<body><script type="text/javascript"> function setAttributeOnload(object, attribute, val) { if(window.addEventListener) { window.addEventListener('load', function(){ object[attribute] = val; }, false); } else { window.attachEvent('onload', function(){ object[attribute] = val; }); } } </script> <div id="navbar-iframe-container"></div> <script type="text/javascript" src="https://apis.google.com/js/plusone.js"></script> <script type="text/javascript"> gapi.load("gapi.iframes:gapi.iframes.style.bubble", function() { if (gapi.iframes && gapi.iframes.getContext) { gapi.iframes.getContext().openChild({ url: 'https://www.blogger.com/navbar.g?targetBlogID\x3d12969692\x26blogName\x3dLearning+Strategies\x26publishMode\x3dPUBLISH_MODE_BLOGSPOT\x26navbarType\x3dBLUE\x26layoutType\x3dCLASSIC\x26searchRoot\x3dhttp://larrydavidson.blogspot.com/search\x26blogLocale\x3den_US\x26v\x3d2\x26homepageUrl\x3dhttp://larrydavidson.blogspot.com/\x26vt\x3d53093167121198245', where: document.getElementById("navbar-iframe-container"), id: "navbar-iframe" }); } }); </script>

Sunday, October 30, 2005

We so-called experts have been wrong for almost 7 years

Those of us who teach math and computer science have been proud of our knowledge that a kilobyte is really 1024 bytes, not 1000. So “Y2K” doesn’t really refer to 2000 but to 2048. Similarly, we believe (and teach) that a megabyte is really 220, or 1,048,576 — not 1,000,000.

But it turns out that we’re all wrong. Furthermore, we’ve been wrong for almost seven years! According to the National Institute of Standards and Technology (the authority on these things), the international standard since December, 1998, has been that the kilo- prefix means 1000. The correct prefix for 1024 is actually kibi-, not kilo-.

Similarly, mega- and giga- are powers of 10, but mebi- and gibi- are powers of 2. You can have two tries to guess what the “bi” syllable stands for in kibi-, mebi-, and gibi-.


Saturday, October 29, 2005

Pythagorean Theorem in so-called real life

Reading this case might prove helpful for some students who think that math is useless in real life (at least those who plan to be lawyers or drug dealers).

But shouldn’t the court have used Taxicab Geometry for its distance metric? (I think that’s equivalent to what the defendant was arguing.)

(Thanks to the pseudonymous Rudbeckia Hirta for this link.)

Labels: ,

Friday, October 28, 2005

Irrationality considered harmful

“I refuse to deal with irrational numbers until they've calmed down,” says one Jeff Schult, who claims that math is a cult.

Read the whole article. I hope it doesn’t represent what Weston students think about math.

We shouldn’t use the words “irrational” and “imaginary” to describe numbers.

Labels: , ,

Thursday, October 27, 2005

Should honors classes be open to all?

At least on political grounds, it’s tempting to argue that honors and AP classes ought to be open to all who wish to enroll in them. It’s also tempting to argue it on educational grounds. We believe in giving everyone a chance; we believe that advanced math courses should be “a pump, not a filter”; we believe that all students should be encouraged to excel to the limit of their ability and interest.

Those are all legitimate beliefs. When I say “we,” I include myself. But it’s only one side of the picture — one that’s overwhelmed by the other side.

First, let’s look at how Weston does it, since that’s what I know best. Every spring (well, winter actually, but that’s another story), teachers make a course recommendation for each student. Sometimes these recommendations are made in consultation with the student, sometimes not. Occasionally a teacher who is on the fence will equivocate; he’ll say, ““I am recommending you for Math 5, but if you really want to take AP Statistics you can do that as well (or instead of Math 5).”

The student, of course, might disagree with the teacher’s recommendation. Suppose she wants to get into an honors or AP course but the teacher has recommended college-prep. If she is proactive, she will approach the teacher and attempt to change his mind. If that is unsuccessful, there is a complex override procedure through which she can get into her desired course without the teacher’s recommendation. The procedure requires a sequence of meetings involving parents, department heads, guidance counselors, etc. — all to ensure that the override is going through with everyone’s eyes open. Then, if there is room in the desired class, the student can enroll in it. This means, of course, that overrides are processed after recommended students are placed in sections.

Why have all these hurdles to jump over and hoops to jump through? Why not have open enrollment? Wouldn’t that give maximum opportunity to everyone?

No, it definitely wouldn’t. Here’s what would happen. My honors class would be overloaded with students who don’t belong there, either because they are unprepared or because they won’t succeed in it for other reasons. This would result in one of two things: classes of 40 or the creation of extra sections. The class ambiance would suffer from the (legitimate) complaints of students who want the teacher to “slow down” and make things easier. Students who belong there wouldn’t get the attention they deserve. As we moved through the first semester, more and more students would be miserable in their math classes and would drop out and move into the ever-more-crowded college-prep sections. By December we would have tiny honors classes and huge regular ones. And don’t say that sections could then be reconfigured; there’s no way that a high-school schedule would permit that, because courses in other subjects would get in the way.

You can find fascinating discussions of this issue on the Web. For example, an entire debate in the Lexington High School Student-Faculty Senate includes this interesting exchange:
Kieft: This is the latest revision of a bill that has popped up in Senate various times, in different forms. This version is simplified, and gets to the point with out a lot of fluff. What you have in front of you is actually two bills. The first gives teacher the right to recommend students without taking into account any requests of the students or their parents. It is not intended to cut off communication between teachers and students, and suggests that a teacher include a written rationale with his or her recommendation, if it may raise any questions. The second bill says that students should have the right to chose disregard the recommendation made for them and move up or down in one course. This limits the number of overrides a student may make — if a student wants to override in many of his classes, he should consider why he is giving many of his teachers the impression that he is not ready for higher level work.

Enders: Although this version improves the bill, I still don’t agree with its original intent. Limiting the flexibility of the process is not the answer — think the better the communication between students and teachers, the more likely the student will be placed correctly.

Burson: What is the current policy? Can teachers currently disregard demands made by students or parents?

Kieft: I don’t think there is anything specifically written down. Mr. Simon described to me the math department’s policy, which entailed students and parents asking for the override on one side of a form, and the teacher filling out the other side as to why the child was recommended for the lower level. At first, this worked well, but with many students asking for overrides, teachers often ask if they plan to override, before making their recommendations, so as to avoid the paperwork. This creates a situation where many students are put in classes above their ability. Also, parents have been known to try to intimidate teachers into recommending their child for a higher level class.

Walsh: The role of department heads in the course selection process is not mentioned in the bill. Once an override is requested, the situation is generally taken out of the hands of the teacher, other than when an explanation of the recommendation is required. As further discussion most often takes place between the students/parents and the department heads, perhaps department heads should be empowered, here.

Kafrissen: A few weeks ago, the faculty was presented with the findings of the Stress Survey. Students said two things: that they had too much work, and that the work was too hard. I can only infer from this that students are taking classes that are too difficult for them, which is likely partially a result of overrides. The Senate tried limiting the number of honors a student may carry, but the proposal was voted down. As students, you have to chose: Do you want the challenge, or do you complain about your course load being too challenging?

David: According to Mr. Pappadonis, the trend in overrides is to take the process out of the hands of teachers and students, in the possible form of a test that a student must pass in order to prove that they have earned the right to be in a higher class. Also, there seems to be a disparity as to what qualifies for an honors class. I think there are too many “honors” classes here in general.

Jehle: The results of the survey also showed that students identified teachers as contributors to their stress. It is irrational not to take the teachers’ opinions into account in the selection process.
The answer to the objections raised in my first paragraph is not to permit open enrollment. It’s to work hard to ensure that all students have the opportunity to succeed at their highest level, so that those who want AP or honors will truly be prepared and will be appropriately recommended. It’s not doing anyone a service to place students in classes that are over their head.

Labels: ,

Monday, October 24, 2005

What is trigonometry?

“Trigonometry is algebra tainted by geometry,” according to one of my students.


Thursday, October 20, 2005

Logarithms and the Hippocratic Oath

I just finished reading The Oath, a novel by John Lescroart. A hospital is suffering from deep financial woes. One character says:
Every day the hospital’s troubles are increasing logarithmically!
I guess there isn’t much that they have to worry about, is there?

The book’s title, by the way, refers to the Hippocratic Oath; a character cites the oft-quoted line, “First, do no harm.” The only problem is that that line does not come from the Hippocratic Oath, contrary to popular understanding. (The Oath does forbid charging tuition to Medical School students, but that’s another story. It also forbids practicing surgery, but that’s also another story.)

Labels: ,

Monday, October 17, 2005

Charging what the market will bear

The folks at TechFusion must be good guys, right? After all, their company is one of WBUR’s underwriters. And they advertise “No Job Too Large or Too Small.” Of course I was suspicious in the first place when I heard their tagline on WBUR and read it on their website:
Where Data is Never Lost
If they don’t know that the word “data” is plural, what do they know?

But that, of course, was not the problem.

There had been a catastrophic failure of the Wildwood Web server, which I use for my website, and which the Weston Math Department uses for its website. Unfortunately the server administrator and sole proprietor was out of town. So I was deputized to take a SCSI disk drive to TechFusion, to see if they could recover our backup data, some of which were on that drive. When they found out that it contained Linux partitions, they said snootily that some people use Linux because they think it will save money, but that they would charge a minimum of $1900 and probably up to $6000 to recover data from the drive!

So much for no job being too small.

We followed Nancy Reagan’s advice.


Tuesday, October 11, 2005

Globe speaks out for Dorchester!

What does the Globe normally say about Dorchester?

Well, the three most frequently reported topics are crime, crime, and crime. So it was welcome news to see a large article right on the first page of Metro/Region in yesterday’s Globe entitled “Visitors won’t discover some city areas via map: Guides omit places south of downtown” — especially when the first sentence of the article was
Where in the heck did Dorchester go?
The article goes on to explain why Dorchester ought to be included in guidebooks and tourist maps:
Boston’s largest neighborhood in both geography and population, Dorchester has about 93,000 residents spread over 6 square miles. The oft-mapped Beacon Hill-Back Bay area, by contrast, has about 26,000 residents in 1 square mile, according to the Boston Redevelopment Authority.

Dorchester is home to Franklin Park Zoo, the John F. Kennedy Presidential Library and Museum, the nation’s first chocolate factory, and the Blake House, which is promoted as the city's oldest house, built around 1648. Except for the zoo and JFK Library, most people who find these attractions live in Dorchester or have friends who do, Taylor [that’s Earl Taylor, president of the Dorchester Historical Society] said.

“It is a major oversight,” said the library’s spokesman, Brent Carney. “This vital part of the City of Boston not only has the [JFK Library], which is one of Boston’s largest attractions, but it has wonderful restaurants, a rich history, and some of the most spectacular views of the city.”


Monday, October 10, 2005

The power of visual representations

In middle- and high-school math classes, we spend a lot of time helping students learn different representations of mathematical relations: words, equations, graphs, tables, etc. One of the big ideas is that a particular representation may be more powerful than others for a particular use or context. Examples start to become routine and repetitive after a while, so I was startled to see one today that I had never seen before: a graph of a function that immediately and dramatically shows the objective difference between the speech rhythms of Harriet Miers and George W. Bush. My erstwhile classmate, Mark Liberman, displays this graph of the waveform of Bush’s introduction followed immediately by Miers’s speech:

As Liberman points out, “it's easy to see where Bush stops and Miers starts.”

So we’re not just imagining it when we think that Bush pauses between phrases too often and for too long.

Labels: , ,

Sunday, October 09, 2005


Conversation overheard in the Math/Science Office the other day:
Ms. X [to Student Y]: I need a babysitter for my kids. Do you babysit?

Student Y: Yes, I do.

Ms. X: You aren’t Jewish, are you?

Student Y: No.
Not knowing Ms. X, you are probably startled by her second question. Sounds anti-Semitic, doesn’t it?


But actually Ms. X is an observant Jew. She was looking for a babysitter for Yom Kippur, and didn’t want to put a Jewish student in the position of driving on such a holy day.


Saturday, October 08, 2005

Hacking, not cracking

It says here that “the word the word ‘hack’ may be losing its negative connotations.” Duxbury High School engineering teacher Chris Connors is sponsoring a contest among his students to see who can come up with the best hack. Sounds like a good idea, as long as people don’t confuse hacking with cracking, as most do these days. Maybe it’s only we old-timers who remember the original — dare I say “authentic”? — meanings of the word “hacker”:
1. A person who enjoys exploring the details of programmable systems and how to stretch their capabilities, as opposed to most users, who prefer to learn only the minimum necessary. 2. One who programs enthusiastically (even obsessively) or who enjoys programming rather than just theorizing about programming... 6. An expert or enthusiast of any kind. One might be an astronomy hacker, for example. 7. One who enjoys the intellectual challenge of creatively overcoming or circumventing limitations. 8. [deprecated] A malicious meddler who tries to discover sensitive information by poking around. Hence “password hacker”, “network hacker”. The correct term for this sense is “cracker”.

The term “hacker” also tends to connote membership in the global community defined by the net... Hackers consider themselves something of an elite (a meritocracy based on ability), though one to which new members are gladly welcome. There is thus a certain ego satisfaction to be had in identifying yourself as a hacker...
(from The New Hacker’s Dictionary)


Friday, October 07, 2005

How to protect your kids: a modest proposal from Scituate

Catching up on Monday’s Boston Globe:
Red-light runners in Boston and Cambridge could soon be handing over some green if the Legislature lets the cities set up cameras at intersections to nab violators... [Name Omitted] of Scituate, who drives often for his sales job, says he does not want the risk of getting more tickets. “It’s expensive enough driving here with parking and having the meter maids catching you,” [Name Omitted] said. “And if my kids were using my car, I’d really be in trouble, because I think they run red lights.”
I admit to mixed feelings about the use of spy cameras, but what do you mean by saying that you would be in trouble? What about your kids? Has it occurred to you that running red lights is a good way for them to get themselves killed?

OK, now I’ll take a deep breath and will calm down.


Thursday, October 06, 2005

Conspiracy theory: more "evidence"

This is a follow-up to my post of 10/5. In a letter to the editor of the Boston Globe today, one Jeff Loja of Halifax says:
It seems abundantly clear that the purpose of ABC’s new show “Commander in Chief”..is to show what life would be like three years from now if Hillary Rodham Clinton (gulp) became president [italicized parenthetical comment in original]... The real purpose of this television show is to make the Bush administration look bad and also work as a pseudo-infomercial for Hillary Clinton’s ’08 campaign.


Principal search

We’re looking for a new principal, as our previous one moved to Georgia over the summer to become an Assistant Superintendent in the Cobb County district. This year we have an interim principal at Weston, as we search for a permanent one. Today our Superintendent met with faculty and students to present some details of the search process: timetable, committee structure, and interview plans. Students will definitely have a voice in the process.

In the meantime, if you’re a student of mine and have strong views (or even moderate views) about the characteristics and attitudes that we should be looking for in a principal, why don’t you become a guest blogger here at Learning Strategies? Just email your post to me, and tell me whether you wish to be anonymous or to be named as the author. You can’t have a voice in deciding the next justice on the Supreme Court, but you can definitely have a voice in deciding the next principal of your high school.

Labels: ,

Wednesday, October 05, 2005

Conspiracy theories

From the right:
THE HILLARY CLINTON ’08 CAMPAIGN AIRED ITS FIRST, HOUR-LONG COMMERCIAL last night. [caps in original] Unfortunately, it came masked as a primetime network TV series... Last night, “Commander in Chief” portrayed conservatives as ruthless, power-hungry, militaristic, Bible-thumping, sexist bigots.
From the left:
Bush never wanted to nominate Ms. Miers, but has done so to appease his wife and/or one or more of his political constituencies. When Ms. Miers fails to get confirmation or withdraws her name from consideration, then he can name the man he really wanted all along, Alberto Gonzales.
Evidence, guys?


Monday, October 03, 2005

Are men malingerers?

According to the Boston Globe:
Men are twice as likely as women to play hooky by calling in sick, according to a recent poll.

The 11th annual Attitudes in the American Workplace poll, reported by the Marlin Co., a workplace consulting firm, showed that in the past year, 14 percent of women reported calling in sick when they weren’t, while 29 percent of men admitted to doing so.
Do you suppose that’s really accurate? If so, what’s the explanation for it?


Sunday, October 02, 2005

Robert Noyce and Bringing down the House

Usually I’m in the middle of reading two books at once — typically a novel and a non-fiction work. But for some reason I’m currently reading a biography that’s definitely non-fiction and a former best-seller that purports to be non-fiction. I have my doubts about the latter.

By a curious coincidence, each book includes a character who lives in Weston.

The biography is The man behind the microchip: Robert Noyce and the invention of Silicon Valley, by Leslie Berlin. Noyce was co-founder of Intel and co-inventor of the integrated circuit; he was also the grandfather of one former and two current Weston High School students. The book combines vivid character descriptions with just enough technical details. It won’t tell you how to get rich — sorry about that — but it does contain one of my favorite quotations about management:
The job of the manager is an enabling, not a directive job... coaching, and not direction, is the first quality of leadership now. Get the barriers out of the way to let people do the things they do well.
The other book is Bringing Down the House: The Inside Story of Six M.I.T. Students Who Took Vegas for Millions, by Ben Mezrich. This claims to be Mezrich’s first non-fiction book (he has written and published half a dozen novels), but many reviews voice disbelief and assert that it’s just another work of fiction. One of the lead characters lives in Weston, which is described as follows:
Twenty minutes from Boston by Mercedes-Benz, Weston was an upper-middle-class enclave separated from the real world by a tree-lined stretch of the Mass Pike. The sleepy New England town was suburbia incarnate: white picket fences, yellow school buses with blinking red lights, colonial homes, lush green lawns, lemonade stands, tennis courts, basketball hoops, tree houses, porch swings, dogs on leashes, kickball and flashlight tag, public schools that looked like prep schools and prep schools that looked like Ivy League universities.
Unfortunately that’s one of the better-written passages in the book. The rest of the book alternates between melodrama and tedium. I don’t know whether it’s fictional or not, but Mezrich too often writes like an advocate of the Dan Brown school of writing.

Labels: , , ,


This page is powered by Blogger. Isn't yours? Made with Macintosh