine Dawson, Julie Osterling, Andrew N. Meltzoff, and Patricia Kuhl

This paper was published in 2000, which is a mark of how removed I've become from the world of autism research. Dawson et al's paper had to have been a major event, because autism is essentially never diagnosed before the age of two.

I had followed her earlier research, which involved looking at family videotapes of babies who would go on to be diagnosed with autism. A lot of us were interested in this, because parents often say that their autistic child developed normally until around the age of 2, then "became" autistic; Dawson was looking for early and subtle signs of the disorder. I remember being confused by her findings, or perhaps by her take on her findings. I don't remember which.

Maybe I'll work up my nerve and take a look at this paper after all....

are we all dyslexic in nonnative languages?

I have no idea whether I'm skimming these things right, but if you're interested in the subjects of reading, dyslexia, and/or foreign language learning, take a look at these papers of Patricia Kuhl's, especially this one: A perceptual interference account of acquisition difficulties for non-native phonemes.

Babies can distinguish all of the phonemes in all of the world's languages, a figure that comes to 600 consonants and 200 vowels, apparently.

Then, over the next months, babies get better at distinguishing the phonemes of their own languages while getting worse at distinguishing the phonemes of all the other languages, a process Dr. Kuhl says is not "subtractive" in nature. (I am failing to understand precisely what she means by "not subtractive" at the moment, but I have an idea, and I can see that it's important.)

Eventually the 5-month old "citizen of the world" becomes a 12-month old American citizen or Japanese citizen or French citizen and so on.

Kuhl has also found that a baby's phoneme-distinguishing abilities predict his language abilities later on.

So..... it strikes me that once you've become a linguistic citizen of a country you may be in an analogous position vis a vis other languages to that of a dyslexic child is vis a vis his own language (only worse, I would think). Once you've become a native speaker, you have acquired a major deficit in phomenic awareness for the phonemes of the foreign language or languages you would like to learn.

I think Michael Merzenich was attempting to use computers to teach English speakers to "hear" Japanese phonemes (possibly by slowing down & stretching out the Japanese phonemes we have trouble distinguishing?)

I wonder whether something like that would make it possible for an adult to regain a 6-month old's ability to hear the phonemes of other languages, thus making it easier for the adult to learn the second language?

This reminds me of something else.

It's been common, in my experience at least, for people who've spent time living in a foreign country to say that they "learned the language by watching TV."

Ed is fluent in French, and he's always said he learned French by living in France and watching French TV. Which never really made sense. He wasn't watching French TV with subtitles. He was watching French TV in French.

Other people who are fluent in foreign languages they picked up as adults have told me the same thing. Not only that, but invariably they advise me to do the same if I want to learn a language to fluency. That an adult can become fluent in a foreign language by watching TV in that language is an article of faith amongst the bilingual, as far as I can tell. (Amongst the bilingual who became bilingual after childhood, that is.)

For sure nobody ever says, "I learned French by reading French."

Well, this makes sense if phonemic awareness is as important to acquiring a second language as it is to acquiring a first. (Is it? Do we know?) In fact, people like Ed make a phonemic argument for learning French by watching French TV, which is that actors speak more clearly than ordinary citizens.

Kuhl's work also shows that there likely isn't a "critical period" for language learning based in time and biology (i.e. the advent of adolence producing some kind of hormonal and/or brain change that makes it impossible to learn to speak an unaccented foreign language thereafter). Instead, the experience of making a "neural commitment" to your own language makes it progressively more difficult to distinguish the phonemes of other languages.

In short, the ability to perceive foreign language phonemes isn't precisely lost, though it is equally not something you could will back into being.


All of this may be deeply wrong.

I'm going to have to stop skimming and start reading.


Just in case it isn't deeply wrong, I'm wondering whether that subscription to Puerta del Sol Audio Magazine I was contemplating a few years back might be a good idea.

Or, better yet, I should go back to my lapsed plan to start watching Spanish & French television every day.


A little PowerPoint can be a beautiful thing.

TIMSS falls apart?

ester left a link to this story:

So why did the federal government quietly decide last year to drop out of an international study that would compare U.S. high-school students who take advanced science and math courses with their international counterparts?

The study, called TIMSS (Trends in Mathematics and Science Study) Advanced 2008, measures how high-school seniors are doing in algebra, geometry, calculus and physics with students taking similar subjects around the globe. In the past, the American results have been shockingly poor. In the last survey, taken in 1995, students from only two countries—Cyprus and South Africa—scored lower than U.S. school kids.


Mark S. Schneider, the commissioner for the Department of Education’s National Center for Education Statistics, says the decision was made after a number of other countries—Australia, Germany and Finland—also decided not to participate. That left Armenia, Iran, Italy, Lebanon, the Netherlands, Norway, Russia, Slovenia and Sweden in the study. “We looked at the countries who are participating, our scarce resources and our overextended staff,” says Schneider, “and we decided to give it a pass.”

The test, which would have been administered to about 4,000 high-school seniors, would have cost the federal government between $3 million and $10 million, Ewing says. The National Science Foundation, which is independent but funded by the government, declined to fund the exam as well.


Advocates for the study are looking for private funders to step in and pay for the test. Patsy Wang-Iverson, who works for the Gabriella and Paul Rosenbaum Foundation in Stockton, N.J., a nonprofit organization that supports math advancement, has been approaching other foundations for money to sponsor the two-and-half-hour test. “We need this money in the next month so that Educational Testing Services [which administers it] can begin the crucial work needed to get the test off the ground.”

I think I know what this is.

My guess is we haven't pulled out of the "regular" TIMSS, which tests 4th & 8th graders. The number of countries taking part in the 12th grade test has always been smaller. I have a memory that Singapore isn't part of it because Singapore doesn't have a 12th grade.

(If radical galoisien or Cassy or someone else who knows the Singapore system can chime in here, that would be great. I'll post corrections, obviously.)

As for me, if Patsy Wang-Iversen thinks we should be part of the 12th grade TIMSS, then I think we should be part of the 12th grade TIMSS. I'll taking my cues from her.

Monday, August 13, 2007

Elizabeth Wissner-Gross

Great minds think alike.

At least I think they do.

I'm thinking that, a year or so ago, Steve H told us about Elizabeth Wissner-Gross' book and website, What Colleges Don't Tell You (And Other Parents Don't Want You to Know).

I don't see her website now.... but here is her blog.

Then today Susan S sent an email telling me about a great book called What High Schools Don't Tell You. She says it's great.

I'm ordering it.

Then I'm going to try to find my copy of the college book, which is around here somewhere....


I am semi returned to email.


(Premack principle rocks!)

the medium is the message

Edmund Bacon, of the Philadelphia town-planning commission, discovered that school children could be invaluable researchers and colleagues in the task of remaking the image of the city. We are entering the new age of education that is programmed for discovery rather than instruction. As the means of input increase, so does the need for insight or pattern recognition.
Understanding Media: The Extensions of Man
by Marshall McLuhan 1964

Ed just found this passage in McLuhan's book.

Ed: "The medium is the message, so there's no need for content, because the medium is the content. Technology is its own content."


"The 21st century won't require knowing content. It will require being able to recognize patterns."

So.....I guess that explains why my district is buying Smart Boards while the parents are raising money to buy books. Forty-three years after Marshall McLuhan announced the end of instruction, the general public is still stuck in the Knowledge is Good stage of cultural evolution.

How Knowledge Helps by Daniel Willingham

zero tolerance

At least one of our ktm-2 regulars lives in Minneapolis/St. Paul, travels the bridge most days, & can see it from office windows. Everyone is OK, thank God, but my own experience with the Northridge earthquake tells me that the trauma will take time to subside.

Today's Times has an op-ed on the subject of bridge maintenance from a former chief engineer of NYC's Department of Transportation. Naturally things are worse than we think.... which I can find funny in other realms, but not in this.

I know bureaucracies work the way they work, and incentives & disincentives work the way they work.

But I'll never get used to it, and I'll never feel anything but contempt for this level of irrational action and decisionmaking.

speaking of which

The bridge collapsed on Monday, August 1.

On August 3 the Sun ran a story:

More than 2,000 bridges in New York State carry the same federal rating of "structurally deficient" as a major highway bridge that collapsed in Minnesota this week, killing at least four people.


According to state standards, New York does not have any bridges that are structurally deficient, a deputy commissioner at the New York City Department of Transportation, Lori Ardito, said yesterday, noting that bridges in the city undergo inspections every two years.

By federal standards, about 15% of New York City bridges are "structurally deficient." At least nine city bridges received the lowest rating on their federal evaluation in 2006, which means they have components requiring replacement, according to a national bridge inventory database maintained by the Federal Highway Administration.

Ms. Ardito said that even the three city bridges that have gotten a poor rating under the state's rating system, including the Brooklyn Bridge, are safe to drive on.

"There's only components of the bridge that are in poor condition. They're actually the ramps leading to the bridge, not the span of the bridge," she said of the Brooklyn Bridge. "If the bridge was deemed unsafe, we would have to close it."

Note the language.

"We would have to close it."

Not: By God we're going to make sure those bridges are in pristine condition or no one's setting foot on them.

I really don't want to hear deputy commissioners of bridges sounding aggrieved and put-upon.

Sunday, August 12, 2007

remembering and forgetting

from a comment left by Le Galoisien:
But really. If they for example, require you to know logarithms, the general attitude is like, "You probably forgot how to do these. Here's a refresher." and you learn the concept over again ... because it is true even the top students in the school forget them because the syllabus is structured in such a way that it is hard to exercise them all year.

I remember the seniors would cry, "awww, you mean we had to remember those?" when there was a rare AP problem that required us to know a trig identity we had learned a year before. And the teachers would respond, "of course. You didn't learn them for nothing," implying it was our fault (but begrudgingly teaching them to us again). But somehow, even though it was partially our fault for not revising the concepts we had learned over the years (even when we had been assigned no work that dealt with them after we finished the unit) I often wonder if it is someone else's fault as well.

I mean, imagine all the time that has to be used reteaching concepts, and generally just in time for the examinations, before we put them in the closet again.

If we reinforced them all along, I wonder if students would save so much time with progress so much quicker that doing linear algebra in your senior year would be no big deal.

That's the story around here, only worse.

Learn percent, forget percent.

Learn percent again, forget percent again.

Repeat, repeat.

Meet with math chair; math chair says class had no business flunking latest test because "they saw that material last year."

inputs, not outputs

I'm realizing, again, how deadly the inputs model is. When school quality is defined by class size, per pupil spending, and number of Masters degrees held by teaching staff (pdf file), there isn't much incentive to design curriculum & instruction that ensures students will actually remember what they've "learned."

In my next life I plan to live on a planet where schools and curriculum designers focus on:

a) how to get content and conceptual understanding into students' long-term memory

b) how to keep it there

Here's Stanley Ocken addressing the National Mathematics Advisory Panel:

My second suggestion is that you investigate and make recommendations regarding common sense issues of pedagogy. It's important to think about the sequence of tasks and knowledge that lead to success in algebra, but it is critical and possibly easier to find out why so many entering college students seem to have forgotten the algebra they learned in school. You could begin by stripping away the obfuscating rhetoric of blind rote and drill and kill. Then you might examine the proposition that repetition and practice, properly implemented, are essential to success in mathematics, just as repetition and practice, properly implemented, are
essential to success in music, sports and the study of foreign languages. You could conclude by identifying prior indicators of successful college math students.

Before they got to college, did they experience rigorous and frequent in-class assessments? Were they required, for example, to master the multiplication facts by the end of third or fourth grade, or were their programs grounded in the principle that it doesn't matter if children master the material this year, since they are going to relearn and re-relearn the same elementary material in later grades? In other words, please investigate the role of basic interventions that clarify the scheduling and rigor of learning goals, these may be more effective and easier to implement than complex manipulations of curriculum and pedagogy.

Here’s my third and final suggestion. Enunciate the importance of a coherent K to 16 mathematics curriculum, one grounded in the principle that K to 12 math instruction must permit and encourage students to prepare for the rigors of calculus. To bring that principle to life, we'll need to see fundamental changes in the dynamics of K to 12 curriculum design.
National Mathematics Advisory Panel (pdf file)
Thursday September 14, 2006

I'm fairly certain the only group of people who measure the success of their instruction by student achievement, which means, among other things, student remembering, are the behaviorists. I may be wrong about that, but I suspect not.

Just what I wanted to hear!

from Lynn G:
FWIW, we started Primary Math 6A today. Kicking and screaming ensued.

Then we opened yesterday's mail and got a very pleasant surprise. My daughter's CMT scores (CT's state testing) arrived and were very good. She got a perfect 400 in math. Math is not her favorite, or strongest subject, but it's one we've focused on at home at length. I see the score as reflecting the coherence of the Singapore Math system.

After much oooohhing and ahhhing, I was able to get her to start 6A.

Right now, she doesn't seem to have any real weak areas. She's doing pretty good in decimals and fractions, so we're just going to charge ahead with the whole program.
That's where I am -- and I can see exactly how this curriculum gets a student to the point of perfect scores on state math exams.

The Primary Mathematics series is the coherent curriculum (pdf file) par excellence. One thing leads to another, and you have problem solving applications from the get-go.

C. has probably done 50 word problems in his entire math-learning career, if that. He has no idea how anything relates to anything else. He's been getting by on brute memory.

Here's how bad it is.

We've been doing the percent lessons in Singapore Math 5A.

That quickly became so "natural" a learning situation that, when I told C. yesterday morning I wanted him to do an entire page of problems, he looked at the page and said, "OK, that looks easy."

And it was easy. He finished in 5 or 10 minutes & got everything right.

The fact is, going back to 3A will probably be fun, especially since the Premack principle is working so brilliantly that yesterday morning (Saturday), at 10 am, C. came into my office, sat down, and said, "What do I have to do today?"

So I think we've got the think-like-a-behavior-analyst aspect of things down, which will free C. to enjoy being able to comprehend, learn, and do 3rd grade math.

That is already happening, in fact.

Yesterday, after he whipped off his one-page problem set, he said, "That Singapore method is really good."

He was referring to finding the percent equivalent of a fraction by multiplying numerator and denominator by the same number.

This is the state of his math education.

Multiplying 6/20 by 5/5 to get 30% is "that Singapore method."

this will give you some idea

When I told Ed I was going to start C. back in 1st semester 3rd grade Singapore Math, he said, "I think that's a good idea."

This brings to mind all those occasions when I wished doctors or special ed teachers would downplay my concerns. Having one's concerns downplayed seems to be a core experience of so many parents of autistic kids, and yet it has never - not once! - happened to me.

No, when I show up with my autistic kids, it's Clear the exits, here they come!

Back when I first started my teach-our-son-math project, Ed was mildly dismissive. He didn't see the big deal; C. was a smart kid; he'd learn math the same way Ed had learned math; etc.

That was irritating.

Ed has become progressively less dismissive as time has gone by, which is also irritating! By last year I was hearing regularly that C. "has no conceptual understanding at all," or "has no idea how to do X," or "doesn't know anything about Y."

I would usually say something like, "He does have some conceptual understanding," or "he does have some idea how to do X," or "he knows something about Y" -- sounding for all the world like a person failing to reflect adequately on her practice.

So, as I say, enough's enough.

I can't keep slicing & dicing it. My son does not know arithmetic, and that's that. (Does not know arithmetic and yet is one point away from "Meets standards with distinction" on the state test. Which is pretty much all you need to know about the NY state math exam.)

speaking of which

I ran across my copy of the New York State Learning Standards for Mathematics 2005 the other day:

Every teacher of mathematics, whether at the elementary, middle, or high school level, has an individual goal to provide students with the knowledge and understanding of the mathematics necessary to function in a world very dependent upon the application of mathematics. Instructionally, this goal translates into three components:
  • conceptual understanding
  • procedural fluency
  • problem solving

I happen to agree with this list.

Not one of them is true of the situation around here.

Plan B

"I stink at teaching percent" wasn't the only result of the 5 to 10 minutes I spent reflecting on my practice.*

my summer and welcome to it

initial plan for the summer: teach C. how to figure percent increase and percent decrease and get a jump on Math A (algebra 1 & geometry) for the fall. Proceed according to advice from Rudbeckia Hirta's dad:

For your summer project, he suggests that you should focus on factoring and anything with fractions. Also multiplying binomials with the distributive law (the infamous FOIL). It's better to get afew basic skills down solidly.
quickly discover C. is nowhere near the point of being able to learn percent increase and decrease. Will have to "firm up" basic percent skills first.

succumb to growing horror as realization that C. does not possess the first clue about percent dawns.

Every lining has its silver cloud

Two nights ago it came to me.

We are going back to the beginning.

As soon as we finish the Primary Mathematics 5B lesson on percent (fantastic!), we're starting page 1 of Primary Mathematics 3A and we're going to work our way straight through to 6B.

Enough's enough.

1. Whole Numbers

  • Place Values
  • Millions
  • Approximation and Estimation
  • Multiplying by Tens, Hundreds or Thousands
  • Dividing by Tens, Hundreds or Thousands
  • Order of Operations
  • Word Problems

2. Multiplication and Division by a 2-digit Whole Number

  • Multiplication
  • Division

3. Fractions

  • Fraction and Division
  • Addition and Subtraction of Unlike Fractions
  • Addition and Subtraction of Mixed Numbers
  • Product of a Fraction and a Whole Number
  • Product of Fractions
  • Dividing a Fraction by a Whole Number
  • Word Problems


4. Area of Triangle

  • Finding the Area of a Triangle

5. Ratio

  • Finding Ratio
  • Equivalent Ratios
  • Comparing Three Quantities

6. Angles

  • Measuring Angles
  • Finding Unknown Angles


REVIEW C (extra review exercises on customary measurements)

the pause that refreshes
upon reflection
Plan B

* 5 to 10 minutes because I don't like reflecting on my practice. I prefer to obsess.