Tall, Dark, and Mysterious

2/20/2006

Everything I ever needed to know, I failed to learn in kindergarten.

File under: Righteous Indignation, Know Thyself, Welcome To The Occupation. Posted by Moebius Stripper at 4:32 pm.

This just in: I come across as blunt, abrasive, aloof, distant, and ostensibly averse to small talk - and damned if some people don’t much care for that.

Pardon me, allow me to clarify: this just in from my supervisor, who took five minutes to get [above] across to me. I knew exactly what was coming halfway into the “Well, I’m not quite sure how to tell you this, but sometimes in large groups…” prelude, but coaxing it out of him any faster would have required me to bypass the requisite small talk and cut straight to bluntness, and never let it be said that I can’t take a hint.

Anyway, this is apparently a problem. Not just to my supervisor, but to the anonymous chorus of indeterminate size (”some people”) that has approached him with concerns about my demeanor. Oh, they all know I mean well, but would it kill me to smile a bit more? Spend more of my lunch breaks indoors with others in the lunchroom, instead of running errands or relaxing at the park? Interrupt my work (which I’m apparently doing quite well, thankyouverymuch), whenever the circumstances demand it, with multi-word commentary about how by gosh, it is raining again, whenever will the madness end?

It’s not that I’m not aware of all of this, mind you; it’s that what others see as friendly banter, I see as distractions from my work - work that no one else in the office can do. I am a task-oriented person, dammit, not a people-oriented person! It’s that, much as I like my coworkers, I don’t come to work to better my social life. It’s that in my metric, it’s better to approach people, possibly bluntly, than it is to mediate your concerns through a third party, so that the offending individual is left suspecting all of the friendly chit-chatters of filing complaints with that party and leaving her to guess whether this modification of her behaviour is enough, because it’s not like she’s had the chance to speak directly (that word again!) with anyone who actually wanted her to modify it. So help me, this all strikes me as remarkably inefficient, not to mention, highly inconducive to creating a pleasant working environment, at least for me. I’m just saying.

In summary: damned if I know what precisely I need to change (goddamn, it’s hard to get straight answers from the directness-averse HR set), and damned if I could make whatever changes are necessary without driving myself insane even if I did know exactly what they were. The good news is, I continue to provide my employer with a sort of specialized expertise that they’ve been seeking for years; and by all accounts, I do a very good job of what I was hired to do.

Call me old-fashioned, but right now, I plan to just continue to do my job well, and I reckon that’ll be enough.

1/26/2006

What do you call it when a person deliberately seeks out psychologically unhealthy attachments?

File under: Righteous Indignation, Sound And Fury, Those Who Can't, Queen of Sciences. Posted by Moebius Stripper at 6:34 pm.

I often forget just how dysfunctional a relationship many of my weaker students have with mathematics.

It’s been a long time since I’ve been surprised at the extent to which such students harbour an unproductive and damaging belief that mathematics is nothing more than a mishmash of symbols and voodoo procedures. After all, this is understandable, what with students being taught that memorizing templates of questions and plugging memorized formulas into their fucking graphing calculators is homologous with “doing mathematics”.

What surprised me for a long time after - at least the first fifty times I encountered the phenomenon - was how resistent these same students are to seeing mathematics as anything other than a collection of disconnected formulas and calculator algorithms.

The other week, I found myself teaching introductory graphing to a handful of students. Partway through a lesson, one student asked me - how do I graph the line in this question? Do I find two points and join them, or should I just find one point and the slope and then graph it that way?

Giddy with delight at this hint of outside-the-box thinking, I replied: you can do it either way you want! It’s your choice! Both of these options are totally valid methods of graphing the line! Two points, point slope, it’s up to you! In fact, you can graph it one way, and then if you want to check your work, you can graph it the other way, and ISN’T MATHEMATICS SUPER?

Pregnant pause. Hesitation. The barely-perceptible tremours of a worldview beginning to collapse unto itself.

There are two ways to do this question?

Yes! Not one, but two (2) ways to achieve the goal of graphing a straight line! Pick one! It’s entirely up to you!

But which way should WE do it?

EITHER way! The easy way! The quick way! Try ‘em both for practice, and then on your homework you can do the graphing questions whichever way you prefer, unless you’re explicitly instructed otherwise!

Facial expression indictating flicker of hope. Oh, so sometimes you’ll tell us which way to do it?

Well, yes, sometimes, because I want to make sure you understand both methods, but in general I’ll -

But which is the right way THIS time?

Do it both ways, and if you did it right, you’ll get the same line both times!

Shock and awe. Oh, we get the same line? No matter which way we do it?

Yes! That’s the point - these two methods are different ways of answering the same question correctly! Remember last class, when we talked about how we can think of a line as a path, and the two methods of being different ways of giving directions? I can say “start at 8th and Burrard and head north”, which is like a point - 8th and Burrard - and a slope - the direction “north”. Or I can say “start at 8th and Burrard, go to 7th and Burrard, and keep going in the same direction”, which is like two points. These are two ways of describing the exact same route. Just like the two points, or the point-slope method, will give you the exact same line.

Pause that gets pregnant, gives birth, and raises twins to adulthood. But which method is BETTER?

SWEET JESUS GOD, THE POINT-SLOPE METHOD, ARE YOU HAPPY NOW?

Remind me why I bother again? Give them freedom, and they beg for a dictator.

12/17/2005

But will they be the sensitive motherly types, or the nagging shrews?

File under: Character Writ Large, Righteous Indignation, XX Marks the Spot, Home And Native Land. Posted by Moebius Stripper at 6:30 pm.

Last night, the three Men Who Would Be Prime Minister (and the One Who Would Abolish The Position Entirely) were asked during the first English debate: what to do about all the heckling in Parliament? How to restore civility to the House of Commons?

To which Jack Layton, feminist, replied:

Well I’ve told my caucus that we won’t shout out and disrupt Parliament. And I think there’s one other thing we should do and that’s have a lot more women in Parliament. I’m very happy that our party has the highest percentage of women candidates ever that any political party has ever presented in an election, 37%. And mark my words - the tone of that house would change if we had a lot more women there, and voting NDP will help make that happen.

Women, see, are more polite than men. Really! Says so right there on TV! And politeness is good, and we want the House of Commons to be more polite, but we can’t very well expect the menfolk to behave by themselves, so let’s bring in more women to set the tone of Parliament. It’s a great deal: Layton gets to send the wimminfolk to do the dirty work, while collecting affirmative action points, all at no cost to himself!

Where have I seen this before? That’s right, grad school. I am leery of most manifestations of affirmative action to begin with, but at least I find a good many of them to be undertaken in good faith; this particular strain, however, is just odious.

Carolyn Ryan, one of four CBC journalists who live-blogged the debate, speaks for me:

Did Layton really just say his party would increase civility in the House of Commons by electing more women? That’s placing a big burden on the gender that produced Sheila Copps, Hedy Fry, and Deborah Grey. Are the female MPs supposed to shush their male counterparts when they get raucous? Should they hold tea parties in the foyer? Will they bring in a “bad-word jar,” with MPs having to pay a twonie every time they heckle? Puh-lease. Why not just promise to elect more polite people as MPs, or discipline the ones you’ve got now?

Why not? I know why not: because Layton knows better than to make promises he can’t keep. Better to set standards that his green women MPs won’t be able to live up to, and let them take the fall when they inevitably fail.

12/5/2005

There is a war between the ones who say there is a war and the ones who say there isn’t

File under: Righteous Indignation, I Read The News Today, Oh Boy, Semitism. Posted by Moebius Stripper at 6:21 pm.

You’ve probably heard of this one by now, if not this year then any of the last ten: Christmas is under attack! And I for one am having trouble choosing sides, because I can’t decide whose position is more compelling. Do I ally myself with the devout Christians who get the vapours whenever someone wishes them a sectarian Happy Holiday? Or should I instead join forces with the sensitive secularists who opt instead to pay due respect to those other religions that celebrate their tree-based holidays by engaging in a frenzy of consumerism in the days weeks leading up to December 25th? These, it appears, are our only choices in this war; “ignore this holiday and the accompanying propaganda entirely” isn’t on the table, which means that just like in a real war, the bulk of the casualties in this one are innocent civilians. As a vegetarian infidel whose family never ever celebrated Christmas, it might seem that I’m predisposed to being more sympathetic to the hippie heathens, but damned if I wouldn’t rather listen to Mariah Carey’s Christmas album on repeat than be subjected to rallying cries like this one here:

“At Rideau Hall, we will be putting up a holiday tree as we find it reflects the traditions of many cultures, and it is inclusive,” Rideau Hall spokeswoman Lucie Brosseau said.

Jesus wept. Not the Christian Jesus, mind you - the other Jesus, the inclusive one who represents the traditions of many cultures.

I assure you that the “we” that finds the history of all traditions great and small to be reflected in the magical Holiday Tree does not include any real-life Jews, Hindus, or Muslims, regardless of what the persecuted Christians may have you believe. And that’s the really mind-numbing aspect of this: the unfounded assumption that people who don’t celebrate Christmas are in fact on board with these inane gestures to pretend that Christmas by another name is somehow a whole ‘nother holiday. No, I would bet hard cash that the “we” that Brosseau references is a subset of earnestly sensitive, yet oh-so-ignorant semi-lapsed Christians who don’t believe in God or Jesus anymore, but who still celebrate Christmas because doesn’t everyone celebrate Christmas? I mean, some people may call Christmas something weird like “Chanukah” or “Diwali” or (God help us) “Ramadan”, but it’s basically the same thing, right? This “we” are the ones who puzzle over whether to put up Christmas trees in deference to their more traditional families and neighbours, or whether they should instead put up more inclusive holiday trees; it never occurs to them that they don’t need to put up trees, period, and that in fact most people in the world - and some even in this very country - don’t. And that some of those people don’t think that the end of December is sacred in any way - or, at least, they don’t think it’s more sacred than other months.

These are the folks who think that nomenclature is the single thing standing between an intolerant Christian society and an enlightened, multicultural one. There’s not a practising Jew in this country, I promise, for whom the generic, inclusive holiday tree - not to be confused with the nigh-identical Christmas tree - brings to mind the story of the Maccabees’ triumph against the Greeks. I assume that followers of religions that don’t even share part of a Bible with Christians aren’t going to be thinking inclusive, tree-inspired religious thoughts just because someone says they should. The holiday tree’s not a Jewish icon, and to pretend that it is - to tell a group of people who don’t adhere to your religion which icons are involved in theirs - that, in my view, is far more offensive than simply displaying bona-fide religious symbols in public. And that’s what pisses me off the most about this war: not the idiotic assumption that saying Happy Holidays constitutes persecution of Christians, but rather the idiotic idea that a few function calls of Replace(”Merry Christmas”, “Happy Holidays”) somehow amount to a genuine understanding of, and respect for, cultural diversity.

So while I’m certainly an opponent of this war, I’m having trouble working up a whole lot of partisan rage over it. Because what do we have? - we have one side insisting that Christmas music and Christmas greetings be ubiquitous…and the other accepting the ubiquity of Christmas iconography and culture but changing a few words here and there; not even thinking about how we have Christmas Day as a statutory holiday rather than a floater - those non-Christians can use their own personal leave time to celebrate their little holidays, after all; and unironically making a point of mentioning Chanukah - the single least important Jewish holiday - whenever they mention Christmas. And both sides fancy themselves martyrs.

It’s almost enough to turn one into a pacifist.

11/24/2005

It’s not a conspiracy theory if it’s actually true

File under: Righteous Indignation, Those Who Can't. Posted by Moebius Stripper at 10:34 pm.

At the risk of engaging in the premature counting of chickens, it looks like I’m going to be involved in something off-blog that will expose my rants about the fucking graphing calculator to a wider audience. Like, wider by a few orders of magnitude. Exciting stuff. Exciting enough that I spent some time today researching the link between Texas Instruments and the math textbook industry that I wrote about a few months ago.

It’s worse than I thought. It’s scandalous, and everyone who has a stake in what students are taught should be outraged.

Here’s a tiny subset of what ten minutes of Googling got me:

  • An alliance between TI and textbook publisher Pearson Prentice Hall: Pearson Prentice Hall and Texas Instruments to Publish Educational Products for High School Math Market. Never mind the creepy abundance of business jargon: far creepier are the repeated references to “increas[ing] student achievement”, “improv[ing] student performance”, “scientifically researched and standards-based instruction materials”, and the like, all waved around without either specifics or support. Just because you say it, doesn’t mean it’s true. Show me the data, Pearson Prentice Hall and TI.
  • Here’s a beautiful example of technology making simple concepts complicated: …The directions for performing these operations differ from calculator to calculator. The steps for a TI-82 are given on page 663 of the textbooks. For other calculators, you will have to consult the manual for instructions. Learn how to use these important functions… Oh, allow me to present a bold alternative to that shit: graph your bloody STRAIGHT LINE by hand, you goddamned punk.
  • Fostering Children’s Mathematical Power: An Investigative Approach to K-8 Mathematics Instruction. Here’s Activity File 0.1 - ZERO. POINT. ONE - in a book about teaching math to children: It may surprise children to learn that some calculations are too hard for a calculator. Encourage them to explore the limits of their calculators for each of the operations. For example, what is the largest addend that can be added on a Texas Instruments (TI) Math Explorer? I’ve got a word for this approach as a zero point first step toward fostering children’s mathematical power, and it ain’t “investigative”. Also: free cookie to anyone who can tell me why the TI in particular is necessary here. The $10 doodad I use to balance my checkbook could do just as well for this, maybe better.
  • Probably the creepiest material of all comes from the TI site itself. Take this, for instance. What do MTV®, Sesame Street ®, the WalkMan®, the DiscMan®, the Game Boy®, and the Brave New World of Mathematics Education ® have in common? A whole hell of a lot, apparently.
  • More from TI. Just…read the title, which I think is more fitting than the good folks at TI realize. I mean, just tie a bow around a big fat red foam A+, and it probably means about as much as a real A+ in a TI-based math class.

And there’s more. Much, much more. The skills-lite, calculator-heavy approach to mathematics education, which produces top high school students that are completely unprepared to do college-level math, won’t last forever. I just hope I’ll be around to bury it.

10/20/2005

Show me the data.

File under: Righteous Indignation, Sound And Fury, Those Who Can't. Posted by Moebius Stripper at 10:56 pm.

What’s that you say? You’re sick of all those long-winded education rants that never go anywhere? Me too! However, I can’t pass up this opportunity to commend the California Commission on Teacher Credentialing for so succinctly summarizing everything that’s wrong with elementary-school-level mathematics education today. And in an exam that every prospective teacher in the state is required to write, to boot - now that’s efficient delivery!

Many people believe children will never learn mathematics if allowed to use pocket calculators. Having spent countless hours memorizing multiplication tables and doing long-division problems unaided by any mechanical device, many adults cannot conceive of anyone acquiring this knowledge without similar effort and practice. ______________. What many people fail to understand is that mathematics is constantly evolving; it is not a fixed body of facts. Students must still learn basic skills, but they do not need to perform the endlessly repetitive exercises that calculators largely eliminate. Youngsters can better use their time—time they would have spent performing long-division problems—to learn mathematical concepts that will enable them to become better problem solvers.

Which sentence, if inserted into the blank line, would best focus attention on the main idea of the passage?

(A) It is true that mathematics is not the easiest subject in the typical elementary school curriculum.

(B) Many of you have doubtless heard about the bitter classroom experiences of students who learned mathematics this way.

(C) There is much to be said for instilling this kind of discipline in students.

(D) Although it was clearly not fun, students trained in this manner rarely forgot what they had learned.

(E) Such views, however, seem to reflect a resistance to change rather than a rational approach to mathematics instruction.

(F) Contrast this instance of common sense with the hallucination that follows.

Just kidding! (F) isn’t an option. The correct answer is (E).

Yes, yes: fish in a barrel are targets for amateur marksmen, I know. But what we have here is a barrelful of tranquilized guppies that been given free reign over early mathematics education, so let’s have a go at it before any more metaphors get mixed:

What many people fail to understand is that mathematics is constantly evolving; it is not a fixed body of facts.

You know, I skewered this one months ago. I even used the word evolved, for crying out loud. My readers found this -

Yes, if there’s one field that has evolved beyond recognition in the past quarter-century, it’s introductory calculus. Why, back when I was a tot, the area of a rectangle was length plus width, the derivative of sin x was 5, and we only had whole numbers, so whenever we needed to compute the area of a circle we had to use pi=3, AND YOU NEVER HEARD US COMPLAIN.

- to be hysterically funny, because it was so over-the-top. Except that…it wasn’t. It was very much beneath the top. It was smack dab in the middle of what those enlightened educators, unlike “many people”, have succeeded in understanding.

Students must still learn basic skills, but they do not need to perform the endlessly repetitive exercises that calculators largely eliminate.

They don’t? Really? I’m not convinced. Let’s see what a cognitive scientist has to say about this!

It is difficult to overstate the value of practice. For a new skill to become automatic or for new knowledge to become long-lasting, sustained practice, beyond the point of mastery, is necessary.

… By sustained practice I mean regular, ongoing review or use of the target material (e.g., regularly using new calculating skills to solve increasingly more complex math problems, reflecting on recently-learned historical material as one studies a subsequent history unit, taking regular quizzes or tests that draw on material learned earlier in the year). This kind of practice past the point of mastery is necessary to meet any of these three important goals of instruction: acquiring facts and knowledge, learning skills, or becoming an expert.

But what does that guy know, anyway? The times (tables), they are a-changin’! Mathematics is evolving! Get with the program!

I’m curious about something, though: is this anti-repetition view unique to mathematics education? Have the musicians among my readers, for instance, noticed a similar trend in music pedagogy? Music is EVOLVING! It is not a FIXED BODY OF FACTS! We have new-fangled technomology that enables students to bypass all that boring stuff, like learning scales! Or…do music students still practice scales, even though scales really aren’t that much fun to practice? I know that when I teach pottery, I spend a fair bit of time focusing on the basic skill of centering the lump of clay, even though it’s more rewarding to throw teapots.

Onward:

Youngsters can better use their time—time they would have spent performing long-division problems—to learn mathematical concepts that will enable them to become better problem solvers.

Joanne Jacobs speaks for me:

I’ve spent countless minutes (that seemed like hours) waiting for students I’ve tutored to multiply 4 times 5 or 3 times 6. Oddly enough, they weren’t adept at understanding mathematical concepts or solving problems.

The idea that students who don’t waste their time learning the boring basics will have freed up valuable time and brain space to become creative problem-solvers is one I’ve seen cited often. It’s an idea that every single mathematics educator with whom I have ever communicated - and I have communicated with hundreds, across several continents, both in person and through this blog - considers to be utter hogwash. But it’s possible that we’re just outliers. It’s possible that on the whole, students who don’t learn their times tables beyond mastery are brighter, bolder, and more creative problem solvers than their predecessors. And if that’s the case, then there should be plenty of statistics to bear that out. And surely the proponents of calculator-based curricula have plenty of rigorous statistical studies at their fingertips.

Let’s see them. Put up or shut up.

Show me the data.

Show me a single peer-reviewed study that indicates that students who were raised with calculators show greater facility and more creativity in problem-solving than those who were raised without. I want to see test scores. I want to see comparisons of performances in university-level mathematics classes between students who were made to memorize and practice their times tables, and those who weren’t. I want to see evidence that learning the basics and learning advanced mathematics are negatively correlated.

Until then, I’m going to rationally resist change, and teach mathematics in the way that my peers and I actually learned it.

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