Learning Strategies

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Labels: books, Dorchester, food, life, linguistics, math, model railroads, movies, teaching and learning, technology, travel, Weston

I enjoyed reading To Darkness and to Death, the fourth book in Julia Spencer-Fleming’s series of upstate New York mysteries featuring a female Episcopal priest. Not that I know much about Episcopalians or their priests, but that only makes these books all the more interesting. Eco-terrorism, real estate development, church politics, and town politics all play important roles. To Darkness and to Death is definitely not one of the best in the series, but give it a try if you want a pleasant diversion in a cold climate.

Labels: books

This post is a follow-up to my post of November 30, where I brought up two points that can illuminate one’s views on the big ideas of algebra:

...we discussed the assignment of partial credit for work in solving a problem — more on this later, but it definitely reflects one’s views on what the big ideas are — and whether the study of algebra is distinct from (and prior to) the study of functions...

Partial credit doesn’t sound like a deep issue, but it really is. All you have to do is gather a group of math teachers, give them a student’s solution to a problem, and ask how many points should be assigned. Regardless of whether it’s out of four (where there are only three partial-credit possibilities) or out of ten (where there are nine), there will be significant disagreements; I reached this conclusion from having participated in such activities many, many times, with various groups of colleagues. And I don’t just mean that one teacher will give two out of four and another will give three, or that one will give seven out of ten and one will give five. No, I mean that one teacher will give nine points and one will give zero! And this is in mathematics, which is supposed to be an objective discipline — unlike English, where such disparities might not be surprising.

So, what does it mean when major disagreements surface in this area?

It usually means one (or both) of the following types of differences:

• differences of opinion about what the big ideas are
• differences in what one values

For instance, consider these three examples of student work that we discussed in the seminar in which I participated in November:

1. The problem read, “The sum of three consecutive odd integers is 81. Find the integers.” One student’s solution was like this:

   Let x = 1^st odd integer
   x+1 = 2^nd odd integer
   x+2 = 3^rd odd integer
   x + x + 1 + x + 2 = 81
                    3x + 3 = 81
                          3x = 78
                            x = 26
   The integers are 26, 27, 28

   How many points (out of ten) is this worth? If a big idea is that odd numbers differ by 2, not by 1, then the setup at the beginning of the solution represents a significant error — especially since the student wrote the word “odd” each time, thus showing that s/he didn’t merely skip over the word “odd” in the problem statement. On the other hand, the solution is otherwise correct, the work is clearly shown, and the answers will even check, being three consecutive integers adding up to 81 (ignoring the word “odd” again). If you highly value all the skills of combining like terms, backtracking to solve an equation, and recording a solution, then the solution is worth a lot of points. But if the idea of consecutive odd integers is important, it may be worth very few points. My colleagues rated the solution all the way from one to nine; I gave it a six.
2. Next we have a different student’s solution to the same problem:
   
The grades on this one ranged all the way from zero to ten! Some teachers gave it only a few points — or even zero points — because no algebra was used. But I was one of those who gave it a ten, because not only was the solution correct but it also showed a thorough understanding of what the problem was asking for, and of course the answer was checked. If an algebraic solution was meant to be required, that requirement should have been specified.
3. Finally, here’s a different problem, along with one student’s solution: “Solve 2(x – 10) &ndash (12x – 4) = 20.”
   
   The issue here is that the student couldn’t read his own handwriting (possibly her own handwriting, but the odds are against that): “20” got transcribed sloppily and then read as 26. I gave it a nine out of ten, since that error struck me as a very minor one. But other teachers’ scores ranged all the way down to zero, on the theory that the student had nobviously never checked his answer. My own values are that checking one’s answer is a big idea of algebra, if we mean that it’s important to understand that what we mean by a solution is a number that will satisfy the equation. But failure to check, especially in a time-sensitive situation where there are no instructions to check, strikes me as a very minor offense.

Your mileage may vary.

The second point that I was intending to discuss — whether algebra is distinct from functions — will have to wait for another post. This one is already too long.

Labels: math, teaching and learning

Although it’s not quite as enthralling as her first book, Tana French’s sequel is well worth reading. In The Likeness, French continues her lyrical writing and fascinating characterization. Cassie Maddox continues from the prior novel, In the Woods, but this time she’s the clear protagonist. The beautiful writing clearly takes center stage in this book, but I also couldn’t help being captured by the interactions among two sets of characters: the police on the one hand, a group of Irish graduate students on the other. Read it for the language, for the characterization, and even for the suspense, though the plot of The Likeness is not really its strong point.

I don’t usually like to quote from Amazon reviews, since they tend to be from random amateurs. As a random amateur myself, what do I need their observations for? But in this case I really have to quote from three, even though I risk sounding like a publisher looking for blurbs:

Tana French has created another sensuous, lyrical, haunting, suspenseful story... Tana French is no lightweight, but she makes the story accessible to anyone who enjoys reading. She has that gift to appeal to a variety of readers — even readers who look for largely escape mysteries. But this is not escape reading; it is the kind of reading that makes you ponder. It is philosophical and it echoes. It has shadows, swirls, hollows, heart,humanity, tension, suspense, whispers, hawthorn, hawthorn, hawthorn... [by switterbug "laughingwild"]

It was truly an exceptional and thrilling read. The way French fleshes out Cassie Maddox, Lexie Madison and the four housemates is truly astonishing. I have always been fond of character-driven plotlines and novels, and French truly impressed me with “The Likeness”. The amount of depth present in these characters — their motivations, relationships, and personalities — was both fascinating and engrossing. This was a book difficult to put down. [by Voracious Reader 326 “College student”]

I couldn’t write a single sentence as well as Tana French if I started now and lived to be a thousand. And she wrote a whole book, two books, of them. Flawlessly. Word after word, sentence after sentence, paragraph after paragraph, until the book is as perfect as it could be. It boggles the mind, it really does... It’s a privilege to read Tana French, it really is. I feel only pity for the person who wrote of the unbelievable plot, I do. This book isn't about a plot, just as Chandler wasn’t about plot, just as we don’t read Shakespeare for the plot. Anyone can do plot; but to give feeling and life, undoubted life, to characters on paper, that is to marvel at. [by Adam Shinbrot]

Labels: books

The waitress at the Legal Seafoods branch in Harvard Square was nervous and very apologetic. “This is my first time opening a bottle of wine in front of a customer,” she confessed. Of course she wasn’t allowed to rest the bottle on the table, and everything was supposed to be perfect.

We assured her that it was OK to put the bottle on the table, and we coached her through the process. The cork came out smoothly. The waitress was just so grateful: “Most people would be upset with me for not knowing how to do this.”

I replied by saying that I’m a teacher and that I believe in being patient while people learn. Doesn’t sound so unusual to me...but then again, I’m a teacher. We left a good tip.

Labels: food, teaching and learning

I recently read Joshua Kendall’s biography of Peter Mark Roget, entitled The Man Who Made Lists: Love, Death, Madness, and the Creation of Roget’s Thesaurus. While this book is fascinating, it’s also deeply flawed — especially for those of us who love lists, not to mention those of us who love thesauri and other reference books.

On the plus side, Kendall teaches us a lot about Roget’s background as a scientist and physician. We learn about his compulsive list-making as a child, whether it be names of farm animals in Latin or lists of the bones in the human body. We learn about his organization of all the concepts of the English language in later life. And we learn a little — but not nearly enough — about Roget’s mental problems and how he coped with them. These problems were relevant, indeed central, to the decision to create the first thesaurus in 1852. Compiling lists of words apparently helped Roget cope with depression, anxiety, and probably Asperger’s, though Kendall only barely touches on the last of these.

On the minus side, the reader gains almost no sense (despite the subtitle) of the importance of the thesaurus to Roget’s life and to the world. It’s just one incident among many. I was looking for details — lots of details — about how the thesaurus was compiled. The lack of details is rather ironic, given the subject of the book. And it reminds me of my issues with The Professor and the Madman. The other flaw is the offhand consideration of the likelihood that Roget had Asperger’s, though of course neither the name nor the disorder was known in the 19th Century. These flaws were not enough to deter me from finishing The Man Who Made Lists, but they certainly reduced my enjoyment of the book and meant that I learned far less from it than I had hoped.

Those who know me will not be surprised that I still have an old copy of Roget’s International Thesaurus, a copy that my father gave me when I was eight years old. As I say, people won’t be surprised that I have this, though they might be surprised that I could lay my hands on it so readily. Anyway, when I was eight, this “new edition” of the thesaurus had been out for nine years, so it slightly predates my own birth. It’s instructive to contrast the arrangement and organization of this edition with the modern alphabetical lists of synonyms that still claim the name “thesaurus.” My copy, published by Crowell, contains the following remarks in the Publishers’ Preface [note the subtle placement of the apostrophe]:

The basic principle of Dr. Peter Roget’s original Thesaurus was the grouping of words according to their ideas rather than the listing of words, as dictionaries do, according to the alphabet. This principle — the secret of Roget’s success — has been scrupulously preserved in the various Crowell editions for over sixty years. [Italics as in original]

The difficulty with grouping words by ideas is that it can be very difficult to find a word, so this edition of the thesaurus contains an index that’s nearly as long as the body of the book. Be that as it may, Roget’s idiosyncratic organization of all possible concepts is a delight, as long as you don’t take it as a given truth. The schema is hierarchical and multi-level. For example, suppose you were thinking about prime numbers, but you couldn’t remember the terminology prime number. You would, of course, look under Class I (abstract relations), Section V (Number), Part 1 (Number in the Abstract), Category 84 (Number), Subcategory 2. You knew that, didn’t you?

Well, no, of course you didn’t; that’s why you needed the huge index. Anyhow, the subcategory in question reads as follows:

complement, subtrahend, multiplicand, multiplier, multiplicator, multiple, submultiple, coefficient, dividend, divisor, factor, quotient, fraction, mixed number, numerator, denominator, decimal, mixed decimal, circulating decimal, repetend, common measure, aliquot part, reciprocal, prime number, totient, quota, differential, integral, fluxion, fluent, power, root, radix, base, exponent, index, logarithm, antilogarithm, modulus.

Note that this is most definitely not a list of synonyms! It’s a list of words that are conceptually related in some way. Reading it, you spot the term you were looking for (“prime number”) and your mind is also captured by a great many other words that are closely or loosely connected. What a loss to use a modern so-called thesaurus, where you probably can’t even find “prime number” unless you already know the phrase, and then you’ll simply find that there are no synonyms.

You can browse through Roget’s Thesaurus and learn something new on any page. All you are likely to learn from a modern thesaurus is some pretentious near-synonyms that will make you a worse writer.

Labels: books, linguistics, teaching and learning

Last night’s New Year’s Eve festivities included watching Juno, which neither Barbara nor I had seen before, even though it was released over a year ago. On the basis of reviews and personal recommendations, I had expected to like this movie. It exceeded my expectations.

I’m sure everybody knows the plot by this point, but I’ll still stay away from spoilers in these brief comments. My major observation is that all of the actors were entirely convincing in their portrayals of various teens and adults, most notably Ellen Page as Juno, who kept reminding me of various Weston students of mine. No students in particular, I hasten to add — just different generic students at different points. J.K. Simmons and Allison Janney were much more genuine than the parents in the typical movie about teenagers, although I kept being distracted because I knew I had seen Simmons before but couldn’t remember where (I’m not good at actors). When I looked him up, I discovered that he plays Dr. Skoda, who appears off and on as the consulting psychiatrist in Law and Order; the temperaments of the two characters are almost identical, thus reinforcing the distraction. Also, Jennifer Garner and Jason Bateman were effective (if a bit creepy) in their roles as the soon-to-be adoptive parents.

Early in 2008 there was some chatter about whether Juno glamorizes and therefore encourages teenager pregnancy. Frankly, I don’t see it. Admittedly, Juno isn’t portrayed as a bad kid, as the right-wingers would prefer; she doesn’t suffer much for her mistake, and her friends and family are all accepting of her. But that doesn’t mean that the movie glamorizes pregnancy, and since Juno immediately decides to have the baby adopted, it shouldn’t encourage the standard worry among adults that a girl will want to get pregnant in order to have a baby who will love her. In fact, since neither Juno nor her family is dysfunctional, what we have here is simply a straightforward tale of how a normal (if rather counterculture) teenager grows up and interacts with adults and with other kids. It’s well worth seeing, just for the quality of the acting if nothing else — but it’s also worth seeing because it’s such a refreshing and captivating story.

I’ll have to ask my student who recently moved to Weston from Minnesota about St. Cloud, where the adoptive parents live in the movie. The director portrays it as a lot like Weston.

Addendum at 8:10 PM:
I wrote the above earlier in the day. But now I’ve just finished watching the first Greater Boston of the year on WGBH, a retrospective of 2008. Emily Rooney’s guest Dan Kelly (identified just as “attorney”) made the following remarks in connection with the supposed but unproved pregnancy pact among girls at Gloucester High School:

The message of all this is not that more birth control is the answer. The message is that Time Magazine picked up on the bandwagon of sensationalizing teen pregnancy, and that bandwagon is out there because of Britney Spears’ sister pronouncing how wonderful it is to be a teen and to be pregnant... The Juno movie, the Juno effect. The Juno movie in a lot of ways was a great movie from my perspective because it showed the dignity of a human life before it’s born. It’s a pro-life movie and it sends a wonderful message to kids. But it also is a movie that glorifies teen pregnancy to some extent. To say that there will not be that many side-effects, that you can get through it, that it is not such a colossally terrible thing, and it also glorifies in some respects teen sex, although I think the message of that movie is that teens are not prepared to have sex and should not be having sex.

This analysis is just plain wrong. The movie doesn’t glorify teen pregnancy, and it doesn’t send a message. It’s not a political document. It’s a story, a work of art, which presents a group of characters and deals with the internal and external conflicts of the main one, just as stories usually do.

Labels: movies, Weston

I just discovered a cool poster-creating applet called Wordle. In their own words:

Wordle is a toy for generating “word clouds” from text that you provide. The clouds give greater prominence to words that appear more frequently in the source text. You can tweak your clouds with different fonts, layouts, and color schemes. The images you create with Wordle are yours to use however you like. You can print them out, or save them to the Wordle gallery to share with your friends.

You can create an image from text that you type in, or from a URL of a blog with an RSS feed. In the latter case, the applet uses all the text it finds at that URL, excluding some common English words (or whatever other language you might choose).

I rather like the result I got by giving them the URL of this blog:

Labels: life, technology

I just finished sending off 104 college recommendations this week.

How many?

Yes, 104. And that was in addition to 21 “early action” recommendations that I sent out earlier in the fall.

But before you conclude that that’s a ridiculously large amount of work for a teacher to have to do, especially during vacation, you need to look at the rest of the story. First of all, these 125 recommendations come from only 13 seniors (all of whom took my honors precalculus class last year), so you can see that they average nearly 10 apiece. That means writing only 13 letters (printed out many times, with each copy signed and stuffed into the appropriate stamped envelopes) and answering only 13 questionnaires (scanned in, and similarly printed out and stuffed). Actually, it’s a tad more complicated than that, since there are still a few colleges that don’t use the Common Application that makes it so easy for high-school seniors to apply to a large number of places, but it’s still basically true.

For each of these students, the total number of applications ranged from 5 to 16. This is Weston, after all. It was the total number of distinct colleges that these students applied to that surprised me a bit: 57. The reason that this surprised me wasn’t the specific number (the famous Heinz number) but the fact that it was so high. In the past, students in honors math courses at Weston tended to apply to the same relatively small number of colleges. But things have changed: it’s now much harder to get into any particular competitive college than it used to be, and as a result it’s unpredictable whether a perfectly qualified student will get admitted to his or her first choice, or second choice, or third choice...

So don’t be horrified by the task of writing 125 recommendations — just by the amount of printing, signing, and envelope-stuffing required.

Labels: teaching and learning, Weston

A completely unsolicited testimonial:

Barbara and I noticed that our 28-year-old gas furnace was behaving erratically, sometimes turning off and on in rapid intervals, and sometimes turning off altogether. We called Micci Fuel Co. to come look at it and fix whatever was wrong. They showed up on time, cleaned and vacuumed the furnace, and explained to us just what they were doing and why. If you’re in their neighborhood, we certainly recommend them!

The furnace works perfectly now.

By the way, conventional wisdom has it that young people aren’t going into businesses like this anymore, so we were pleased to see that one of the guys who showed up was in his twenties.

Labels: Dorchester