kitchen table math, the sequel: 3/2/08 - 3/9/08

Saturday, March 8, 2008

here to stay

For Katelin E. Dutill, high school began as soon as she woke up each day. During her senior year she would tackle her hardest courses first, while her 20-month-old sister was still asleep. That often meant taking a math or chemistry test and then turning to the teacher's manual to grade it, or logging on to her Advanced Placement macroeconomics course. Later she might read for her literature class while keeping one eye on her sister, or conduct Internet research for her paper on the historical accuracy of F. Scott Fitzgerald's novels.

This fall Ms. Dutill, who has been home-schooled since kindergarten, is experiencing a classroom for the first time, as a freshman at Cornell University. She is one of thousands of home-schoolers entering colleges and universities around the country. The home-school movement, once considered the domain of religious fundamentalists and hemp-wearing hippies, is all grown up and going off to college.

While exact numbers are hard to come by, recent estimates by the U.S. Department of Education place the home-schooled population at more than one million, or about 2 percent of the school-age population. As recently as 20 years ago, home schooling was effectively illegal in many states. Today its students are edging toward the mainstream — and are eyed by some colleges as a promising niche market.

Home-Schooled Students Rise in Supply and Demand (private)
by Paula Wasley
The Chronicle of Higher Education
Volume 54, Issue 7, Page A1
From the issue dated October 12, 2007

onward and upward


The home-school movement, a once-marginalized segment of the educational community, is all grown up and going off to college. As colleges across the nation report increasing numbers of applications from home-schooled students, policies have been developed to evaluate these candidates. Translating years of independent study into something that resembles a high-school transcript can be tricky for the home-schooled applicant, and even more challenging for the admissions officer assessing it. Without traditional points of comparison, like class ranking and grade-point averages, colleges tend to fall back on standardized-test scores. Many require that home-schoolers take two or more SAT 2 subject tests in addition to an SAT or ACT. The Common Application, a format used by more than 300 colleges, has added a supplement for home-schoolers. Home-schooling guides now offer advice on compiling transcripts and highlighting the advantages of home schooling in application essays, as do independent consultants, who offer the same sort of college counseling available from traditional high-school guidance personnel. Often a late hurdle in the admissions process for home-schooled students is persuading colleges that they have the social smarts to get along with traditionally educated peers, although experts who have tracked home-schoolers' academic and social performance in college have found little difference between their transition and that of their peers. This lingering attitude has prompted one home-schooled student now enrolled in a large urban university communications program to liken the co-op he sometimes attended with a very small, very private school and tell classmates simply "I went to a private school."

Home schooled students rise in supply and demand
Chronicle of Higher Education, v54 n7 pA1 Oct 2007


not going away

professors who home school, part 1

This article is so great I'm going to spread it out over several posts.

If you want to bring a conversation to a dead stop on the academic cash-bar circuit, just mention casually that you are home schooling your children. You might as well bite the head off a live chicken. Most professors are likely to be appalled, and those who are not will keep their mouths shut. Still, all indications are that the number of families who home school is growing rapidly - somewhere between 5 percent and 15 percent per year, according to the U.S. Department of Education — and the number of home-schooled children now hovers somewhere between one and two million. A recent Phi Delta Kappa/Gallup poll indicates that 41 percent of families had a positive view of home schooling in 2001, as opposed to only 16 percent who did in 1985. By almost every measurable outcome, home schoolers in general outperform their public-educated peers, and many colleges are beginning to rework their admissions procedures to accommodate the growing numbers of home-schooled applicants.

For Professors’ Children, the Case for Home Schooling
by W. A. Pannapacker
Chronicle of Higher Education, v52 n17 pB14-B15 Dec 2005

I repeat.

Home schooling isn't going away.

home school factoid

The United States Department of Education last did a survey on home schooling in 2003. That survey did not ask about full-time in-home teachers. But it found that from 1999 to 2003, the number of children who were educated at home had soared, increasing by 29 percent, to 1.1 million students nationwide. It also found that, of those, 21 percent used a tutor.

The Gilded Age of Home Schooling
by Susan Saulny

Do we have data more recent than 2003?

gilded age

In what is an elite tweak on home schooling — and a throwback to the gilded days of education by governess or tutor — growing numbers of families are choosing the ultimate in private school: hiring teachers to educate their children in their own homes.

Unlike the more familiar home-schoolers of recent years, these families are not trying to get more religion into their children's lives, or escape what some consider the tyranny of the government's hand in schools. In fact, many say they have no argument with ordinary education — it just does not fit their lifestyles.

Lisa Mazzoni's family splits its time between Marina del Rey, Calif., and Delray Beach, Fla. Lisa has her algebra and history lessons delivered poolside sometimes or on her condominium's rooftop, where she and her teacher enjoy the sun and have a view of the Pacific Ocean south of Santa Monica.

"For someone who travels a lot or has a parent who travels and wants to keep the family together, it's an excellent choice," said Lisa's mother, Trish Mazzoni, who with her husband owns a speedboat company.

The cost for such teachers generally runs $70 to $110 an hour. And depending on how many hours a teacher works, and how many teachers are involved, the price can equal or surpass tuition in the upper echelon of private schools in New York City or Los Angeles, where $30,000 a year is not unheard of.

Other parents say the model works for children who are sick, for children who are in show business or for those with learning disabilities.

"It's a hidden group of folks, but it's growing enormously," said Luis Huerta, a professor of public policy and education at Teachers College of Columbia University, whose national research includes a focus on home schooling.

The United States Department of Education last did a survey on home schooling in 2003. That survey did not ask about full-time in-home teachers. But it found that from 1999 to 2003, the number of children who were educated at home had soared, increasing by 29 percent, to 1.1 million students nationwide. It also found that, of those, 21 percent used a tutor.

The Gilded Age of Home Schooling
by Susan Saulny
New York Times
June 5, 2006

Home schooling isn't going away.

rough draft

angry wife of administrator

from palisadesk

angry teacher

I think we should invite this man to join our Karen Pryor club.

see also:
yelling doesn't work

Because not just anybody can summarize the news...

Great post about the recent California homeschooling ruling over at Protein Wisdom.

"First parents are told they have no rights beyond the public school threshold, now they are told they have no right to opt out of government schooling."

Thinking about this in a larger context, Jeff G. of Protein Wisdom recalls a US 9th Circuit ruling in which the judge determined that parents "have no constitutional right, however, to prevent a public school from providing its students with whatever information it wishes to provide, sexual or otherwise.”

Friday, March 7, 2008

can o'worms

"A primary purpose of the educational system is to train school children in good citizenship, patriotism and loyalty to the state and the nation as a means of protecting the public welfare," the judge wrote, quoting from a 1961 case on a similar issue.

Homeschoolers' setback sends shock waves through state

This is going to come as news to ed schools. (scroll down for the "rah rah America" passage)

see also:
ed school prof contemplates German aggression or lack thereof
Skewed Perspective
eduwonk on the whispering campaign

Schwarzenegger Denounces Homeschool Ruling

"Every California child deserves a quality education and parents should have the right to decide what's best for their children," the governor said in a statement. "Parents should not be penalized for acting in the best interests of their children's education. This outrageous ruling must be overturned by the courts and if the courts don't protect parents' rights then, as elected officials, we will."

Schwarzenegger denounces 'outrageous' homeschooling ruling
San Francisco Chronicle
Jill Tucker and Bob Egelko, Chronicle Staff Writers
Friday, March 7, 2008

Thank You, Karen Pryor

After hearing Catherine talk about Karen Pryor's Don't Shoot the Dog, I decided it was time to give it a go. (I gotta say, Catherine, your recommendations are usually spot on.)

My local library didn't have it, but I was able to track it down via state-wide interlibrary loan. This is actually a good thing -- normally, I can buy a book or get it from the library, and then I put it off and never really get to it. But -- interlibrary loan! No renewals! Get cracking!

I started it this morning during my warmup on the treadmill, and only got about 10 pages in before I started running and it got too bouncy to read. Finished up, checked in with the family, wasn't thinking about it, then went to go take a shower.

Once in the shower -- BAM!

I got it.

When I'm depressed, I engage in "retail therapy," and I'm training myself to be depressed. When I'm nervous, I eat treats, and I'm training myself to be nervous.

What am I training my kids to do? What am I training my husband to do?

Catherine -- if you set up a discussion group, I am so in.

(This, admittedly, may seem a bit simplistic. But it was quite the "aha!" there in the shower.)

Response to California Homeschool Ruling

The HSLDA has responded as follows:
There are two appellate options at this time.

First, we have been told that the family is appealing this decision to the California Supreme Court with their California counsel.
HSLDA will file an amicus brief on behalf of our 13,500 member families in California. We will argue that a proper interpretation of California statutes makes it clear that parents may legally teach their own children under the private-school exemption. However, if the court disagrees with our statutory argument, we will argue that the California statutes as interpreted by the Court of Appeal violate the constitutional rights of parents to direct the education and upbringing of their children.

HSLDA welcomes other organizations and persons to assist with the amicus process so that a full defense of home education, religious freedom, and parental rights can be given to the California Supreme Court.

The second appellate option is to seek to have this particular decision “depublished.” Depublication is a decision that can only be made by the California Supreme Court. If the Court determines that the decision should stand, regarding this family, on the facts presented, but that the general pronouncements of law for all of homeschooling should not be determined by this case, then the Court has the option of “depublishing” the Court of Appeal’s decision. This would mean that the case is not binding precedent in California and has no effect on any other family.

HSLDA will take the lead in an effort to seek to have this case depublished.

You can sign the online petition requesting the the court depublish the ruling HERE.

UPDATE: California Homeschool Network is a good place to check in for the latest updates on the homeschooling ruling. CURRENT EVENTS OF INTEREST.

Thursday, March 6, 2008

Happy Birthday Dr. Seuss!

"I think killing phonics was one of the greatest causes of illiteracy in the country."
-Dr. Theodore Seuss Geisel in an interview with Arizona Magazine in 1981

Permission to Forget

I often ask educators in my seminars what percentage of the school year is spent teaching content students should know prior to entering their course. The answers are typically from 25 percent to 50 percent with some percentages even higher.

Permission to Forget by Lee Jenkins

Easter preparations

A brand new blog!

By someone we know and love.

Fordham's take on the upcoming Math Panel report

Fordham is in line with Concerned Parent so I'm thinking I've been too grim in my reaction thus far:

The final report of the National Mathematics Advisory Panel will be released next week, and indications are it will contain several solid proposals while also avoiding many of the contentious "math wars" issues. According to the Wall Street Journal, the panel's big recommendation for fixing the country's "‘broken' system of mathematics education" is a "laserlike focus on the essentials." Essentialists ourselves, we think that's a fine idea. And the benchmarks the panel puts forth "mirror closely a September 2006 report by the National Council of Teachers of Mathematics," which is cause for optimism because the 2006 document (unlike sundry earlier NCTM products) was well done (see here). Math panel chairman Larry Faulkner believes "it's time to cool the passions" that divide those who prefer traditional arithmetic instruction from advocates of "fuzzy math." Therefore, next week's report does not specify which instructional method is superior, nor does it take a position on whether students should use calculators in early grades. But a "laserlike focus" is fundamentally at war with fuzziness, so the panel's findings are certainly a positive development, maybe as important to math education as the National Reading Panel's were to reading.

It will be interesting to see how things develop.

Thomas Jefferson Education Consortium

Concerned Parent left this link -- hadn't heard of these folks.

Thomas Jefferson Education Consortium

I'm going to be reading....

World Math Day Sets New Record

Yesterday, March 5th, was World Math Day. Apparently over a million students from over 160 countries logged on to participate in the online competition to set a world record. The new world record is 182,455,169 correct answers. Tatania of Team Australia, took top honors with 65,199.

The response to World Math Day was so overwhelming, they have extended access through Sunday, March 19th for those already registered. If you haven't registered, however, you're out of luck until next year.

more money for ed schools

Court: Parents must have teaching credential to home school kids

LOS ANGELES (AP) — California parents who don't have teaching credentials no longer can home school their children, according to a recent state appellate court ruling.

"Parents do not have a constitutional right to home school their children," Justice H. Walter Croskey wrote in a Feb. 28 opinion for the 2nd District Court of Appeals.

Noncompliance could lead to a criminal complaint against the parents, Croskey said.


What does a criminal complaint entail?

Wednesday, March 5, 2008

the compleat constructivist

See One, Do One, Teach One

The title refers to how medical interns learn procedures. But it is also true elsewhere. From the Public Education Network Weekly Newsblast, this short article covers two studies:

The goal of a new study from Vanderbilt University was to examine whether explaining to another person improves learning and transfer. In the study, four- and five-year olds solved multiple classification problems, received accuracy feedback and were prompted to explain the correct solutions to their moms, to themselves or to repeat the solutions.

The study found that generating explanations improved problem-solving accuracy following the test, while explaining things to the mother led to the greatest problem-solving transfer. This indicates that explanation prompts can facilitate transfers in children as young as five years and reveals that it matters if the mother is listening. Even though it is possible that prompting children could be a substitute for the positive influences of a listener, there is reason to suspect that explaining to another person improves learning.

People often produce more detailed and explicit explanations and justify their ideas more when they are doing so for other people rather than just for themselves. And young people adjust their speech based on the age of the listener. It follows that explaining to others may increase motivation and also support more complete and explicit knowledge. This improved knowledge could be more easily transferred to new situations and problems.

The Vanderbilt study’s sentiments seem to be echoed in a new piece in Teacher Magazine written by Kathie Marshall (second link). Marshall begins by noting that a great deal of research has been conducted on the importance of student discussion and its prevalence in class. However, research from Martin Nystrand finds that eighth graders spend an average of 50 seconds per class in sustained conversation, with ninth graders spending only 30 seconds. So Marshall set out to see if discussion could help improve struggling students.

After four weeks, Marshall was amazed at the results of this strategy. Many ‘C’ and ‘D’ students were suddenly performing at the top of the class and were highly engaged in their work. One student wrote in her notebooks that "I like this class because in our other classes, we get in trouble if we want to talk about what we are learning."

Learning from Explaining: Does it matter if mom's listening?

Best Practices: Getting to Comprehension in the Classroom by Kathie Marshall Feb 19, 2008

National Math Panel report coming right up

WSJ has an article in today's paper.

Assuming this article is correct, I would say the panel report will net out as a good day for TERC & c. and a bad day for the science of teaching.

The group said it could find no "high-quality" research backing either traditional or reform math instruction. The draft report calls a rigid adherence to either method "misguided" and says understanding, which is the priority of reform teachers, and computation skills, emphasized by traditionalists, are "mutually supported."

Number one: there is a massive body of research showing that direct instruction is effective while discovery learning is not. (pdf file)

Number two: "Rigid adherence" to the "method" of direct instruction isn't rigid adherence. The whole point of direct instruction and precision teaching is to respond directly, rapidly, and flexibly to the actual, living, breathing students before you. This is why direct instructionists and precision teachers spend so much time taking data.

Number three: yet again instructivists are defined as "traditionalists" who obsess over "computation skills."

It's as if the only math that exists in the known universe is K-5 arithmetic.

[note: Concerned Parent thinks the report may not be as grim as I'm thinking - I hope she's right.]

A school survey that asks about tutoring

The problem of schools failing to account for the effects of outside tutoring when boasting about their test scores has frequently been brought up on KTM, and it came up again in the comments section of this post.

Well, the Bridgewater-Raritan school district in New Jersey has a survey out that asks several questions about outside tutoring. Here are some:

11. Does your child receive any form of tutoring extra help in math by someone other than a family member?

12. Why do you get extra help in math? a)
My child is doing fine in math, but I want her/him to do even better. b)
My child has difficulty with math and needs extra help. c) I’m dissatisfied with the math curriculum, and the tutoring makes up for that.

(Question 12 is important in order to learn if tutoring is being used primarily to help kids to gain an edge in competitive environments, as many schools claim.)

13. What type of tutoring/extra help do you utilize? a) Kumon, Huntington Learning Center, Sylvan Learning Center, or other professional tutoring service. b) Paid private tutor c) Extra help from classroom teacher

(In some school districts, it might be advisable to add a fourth option for question 13: Paid private tutoring from teachers in my child’s school. I was amazed to learn that this occurs; it doesn’t seem ethical.)

15. About how much does it cost you a month?

16. Does the tutor provide different techniques and strategies than those your child is learning in class?

Parents who post on this B-R forum are dissatisfied with their school’s choice of Everyday Math. This survey seems like it will capture important tutoring information for them. I would love to have my school send out something similar.

Monday, March 3, 2008

Problem Solving and Writing Proofs

in this post, Catherine asked:

What I read over and over and over again is that the pinnacle of mathematics achievement is the "ability to solve problems."

Isn't that wrong?

How does that square with "the ability to write proofs"?

I'm asking because I don't know.

From the perspective of a working mathematician, the pinnacle of math achievement is, in fact, the ability to solve problems. For many mathematicians, problems come from the real world; for others, they come from tiny slivers of the rareified math world, but in both cases, a mathematician needs a problem. A mathematician without a problem to solve is a fish out of water.

So what's a problem? Well, it's something that can be solved.

A solution is, basically, a Single Answer. A truth. A statement of fact. It might involve a lot of generalities, so that various cases break down into more answers, but if you've solved the problem, then you've solved ALL of those cases, however many there are. And if you've solved them all, then you've found a Truth--a solitariness that made them all part of your singular solution.

A proper solution is not an opinion. It's not a work of art that's open to interpretation.

A proof is a certain way of showing that your solution isn't just an opinion, isn't open to interpretation.

Basically, it's the "show your work" step. In calculus, or arithmetic, we show our work by doing calculations. But at some point, problem solving involves REASONING. And "Show your work" means explaining your reasoning.

A math problem is a kind of special problem where Everything Is Well Defined, and the goal is to Generalize As Much As Possible, But No More. In math problems, you know what all of your known knowns are, and all of your known unknowns. Those unknown unknowns aren't here--they've been defined away. That's where the proof comes in: the proof tells you what you assumed, and what you predicated your reasoning on. You don't need to say "because 3 * 5 is 15", but you do need to say "because we're working with the rational numbers" or "because 7 is prime".

Generally, a mathematician is trying to find a specific Truth that applies to a whole lot of instances of problems, because to him, that's all One Problem to Solve, and he'll be better at "problem solving" if he can show a solution to a LOT of problems at once. A proof is a really good method for doing that.

Here's how a mathematician actually solves a problem: First, he does problem solving. And after a lot of problem solving, he starts to distill what is true and common to all of his solvings. And then, if he really wants to nail the problem, so that all problem of the future problems of the same type can be solved, he is going to find the proof.

Here's a math problem: I've got a triangle. One angle is a right angle. I know the lengths of both sides of the right angle. What is the length of the hypotenuse?

The way a mathematician would solve this problem would be to evaluate what they know. They might start by trying to solve it for some specific triangles, with specific lengths. But while this doesn't seem like a lot of information, to a mathematician it is, because a lot of information here is hidden. But to a mathematician, Everything Is Well Defined. So by knowing you've got a triangle, you know a lot. And by knowing you've got a right angle, you've got a lot.

So the mathematician solves the problem first for a specific triangle. And then for a few more. And a few more. And at this point, he's sure he's onto something. But then he thinks about if he can generalize his answer, so it's true for any triangle. Well, no, he can't, he finds out. It's not true for ANY triangle, but it is true for every RIGHT triangle. And then he realizes what's true: that he can turn that "solve the length of the hypotenuse" into a proof, and the proof will ALWAYS tell him the length of the hypotenuse. So the problem solving then becomes "form this thing into a proof: a proof that the square of the length of the hypotenuse is the sum of the squares of the legs of the right angle in a right triangle."

Writing proofs is a form of problem solving where you are trying to find the Truth in a way that is convincing to those who don't know the answer just by looking at it. It's a convenient way to solve a whole set of problems at once. To a mathematician skilled at proofs, solving it for a whole set seems like less work than finding the answer for a specific instance. But you've got to know enough, and believe enough in the answer to be able to turn "solving a problem" into a proof.

Update: if you look carefully at this, you might be horrified to see something like Constructivism here. The difference is that the mathematician has an exceptional amount of mastery, and so the constructivism that they undertake is not aimless, confused, misguided, or pointless. It is carefully aimed in certain directions by their extensive (in both breadth and depth) mathematical experience.

Dyscalculia: What Is It? International Dyscalculia Awareness Day

Dyslexia is a nickname for "Specific Learning Disability--Reading", listed as 315.0 in the Diagnostic and Statistical Manual-IV (DSM-IV). Most people understand that dyslexia is a persistent difficulty with reading, despite good instruction and at least average intelligence.

There is also a Specific Learning Disability -- Mathematics (315.1, DSM-IV), known as dyscalculia.

The Dyscalculia Forum chose today as the day to raise awareness.

According to the National Center on Learning Disabilities (NCLD):

Dyscalculia is a term referring to a wide range of life-long learning disabilities involving math. There is no single form of math disability, and difficulties vary from person to person and affect people differently in school and throughout life.

Here's an index page on math and LDs from NCLD. Here's LDOnline's index page on math disabilities. Here's an overview of math disabilities in children from SchwabLearning. Anna J. Wilson's Dyscalculia Primer and Resource Guide.

There are also a couple of good videos on Youtube: start with Dyscalculia: It Is Not Only Trouble With Math.

Sunday, March 2, 2008

coming soon to a school district near you

performance based assessment !

In designing a new corner cabinet for our family room, my family and I had to figure out how deep to make it so that the TV we currently have would fit. We want the new cabinet to be the same length on each side (along the two walls). Here is an overhead view:

How long should each side of the cabinet be? Show all of your calculations and explain how you approached and solved this problem.

Exemplars K-12

And you thought kids hated math now.

Susan Wise Bauer on the Young Writer

I have to jump on Silly Old Mom's post about Susan Wise Bauer's new writing program, Writing With Ease: Strong Fundamentals. As Susan so aptly pointed out in the comments, "She just nails it."

Written language is an unnatural foreign language, an artificially constructed code. Compare written dialogue with any transcript of an actual conversation, and you’ll see that written language has entirely different conventions, rules, and structures than spoken language. The rules of this foreign language must be learned by the beginning writer—and they have to become second nature before the beginning writer can use written language to express ideas.

This is why so many young writers panic, freeze, weep, or announce that they hate to write. Try to put yourself in the position of the beginning writing student: Imagine that you’ve had a year or so of conversational French, taught in a traditional way out of a textbook, with practice in speaking twice a week or so. After that first year, your teacher asks you to explain the problem of evil in French. You’re likely to experience brain freeze: a complete panic, a frantic scramble for words, a halting and incoherent attempt to express complicated ideas in a medium which is unfamiliar. Even another year or two of study won’t make this kind of self-expression possible. Rather, the conventions of the French language need to become second nature, automatic—invisible to you—so that you can concentrate on the ideas, rather than on the medium used to express them.

The same is true for young writers. Ask a student to express ideas in writing before she is completely fluent in the rules and conventions of written language, and she’ll freeze. She can’t express her thoughts in writing, because she’s still wrestling with the basic means of expression itself.

I have become convinced that most writing instruction is fundamentally flawed because children are never taught the most basic skill of writing, the skill on which everything rests: how to put words down on paper.

Susan Wise Bauer
"Why Writing Fails"

More on Test Taking Strategies

This always gets a big laugh when I do a Singapore Math Teacher Training:

Student's Misguide to Problem Solving

Rule 1: If at all possible, avoid reading the problem. Reading the problem only consumes time and causes confusion.

Rule 2: Extract the numbers from the problem in the order they appear. Be on the watch for numbers written in words.

Rule 3: If rule 2 yields three or more numbers, the best bet is adding them together.

Rule 4: If there are only 2 numbers which are approximately the same size, then subtraction should give the best results.

Rule 5: If there are only two numbers and one is much smaller than the other, then divide if it goes evenly -- otherwise multiply.

Rule 6: If the problem seems like it calls for a formula, pick a formula that has enough letters to use all the numbers given in the problem.

Rule 7: If rules 1-6 don't seem to work, make one last desperate attempt. Take the set of numbers found by rule 2 and perform about two pages of random operations using these numbers. You should circle about five or six answers on each page just in case one of them happens to be the answer.

You might get some partial credit for trying hard.

Credit goes to Lynn Nordstrom for this piece. I've received it a couple of times in my email over the years. If anyone knows the source, I'm happy to credit them!

Looky what I got on pre-order!

In addition to the upcoming FLL4, I've put in a pre-order for Susan Wise Bauer's new writing curriculum series, The Complete Writer. It's designed to work with the First Language Lessons series. Woo hoo!