kitchen table math, the sequel: 11/11/07 - 11/18/07

Saturday, November 17, 2007

let's not and say we did

Dear Visitors,

As you browse through this site, reading the text and looking at the images of students busy learning and interacting, it should become evident that the Trevor program strives to engage students in activity-based learning. Encountering new information in this environment, students are at the beginning of their journey as life-long learners. The Trevor faculty and administration design programs that keep students moving forward, absorbed in every moment. Whether they are learning about the value of sharing or sharing their interpretations of a Shakespeare sonnet, they are actively discussing, writing, drawing, communicating, asking questions and embracing each new opportunity. At Trevor, teachers ask questions and hesitate to provide easy answers. They design experiences, environments and the means by which students may take ownership of their own knowledge, and answer questions for themselves. Students learn how to learn.

We hope that these pages can shed some light on our very comprehensive and exciting programs.

30,000 bucks a year for activity-based learning.

I think not.

bonus points for technology!

An important element in support of these curricular and learning goals is the presence of sophisticated technology....With growing awareness of the educational power of the Internet and information technology, teachers are incorporating more of its content into their curriculum in every subject area. Every High School faculty member has a laptop computer, thus enabling students and teachers to broaden their communications beyond the classroom and Common Room.

Trevor Day School

High-Tech Heretic by Clifford Stoll

clicker training for officemates

The Office - The Jim Trains Dwight

Posted Feb 06, 2007

Using Pavlov's teaching theory, Jim teaches Dwight to want mints.

Cat chapter finished.

Horse chapter commenced.

My editor said last week, "You've hit your stride." Ed said, "No, you've hit your sprint."

resolution: I am reforming my work habits.

I feel confident I can do this because between the last book and this one I reformed half my work habits. So it can be done.

Next time I'm reforming the other half.


Clicker training is going to be one of those life-altering discoveries, I'm thinking. Andrew needs clicker training pronto, and I'm trying to figure out whether I could use it to teach C. how to factor trinomials in the form of ax^2+bx+c. Seriously. I'm pretty sure this is possible.

I wonder if you can clicker train yourself.

Friday, November 16, 2007

A young writer's work in progress

Just when I was wondering if my daughter's writing program was taking her somewhere, it all came together in Lesson 11, Writing a Complete Essay. When she got to Lesson 12, Evaluating Your Essay, I was feeling pretty good about choosing Grammar & Writing 6 by Curtis and Hake.

In Lesson 10, she was provided with the thesis statement "I can do things to make the world a better place." After brainstorming for supporting ideas, she finally put it all together in Lesson 11 and by Lesson 12 had come up with the following:

Even though I may be only nine years old, I can make a big difference in this world. There are small things I do that will make the world a better place.

One important thing I do is protect natural habitats. I do not feed wild animals because it disrupts the balance of nature. I pick up my trash and sometimes even clean up other people’s litter. I also try not to disrupt the order of natural habitats by using paths instead of trampling over plant life when I am outside.

When I am inside, there are certain things that I do to conserve natural resources. I turn off lights when I do not need them. I make sure I turn off the faucets when I am finished using them. One other thing I do is keep my showers brief so that I do not waste water.

Recycling is yet another important way to care for our environment because it saves trees, water, energy, and landfill space. I carefully sort out items that can be recycled and place them in a special bin. I try to find new uses for things instead of buying something new. Finally, I use recycled paper and biodegradable products whenever possible.

When all is said and done, taking care of our planet is a huge responsibility but I am able to do things that make the world a better place. I can protect natural habitats, conserve natural resources, and care for our environment by recycling. If I can make a big difference by making small changes, maybe you can too.
This is a huge milestone for my very reluctant writer. She is extremely bright and very verbal, but she doesn't consider herself a writer. This process guided her through each step of the writing process in a way that makes sense. She doesn't just know that she's supposed to write an introductory sentence, topic sentence, supporting statement, etc., she knows what this means. She also understands the importance of transitions, sequence, and the level of detail that come into play in writing an essay. Hake has unraveled the mystery of writing by providing her with an easy to follow recipe. As far as I can see, it's working quite well so far.

I particularly liked the fact that even after Lesson 11 when the essay was quite good, in Lesson 12 she was asked to go back and evaluate her writing critically because writing is always a "work in progress." Mary Hake reminds the young writer "The knowledge that writing is a process should guide your thinking throughout the construction of an essay." She then goes on to prompt the writer with questions which help the self-evaluation process move along.

As a disclaimer, I have to say that I don't believe the writing component would work as well without the grammar, dictation and journaling exercises. There is a sequence to the lessons and we have been following the suggested schedule. My daughter also consistently outlines and summarizes information in her world history lessons and this has fine-tuned her writing further. Book reports on classic literature are part of her studies as well. Nevertheless, I don't believe she would have been able to write such a logical, clear and well-thought out essay pre-Hake Grammar & Writing.

My next task as her teacher, is to finish reading Writing to the Point by Kerrigan. From what I understand so far of Kerrigan's approach to teaching writing, it seems to fit in very well to the Hake approach to teaching a much younger writer.

Who knew that learning to write could be so logical and presented so very clearly.

Grammar and Writing
Christie Curtis & Mary Hake

Fair Use for Public School Teachers

Cross-posted on

fair use in the classroom

A month ago I wrote about a Florida A&M University law professor's decision to use questions out of a test-prep guide for a significant portion of the final exam. In Using Test Questions from Prep Guides - Ethical, Legal? I said:
"Reproducing questions from review books happens frequently in New York. We have state-issued curricula for most all high school subjects with a statewide final exam. Barron’s publishes review books for these state exams and it is very common for teachers to make unit tests from questions taken directly from the review books. No one really complains [other than that it suggests a classroom teacher is “teaching to the test”], but I find it highly unprofessional and unnecessary at the post-secondary and especially at the law school level."

I wanted to elaborate a bit on the rules by which New York State teachers - and those nationwide - must abide when using someone else's material.

There are four basic conditions to meet fair use requirements [from the House Judiciary Subcommittee]:

1. Brevity - a single poem, passage, short story, etc. is used;

2. Spontaneity - the material is included close to the time when the material is used;

3. Cumulative use - "generally no more than nine occasions per teacher per term"

4. Notice of use - credit to the author must be given with year of publication and appropriate copyright symbol.

Brevity. The intent of fair use is, generally, grounded in brevity. Teachers [and anyone creating instructional content] depends on passages, illustrations and small pieces of work to develop curriculum. Most K-12 teachers don't have a problem here.

Spontaneity. I find this a bit troubling. How many times have we chided students for leaving their work until the last minute? But if you're a teacher in New York, go for it - your use of copyrighted material is fair if you put yourself in a position that necessitates a shortcut.

Cumulative use. I've got to admit, I'm a bit puzzled by 9 uses as a threshold - it seems arbitrary, though I doubt this is ever policed. How one could use the same material 10+ times in a term and still profess that one is advancing a student's course of study at a reasonable pace is beyond me.

Notice of use. This is where teachers usually stumble - they just don't bother to credit the original authors. But satisfying point #4 is easy provided that you're committed to respecting the intellectual property of others. Author's name, the larger source, publication date, copyright symbol - the end.

I don't expect teachers or anyone else to document ad nauseum every bit of intellectual property they decide to use [it's faddish in the ed-tech community to cite image sources to the nth degree on blogs, something which I don't bother to do unless it's real intellectual property/art]. But showing the most basic respect for another's work by labeling it properly is a necessity - it shows our students that their future work will be credited and that their teacher is a competent scholar.

Browse a detailed summary of Basic Books, Inc. v. Kinko's Graphics Corp. if you're so inclined. And if you can't be bothered, at least take those four baby steps that fair use requires. It isn't hard.

from short term memory to working memory

This is a terrific short summary of the transition from short term memory, the concept I was taught in college, to today's notion of working memory.

I don't know whether this is the best account of how this idea has evolved, but it does coincide with the changes I've seen over the years.

I heart Clippy

I may be the only person on the planet who liked Clippy. (scroll down)

I wonder if my computer would go sprong if I installed the Clippy applet.

Also, I have no idea how to lock my computer. Good thing I don't work in an office. Of course, if Andrew carries on the way he's been carrying on, any day now he'll start goating people's computers.

That will be the last straw.

finding the basic principle

What about teachers? Were there teachers who were pretty important to you?

Nora Ephron: Yes. I had a couple of great, great teachers. The teacher who changed my life was my journalism teacher, whose name was Charles Simms. I always tell this story. I love it. I had already decided that I was going to be a journalist. I didn't know why exactly, except that I had seen a lot of Superman comics. Lois Lane and all of those major literary characters like that, but Mr. Simms got up the first day of class, and he went to the blackboard, and he wrote "Who, what, where, why, when, and how," which are the six things that have to be in the lead of any newspaper story. Then he did what most journalism teachers do, which is that he dictated a set of facts to us, and then we were all meant to write the lead that was supposed to have "who, what, where, why, when, and how" in it.

He dictated a set of facts that went something like, "The principal of Beverly Hills High School announced today that the faculty of the high school will travel to Sacramento, Thursday, for a colloquium in new teaching methods. Speaking there will be Margaret Mead, the anthropologist, and two other people." So we all sat down at our typewriters, and we all kind of inverted that and wrote, "Margaret Mead and X and Y will address the faculty in Sacramento, Thursday, at a colloquium on new teaching methods, the principal announced today." Something like that. We were very proud of ourselves, and we gave it to Mr. Simms, and he just riffled through them and tore them into tiny bits and threw them in the trash, and he said, "The lead to this story is: There will be no school Thursday!" and it was this great epiphany moment for me. It was this, "Oh my God, it is about the point! It is about figuring out what the point is." And I just fell in love with journalism at that moment.

I just fell in love with the idea that underneath, if you sifted through enough facts, you could get to the point, and you had to get to the point. You could not miss the point. That would be bad. So he really kind of gave that little shift of mind a major push. I just fell in love with solving the puzzle, figuring out what it was, what was the story, what was the truth of the story.

interview, Nora Ephron

Ed told me that when his first wife was learning to do radio journalism her boss kept telling her she was "backing into the story." Ed remembers being fascinated by that: backing into the story.

Print journalists call it burying the lede.

She would go into the radio booth and read the text she'd written; then the guy would tear it apart.

Temple has a wonderful way of talking about not backing into stories and not burying the lede and such. She calls what she learned to do in college find the basic principle. Temple figured this out on her own. She would have a mass of facts, figures, and concepts she had to master for a course and her working memory was too limited to hold more than a couple of them at the time, so she had to find a work-around.

Her workaround was to find the basic principle, the one idea from which all the other ideas flowed logically. Then that one idea would work as a cue, helping her to remember all the other ideas.

Of course, everyone's working memory is severely limited. The idea used to be that working memory could hold "the magical number 7 plus or minus 2" items. But these days people are saying the magical number is closer to 3 or 4.

I don't think Temple's working memory is any more limited than a typical person's; I think the real problem is that her working memory is slower. She told me once that the reason she can't do mental math is that if she's adding 12 to 29, say, by the time she's able to close the 9+2 "window" in her mind's eye (another term for working memory), she's forgotten 10+20. If she does manage to retrieve 10 + 20, she's forgotten 2+9, carry 1.

I back into my story all the time. Then some editor will tell me to fix it and I do. This has happened enough times that these days, after finishing a draft, I try to figure out how much introductory stuff has to go. It's not easy.

It's gotten easier since I discovered William J. Kerrigan's Writing to the Point. Which reminds me. I have to scan some more of Kerrigan's book and get it posted.

Judging by the essay Concerned Parent's 9-year old daughter just wrote, I'd say Hake's Grammar and Writing the closest thing we've got in print to Kerrigan. Hake wrote the Saxon Math books 5/4 through 8/7, then decided to write a "Saxon Grammar," too.

The Magical Number 4 in Short Term Memory: A Reconsideration of Mental Storage Capacity
by Nelson Cowan, 2001

William J. Kerrigan and Allan A. Metcalf
Paperback: 192 pages
Publisher: Harcourt; 4th Ed edition (January 1987)
Language: English
ISBN-10: 015598313X
ISBN-13: 978-0155983137

Thursday, November 15, 2007

NCLB, ESL and Long Division

From US News & World Report

The fifth graders are learning division in small groups in the Fairfax County, Va., classroom, but Carolina, a girl from El Salvador who speaks broken English, is having a bit of a hard time. She has figured out that 162 divided by 12 equals 13 with a remainder of 6, but she can't come up with a story to write that shows she understands the problem. "No entiendo," she whispers to her friends. I don't understand.

She's struggling, not because she doesn't know the math, but because she can't come up with a story. This is so wrong-headed on so many levels, not the least of which is what it is doing to this girl's confidence in her own mathematical abilities, which could (in another time and place) prove to be exceptional.


Tuesday after class, I met Martha. She's retired, in her 60s, she's a tutor, and she's misplaced (to say the least). I'm glad she's volunteering, but she has no experience teaching ESL, and she has no idea what she's doing (which she readily admitted). I suggested that she move to the literacy program for native English speakers.

Anyway, Martha wanted tips, and she veered into grammar, and then into "We should go back to teaching Latin so people will learn grammar." We had a long discussion about this. There's no point reproducing it here, but if you're interested, my abbreviated
response is here.

Now, I have about 20 more essays to read and comment on.

Newsflash – Middle-schoolers hate math homework

For Catherine, and all the other afterschoolers out there:

A national Raytheon survey found that 84 percent of middle school students would rather clean their rooms, eat vegetables, take out the garbage and to go to the dentist than do their math homework.

From Discovering the magic of math

Wednesday, November 14, 2007

Tuesday, November 13, 2007


I just love it when the directions for grammar exercises -- written by university English faculty, and posted on university servers -- are themselves ungrammatical. See here, specifically the second clause of the second sentence.


Monday, November 12, 2007

Sundseth on fractions

This is funny.

I was Googling images of fraction multiplication and I found this. (Look down towards the middle.) The funny thing is, Doug didn't make that drawing. That's Carolyn's.

help desk - number pattern

Primary Mathematics Intensive Practice 3A, U.S. Edition
p. 8

I absolutely cannot see what comes after 628.

Having looked the answer up in the back of the book, I absolutely cannot see why 862 should come after 628.

I hate number patterns.

Sunday, November 11, 2007

string theory is me

Andrew is downstairs watching a show on string theory on C's computer.

Last night he was watching something on relativity.

Andrew still can't talk; can't do math (that I know of); doesn't appear to read much beyond the basics.

But he's watching string theory.

Of course, maybe that makes sense. I can talk, do (some) math, and read way beyond the basics, but when it some to string theory, I have no clue. Maybe unlike Andrew I'm spending too much mental energy on all that other stuff to have anything left over for physics.

my dream school


The Browning School is known for being small, structured, and focused. Classwork and assignments are framed around relatively short timelines, with clear, consistent, expectations. The atmosphere is one of adults in charge, teacher directed- child focused. The curriculum is a medley of constantly evolving research and material as well as traditional programs that have always been a part of the Browning experience. The faculty work together to create an interdisciplinary course load that reinforces and builds upon a sequential academic experience.

Mission Statement

Founded in 1888 as a college preparatory school for boys, The Browning School continues its commitment to the goals of John A. Browning: the pursuit of academic excellence and a lifelong love of learning, the belief in the dignity of the individual, the development of personal integrity and responsibility to the broader community.

The Browning boy develops amid these values: the Browning alumnus is a good citizen, sensitive to the needs of others, respectful of divergent yet informed opinions.

He is, in the best sense of the word, a gentleman.

The Head of the Upper School was a journalist.

The Browning School

help desk

I'm in the thick of my cat chapter, and I'm stumped.

What would laterally compressed canines be? I'm assuming this phrase means canines that are squooshed together in some way -- that is, there's a smaller gap between the two canines in a cat than in a dog -- but I don't know.

Cats are preeminently adapted to be predators. They have laterally compressed canines, rooted in mechanoreceptors, that hold food and permit them to dislocate the vertebrae of prey in one bite.

Clinical Behavioral Medicine for Small Animals
Karen Overall
St. Louis: Mosby, 1997
page 55

I'm not managing to visualize this at all.

Overall's book is fantastic, btw. Expensive and fantastic.

The other marvelous book I've found is Dennis C. Turner & Patrick Bateson's The Domestic Cat: The biology of its behaviour. The subtitle is a bit misleading, because the book has far more to say about behaviour than biology, making it far more interesting than you would imagine from the title. You can look at the book on Google (previous link); here's the Cambridge Press page.

Last and also least if you're trying to write a book about animal welfare, We Are the Cat is pure pleasure. Brilliant writing.