A lot of adults are complaining that teens are “illiterate” in their writing, especially in email messages — you know, “kids these days…” and all that — but that’s not what I’m seeing. The abysmal level of teenage writing is usually attributed to their addiction to text messaging, a.k.a. texting. For example:
The youth of Ireland are becoming increasingly poor spellers and writers, and their love of text messaging on cellphones is a major reason why, according to the Education Department.
In a report published Wednesday on national test results in English for about 37,000 students aged 15 and 16, the department’s Examination Commission said cutting-edge communications technology has encouraged poor literacy and a blunt, choppy style at odds with academic rigor.
“Text messaging, with its use of phonetic spelling and little or no punctuation, seems to pose a threat to traditional conventions in writing,” said the report written by the department’s chief examiner, whose identity is kept confidential to safeguard the integrity of tests.
The report branded today’s teens “unduly reliant on short sentences, simple tenses and a limited vocabulary.”
…
Ireland is among the world leaders in cell-phone use — in part because of traditionally high costs for conventional phone lines — and surveys indicate that a majority of children have their own mobile phone by age 12, with the most enthusiastic texters sending more than 250 a week.
Yes, that happens to be Ireland. But we hear the same kind of complaints in this country as well. However, as I said above, that’s not what I’m seeing. Of course I may have a very skewed sample, consisting primarily of Weston students, but since I’m not pretending to be doing a statistically valid survey I’ll go ahead with my observations, skewed though they may be. Here’s what I see. I’ll stick to email, since that’s where we’re most likely to see overly informal writing:
Most students know how to address adults (teachers, at least) in their writing, even when using email. The big exception is the capitalization of the pronoun “I,” which often appears uncapitalized. Otherwise their grammar, style, punctuation, and spelling are all pretty reasonable. I’m not claiming that we have works of literature here — merely that the quality of writing is close to that of adults.
To gather my evidence, I looked at 20 consecutive email messages written by my students in October. (As I say, it’s certainly not a rigorous survey, nor was it meant to be.) Here they are in their entirety; I have omitted no messages, nor have I edited anything beyond adding message numbers and altering students’ names. Judge for yourself.
1 Hey Mr. Davidson,
I hope that i could get a recommendation from you. I’m sorry i couldn’t get to you earlier about the recommendation letter.
To make it easier for you, i’ll be sending the info you need over email. However since i do not have the finalized list of the colleges that i would like to apply to, is it possible to hold onto the the rec. till i can get you the list of colleges? After i’ve narrowed my list down i’ll be able to give you the letters that you need to send them off in. Thanks a lot.
2 Hey Mr. Davidson,
I am doing a lot better today, yesterday and Tuesday were truly awful though, so although i’m not 100%, I feel “relatively GREAT” and it was very nice to get back to school today. I stopped by your desk after school to talk about what I missed and you weren’t there, but luckily I’ve been getting filled in pretty well from classmates, and borrowed a textbook, so i’m not behind, and just may need some help completing tonights assignment. I noticed a note on your desk that said you will miss tomorrows class, is this true?
Thanks for the check-in, I appreciate it, and I hope to see you soon!
3 Hi Mr. Davidson,
This is Stu Dent in your H block Geometry class. I’m just wondering
what days you free after or before school this week before the 18th?
Thanks alot!
4
On the westonmath website for #6 on tonight’s homework I’m not sure what the &ndash means. Should I assume the question is for (X+2)^2?
5 Hi Mr. Davidson,
I was wondering if there was a possibility I could meet with you tomorrow morning regarding proofs as I am confused going about proving them especially with word problems such as the one with the bus and railroad for example. I’m willing to come whenever you are available (except maybe not 3:00 AM in the morning!).
6 Hi Mr. Davidson
I’m having some trouble with the domain and range part of tonight’s homework, as well as the Dr. scheme questions. Could I meet with you at 7:15 tomorrow morning to go over it?
7 Hi Mr. Davidson
I’m in your Honors Geometry class Block F. I just have one question. For the sample problems you gave in the book, I’m not quite sure what method I should use to solve the last question, number 43. I usually use guess and check, but I know there could be an equation to solve it, but I’m not quite sure what the equation is.
8 Hello Mr. Davidson,
I have registered onto the math blog site and I was wondering how to do I actually post a blog since I have not been able to find the button that allows me to actually make a post.
9 Hi Mr. Davidson,
Tomorrow I have a study hall first and last block. I was wondering if you were free either of those blocks so that I could go over the test with you.
Thanks!
10 Hi Mr.Davidson,
I went over the clock problems with a friend and now I understand it so I don’t need to meet with you! Thanks
11 Hi Mr Davidson,
Could i see you tommorow morning before school starts to go over some test questions and concepts? Thanks
12 Hi Mr. Davidson,
I’m in your F Block Honors Geometry class. I just have one question. On the test, on problem 3, for the collinear points question, I think it was the last one. I got that question wrong because I said the points were collinear. I don’t know why, though, its wrong. Can you please explain it to me so I don’t make the same mistake on future test or quizzes?
Thanks,
13 Hello,
I just submitted the post that I created on the blog website.
I did not remember how to make the math look like math.
Also, when I try to preview it, it says “Sorry, no posts matched your criteria.”
I probably did something wrong and I’m not really sure how I can fix it.
Thanks,
14 Hi Mr. Davidson,
I think I may have left my math book in your class on Friday. If you have it could you please let me know and I can get it on Tuesday.
Thank you very much and have a good long weekend!
15 It is Stu Dent. I have contacted you because i finished my blog, and saved it, but then logged out, and it seems now that the website could be messed up, because when i try, it says “Cheatin’ Uh.” I will continue to try, but could you please respond, because i would like to have my post up.
16 Hi Mr. Davidson,
This seems like forever ago, but at the end of last year you said you could help me out by writing my college recommendation. I have the form from the school and the forms from CommonApp.org almost ready to give you, so I thought I should let you know where I am/remind you. I am applying to one school Early (November 1), so I also have an envelope from that school, and then I will bring the rest later when I decide what schools I am going to apply to Regular (January 1).
Would you like to meet with me before you write it? Or can I just drop off the packet of papers with you?
I only have one free, so if we met it would probably have to be either in the morning, during lunch, or quickly after school.
Thanks for all your help,
17 Hi Mr.Davidson,
My parents and I discussed my last quiz and test grades we thought
that maybe I should consider taking the CP geometry course. Do you
have any input on this and is there an F block CP geometry class?
Please let me know.
Thank you,
18 Mr. Davidson
So i know it’s been a while since we’ve talked but I was wondering if you need anything from me for teacher recs. I will have the envelopes and teacher rec form to you for Thursday. May I drop it off Thursday after school? I am actually just giving you the info (envelope, due date) for the school that I am applying early to because I still have to finalize my other schools. I will tell you the rest of the schools as soon as I finish my list. I hope that’s okay.
Thanks,
19 hi mr. davidson!
its Matilda. well i was talking to Stu Dent and he tried helping me with the blogging but it wouldnt work. and he said that i had the same problem as him and the admin messed up the account or something like that. i couldnt write the blog! let me know how to fix it. see you tomorrow!
20 Hi Mr. Davidson, I’m finishing up the teacher recommendation package that I plan to give to you tomorrow in school. There are a few things that I can include if you feel that you need or want them: my activity list, parent brag sheet, the teacher rec Basic Questionnaire, etc. Would you like me to include any of these in your package?
After spending a totally absorbing 90 minutes at Harry Potter: The Exhibition, I still don’t know why it’s at the Museum of Science of all places — what’s the connection with science? — but I highly recommend it nonetheless. The exhibition consists mainly of actual props, sets, and costumes from the filming of the Harry Potter movies, supported by small amounts of textual commentary and other related material. By far the most striking aspect of the show is the exquisite attention to detail; every tiny bit of the handmade costumes and other props has been carefully crafted and expertly weathered so has not to look new. The verisimilitude has been enhanced by the context in which the materials are set — sometimes actual scenes but more often just sets that are suggestive of the scenes used in the movies. Even the usual store that you are forced to walk through when leaving the exhibit is entrancing, as it is made up to look like various shops from the movies. The exhibition will be there until February 21; don’t miss it!
Incidentally, it struck me as I was walking through the exhibits that there is a deep connection with model railroading here. I was asking myself why I would be interested in costume design, a subject that actually doesn’t interest me at all. And yet the costumes were among the most fascinating artifacts on display. Halfway through it hit me: even though everything was 1:1 scale, it’s a lot like a model railroad! The attention to detail created a miniature world that selectively reflects the real world but veers off into fantasy in various ways. I once again thought of imaginary gardens with real toads in them. See a post I wrote four and half years ago, which was actually about math but could equally as well have been about model railroading; it’s just that everything is intertwingled.
If you’re a long-time reader of this blog, you will recall that I wrote a post four years ago entitled, “Ban Comic Sans!”, in which I linked to the ban comic sans site. Now Gizmodo has a new take on the matter in John Herrman’s list of Eight Regrettable Tech Inventions:
Vincent Connare, and Comic Sans: Font of choice for kitschy restaurant menus, passive-aggressive office notices and the worst websites on the internet, Comic Sans is merely a lame font, made evil by its endless, widespread use. From the WSJ, the creator on his most maligned creation, which was originally intended for use exclusively in Microsoft Bob: “He cringes at the most improbable manifestations of his Frankenstein’s monster font and rarely uses it himself, but he says he tries to be polite when he meets people excited to be in the presence of the creator.” Connare’s penance has already been paid: Microsoft owns the font, so he couldn’t earn any royalties from its viral — and I mean that in the worst way possible — spread.
“Do you know about the Xerox Alto and Xerox Star computers from back in the ’70s?” asked one of my fifth-graders in The Saturday Course.
“Yes,” I replied, “but I’ve never before met a fifth-grader who knows about them!” This mut have been ancient history to him.
He went on to tell me that the Alto was the first computer to use windows, menu, and a mouse, but that Xerox’s marketing department wasn’t able to sell it to home users.
Actually, I wrote once before about a Saturday Course student who surprised me with her wisdom and knowledge — and that was a fourth-grader that time — so I guess I shouldn’t have been surprised. But this blast from the past was definitely unexpected.
Check out the blogs for all of my classes! We rotate each day that a class meets, so that students take turns posting class notes. So far this has led to a number of positive effects:
- Students who miss class for any reason have a resource for finding class notes.
- Students who were present in class but have inadequate notes (yes, this has been known to happen, even in Weston) have a backup.
- Students get the experience of taking and writing up detailed notes for a real audience to read.
- Misconceptions are revealed to me way in advance of the next quiz or test, as I can sometimes see that a student misunderstood what was done in class.
The first three effects were expected, but I hadn’t anticipated the fourth.
Little Brother, by Cory Doctorow, is billed as a “Young Adult” Novel. And so it is. But, like several other “Young Adult” adults, it is worth reading by not-so-young adults. This is an homage to 1984 — hence the title — set in the current world of technology, teenage hackers, and paranoia about national security. The fundamental conflict is between the Department of Homeland Security and a 17-year-old wiz named Marcus, who initially goes by the handle of W1nst0n (no coincidence there) and soon becomes M1k3y. Doctorow, who may or may not be related to E.L. Doctorow, has made the novel available for free download, although in my case I checked the excellent audiobook version out of the library.
Anyway, I enthusiastically recommend this book to anyone who is interested in politics, technology, education, and their intersections. Marcus is an engaging and believable protagonist, whose conflict with the DHS forms the central theme of the novel. The idea of a teenage hero who successfully fights the establishment is, of course, not new to science fiction, but Doctorow handles it with particular skill and interest. The novel is particularly authentic in its depiction of cryptography, Internet security, and other technical matters — but it still makes a convincing account to those who are not entranced by such topics. As a teacher, of course, I was particularly taken by the issues that Marcus’s school had with him, and by the San Francisco school district’s attempt to fire his social studies teacher, who was only attempting to teach the class about the Declaration of Independence and the Bill of Rights (subversive documents, of course). The result is a somewhat chilling but ultimately convincing tale. Do read it!
Vincent Rossmeier has written a refreshing article in Salon entitled “Is the Internet melting our brains?” Essentially an interview with linguist Dennis Baron about his new book, A Better Pencil, the article counters much of the typical hand-wringing in the mainstream media and academia:
Facebook is ruining our social relationships; Google is making us dumber; texting is destroying the English language as we know it. We’re facing a crisis, one that could very well corrode the way humans have communicated since we first evolved from apes.
While I’m sure that many of my students spend too much time on Facebook and too much time texting, I’m equally sure that their social relationships and their use of English were no better before they indulged in such activities. I’ve reserved Baron’s book from the library, and I’ll post a review here (but only after I’ve read it).
How nice to see a website that actually recognizes Dorchester as a neighborhood of Boston! Povo not only lists it prominently, but its description is an accurate portrayal of Dorchester’s many virtues:
Dorchester is the largest geographic and most populated neighborhood in the city of Boston. Home to Dot Ave., it is also Boston’s most diverse neighborhood, with large pockets of African Americans, Irish, Vietnamese, Caribbean, and South and Central American residents. In recent years, the neighborhood has seen an influx of young working professionals, working artists (in areas like Lower Mills, Peabody Square, and Savin Hill), and a growing GLBT community along Dorchester Avenue, while it’s still predominantly a working class neighborhood and a thriving center of immigration. The neighborhood also includes vast economic diversity. Housing varies incredibly from housing projects in places like Bowdoin/Geneva and Franklin Field to stately Victorian homes in places like Ashmont Hill and Melville Park.
Contrast this paragraph with the usual treatment. Other websites almost always do one of the following:
- They ignore Dorchester completely, because they think it has little to offer out-of-towners. For example, here’s Fodor’s list of “Places to explore” in Boston:
- Alternatively, they notice nothing about Dorchester except for its crime, which is so well publicized by the media. For example, here’s a sentence from a movie review written halfway across the country, in Madison, Wisconsin:
The Dorchester neighborhood is a tough one, mostly lower working class, dotted with slummy bars where drug-related shootings are a regular occurrence.
So check out Povo for the straight scoop with a positive POV that’s not written by the real-estate industry.
For years now I’ve been fascinated and bothered by hierarchical systems of organization, starting with the Dewey Decimal System and progressing to typical org charts in businesses and hierarchical file systems on computers. On the one hand, the systematic structure appealed to me; on the other hand, it was clearly much too rigid. Even as a kid I was perplexed by the problem of shelving interdisciplinary books in a library, and I still pester librarians about that issue. (It’s no coincidence that my favorite book is Gödel, Escher, Bach.) A place for everything, and everything in its place…but no, that doesn’t work. And as soon I became an avid computer user I got frustrated by files that belonged in multiple places; alias are nice, but they’re a workaround, not a solution.
I’m still of two minds about this. I like the fact that the email in my gmail account is mostly sitting in one huge pile, where I can use the power of tags and fast searching to retrieve what I want. But another email account, which I access through Apple Mail, is nicely organized into folders and subfolders. Except…does a message from Paul dealing with teaching math at CSA go into the Paul folder or the math folder or the CSA folder? Folders aren’t really right.
Continue reading Everything is Miscellaneous
During yesterday’s Massachusetts Math League meet in Westford, a cell phone belonging to a student from a nearby high school (neither Weston nor Westford) emitted a tone during the first round. She pulled the phone out of her pocket, looked at the screen for awhile, pressed a button, and put it away. The proctor, assuming that she had received a text message, reported the incident.
The girl claimed that it was merely a “low battery” message.
Perhaps that’s all it was. Probably in fact that’s what it was. But it was still a gross violation of the rules, which prohibit not only the use of cell phones when competing but even the presence of cell phones in the room. Students are supposed to keep their phones in the prep room and not carrying them into the competition rooms. They know the rules.
If, of course, a student turns off her phone and puts it in her pocket, no one will know if she has brought it into the competition room. But that’s not what happened here. So she received a zero for the round, affecting not only her own score (reducing her possible total from 18 to 12) but also her team’s score. Perhaps that penalty was not sufficiently severe.
And the moral is…
Yesterday was an “abbreviated Wednesday” at Weston High School, since the afternoon was devoted to a Professional Development Day for teachers. We focused on the subject of interactive whiteboards (IWBs); many of our classrooms have recently been equipped with either an ActivBoard or a SmartBoard, and we badly need training in how to use them effectively. An ActivBoard was installed in my classroom over the summer, and I’ve attempted to use both their own software and the SmartBoard software with the ActivBoard. Although they are competing brands (and the hardware is different), the software is reasonably compatible and somewhat similar.
Somewhat — but definitely not entirely. As a result of the workshop, I have decided to give up on the SmartBoard software and return to the ActivBoard software, which definitely is closer to meeting my needs as a teacher. I wouldn’t pretend to have done anything like a thorough analysis of their relative strengths and weaknesses; all I can say is that there are several tasks that don’t work as well (or apparently don’t work at all) on the SmartBoard. But take this with a grain of salt, since the information that I don’t yet know about either one would fill a book. There is a small amount of evidence (not definitive, but still…) that the ActivBoard software works better on Macs and the SmartBoard software works better on Windows. My conjecture — with no evidence at all — is that this difference arises because the ActivBoard software was probably developed on Macs and the SmartBoard software on Windows; when each is ported to the other platform, it’s never quite as effective as the original.
The bottom line, of course, is whether either of these products helps kids learn better and helps teachers teach better, or whether they are merely cool toys. They both have a somewhat useful feature that one’s notes on the whiteboard can be captured as computer images and then posted on a website. Then absentees can find class notes and students who were present in class can check their own notes against what was written on the board. Frankly, though, I’m skeptical of this feature, at least for the absentees: class notes in a math class are almost entirely cryptic to anyone who wasn’t there to listen to the class and participate in it. Maybe it works in other subjects. As for other features of the interactive whiteboards, the jury is still out concerning their effectiveness. The only study I’ve seen so far is “The Interactive Whiteboards, Pedagogy and Pupil Performance Evaluation: An Evaluation of the Schools Whiteboard Expansion (SWE) Project: London Challenge,” which draws the following conclusions (you’ll have to work your way through the educationese):
The main findings are that the SWE scheme substantially increased the number of IWBs in use in London secondary school core subject departments. As a technology, IWBs adapt well to the kind of whole class teaching environment favoured in secondary school core subjects. Their actual use varies according to the teacher, and between subject areas.
The transformation of secondary school pedagogy is a long term project. The use of IWBs can contribute to this aim under the appropriate circumstances. Discussion of pedagogy should precede and embed discussion of the technology. Successful CPD is most likely to be effective if it supports individual teachers’ exploration of their current pedagogy, and helps identify how IWB use can support, extend or transform this. Discussion of the relative strengths and weaknesses of different ways of using the technology for particular purposes should be part of the on-going work of a department. Although the newness of the technology was initially welcomed by pupils any boost in motivation seems short-lived. Statistical analysis showed no impact on pupil performance in the first year in which departments were fully equipped. This is as we would expect at this stage in the policy-cycle.
…
There are potentially some drawbacks to the ways in which IWBs are currently being used. The technology can:
- Reinforce a transmission style of whole class teaching in which the contents of the board multiply and go faster, whilst pupils are increasingly reduced to a largely spectator role;
- Reduce interactivity to what happens at the board, not what happens in the classroom.
Those with responsibility for the rollout of the technology and training for best practice in its use need to be aware of these dangers and help refocus discussion amongst colleagues on their pedagogic aims so that teachers harness what the
technology itself can do in the light of their broader pedagogic purposes.
Further research and exploration of how peripherals can mediate the focus on action at the front of the class, and create more space for pupil involvement in the creation of lesson content is needed. Amongst practitioners, this kind of exploration currently flows from teachers already committed to using any technology in this way, i.e. bending the technology to their own pedagogic intent.
As I say, the jury is still out. As with so many technological advances, its success may all hang on adequate teacher training.
We’re studying some 20th-Century mathematics in Precalculus class these days. This situation is unusual in high-school math, where most of what we study goes back at least 300 years, not to mention 2300 in the case of most of our geometry. In order to give some historical context, to show why some revolutionary ideas appeared at the end of the 19th and beginning of the 20th centuries, I gave a mini-lecture on the intellectual ferment at the time in other disciplines, including sciences (Darwin, Einstein, etc.) and arts (Monet, Stravinsky, etc.). When I described the riot that developed on the Paris premiere of Stravinsky’s Rite of Spring, the class naturally wanted to hear an excerpt. That’s fair enough, and of course I should have prepared one, but the interesting point is what happened when I said that I didn’t have one with me. “You can find it on YouTube,” said several students at once.
“Why didn’t I think of that?” was my reply. Of course they didn’t really know that it was on YouTube, but they correctly concluded that it must be. I’ve been using the Internet since before it was the Internet (since 1978, in fact), and I’m both comfortable with it and knowledgeable about it, but why didn’t it occur to me to check YouTube? The quick answer is that it has only been possible in the last couple of the 31 years of my Internet use, but still…
Teachers and parents, of course, know that when they have a technology question they should ask their kids. But I’m supposed to be the expert. So it bothers me that I didn’t think of YouTube. I learned last year that we can find math lessons there, after all. (More on that in a later post.)
So, why do I have a Facebook account if I don’t do anything with it?
That’s an easy question. I have a Facebook account because some of my students kept pestering me to set one up. Apparently Facebook is absolutely essential to high-school life. And several other Weston teachers are on Facebook; why shouldn’t I be?
So I gave in. Being mildly concerned about privacy issues as a public-school teacher, I set up some limitations: I don’t show my birthday, my political views, or my religious views; I don’t post my address or phone numbers; and I don’t check “Friends may post to my Wall.” I’ll accept friend requests from current and former students, but I won’t initiate them. These restrictions seem excessive to my students, but I’m comfortable with them.
The problem is that I don’t know what to do with Facebook! I already have a blog (you’re reading it now), and I am totally comfortable with email and IM, having used both since 1978. But the whole concept of a social networking site like Facebook eludes me. One thing that students tell me is that they use it to send messages to classmates — when they’re organizing a class party, for example — and that use makes sense to me. But why do they want all of their “friends” (hundreds of them, in some cases) to read personal messages that might apply to just one person or at any rate might not be public information?
Some day, perhaps, someone will give me a clear explanation of what I want to do with my Facebook account. In the meantime, there it is, and I check it every two or three days…
For other opinions, see Would you track your health on Facebook.
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:
One of my students asked me why his textbooks aren’t available for Kindle. Currently the typical Weston student’s backpack weighs 42 pounds*; Kindle weighs only ten ounces! Aside from everything else that’s available for it, imagine replacing your math book, your English book, your science book, your history book, and your Latin book (not to mention the extra book for the student taking two math courses or two sciences or two languages…) with a single light-weight device. It would be much cheaper for the publishers, too.
So why hasn’t anyone jumped on this opportunity? Save our students’ backs!
________
*Actually, I made this figure up. But the reality is probably all too close to that.
Having been an enthusiastic iPhone user for the past four months, I’m not surprised that many of my students want to play games on it (at least those students who don’t have iPhones themselves; this is Weston, after all). That’s a good excuse for installing games, isn’t it? Or do I just want to play them myself?
Maybe so, but at least the recommendations still came from the students.
Here’s what I have, in alphabetical order:
- First is Dactyl, a game of hand-eye coordination. Not unexpectedly, I’m terrible at Dactyl and can’t possibly compete with my freshmen and sophomores on the math team.
- Then comes Enigmo, which I haven’t learned yet, so I have no opinion on it. But my students tell me that it involves physics and problem solving, so it must be good.
- Then we have Labyrinth Lite, an astonishingly faithful reproduction of the classic wooden labyrinth game. Tilting the iPhone backward and forward in two directions exactly mimics the physical game, even to the point of accurately reproducing the momentum and sounds of the real-life steel ball.
- The silliest game that used to be on my iPhone is Scoops. Scoops of ice cream fall from the sky, and you move your cone left and right in order to catch the scoops while you avoid onions. Onions? Yes, onions. I’ve removed Scoops, even though a certain sophomore disapproves of my doing so.
- Then there’s Tetris, though I’m currently using the unauthorized knock-off called Tris, which I installed shortly before it got kicked off the Apple Store. Maybe I’ll get the real thing, as Tris rotates the tetrominoes counterclockwise rather than clockwise as nature intended.
- Finally we have my current favorite, Trace. It’s hard to describe this one, but it’s addictive and not time-pressured, so try it yourself!
Of course I also play Sudoku a lot, but that’s really a puzzle, not a game.
What’s next? Scrabble, perhaps? Or SimCity? Is the screen big enough for either of them?
I recently installed an unusual application on my iPhone: Ocarina. This program turns your iPhone into a four-hole ocarina, with the holes outlined on the iPhone’s touch-sensitive screen. But the really cool thing is that you actually blow into your iPhone to simulate blowing into the ocarina! Try it: it really works!
Many of my students agree that this is really cool, although some adults think that it’s a waste of time. I don’t really understand their point of view, since they are likely to spend their time on useless things like watching football games, but anyway….
The reason that I had to demo this product for my precalculus class is that we have just finished studying the use of trigonometric and exponential functions to model musical sounds, and one of the issues that arose is what the dependent variable represents when graphing an oscilloscopic rendering of a tone. Sure, if Middle C is 262 Hz, we notice that the frequency is 262 cycles per second since the period of the independent variable is 1/262 of a second. But what does the y-axis represent? We say pressure, and we may measure it in pascals or mV, but what does this have to do with the loudness of a sign? The direct analog construction of the iPhone ocarina application — with no intermediate abstractions of digital software — provides a clear understanding of this phenomenon, since the user’s breath blowing into the iPhone moves the membrane of the microphone, illustrating pressure in a literal way.
The Josephson Institute Study of the Ethics of American Youth has been widely reported on such widely varied outlets as National Public Radio, Fox News, and Yahoo News. They report “a troubling picture of our future politicians and parents, cops and corporate executives, and journalists and generals.”
I do agree that their picture is troubling, but something about their analysis makes me uneasy. First let’s look at their results:
More than one in three boys (35 percent) and one-fourth of the girls (26 percent)…admitted stealing from a store within the past year.
…
A substantial majority (64 percent) cheated on a test during the past year (38 percent did so two or more times).
…
As bad as these numbers are, it appears they understate the level of dishonesty exhibited by America’s youth. More than one in four (26 percent) confessed they lied on at least one or two questions on the survey. Experts agree that dishonesty on surveys usually is an attempt to conceal misconduct.
The justification, of course, is that “everyone else does it.” That may explain the cognitive dissonance:
Despite these high levels of dishonesty, the respondents have a high self-image when it comes to ethics. A whopping 93 percent said they were satisfied with their personal ethics and character and 77 percent said that when it comes to doing what is right, I am better than most people I know.
So, how do we interpret all of this? As a teacher of teens, I have to be troubled by these results. (I’m ignoring the self-reported accounts of using the Internet to cheat, as that’s a remarkably gray area.) But the report doesn’t quite ring true, despite the assurance that “These statistics have been verified by the Department Chair, Decision Sciences & Marketing, Graziadio School of Business & Management, Pepperdine University.” Maybe I’m in an atypical situation, but I just can’t believe that over half of my students have cheated on a test during the past year. I don’t want to be flippant, but maybe it depends on what the definition of “cheat” is. Maybe I’m just unobservant, but I don’t see students using notes on a no-notes section of a test, and I don’t see them texting on their cell phones, and it’s hard for me to figure out other ways in which they might be cheating. I do hear of the occasional student in other classes who texts during a test or sneaks in notes, but I just don’t see it, and it seems rare and exceptional. I guess I have to look into this matter further.
What’s a meme? Well, those of us who have spent too many years on the Internet (from its inception in 1969, actually, when it was called the ARPAnet) and those of us who have read The Selfish Gene, by Richard Dawkins, know what a meme is. Although the Wikipedia article on memes is far too long and leaves a lot to be desired, it definitely includes the correct definition:
A meme…comprises any idea or behavior that can pass from one person to another by learning or imitation. Examples include thoughts, ideas, theories, gestures, practices, fashions, habits, songs, and dances. Memes propagate themselves and can move through the cultural sociosphere in a manner similar to the contagious behavior of a virus.
That’s clear enough, so why is the word used incorrectly these days by so many people, some of whom should definitely know better but most of whom have never learned what a meme really is? Many writers seem to think that a meme is an informal quiz or questionnaire that is passed around by email or by the Web, often of the “you are a _____” variety. Now you can see both the similarities and the differences here: Do they propagate themselves, or do users intentionally transmit them? Are they cultural ideas and behaviors, or are they questionnaires? The word is definitely losing most of its import these days!
As a teacher, I suppose I’d better cite some sources for this claim. I’m sure that some of my colleagues would be aghast that I cited Wikipedia as my source for the correct use of a word, but so be it. As for the current incorrect use, I am reluctant to cite either email messages or websites of friends — for obvious reasons — but I can probably find similar use by strangers without much effort. Let’s see… most of the initial hits from a Google search actually lead to the correct usage (much to my surprise), but I’m sure I can also find the usage I object to… OK, here are a few:
That’s enough. You get the idea. What’s up here?
By this point I’ve taught simplified versions of the RSA algorithm to ten different cohorts of teens: four years’ worth of Honors Algebra II students at Weston High School, juniors for four summers at Crimson Summer Academy, and two years’ worth of college-prep Algebra II students at Weston. Tweaking the details as I’ve gone along, and benefitting from changes in technology, I’ve learned a lot from these experiences.
There are several types of benefits for the students. Some benefits are conceptual, involving understanding ideas about public-key cryptography, ranging from technical questions like how a cryptosystem can use a public key, why that’s necessary, and why it’s secure, to public-interest issues like whether we can trust so-called “secure” financial transactions on the Internet. I could have predicted these benefits; the unit was designed to try to achieve them, after all. And I could have predicted the success of some of the more concrete mathematical benefits as well, since RSA involves exponentiation, prime numbers, modular arithmetic, factoring, representation of characters as integers, and other operations with numbers. But a third type of benefit is more of a surprise: because the technical details are complicated, and even a single mistake can doom the effort to failure, most of my students have been doggedly persistent in paying attention to details and getting them right. Too often we can fall into the trap parodied by Tom Lehrer: “The important thing is to understand what you’re doing rather than to get the right answer.” We give so much partial credit that a student can get a B without ever producing a correct result. Part of the way that my colleagues and I have avoided this trap with RSA is that our sequence of activities and assignments concludes with a two-way exchange of messages: each student sends me a message using my public key, and I reply with a message using the student’s public key. This gives everyone practice in figuring out their private and public keys, enciphering, and deciphering. But fewer than half the kids get it right the first time, since there are so many opportunities to make mistakes. Unlike the usual math problem, they can’t settle for having a couple of points taken off; the message simply won’t work. So they try over and over again — sometimes four or five times — in order to get it right. If they don’t, I can’t read their message, or they can’t read mine.
If you’re interested in checking out how I’ve simplified RSA so it can be studied at the level of Algebra II, take a look at my worksheets, starting at RSA Phase One. (If you keep incrementing the “1” in that URL, you’ll find the next three worksheets at the expected URLs.)
No, this isn’t another one of those essays about the usefulness of technology in teaching math. This is a response to a fascinating post in Heather’s Comparative Childhood blog, in response to a newsletter from her daughter’s middle school. Here’s an excerpt from the newsletter:
Cell Phones, I-Pods, MP3 players, any other electronic devices are not permitted for student use at any point during the school day. If these items are seen or heard during school hours, they will be confiscated and a parent will have to pick up the device from your child’s house office.
This seems pretty reasonable, especially since the careful wording doesn’t prohibit possession of such devices, merely their use or visibility during the school day. And, of course, it is a middle school.
Heather’s post includes the following observations:
Is there ever a circumstance in which the presence and use of an iPod (or cell phone or MP3 player or digital camera or gameboy or fill-in-your-electronic-device-of-choice-here) is justifiable in a school setting? I guess I’m taking the perspective of the teacher on this one. There is nothing more annoying than someone’s cell phone going off during a lecture. And there is nothing more rampant in university settings than “creative” new ways to cheat during examinations. I can’t believe that the use of electronics for cheating begins at the college level.
My understanding on the ban of cell phones in public schools was that it was originally put in place to prevent drug deals going down on the school premises. But now cell phones could be used for anything from covertly cheating by sending text messages to voyeuristic photography in the ladies room to remotely setting off bombs. I won’t waste my space here, but we need only use of imagination to think of the ills of other electronics in the school settings. Nintendo DS’s create their own network within a local range.
These are eminently reasonable comments, but I need to take a different point of view, even though Heather is trying to take the perspective of the teacher. Of course she’s absolutely right that it is annoying and disruptive for a cell phone to ring during class, and she is also absolutely right that they need to be prohibited during tests, as they can be used for cheating (as Weston students know all too well). But there are also too many valuable uses of these electronic devices for them to be banned entirely in school — at least in high school, and I suspect in middle school as well. At Weston High School we ban cell phone use (or even visibility) in the classroom, but not in the cafeteria or outdoor areas; iPod use is left to the discretion of the teacher. Cell phones are a valuable way for students and parents to get in touch with each other, so students should be allowed to use them outside of the classrooom. And MP3 players may help many kids concentrate in noisy situations or just when taking a test; while I certainly don’t allow kids to shut out the world during a class discussion or lecture, I think it can be valuable to do so when trying to concentrate on individual work. I admit that there’s a small chance that a student may use an iPod for cheating, but that’s a lot harder than texting on a cell phone, which is currently the preferred method among high-school students and Boston firefighters. Of course a variant of the method used by the firefighters would be very difficult to prevent in school settings:
…a group of Boston firefighters took turns going into a men’s room at the Quincy middle school and sent answers via text message on their cellphones to colleagues in the testing room.
We can easily prevent this precise method of cheating in school by allowing only one student at a time to go to the bathroom and by banning cell phone use in the classroom during the test, but how do we prevent texting between a student who goes to the bathroom during the test and a classmate who has already taken the test and is currently in the cafeteria during a free period? Temporarily confiscating cell phones at the beginning of the test is the method preferred by some teachers. That works well…except for kids who have a second cell phone hidden away.
And while I’m looking at Heather’s blog, let me recommend several of her recent posts, especially the ones entitled “Wow” and “What would Jesus do, indeed”.
I have just finished reading Double Vision, by Randall Ingermanson. This science fiction thriller has a great concept, but the execution is disappointing. On the plus side, the novel speaks effectively to those of us who have worked in the computer industry, especially if we have any interest in computer science and physics. Knowing something about RSA and factoring certainly helps, but it isn’t necessary. Knowing something about quantum computing might also help — but since I know almost nothing about that field, how could I be sure? Anyway, the idea behind the book is fascinating, and the fact that the protagonist is a computer programmer with Asperger’s makes it fit into my accidental recent theme of Asperger’s Syndrome. However, there’s also the minus side: implausible characterization, poor writing (à la Dan Brown), unbelievable plot, and excessive Christianity. Worse yet, there’s a subsubplot concerning Jews for Jesus, and if anyone can explain to me how that organization is distinct from Christians, please let me know.
In one of those typical synchronicities, two of my students have just asked me how they can create their own blogs — a Weston sophomore yesterday, and a Saturday Course fifth-grader today. The Weston student suggested that I should post the answer in my blog, so here it is, short and sweet:
- Go to www.blogger.com.
- Follow the 3 easy steps displayed on that page.
That was easy®, as they say at Staples.
Another of the great ones is gone. Scientist, science fiction writer, and visionary Arthur C. Clarke died the day before yesterday at age 90. He is best known for the novel 2001: A Space Odyssey, on which the eternally rewatchable movie of the same name was based (though they were written simultaneously!). But he made so many more contributions than that. The Wikipedia article on him provides a fairly decent summary, including links to various obituaries. I particularly recommend the article about him by fellow writer David Brin, in the Daily Kos of all places. The NPR story on yesterday’s Morning Edition was an effective four-minute vignette.
I particularly remember Clarke’s observation that “any sufficiently advanced technology is indistinguishable from magic,” as well as his agreement with the late, lamented Isaac Asimov that each would refer to himself as “the world’s second best science fiction writer.” As Asimov wrote in his autobiography:
Arthur Charles Clarke was born toward the end of 1917 in Great Britain. He is another science fiction writer who has been thoroughly educated in science and he did extremely well in physics and mathematics.
He and I are now widely known as the Big Two of science fiction. Until early 1988, as I’ve said, people spoke of the Big Three, but then Arthur fashioned a little human figurine of wax and with a long pin.
At least, he has told me this. Perhaps he’s trying to warn me. I have made it quite plain to him, however, that if he were to find himself the Big One, he would be very lonely. At the thought of that, he was affected to the point of tears, so I think I’m safe.
I’m very fond of Arthur, and have been for forty years. We came to an agreement many years ago in a taxi which, at the time, was moving south on Park Avenue, so it is called the Treaty of Park Avenue. By it, I have agreed to maintain, on questioning, that Arthur is the best science fiction writer in the world, though I am also allowed to say, if questioned assiduously, that I am breathing down his neck as we run. In return, Arthur has agreed to insist, forever, that I am the best science writer in the world. He must say it, whether he believes it or not.
I don’t know if he gets credited for my stuff, but I am frequently blamed for his. People have a tendency to confuse us because we both write cerebral stories in which scientific ideas are more important than action.
Both Clarke and Asimov were science-based writers of science fiction; neither was a prose stylist, but both of them stuck to a transparent style that let the content of their writing shine through with great clarity.
Yesterday afternoon we had a half-day workshop on Maple, a computer algebra system. At least that’s how we think of it, but here’s the description on their website:
Maple is the leading all purpose mathematics software tool. Maple provides an advanced, high performance mathematical computation engine with fully integrated numerics & symbolics, all accessible from a WYSIWYG technical document environment. Live math is expressed in its natural 2D typeset notation, linked to state-of-the-art graphics and animations with full document editing and presentation control.
Users can perform everything from instant “in document” calculations to highly complex mixed symbolic and numeric programming involving millions of terms, at any precision desired. Maple’s intelligent technical document environment addresses the full spectrum of needs and requirements from high school students to advanced commercial research.
The question, of course, is how we can use this software productively in the context of high-school math courses. We looked at several possibilities yesterday, ranging from expansion of powers of trinomials to 3-D graphing. For instance, suppose we want to calculate the fifth power of a trinomial. If we simply type the appropriate expression, it gets echoed back:
But if we ask Maple to expand it, it does so:
And then suppose we want to solve or plot a system of three equations in three unknowns. Maple will do both:
This is just a beginning. We don’t know yet how we’ll use it, but it surely promises some major expansions of what we can do in high-school math.
According to the badge that I’ve pasted into the right sidebar, this blog requires a high-school reading level. I was glad to see that it passed that test, even though only a small part of my audience actually consists of high-school students, and many of those are surely reading at the college level. But a large number of adults read at or below the high-school level, and everybody finds it easier to read pieces that are written at a lower reading level.
After I wrote that paragraph, I wondered what the statistics are. In particular, what is the reading level of the average American adult? It turns out to be surprisingly difficult to get a valid answer. There is plenty of material giving figures (though inconsistent ones) about the shockingly large number of American adults who read at the third-grade level or below, who are unable to read a poison label, etc. In particular, Jonathan Kozol provides a wealth of material about functional illiteracy and its connections with race and class.
According to Blogger, this is my 500th post! It’s hard for me to believe that I’ve written 500 of these short (and sometimes not-so-short) essays. One of my Weston students asked in class why anyone would bother keeping a blog, and I didn’t have time to answer him right then; I’d better get around to doing so real soon now. There must be something that drives me to write so much.
I can’t speak for anyone else, but the truth is that I often feel impelled to share my thoughts with others, and blogging is a good way to do so. It’s not the main reason I became a teacher — that’s more a matter of my interest in seeing people learn and helping them do so — but it’s surely a secondary reason, both for me and for many other teachers. For my entire teaching career I have wanted people to become better thinkers and better problem-solvers, so I want to help lead them in what I see as the right directions. Those people might be my students (in Weston, at The Saturday Course, at the Crimson Summer Academy), or they might be my colleagues or the general public. Blogging is just one of the ways I can reach them. I’m pleased to have kept it up for 500 posts, and I’m looking forward to 500 more.
Mark Bernstein has an observation and a question:
I no longer trust my email. If you send me mail, I will probably receive it, but I’m far from certain that it won’t be lost in the vast deluge of spam.
Meanwhile, Eudora is obviously past its sell-by date; my spam bucket overflows every month, and apparently Eudora crashes when it has more than 32,768 messages in a mailbox. With a mere thousand spam messages a day, that’s suddenly a very real possibility.
Do grownups rely on mail.app? Is there another option?
I definitely rely on mail.app, and mail almost never gets “lost in the vast deluge of spam.” Here’s my setup:
- Most spam gets caught by spamassassin on the server, which sends it on to me appropriately marked.
- I then have a mail.app Rule that puts such messages into my SPAM mailbox without ever appearing in my Inbox.
- Spam that gets through the spamassassin filter unscathed might then be caught by mail.app’s Junk Mail filter. In that case it gets automagically routed to my Junk mailbox by another mail.app Rule.
- A tiny amount of spam manages to evade both filters. I manually mark it as Junk.
- I have separate Rules that delete all mail over a week old from both the SPAM and Junk mailboxes, so that I have a chance to look them over if I wish. I have almost never had any false positives, but they do occur every once in a while.
Data from a single day (yesterday):
| Spam messages caught by spamassassin on server |
212 |
| Spam messages caught by mail.app’s Junk Mail filter |
14 |
| Spam messages that avoided both filters |
2 |
| False positives |
0 |
| Legitimate messages |
52 |
A reader of both this blog and Adam Gaffin’s Universal Hub asked why I’ve turned off comments in my blog. Naturally he had to ask the question on Universal Hub. I replied as follows:
I have comments turned off because they tend to generate flame wars and spam. Adam’s blog is meant for general discussion, but as a public-school teacher I can’t be in that position. You can imagine what would happen if somebody posted something inappropriate and it appeared on my blog (even though I wasn’t the author of the comment). No schoolteacher can allow his or her blog to become a public forum.
Coincidentally, I received an interesting rant by email in response to my post from yesterday concerning Huckabee’s so-called Fair Tax. My point had simply been that I wanted to illustrate one of the widespread errors that adults make in applying middle-school math, but it engendered a long rant from one of Mike Gravel’s campaign directors. [How weird is that? Politics makes strange bedfellows, including the two Mikes.] He had a point, at least a political and economic point, but it had little to do with the math, which, as he himself pointed out, he apparently understood. My point was simply that an n% tax is a standard concept from a mathematical standpoint, even if there might be motivation for redefining it for political reasons. While this writer’s rant wouldn’t have been unacceptable on the “public school teacher” grounds that I cited above, I still can’t open my blog to unmoderated comments, and I don’t have time to moderate.
This is a follow-up to my post of December 26. There are two separate and distinct issues here:
- Has there been a decline in ethical attitudes and behavior among students in recent years?
- Are some lines that used to be bright now in fact just shades of gray?
Let’s take them one at a time. First, I suspect that every generation believes that there has been a decline in ethical attitudes and behavior. But unfortunately the usual citations are highly questionable. For example, consider the following (attributed to Socrates via Plato):
The children now love luxury; they have bad manners, contempt for authority; they show disrespect for elders and love chatter in place of exercise. Children are now tyrants, not the servants of their households. They no longer rise when elders enter the room. They contradict their parents, chatter before company, gobble up dainties at the table, cross their legs, and tyrannize their teachers.
What a great example! But apparently it doesn’t actually come from Plato, even though it has been floating around the Internet for years. Oh, well.
Despite quotations that might be spurious, it is hard to believe that there has been a recent decline. We usually view the past through rosy glasses. I just wish there were more actual evidence.
The second issue is probably more telling. Bright lines are easy when cheating is difficult. They become gray when cheating is easy. Not very many students are likely to go to the trouble of writing illegal notes on the back of a label affixed to a water bottle, though that kind of cheating is not unheard-of. But downloading a verboten copy of a song or a video is all too easy. As is making photocopies of copyrighted text. (Do you know any teachers who have done that?) Ease of cheating doesn’t make an act any more or less unethical, but it certainly makes it more likely. And the lines have become grayer. What is “fair use”? Can I photocopy some material for a class when I don’t have time to get permission? Can I do so when I am unlikely to get permission? What if it’s a single paragraph? What if it’s a whole chapter? What if the book is out-of-print? What if a student doesn’t cite a source for “commonly known” facts? What if a teacher copies a problem? What if s/he copies a problem and makes a small change? The lines aren’t so bright now that we have the technology to copy material off the Internet and to make photocopies of printed matter. Let him who is without sin…
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