kitchen table math, the sequel: 8/22/10 - 8/29/10

Saturday, August 28, 2010


Speaking of Andrew behaving well, I've got my magic clicker out again.

source: Arcata Pet Supplies

and see: TagTeach autism

in Borders today

We picked Andrew up at camp today and learned that he had a fantastic week --- he was the best camper in the place, his counselor said.

Then he added, gesturing to his chums sitting under the canopy, "They would all say the same."


He did pretty well in the car until we stopped at Office Max to pick up poster board for the Big Calendar that's going to change everyone's life around here.

Big tantrum at Office Max & then in the car 'cause he'd spotted a Borders and wanted to go there. But since he'd managed to pull himself out of it by the time I'd made my purchases, we decided to go to Borders after all.

And guess what I found in the school section?

A Frank Schaffer Singapore Math 6B Math Practice workbook.

Plus a lot of terrific Kumon workbooks (those are the two next to Singapore Math Practice.)

The cover of the Singapore math book says, "Activities based on the leading math program in the world--Singapore Math!"

introduction to Singapore Math - Level 3 (pdf file)
Andrew comes home from camp - July 2008

Mallard Fillmore lays it on the line

The cartoonist who does Mallard Fillmore either attended ed school at one point, or knows people who are in education:

reading on iPhones and Kindles

Speaking of dyslexia and visual deficits, I never got around to posting this link:

My iPhone has revolusionised my reading

A friend of mine tells me that her child, who has dyslexia, reads much more easily on the Kindle.

dyslexia is visual not phonological - ?

A few years ago, when I asked Daniel Willingham what journal I should read on the subject of cognitive science, he recommended Trends in Cognitive Sciences.

Yesterday, as I was trawling the journal for articles on habit learning, I came across an article from January 2010:  Dyslexia: a deficit in visuo-spatial attention, not in phonological processing by Trichur R. Vidyasagar and Kristen Pammer.
Developmental dyslexia, a specific difficulty in reading despite adequate learning opportunities, affects from 5 to 10 per cent of the population [1], but there are many manifestations of reading failure (Box 1). The etiology of dyslexia itself has been hotly debated for a long time. Theories have ranged from the reading disorder being a high-level learning disability, to a visual perceptual defect. Although it is generally recognized that a majority of poor readers have severe problems in phonological awareness [2,3], it is still an open issue whether the causal deficit in dyslexia is necessarily phonological. The debate is particularly timely in light of recent reevaluations – especially in the USA, Australia and UK – of how children learn to read.

In this paper, we present evidence for an alternative possibility, namely that a fundamental defect in the visual pathways, with or without a corresponding defect in the auditory system, can potentially cause a cascade of effects that can ultimately manifest as a reading problem, including phonological impairments. Understanding the mechanisms underlying dyslexia allows better informed policy making with regard to teaching and remedial intervention.


Pre-reading phonological skills predict later reading failure, and phonological interventions have been demonstrated to be successful [2]. However, there are a number of reasons why poor phonological coding might not be the whole story, or even be an etiological factor in dyslexia. Some cases of dyslexia are clearly not phonological, for example where the reading errors are for irregular words, not non-words, and impairments in reading non-words are not always matched by deficits in phonological awareness [4,5]. There are reports of children [5,6] and adults with brain damage [7,8], who have difficulties in non-word reading but nevertheless exhibit good phonological awareness. Such evidence should, at the very least, lead us to question the causal link between a phonological deficit and dyslexia.


Misordering of letters and reversal of letters in a word are common complaints from dyslexic readers, and sensitivity to spatial sequencing of the constituent components of text-like object arrays predicts reading in adults [12] and children [13]. Such difficulties in ascertaining the sequence of letters in words cannot be easily explained by phonological deficits. Studies of neurophysiological bases of pattern and object recognition indicate that such sequencing of letters is a non-trivial problem for the brain.

Trends in Cognitive Sciences Vol.14 No.2

reading on iPhones and Kindles

Friday, August 27, 2010

is Saxon Math different?

Jean wrote:
It's my understanding that the new look also reflects a new owner and a different approach--not so "Saxon-y." Some folks are quite annoyed about this. I'm not sure what I'll do--my daughter is in 76 and I'm a fan, and I'm wondering if I'm going to like the new editions as much.

Art Reed wrote:
I have never seen a "Math Cat" before although several of my senior high school calculus students thought they were "Cats."

If you would take a look at the January 2010 news article at Using Saxon Math I believe your question about which editions of John Saxon's books are still valid - and will be for several decades - will be answered.

If you still have questions you can reach me at my office at (580) 234-0064 (CST) during normal office hours.

true or false

(warning: four-letter words)

In The Know: Are Tests Biased Against Students Who Don't Give A Shit?

thanks to Susan S!

Cliff's Notes to the rescue

This image, from the Cliff's Notes page on Regular Pyramids, showed me how to solve the Blue Book problem I was stuck on.

The problem:

The pyramid show above [not drawn to scale] has altitude h and a square base of side m. The four edges that meet at V, the vertex of the pyramid, each have length e. If e = m, what is the value of h in terms of m ?

(A) m ÷ square root of 2
(B) m x square root of 3 ÷ 2
(C) m
(D) 2m ÷ square root of 3
(E) m x square root of 2

answer: A

source The Official SAT Study Guide, 2nd edition, p. 401

help desk - Blue Book

I can't do problem number 20 on page 401 in the Blue Book. At least not so far.

If you have the book, can you post the solution in the comments threat? I need the solution, not the answer: I have the answer. Have not yet tried to reverse engineer from the answer to the solution. That's next.

I'll scan the problem and post later on.


update - 10:33

solution here

The Official SAT Study Guide

Thursday, August 26, 2010

new look

Googling Saxon Math a couple of posts back, I learned that the Saxon books have "a different look."

Barb's People Builders

They sure do.

My books look like these.

Buy used Saxon Math

I need a cat.

VR on using backgammon to teach probability

VR wrote:
I have been playing chess with my son for a few years. Chess is deterministic. In order to introduce him to probability concepts, I have started to play backgammon with him and bought him the "Backgammon for Dummies" book, which uses probability concepts to explain what is good play. Other games, such as blackjack and poker, can be used to teach probability. Many good games players can calculate probabilities well, even if they never read a book using the mathematical terminology Allison mentioned. Maybe books on those games can be used to teach probability in a palatable way.
Great minds think alike!

At some point, looking for self-teaching resources on probability, it came to me that I ought to stop trawling Amazon for introductory books on probability and start looking for introductory books on  card-playing.

Or card counting - ?

fyi: A lot of the Dummies books are terrific, I think. The book on public relations is very good, and I've just bought Grammar for Dummies because Stanley Fish said he likes it.

A few years back, I had a scheme to purchase all of the Dummies books and dedicate an entire bookshelf to them, the way people used to buy World Book Encyclopedias and give them pride of place.

Backgammon For Dummies

Allison on why there is relatively little help available for people self-teaching probability

I believe there are several reasons why there is so little help for discrete probability at this [beginning] level:

1. It requires significant mathematical maturity to even begin to understand what's going on.

2. Almost no one understands probability anyway.

3. Even if you do understand, it is extremely difficult to be careful and precise enough to never make a mistake in describing the problems or wording the solutions.

4. Most of work in discrete probability rewards cleverness. Few methods for tutoring individuals, or supporting individuals in their own learning can teach cleverness.

I'll elaborate on these in another comment.

But this is where you should start: Schaum's Outline of Theory and Problems of Probability (2nd edition)

as smart as a 5th grader

Competition Math: for Middle School (Volume 1)
p. 48

More evidence that "repeating the same lesson over and over" works as well as Howard Gardner's Chinese teachers said it does. I knew how to solve this problem within a few seconds of looking at it, and the reason I knew how to solve this problem within a few seconds of looking at it is that I used the difference of two squares to rationalize denominators many, many times while working my way through Saxon Math.

Competition Math: for Middle School (Volume 1)

ego depletion

The Unbearable Automaticity of Being
John A. Bargh, Tanya L. Chartrand
American Psychologist
1999 Volume 54, Issue 7 (Jul)
Pages 462-479 

Apparently eating radishes instead of available chocolates is a bad idea for any number of reasons.

what do parents think?

This is interesting:
Overwhelming numbers of the public link job opportunities and economic success to education preparation, but almost one-half of parents believe today's graduates are less prepared for work or college than they were.
2010 survey - PDK (pdf file)


I would have predicted that the general public feels this way but not necessarily parents specifically.

I wonder if a majority of parents say students in their local schools are better prepared than students coming out of other schools --- ?

PDK poll

Quick post before I get back to work.

A few weeks ago we were talking about whether there is opposition to charter schools in suburban districts. Given the comments people left, I believe there is.

So it was interesting today to see that the new pdk poll includes this bullet point in the press release (pdf file):
We like public charter schools more every year! We’d be happy to have new public charter schools in our communities and more throughout the United States. 
Phi Delta Kappan was once described to me as the flagship of the constructivist movement; it's got to be one of the most important journals in public education. If pdk is phrasing a 'pro' finding on charter schools this way, I take that as a sign.

Wednesday, August 25, 2010

Math in Ukraine - some impressions from my trip

I spent July in Ukraine, visiting my family and friends. My son (now almost 9) finally realized that mom and dad are not the only relatives he has. Anyway, from our observations of life of kids (school age) and interactions with people, a few things really stand out. And math is one of them.

First, for my son, the trip was educational in many respects. Learning to multiply two- and three-digit numbers in his head seemed easy for him. My husband's grandmother, 73 years old, a teacher for 50 (!) years and still going - taught my son the method of mental multiplication in less than an hour. And mind you, she teaches high school language and literature (both Russian and Ukrainian). My son loved it!

Second, one really needs to calculate fast there...(I forgot that in all these years in the states). Food is bought primarily at the farmer's markets. And any "sales person" (most often, a farmer's wife or a kid), will calculate the price for "2kg and 400g of tomatoes" in their heads. And you'd better be as fast as they are, or you may be cheated. I felt pretty safe sending my son to do shopping - at least I was sure he can calculate the right change.

Third, my son played with some random kids - in the streets, on the beach, -some were younger, some were older. But even the younger kids act and look more mature then my son. All of them could do multiplication, division, addition, subtraction fast and efficient in their heads. And most of the kids are really physically fit. They run, climb, walk. My son could not compete with them (and comparing to his classmates here, he is pretty skinny and well trained!)

Fourth, Ukraine changed the years of schooling to 11 (they tried 12 for at least 5 years); kids still can officially finish their schooling after 9th grade. Those who do not want to continue being in school, can go to vocational/technical schools or start working as they are.

Fifth, the official workload of a teacher (full-time position) counting the time in-from of the students is... 18 hours a week! The rest of the time is for planning, meetings, collaboration. The workday ends "as soon as everything is done". Kids are in school usually until 1 or 2 pm. No more than 7 periods a day (and that's more than I had when I was in school - never more than 6!) .

Schedule is different for every day of the week; the courses are still taught in vertical strands - physics begins in grade 6 and continues until grade 11, twice a week etc. Algebra begins in grade 6, along with geometry ( but taught as separate subjects) . I think they added more of calculus to 11th grade, but kept the earlier grades with the same sequence/pace as I had.

By any means, I was glad to learn that elementary/middle grades education is still solid in Ukraine. Because later -well, it too late!

(By the way, Ukraine does standardized testing - in 11th grade, math and language/literature. The results are submitted to colleges/universities. The results count for kids, but not for teachers. As my husband's grandmother put it, in the last grades, it is too late to teach things that were supposed to be learned earlier. But for the promising kids, the kids who showed that they want to continue their educations - the teachers ensure that the test are passed well (if you know what I mean).

As we returned to the US, unfortunately (or fortunately), I keep seeing and comparing. My son wanted to take karate classes. But I do not see the instruction/learning. I see "Mommy's treasure" - Good job! Did you have fun, my dear? And I look at that "dear" and at my son and I see them doing a lousy kiba-dachi and fooling around. And I really wish that instructor would yell or better hit my son (well, it's karate, you do things for a reason!) so he learns fast and effective - humility, obedience, and the right position. Well, we'll get home and my son will owe me 40 push-ups.

Art of Problem Solving

I've been only dimly aware of the Art of Problem Solving web site for lo these many years, so I'm glad kcab steered me over to them web site today.

Here's an article on AoPS from 2007 (pdf file).

Week 7

Debbie Stier

How can it be Week 7 already?

I really need that Big Calendar.

Debbie Stier's big calendar
the big picture
blank calendar template (pdf file) 
self-charting increases motivation 
what is one year?  

arithmetic is habit-forming

Debbie Stier is having the same experience I did when I first started reteaching myself math.

instructional practice

I was looking for an old ktm post about Kumon this morning, and when I found it I rediscovered the concept of instructional practice, meaning practice that teaches.

I think that's probably what the Arlington Algebra Project's sections on probability provides.


Are there resources you like for teaching oneself beginning probability?

Someone (either lgm or lsquared, I think) recommended the Arlington Algebra Project, which looks like it's probably terrific for my purposes - though it lacks an answer key, which is not good.

I'll also be using this site (thank you!)

Anything else?

I wonder if I should take the AP statistics course at ALEKS.


kcab recommends The Art of Problem Solving, which turns out to have a course that sounds like exactly what I need: Introduction to Counting and Probability

Thank you!

spaced repetition

Because I remained in the third form [grade] three times as long as anyone else, I had three times as much of sentence analysis, learned it thoroughly, and thus got into my bones the structure of the English sentence. The essential structure of the ordinary English sentence is a noble thing.

Winston Churchill
quoted in Sentence Composing for College

spaced repetition
spaced repetition and the chorus effect

in today's mail

from the 25th Anniversary edition of the Harvard Education Letter:
[Jerome Bruner’s “Man: A Course of Study”] was my first deep exposure to progressive education, and I liked what I read, heard, and observed: the hands-on experiences, the deep exploration of inviting topics, the belief that the questions asked are as important as their answers, and that the reasoning behind questions and answers is crucial. I became a card-carrying enthusiast of progressive education, American style.


As one personally committed to progressive education, I was well prepared for my initial visits in the early 1980s to the small northern Italian city of Reggio Emilia, home of what are widely regarded to be the finest preschools on the planet. Initially launched in the post-World War II era, these municipal school operate on the assumption that children’s natural curiosity should be the centerpiece of education. An object (or experience) that captures the children’s attention—a shoe, a fax machine, a rainbox, a birdhouse, or a carved lion at the central Piazza—can become the focus of curriculum for weeks, even months. As the young students explore this fertile object, they have the opportunity to draw on the “hundred languages” that are the birthright of every child—their senses, available media and symbol systems, the arts, the sciences, the natural world—to gain relevant insights into the various spheres of life in which these objects occupy a role. What is learned and created each day becomes the starting point for the following days’ activities. And these learnings are publicly displayed – or “documented”—so that teachers, parents, and other children can share in them and build on them.

Alon with other educators, including my mentor Jerome Bruner, I have visited, studied, and learned from the Reggio Emilia approach for 30 years. This flagship educational enterprise has changed my mind about what is possible to achieve with young children, the importance of group—as opposed to individual—learning, and the role that can be played by documentation of learning over days, weeks, and even longer stretches of time. I have also learned how a single educational experiment—conceived 50 years ago by a determined grouop of citizens—can affect practices all over the world.

Yet shortly after visiting Reggio Emilia for the first time, I undertook a series of trips to China. There I found that my progressive educational philosophy—Italian as well as American style-was sharply challenged. In classrooms in major cities around the country, I saw the same “prefabricated” lessons presented in essentially the same manner. Little latitude was permitted to either teacher or student. Indeed, in one college class in psychology, I was shocked to observe obviously talented students simply repeating the same lesson over and over. When I challenged the teacher about what seemed to be an obvious waste of time, we had an unproductive conversation that she finally terminated with the terse remark, “We’ve been doing it this way for so long that we know it is right.”

Yet I was also surprised by some of the positive results. In a first-grade art class, I watched the students slavishly copy a model over and over. I wondered whether these six-year olds could use their developing skills to portray an unfamiliar object—in this case, an Italian stroller that they could not possibly have seen before. Although the teachers protested when I proposed this assignment, I stuck to my guns. To everyone’s astonishment, the students were able to draw the stroller with considerable skill—far greater aptitude than would have been shown by most American youngsters. This experience convinced me that an effective education can begin with a singular focus on skill building rather than on the play of unfettered imagination, and that the skills that are developed, often precociously, have the potential to be mobilized to more creative ends.

From Progressive Education to Educational Pluralism
by Howard Gardner
Harvard Education Letter
September | October 2010

Sunday, August 22, 2010

SAT question

Of 5 employees, three are to be assigned an office and 2 are to be assigned a cubicle. If 3 of the employees are men and 2 are women, and if those assigned an office are to be chosen at random, what is the probability that the offices will be assigned to 2 of the men and 1 of the women?
Answer Choices:

(A) 1 / 3
(B) 2 / 5
(C) 1 / 2
(D) 3 / 5
(E) 2 / 3