Learning Strategies

Check out the great photos at <legnangel.livejournal.com/564026.html>. I wish I could read the Russian text, but maybe Boris can help.

Anyway, the question for me is why this collection resonates for me at several different levels. For one, the miniature figures look like — and might in fact be — model-railroad figures that have been repurposed. The use of food items, actual-size rather than scaled down, sets up a feel of Gulliver’s Travels, a feeling that’s very different from the miniature world of model railroading where absolutely everything is perfectly to scale. This tension is amusing, attention-getting, and fascinating.

There’s also an interesting connection with mathematics, where we are often concerned with models and representation. What happens when there’s a clash between two representations of different scales? Does this incongruity create delight and humor?

I’ll resist saying that it’s food for thought.

Labels: model railroads, teaching and learning

Just got back from Sel de la Terre. Highly recommended for a wonderful birthday dinner with that Provençal flavor.

Labels: food

There are several blogs that I read regularly. One of my favorites is Learning Curves, by the pseudonymous math professor Rudbeckia Hirta. She goes to some lengths to hide her real name, as well as the the name of the university somewhere-in-the-South at which she is head of the Mathematics Department. Not that she’s unwilling to leave some clues for the knowledgeable: she has posted photos of herself, a map of her neighborhood, a shot of the Math Department’s building, and even pix of her house. So it’s clear that anyone who knows her or is associated with her university will know her secret identity. Apparently she’s protecting herself from strangers, not that I’m nosy enough to try to figure out who she is or where she teaches.

In any case, Ms. Hirta recently wrote about the TI graphing calculator and Apple’s Grapher software:

It’s no secret that I’m not a big fan of the graphing calculator.... Now that I have found Grapher in the Utilities folder inside my Applications folder (that, among other things, makes very pretty graphs that can be output as .pdfs), my limited needs for the graphing calculator have waned somewhat.

This post got me thinking about calculators and graphing. It’s the second recommendation that I’ve received recently for Grapher, so I really have to check it out. One user describes it as “very useful and frustrating,” which is not particularly encouraging. The documentation is daunting, but clearly there isn’t enough of it. Sigh.

Oh, well. I’m going to have to explore it anyway, since it promises to be a useful tool for me and for other math teachers. It does 2-D and 3-D color graphs, animations, polars, parametrics, and so forth — but I don’t really have any overall sense of its capabilities.

And what about the TI graphing calculator? This device has become ubiquitous in American high schools, and quite common in colleges. It clearly does a lot of good things for students, but it just as clearly has done a lot of harm. Let’s look at four examples of what Texas Instruments claims as its principal virtues [numbers added]:

1. A high school math teacher who works with students at a school geared toward the arts, finds that TI technology helps him overcome the disinclination toward math exhibited by many of the students, while it also enhances his own professional growth.


2. An Arkansas teacher with a long history of implementing technology in the classroom uses TI handhelds and related peripherals to introduce his students to the latest analytical and problem-solving techniques in math and physics


3. At-risk students receive a boost through programs that use TI graphing handhelds to reinforce basic mathematical concepts and prepare them for Algebra 1.


4. TI-83 Plus and TI-89 handhelds help Pre-Calculus and Calculus students at North Shore Senior High School visualize concepts and achieve higher passage rates on the AP Calculus exam.

I’ve deliberately selected a variety of success stories. Of course this is advertising by TI, but that doesn’t mean that we should dismiss the stories out of hand. Note the four different themes here: #1 claims that the calculator increases motivation for many students, #2 says that it gives access to the newest and (perhaps) best techniques of problem-solving, #3 points out advantages for at-risk pre-algebra students whose skills are not up to par, and #4 addresses the opposite extreme, students preparing for AP exams in calculus.

As I said, we shouldn’t dismiss these stories out of hand. Far from it: even without following the links to read the details of these four stories, I don’t doubt that they provide significant arguments for the benefits of using the graphing calculator. It can clearly be a great help for a wide variety of students in a wide variety of courses.

Then why does its use distress so many math professors, including but certainly not limited to Rudbeckia Hirta? Does it also distress high-school math teachers?

Indeed it does. While the graphing calculator can definitely provide motivation and assistance, it can also foster inappropriate dependence. For example, if a student can’t multiply a number by ten or by negative one without whipping out his calculator, he is demonstrating an unfortunate lack of number sense. Now there are probably a few people who would never succeed in multiplying by ten without a calculator, but surely most students can develop that much number sense before high school. The calculator is hindering their learning, not helping it.

Insofar as the calculator is a substitute for skills that ought to be learned, it’s a harmful tool. Of course we’re going to have disagreements about what those skills are. Should a high-school student be able to divide one number by another, using just pencil and paper? Most of us would say yes, but certainly not all of us. Most of us would say that it’s OK to use the graphing calculator to perform long division most of the time — after all, we do it ourselves — but there still need to be enough contexts in which we ask kids to do it without a calculator. On the other hand, most of us would say that there is no longer a need for a student to learn to perform square roots by the pencil-and-paper algorithm, and most of us have forgotten the details of that algorithm oursleves. (On the third hand, we would want any high-school student to be able to determine whether 8.25 or 8.75 is closer to the square root of 70 — without a calculator, of course.)

These ideas led me to divide most tests into two sections, one allowing calculators and one forbidding them. But I don’t do that in every class, having been burned a few years ago by a parent who threatened to sue the school system if we didn’t allow her son to use a calculator on every math problem. More on that in a later post.

Labels: teaching and learning, technology

Almost 25 years ago, my friend and colleague Phil Lewis wrote an article for Kaleidoscopes called (if memory serves) “Subject to Gates and Bars.” If I were better organized, I would be able to find that article; Phil always describes me as mentally organized but physically disorganized, and it’s physical organization that’s needed in order to find a hard-copy back-issue of Kaleidoscopes. So I’ll have to go from memory here...

What brought Phil’s article back to mind was a recent discussion at Weston about students in precalculus whose algebraic skills are not up to the job. Our current curriculum rightly has a major emphasis on big ideas — on concepts rather than manipulations. This isn’t Tom Lehrer’s new math, where he said in his famous line, “The important thing is to understand what you’re doing rather than to get the right answer.” We do pay attention to right answers, and to the mathematical skills that are needed to get those answers.

Nevertheless, we subordinate skills to concepts, as we should. The problem lies in Lehrer’s italicized “rather than”: the line is amusing because we all know that it’s essential to understand what you’re doing and to get the right answer. This, of course, is what’s wrong with the so-called “Math Wars,” in which skills and concepts are portrayed as being opponents rather than partners. But what do we do with students whose understanding of concepts is sufficient for them to earn B’s but whose command of skills is insufficient to thrive in the next course? Having separate grades for skills and concepts would be an administrative and pedagogical nightmare, so don’t even bother suggesting that route. A more productive recent suggestion has been the use of placement tests: no matter what his or her grades might be, a student should not be able to move into precalculus without demonstrating a sufficient command of algebraic skills. (This proposal wouldn’t have to be limited to precalculus, of course, but that’s where the problem crops up most severely.)

What would be the effect of creating additional bars in the way of a student’s mathematical progress? An optimist might say that a placement test would actually be an additional gate to pass through, not a bar to further progress. The optimist would claim that a student who fails to demonstrate sufficient competence in algebraic skills would have the incentive to learn what s/he doesn’t know, would pass the test on a second or third try, and would then be qualified for precalculus.

Sounds a bit too much like No Child Left Behind and MCAS for my taste. Would it really work? I don’t believe the rosy scenario.

Admittedly, I’m usually an optimist, but in this case I see much more of a downside than an upside to the idea of putting additional bars in the way of students who want to take precalculus. The principal negative effect would be to widen the achievement gap at a time when we want more students of color to be taking calculus (and therefore precalculus before that). In a series of workshops last year, we were exhorted to find ways to narrow the gap — to get more black students, more Hispanics, and more girls into advanced placement math courses. I don’t see how we’re going to do that if we put more barriers in their way.

I’ve also heard a variant of the placement-test proposal: require a score above a certain cut-off in order to receive a grade of A in Algebra II (or other feeder course, if applied elsewhere than precalculus). In that case the test would not be a bar, since it would not be a ticket of admission to precalculus; it would merely be a gate that a student could pass through with eyes wide open, knowing that s/he does not yet have the recommended skills for precalculus. But I suspect that this variant might be the worst of both worlds: it would still discourage certain students, thereby widening the achievement gap; and it would let others who aren’t truly prepared for precalculus pass through anyway.

More thoughts to come...

Labels: teaching and learning, Weston

• Tuesday afternoon at 4:20 — I took my iBook to the Cambridge Apple Store, having made an appointment earlier in the day at the so-called Genius Bar. (CDs and DVDs were ejecting less than 50% of the time. Worse yet, the mechanism was sometimes scratching the discs.) The Apple guy, who was helpful and knowledgeabe, told me to expect the computer back in about a week and a half.


• Tuesday afternoon at 4:42 — I received an email message from Apple saying, “We have received your IBOOK G4 (EARLY 2004) for repair. The Apple Store CambridgeSide will send it to the Apple repair center.”


• Wednesday morning at 9:51 — I received an email message from Apple saying, “Your IBOOK G4 (EARLY 2004) has reached our repair center. We will notify you by email when the repair is complete.” The repair center is in Memphis.


• Wednesday evening at 8:39 — DHL reports that my computer was picked up in Memphis.


• Wednesday evening at 8:41 — I received an email message from Apple saying, “Your service request has been completed and your IBOOK G4 (EARLY 2004) is on its way. Please allow two business days for delivery.”


• Thursday morning at 8:04 — DHL reports that my computer had arrived at their facility in Newton.


• Thursday morning at 9:20 — My computer arrived and was signed for in Weston.

Wow! There’s nothing like delivery ahead of the promised date. Not only was Apple super-fast, but DHL took less than twelve hours on a promise of “two business days.”

Labels: technology

All I can do is shake my head in amazement:

About one out of five Americans believe that winning the lottery is the most practical way of attaining personal wealth, according to a survey released in January by the Financial Planning Association and the Consumer Federation of America. Among Americans with salaries of $25,000 or less, 38 percent believe the lottery is the way to go.

This comes from <http://www.bankrate.com/bos/news/BoomerBucks/20060111a1.asp>; the survey cited is at <http://www.consumerfed.org/pdfs/Financial_Planners_Study011006.pdf>.

Labels: math

No, that’s not a typo. I don’t mean the Harvard Coop; I’m referring to the forced resignation of Harvard President Larry Summers, which Alan Dershowitz rightly calls a coup.

Definitely read Dershowitz’s column!

I do have a certain bias in favor of the faculty, not only as a full-time teacher during the year but also as a teacher at the Crimson Summer Academy at Harvard. And I do have a certain bias in favor of the left in left-center conflicts. Despite these biases, I have to say that Dershowitz is right on the money in his analysis:

Summers was being condemned for expressing views deemed offensive by some of the faculty. I personally disagreed with some of Summers’s statements, but that is beside the point in an institution committed to academic freedom and diversity of viewpoints.

Do note that it was only one faculty — the Faculty of Arts and Sciences — that was about to express a lack of confidence in Summers. All evidence suggests that he still had the confidence of the Law School faculty, the Medical School, the School of Public Health, the Kennedy School of Government, and so forth. Only one faculty out of twelve was going to proceed with a no-confidence vote, and even they might have evinced only a plurality, not a majority. Admittedly the Faculty of Arts and Sciences is the largest and most important of Harvard’s various faculties, but still....

Summers does suffer from a lack of tact, like his erstwhile colleague John Silber. Both of them say what’s on their mind, whether it’s politically advisable or not. Some people even claim that Summers has Asperger’s Syndrome. Maybe so, but at least in public schools we don’t react to people with Asperger’s by voting them off the island.

Summers, by the way, was widely misquoted in the media when they reported on his famous remarks on women in math and science. But I’ll save that for another post.

Finally, a few additional quotations from Dershowitz’s piece:

[The radical academics were] insisting on complete freedom of speech for those with whom they agree — free speech for me but not for thee!

It was arrogant in the extreme for a plurality of a single faculty to purport to speak for the entire university, especially when that plurality is out of synch with the mainstream of Harvard.

Now that this plurality of one faculty has succeeded in ousting the president, the most radical elements of Harvard will be emboldened to seek to mold all of Harvard in its image. If they succeed, Harvard will become a less diverse and less interesting institution of learning governed by political-correctness cops of the hard left. This is what happened in many European universities after the violent student protests of the late 1960s. It should not be allowed to happen at Harvard in the wake of the coup d’etat engineered by some in the Faculty of Arts and Sciences.

Labels: life, teaching and learning

So we finally gave in and got a TiVo box. I think it was a recommendation by Ira Glass that did the track. Most of the setup was painless, but it’s been very frustrating trying to connect it to our wireless network. So far all the USB-to-wireless adapters are either back-ordered or strangely incompatible. I don’t really want to string cables all over the place in order to hook the machine up to the phone or by Ethernet to our Airport Express. And anyway, using the phone seems to cause problems for our DSL, and using Ethernet just replaces the USB-to-wireless adapter search with a USB-to-Ethernet adapter search. Grrr!

Labels: technology

Does the iPod steal music’s soul? Do these numbers make sense?

Here are the views of Tony Brummel, founder of Victory Records:

iTunes “makes music disposable. It makes it a faceless impulse item. It steals its soul,” according to Macworld UK. Brummel asks why consumers should be allowed to “cherry pick” specific songs, thus “cannibalizing full length album sales”... Brummel points out that if the major labels wanted to force Apple away from the set-pricing model, they would all pull out their music from iTunes. “Focus on the 96 percent which is traditional retail. Traditional retail supports music 1,000 times more than iTunes does.”

Labels: math, teaching and learning, technology

Early in April, our entire math department will be participating in a workshop on “redefining our major curriculum units”. At this point I have some very preliminary thoughts, some of which I’ve discussed here previously:

• Many mathematical applications that are important at the beginning of the 21^st Century receive short shrift from the high school math curriculum, even at intellectually progressive high schools such as Weston. For many years — at Weston and elsewhere — I’ve been beating the drum of cryptology, which has many claims on a significant place in a high school math program: it shows uses of linear functions, number theory, systems of equations, matrices, and exponential functions; it’s interesting and motivating for a significant number of students; it’s truly important in our current world of heavy Internet usage; and it provides ample interdisciplinary tie-ins. Nevertheless, cryptology is nowhere in the curriculum of most high schools, and at Weston it appears only in honors-level Algebra II.
  
  Similarly, it’s essential for future voters to understanding procedures and models of voting. But those topics appear nowhere in the high-school curriculum — neither at honors nor at college-prep level, neither at Weston nor elsewhere. We’re emphasizing mathematical models these days, as we should be doing, but some of those models ought to be of voting systems
  
  And then there’s game theory, another topic of increasing importance in the new century. Where does that occur in our curriculum? Only in a course taken by a tiny number of students who are not comfortable with the symbolic manipulations found in precalculus. This course, Applied Discrete Math Concepts, is a fine opportunity for the few kids who take it, but game theory ought to be found in the curriculum for all students.


• At some schools, including Weston, math teachers invest a lot of time in thinking about themes, tools, and techniques. We talk about big ideas, such as representation and variable. And we talk about the details that are necessary to implement those big ideas, since the devil is in the details. And we talk about the tools and techniques that students ought to be learning as aids both in their future math and in other endeavors.
  
  Perhaps we need to place more emphasis on certain themes, such as transformations, which could weave their way into every year’s math course. And we should rethink our use of tools, whether they are mathematical tools such as matrices (applicable in many courses) or technological tools such as the graphing calculator or the Geometer’s Sketchpad.


• We’ve made a valiant effort in our project of integrating computer programming into the regular math curriculum, but we still have far to go. In particular, programming is not integrated into enough units; it’s too scattered, and as a result a student may go a whole year without doing any. Last June, three of us delivered a paper at the TeachScheme Tenth Anniversary Workshop, in which we made the point that programming should be a regularly available tool at a student’s fingertips. But no one will develop enough facility to make this possible unless programming is a regular, not sporadic, part of the curriculum.


• Finally, we always assume that honors curricula are a superset of college-prep curricula, and therefore an honors course is “better.” If a topic is in college-prep Algebra II, we know it will also be in Honors Algebra II, but not necessarily vice versa. Maybe this principle is wrong. Maybe college-prep and honors should be slightly different courses, where surely there’s something extra to be learned if you take honors, but where you also miss something if you do that. There would be a trade-off that would require some thinking; the honors course wouldn’t automatically be perceived as better.

I would welcome ideas from any students, teachers, parents, or anyone else who reads this blog — either additional ideas of your own, or feedback on the ones I’ve suggested. Let me know!

Labels: teaching and learning, Weston

Today’s Boston Globe reports on the appointment of new principals to both of the high schools in Newton. One candidate, Jennifer Price, had been a finalist for the position at Weston, though she was not the one ultimately chosen. (See my post of February 9.) I am delighted by the choice of our new principal, Anthony Parker, but I would have been equally happy with Ms. Price. I don’t know anything about the other new Newton principal, Brian Salzer. Anyway, the Globe’s story about the appointments of Price and Salzer has the following inflammatory headline, written of course by an anonymous headline writer:

Gay principals soon take helm at both Newton high schools

The article itself, by Matt Viser, isn’t at all inflammatory — in fact, it’s reasonable, positive, and even complimentary. For example:

Brian Salzer, 38, who will be the principal at Newton South High School, comes from Sauk Prairie, a small Wisconsin school district near the state capital of Madison, and was the first openly gay principal in Wisconsin.

Jennifer Price, 34, is a doctoral student at Harvard’s Graduate School of Education who lives in Newton with her spouse and their two young children. She takes over at Newton North High School in July.

“In the end it’s about our leadership and what we do in the schools,” Price said yesterday of the dual appointments.

Nathan Bonneau, a spokesman for the Massachusetts Secondary School Administrators’ Association, said he wasn’t aware of any other openly gay principals in the Bay State, but could not say definitively whether Salzer and Price are the first.

Many parents said yesterday that the sexual orientation of the principals is not important.

...

Superintendent Jeffrey M. Young said that Salzer and Price were hired because they were “the two best principals.”

“People should judge them on the way they do their job,” he said. “I am thrilled that they’ll be joining our staff.”

Labels: Weston

I’m currently reading The Bookman’s Promise, another Cliff Janeway mystery by John Dunning. If you don’t know this series, run to the nearest library or bookstore — at least if you love books. Dunning’s protagonist is a bookman, defined in Merriam-Webster Online as

1. one who has a love of books and especially of reading


2. one who is involved in the writing, publishing, or selling of books

Janeway is both. More particularly, he is a former cop who now sells rare and used books. Dunning makes this unlikely combination plausible, and he makes the world of rare books come alive. Anyone who’s fascinated by books — not just their content, but also their form and their heft and their typography and their bindings — will enjoy the entire Janeway series.

The Bookman’s Promise is Dunning’s third Janeway book. It contains some interesting history, a bit too much violence, and unfortunately not quite so much fascinating detail about the book business as the first two books offered the reader. Of course, since I haven’t finished this one, I can’t really give a considered opinion yet. But so far it’s well worth reading, even if it’s a notch below Booked to Die and The Bookman’s Wake.

Labels: books

How we can solve the dismal state of so many of our schools that are educationally inadequate? We all know that throwing money at the problem won’t help, don’t we?

“Throwing money at the problem isn’t going to help,” says Stacey Turner.

“Educational problems can't be solved by throwing money at them,” writes Paul Ciotti of the Cato Institute.

“First lady Laura Bush was probably right when she said recently that it was time for us to pay more attention to boys. That is more likely to produce a solution than throwing money at a reorganization of our school,” writes economist James McCusker.

“Throwing money at the worst schools only rewards poor performance,” writes Kathleen Vail, Senior Editor of the American School Board Journal.

These people are confusing sufficient conditions with necessary conditions. Sure, throwing money at a problem isn’t sufficient to help, but it’s often necessary. It’s amazing what money can accomplish when it’s accompanied by thoughtful, research-based activities performed by the right people. With that combination, throwing money at a problem is exactly what’s needed.

Labels: teaching and learning

We don’t have to like Bill Gates, and we certainly don’t have to like Microsoft, but we do have to admit that Gates has changed. He’s making an impact by doing fine work as a philanthropist, and occasionally he’s even right on technical issues.

One correct bit of technical vision goes back about 20 years, when I was attending a meeting of the late, lamented Boston Computer Society (b. 1977, d. 1996), at which Bill Gates was the featured speaker. At this point I couldn’t remember very much about that meeting, but I do remember the Gates vision of a software world without applications. It struck me as supremely right that we shouldn’t have to launch Word in order to compose text, Excel in order to calculate, Photoshop in order to edit an image, and Lisp in order to program. Of course there have been many lame attempts at software suites and even integrated applications, but that’s not the point. The vision — still in the future today — is the software equivalent of writing on a whiteboard, where you just write, and your mind does whatever needs to be done without partitioning itself into a word processor, a spreadsheet, an image editor, and a programming language.

Much more recently, the Bill and Melinda Gates Foundation has been funding a variety of educational initiatives, including a drive for smaller schools. While there are certain virtues to having large schools, those virtues almost always come down to providing resources that small schools can’t afford. And there are other solutions to the resource problem, including the Internet and community-based activities. Gates is right about small schools:

Many high schools are just too big. Over the last half-century, average school enrollment has increased fivefold. These large, impersonal institutions are failing to teach young people what they need to know to lead meaningful lives, succeed in college, and earn a decent living. This is disproportionately true for children from low-income neighborhoods. Students in large high schools also report having few significant relationships with teachers and mentors, in large part because teachers see so many students every day that it is almost impossible to build any sort of relationship with most of them.

Finally, the Gates Foundation has been involved with important world-health ventures that focus on underserved communities, reportedly including Partners in Health, the organization founded by Paul Farmer. The stated mission of PIH is:

to bring the benefits of modern medical science to those most in need of them and to serve as an antidote to despair. We draw on the resources of the world’s leading medical and academic institutions and on the lived experience of the world’s poorest and sickest communities.

Labels: life, technology

I’ve just finished listening to an audiobook, The Anglo-Irish Murders, by the Irish author Ruth Dudley Edwards. Rates a cautious thumbs-up from where I stand. But I learned from a former boss that where you stand depends on where you sit; in other words, opinions change when you change positions. (Notice what happens when a small-government advocate gets into the White House, for example.) I suppose that if I suddenly became an Irish Catholic, or an Irish-American Catholic, my POV on this book would be different, but that will have to remain nothing more than a thought-experiment.

The audio version is beautifully read by Bill Wallis on a $64.95 CD (that’s why you check it out from the library). Wallis endows the characters with individual personae and immediately takes the listener into the world of the story. He makes the experience feel like watching a play performed by a dozen excellent actors.

It’s obvious from the title that this book is a murder mystery; what’s not so obvious (unless you’re familiar with the author’s previous works) is that it’s also a satire. At least it’s not obvious until you’ve read the first couple of pages, by which point no doubt is left. The plot revolves around a conference on Anglo-Irish multicultural sensitivities organized by the Brits and held in a somewhat secluded castle in Ireland. Conferees are being killed off one by one — sounds a bit like Agatha Christie’s And Then There Were None, doesn’t it? And yes, along with being a political satire, it is also a parody of the Christie work. In a touch of post-modern self-reference, one of the characters even makes the comparison explicit. Although not connected with the parts of the satire that focus on Anglo-Irish relations and the IRA, the Christie parody matches the portions of the satire that deal with political correctness and ethnic stereotypes.

I usually pay no attention to reviews posted on amazon.com, since they’re typically written by uninformed members of the public whose opinions are of little value. (It reminds me of Tom Lehrer’s line that “the reason most folk songs are so atrocious is that they were written by the people.”) But of course not all posted reviews are dumb; occasionally one comes across a review that’s well-written, articulate, compelling, and wrong. Such is the wrong-headed piece by Brian Callahan, an Irish-American who has let where he sits control where he stands. Missing (or rather denying) the satire, he writes as if the views of the characters reflect the views of the author:

Outlandish characters like an Indian and a Japanese are shown to be wise men, even though vilified by racial epithets by the British baroness in charge of the conference in the castle... The author goes so far as to claim that the Irish Potato Famine was not an example of British inhumanity, but just “a spot of bad management”... the author’s polemics against the entire Irish race and against the Catholic Church in particular ruined the book for me.

I don’t know about the Irish “race,” but the polemics are the characters’, not the author’s. It’s true that the Catholic Church doesn’t come out so well in this novel, and perhaps Callahan is also basing his judgment on the author’s non-fiction writings, though that’s hardly a fair technique when reviewing a work of fiction. For example, on her website, Ruth Dudley Edwards refers to her native Ireland as “a country culturally conditioned by an authoritarian church to suppress any questioning of orthodoxy.”

The novel’s satirical descriptions of political correctness and ethnic sensitivities are amusing and to the point, though they begin to wear on the reader (listener) after a while. That’s my only real reservation about this mystery: about halfway through, it begins to be much of the same over and over again. But I still recommend it.

Labels: books

On February 3, President Bush was addressing a crowd at Intel concerning the importance of studying math and science:

A lot of people probably think math and science isn’t meant for me — you know, it seems a little hard, algebra. I understand that, frankly.

Do we really want our leader to be telling people that he finds algebra difficult, even when he’s being funny and self-deprecating?

It reminds me of a controversy from 1992. Remember when Mattel released a talking version of another American icon, the world’s best-selling doll, Barbie? One of the random remarks uttered by the talking Barbie was, “Math is hard.” For those girls who looked up to her as a role model [??], this opinion apparently discouraged them from thinking they could do well in math, especially when it was packaged with other utterances such as “Shopping is fun.”

Bush says algebra is hard; Barbie says math is hard. Barbie says shopping is fun; what does Bush say is fun?

Labels: math, teaching and learning

An interesting resonance among four recent but different news and/or entertainment items:

• Last month, students in a certain well-regarded suburban high school report that “other kids” (of course it’s always other kids) have been selling or giving Ritalin to their classmates as a way of boosting energy, getting better grades, and incidentally getting high.


• On Wednesday’s episode of Law & Order, a teenager murder denied responsibility for his acts because of his medication (a fictional one that seemed to be a combination of Ritalin and Prozac). Then it turned out that he hadn’t even been taking it, but had been selling or trading it to his classmates.


• In yesterday’s Dorchester Reporter, former Dorchester District Court Judge James Dolan writes about personal reponsibility:

  Two Milton youths, undoubtedly with the support and encouragment of family members, have begun lawsuites to establish their schools violated their civil rights. One, a Milton High School senior, charges that boys are discriminated against in the school system and cites as an example that girls do better academically than boys.... He proposed remedial action such as pass/fail marking. That would blur the distinction between the academically gifted and others either not as talented or hardworking.
  
  ...The other suit is against Milton Academy, brought by a former student...charged with statutory rape and expelled. The suit suggests that the school failed to inform them there was anything wrong with that. Had the student handbook indicated that kind of behavior was not tolerated, he probably would have avoided that conduct.

• Yesterday, there was a story on Marketplace (NPR) about this — not about any particular school, but about selling Ritalin as a nationwide problem, especially in colleges.

Labels: teaching and learning, Weston

The other day I turned on the radio to hear someone say, “Sure, there’s diversity in Weston. They have doctors and lawyers.” But now we have a more convincing sign of diversity: a black principal!

The Superintendent of Schools just announced the appointment of Anthony Parker as the new principal of Weston High School. Of course we’re supposed to be color-blind and not notice that Parker is African-American. We’re thrilled that he’s a calm leader with 13 years of experience in Newton, the next town over; that we all immediately liked and respected him; and that he’s clearly a good listener with good values. Most intriguingly, he used to be assistant editor of Sojourners Magazine, a lefty Christian magazine focused on peace and social justice. Consider, for example, the first full paragraph that we currently see on the Sojourners website:

Passage of the budget will result in cuts to health care, child support, and educational assistance for low-income families. At the same time, Congress is planning to provide more tax cuts for the wealthiest Americans.

Parker is a graduate of Earlham, has a master’s degree from Harvard, and is currently a doctoral candidate at BC. These are great credentials; nobody will say that he got the job just because he’s black.

Nevertheless, it’s going to shake things up a bit to have a person of color as our principal. And that’s all for the good.

Labels: teaching and learning, Weston

The day before yesterday, it was getting to be too late to cook dinner after I picked up Barbara in Watertown...and we would have had to defrost something anyway, or go grocery shopping on the way home...which would have made it even later... Anyway, this was a good excuse to try the new restaurant called South, which was right on our way on Dorchester Street.

You might think that a restaurant called “South” serves southern cuisine, but you would be wrong. Or you might think that it’s in South Boston, and in that case you would be right. But to make full sense of the name, you have to understand the truly ambitious plans of their parent organization, the Trinity Restaurant Group. Along with South, they are about to open North (in the North End, of course), East (in East Boston), and of course West. I don’t remember where West is going to be. West Roxbury? West End? I just we’ll just have to wait to find out.

Unfortunately the pattern is broken by Ocean, a seafood restaurant in Southie that will open before West. It’s always crushing for us math people when we think we’ve detected a simple and convincing pattern and then find a counterexample. Sigh.

Anyway, I am delighted to report that Barbara and I had an excellent experience at South, and we highly recommend it (even though that might be premature after only a single visit). On arriving there, we encountered a good omen: a parking space on the street right in front! For Southie, that’s pretty remarkable. Our good luck continued to hold. We had two different salads, both of which were pristinely fresh, crisp, lightly dressed, and beautifully arrayed. Barbara had a huge ribeye and I had the prime rib, each of which easily provided a second meal’s worth of leftovers. More important, both were flavorful, tender, and cooked exactly as ordered. Vegetables and potatoes were varied and also cooked just right. We had no room for dessert, of course, but I can vouch for the espresso. The wine list contained a lot of good choices; it was pricey, like almost every other wine list, but not unreasonably so. Finally, the service was consistently attentive — a bit too far on the friendly side of the friendly/professional line, but maybe that says less about the waiter than it says about me. Try it out yourself!

Labels: food

High-school students want to take more and more Advanced Placement courses these days. And we’re encouraging them. At Weston we have altogether too many students who want to skip the second half of precalculus and take AP Statistics instead — all because it comes with that “Advanced Placement” imprimatur. They’re bolstered by Newsweek, which rates high schools by the number of students taking AP courses — not even by the number who do well on the AP exams, but just by those enrolled:

Students who take AP exams — even if they don’t do well — are better prepared than those who don’t.

Weston is #4 in Massachusetts by this strange criterion. Of course we know we’re #1 by any reasonable criterion, right?

In his recent State of the Union address, President Bush made it clear that he agrees with the AP mania:

Tonight I propose to train 70,000 high school teachers, to lead advanced-placement courses in math and science.

Now it’s certainly true that Americans need to learn more math and science. And it’s certainly true that a lot of American students would end up stretching their mathematical knowledge and skills if they prepared for and took AP courses. But at what price? On NPR’s All Things Considered yesterday, there were a couple of fascinating interviews within a single story. One was with Maria Klawe, outgoing Dean of Engineering at Princeton and incoming president of Harvey Mudd College, who “worries about the President’s emphasis on advanced placement classes”:

We need good teaching at all levels, not just in the final years of high school....

The most important thing is that we simply don’t pay our teachers enough to attract people with the kind of training we need in mathematics, science, or computer science... India not only produces a much higher number of computer science graduates than we do; they also teach computer science throughout K-12. So, for example, virtually every student in India will learn to program before they’re 15 years old.

If you look around the world, the places that have students performing well in math, science, or computer science are places that value their teachers. They give their teachers excellent training, they pay their teachers much better than we do... There has been a fair amount of research looking at how China teaches mathematics, and one thing that came out of that was that the teachers themselves are extremely creative. It’s not that they’re teaching exactly the same way year after year. They’re constantly experimenting with their students, looking for new approaches to teach abstract concepts. And I think one of the things in the US that we think is going to work is that we think we’re going to come up with the right textbook, or the right set of exercises, the right curriculum, and then give it to everybody and it will solve the problem. And of course it doesn’t, because teaching is not a rote activity.

The other interview was with Eric Walstein, advanced math teacher at Montgomery Blair High School in Silver Spring, MD, who said this:

One of the things that schools do, whether they realize it or not, is that they pull the intuition from the kids’ brains. As they come through elementary, middle, and high school, the students become less and less intuitive. But that’s exactly what we want to promote: their intuition.

Are AP courses the best vehicles for solving these problems?

Labels: teaching and learning, Weston

On February 15, Weston High School will be holding a Sudoku challenge in the Library for the first 30 students to sign up.

On March 10-11, the first World Sudoku Championship will be held in Lucca, Italy.

Labels: teaching and learning, Weston

You may have heard that dogs have masters but cats have staff. It’s true. Even though Barbara and I are privileged to share our house with five cats — well, actually six at the moment, since we have temporary custody of a foster cat whose human is in England for the year — we still celebrated the new year by eating dinner at our favorite Chinese restaurant on Chinese New Year’s Eve.

The next day — Chinese New Year — we liked this cartoon:



I showed it to one of my students and asked her to please arrange for the insertion of a Year of the Cat in the Chinese Zodiac. She couldn’t do that, but she did send me the explanation for why the first year in the cycle isn’t named for the cat, as one might expect, but for the rat of all things.

Labels: life

According to the National Survey of America’s College Students (NSACS) — a study conducted by the American Institutes for Research and funded by The Pew Charitable Trusts — American college students know even less math than we had thought:

Approximately 30 percent of students in 2-year institutions and nearly 20 percent of students in 4-year institutions have only Basic quantitative literacy. Basic literacy skills are those necessary to compare ticket prices or calculate the cost of a sandwich and a salad from a menu... they are unable to estimate if their car has enough gasoline to get to the next gas station or calculate the total cost of ordering office supplies.

They cite the “basic” questions, which most students answered correctly, but unfortunately I was unable to find the actual questions that most students were unable to answer. Estimating the amount of gasoline to get to the next gas station or calculating the total cost of ordering supplies might or might not test important math skills.

Labels: math, teaching and learning

There’s a possibility that Weston may return to a traditional exam schedule after a decade or so of not having one. There have been many justifications for not having a final exam week:

• An emphasis on exams increases stress.


• Students can’t learn anything from exams that are given the last week of school, since they never see the corrected exams.


• Massachusetts state law requires 990 hours of instruction, and a day that contains nothing but one or two exams won’t count for enough hours.


• Exams are not appropriate for all teachers/courses. Not all teachers are willing to give exams.

So for years we’ve had the worst of both worlds. A majority of courses give exams, but students have regular classes in some subjects on the same days as they have exams in other subjects. This is the pessimal solution. How can a student concentrate in geometry when s/he has already taken a geometry “final exam” and will be taking a physics final exam the very next period?

But it looks as if we may be shifting back to the usual system of having a week devoted to nothing but exams. This traditional system has many advantages:

1. On a given day, students can focus on one or two exams, without other obligations such as regular classes getting in the way. Stress is reduced, not increased.
   


2. Students are prepared for the process of reviewing and connecting large amouns of material for an exam, which they will have to do in college.
   


3. Students aren’t left with the artificial attempt to continue working in a course after they have taken a so-called “final” exam.
   


4. Teachers have time to correct exams, since they’re not teaching classes at the same time.

If it’s important to review and make connections within an entire semester or year’s worth of material, then it’s important for kids to focus on exams and nothing else for four or five days at the end of the year.

For the first year in a decade, a traditional exam week may finally have the support of the administration, the Principal’s Advisory Council, student government, and a majority of departments. Let’s hope that it really gets approved.

Labels: teaching and learning, Weston

President Bush (on CBS today):

My job is not only Commander-In-Chief but educator-in-chief. And I needed to say to the people, you bet it’s tough.

George W. Bush as educator-in-chief? Hmmm...

Labels: teaching and learning