Showing posts with label New York Times. Show all posts
Showing posts with label New York Times. Show all posts

Thursday, March 7, 2013

The State of Education


Over at Motherlode today, K.J. Dell'Antonia doesn't buy what Hope Perlman is selling. And as biased and immersed as I am in the New England academic scene, I totally agree. 

Hope Perlman doesn't believe parents who say they are not stressed out about the college application process:

      "Furthermore, I have dear friends who seem to agree with Levine. I’ve been in conversation with them about their college hopes for their children and they’ve looked me in the eye and told me they really, really don’t care if the college their child attends is prestigious, as long as it’s the right fit. And I’ve looked right back at them, impressed, but ultimately unable to believe they really mean it."

I'm sorry, Hope, but I, like K.J., really mean it. I was raised in a wealthy, academically-oriented town with one of the best public high schools in the state. Today, I teach at an academically accelerated New England middle school, in a town just a stone's throw from Dartmouth College, and I still really mean it. When presented with the range of ivy to state, I chose state for myself, all the way from kindergarten to graduate school. I reveled in my education (Dover-Sherborn High School, B.A., University of Massachusetts at Amherst and J.D., University of North Carolina at Chapel Hill). Because I was self-directed, ambitious, loved learning, and was allowed to negotiate on my own behalf from an early age, I got so very, very much out of my education.

Consequently, these skills of self-advocacy are some of the most important skills I teach today in my middle school. I want to make sure my students will get what they deserve everywhere from Harvard University to Bunker Hill Community College. I was raised to fight for my right to take any damn class I wanted, opt for every extracurricular activity I could make time to attend, and a giant, intimidating, populated state university gave me just about every opportunity I could have hoped for. 

K.J. Dell'Antonia is absolutely right. Dollar for dollar, public higher education kicks private education's ass. With some solid skills in self-advocacy and the confidence to stand up for what you deserve, most public colleges will give their students what they need to be truly successful. 

Thanks, K.J. for the reminder. As I move toward my oldest child's college application process, I appreciate the perspective, the calming sentiments, and the dose of sanity. 

Sunday, January 20, 2013

In Both Countries it Was Clearer Than Crystal


The stars have aligned and my love of literature has come full circle. I am teaching Dickens' A Tale of Two Cities at the same time that my fourteen year old son has (finally) agreed to read this, one of my favorite books. I think Ben (the aforesaid son) has finally given in because I said I came to love it in sixth grade when my teacher, Mr. Akeley, read it aloud while we ate our lunches. Ben's in 8th grade, so I think he sensed a challenge. 

Yeah, that's right, a gauntlet was tossed down, and I can win. But only if he loves the book.

So. Taking a cue from a post I did a while back for Great Expectations, I'm doing the same for the first book of A Tale of Two Cities. This is for my students, their parents, and my son. Accordingly, all page numbers in my notes refer to the text I like to use in my classroom, the EMC Masterpiece Series Access Edition. I like the notes in the margins and use them as quiz questions.

Oh! And Katherine Schulten, the august and editorial genius of The New York Times Learning Network. She became my editor last summer when she asked me to write some critical thinking quizzes for The Learning Network. She was a teacher in Brooklyn for ten years, has been a curriculum writer since the invention of fire, and has won all kinds of awards for her work in education, but she has one major failing. She does not love A Tale of Two Cities. 

Today, I made a bet with her: one lunch in the New York Times cafeteria (notably not excluding the sushi bar) that I can make her love this book. The stakes are high, people, and I'm playing for keeps.

Brace yourself, Ben and Katherine, because this will be one wild ride.

Book the First - Recalled to Life

Chapter One: The Period

As we go through this novel, remember that Dickens published it in installments. In the tradition of serial writers and dramatic television series writers throughout history, that calls for some really great cliffhangers, and Dickens delivers.

"It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity [skepticism], it was the season of Light, it was the season of Darkness, it was the season of hope, it was the winter of despair..."

Yeah. I know you know that one, and it goes on for a while. 

This paragraph is one of the most famous in all of literature. I like to bring in some other famous first lines when we talk about this one in order to compare/contrast. Moby Dick ("Call me Ishmael") and Pride and Prejudice (extra credit for the students who memorize this one: "It is a truth universally acknowledged, that a single man in possession of a good fortune must be in want of a wife.") top the list. 

This first paragraph is easy at first - best/worst, wisdom/foolishness, belief/incredulity, Light/Darkness, hope/despair - but goes off into stuff that only readers in Victorian London will understand. But that first part? That first part is killer. It's the contrast of opposites - a rhetorical device called antithesis. Antithesis is about the setting up opposites for effect, and to take it one step beyond the pale, there's another rhetorical device that defines serial antithesis called isocolon. This first paragraph is one massive example of isocolon, and it's chock full 'o examples of allusion to the Enlightenment ("Light," "Dark"), Genesis ("Light," "Dark"), Revelations ("clearer than crystal"), Matthew ("loaves and fishes," 14:17), and some verbal irony. "Things in general were settled forever." Um, no. They were the exact opposite. Totally unsettled in the short term. 

This is why Tale of Two Cities is perfect for the 8th grade. Middle school students are smack in the middle of so many things, notably their transition from literal to figurative thought. This transition is not about "smart"; it's about neurological development. Sorry, parents of kids who have been accelerated in school, but this ability to connect can't be taught. I can present metaphor and allusion until I turn blue, but those sort of connections just have to happen on their own sweet neurological time. These connections must be made in the brain before my students can make the leap from concrete understanding of literature to the symbolic, abstract, figurative wonderland that is the stuff of mature reading. I've written about this transition before, the moment when a student moves from the world of black and white to one of technicolor. I call it the "Dorothy Moment," and I am forever grateful to be there when it happens to my students. For seventh graders fortunate enough to make that leap, it tends to happen during Great Expectations. If it happens in 8th grade, it happens during A Tale of Two Cities. The allusions, metaphors, and symbols are just too thick on the ground, and even the most immature 8th grader can't help but trip on a few. 

But back to the text. 

You can just relax through some of the incomprehensible references of the next couple of pages, because all that stuff about the Cock Lane Ghost and the sister of shield and trident (Britannia), people being buried alive after not kneeling down to monks (the execution of Chevelier de Barre in 1766; he did not take his hat off at an inopportune moment in front of church members), and the state of rampant lawlessness in England is only comprehensible to people who lived and read the newspaper during Dickens' lifetime. Don't worry about it. Dickens is setting the scene. Here are the relevant points:

1. Things were bad in England. Worse, actually, than in France, where much of the action of this novel will take place. Lawlessness reigned, no one trusted anyone else, and people were put to death for everything from the worst to the most trifling offenses. The country was overrun by burglars and highwaymen (this will be important in chapter 2). 
2. Dickens uses a lot of irony and dark humor to convey how bad things actually were. "Dear old year one thousand seven hundred and seventy-five" (3) is ironic. It was not, in the least, "a dear old year." It was horrific. 

One last note. Note the mentions of the Woodman, Fate and the Farmer, Death. Keep these allusions in mind. This paragraph (2) just beautiful, just so...oh, dear, so lovely. 

"It is likely enough that, rooted in the wood of France and Norway, there were growing trees, when that sufferer was put to death, already marked by the Woodman, Fate, to come down and be sawn into boards, to make a certain movable framework with a sack and a knife in it. terrible in history." (2) 

This quote refers to the trees that will someday become guillotine. That have already been marked for that purpose. Fate, the Woodsman, already knows. It's already done. The trees are growing, they will be felled, the guillotine will be made, and the Revolution will take place. Capital F-Fate has determined it all. 

"It is likely enough that in the rough outhouses of some tillers of the heavy lands adjacent to Paris, there were sheltered from the weather that very day, rude carts, bespattered with rustic mire, snuffed about by pigs, and roosted in by poultry, which the Farmer, Death, had already set apart to be his tumbrils of the Revolution." (2) 

See? Again, it's already done. Death has already decided which farmer's carts will serve as the tumbrils (carts) that will transport what used to be farmers' harvests but which will now be the prisoners of the Revolution to the guillotine. Done. Over. Don't even try to pretend the future is not set in cobblestones. 


Chapter Two: The Mail

Jarvis Lorry (the "he" of this chapter), an employee of Tellson's Bank in London (and its profitable Paris branch) is on the Dover Road (the road between London and Dover, about 71 miles long) in a mail coach - hence "The Mail."

The coach at Shooter's Hill, about 8.5 miles outside London, when it gets stuck in the much and mire and fog. At this point, I tend to gesture back one year to our reading of Great Expectations when we talked so much about the fog and "clammy and intensely cold mist" (4) and its ability to create a mood of tension and uncertainty. That's what's going on here. The passengers have to get out and push. No one trusts anyone else, everyone is freaked out, and the coach is stuck on a hill. The horses are shaking and breathing so hard that the motion is transferred to the coach and, well, yikes. 

A messenger approaches the coach from "T, and Co." (Tellson's Bank), looking for Jarvis Lorry. Everyone else is frightened and hangs back. The message for Jarvis Lorry (after some paranoid back-and-forth between the coach drivers and the messenger) is: RECALLED TO LIFE. No, you are not supposed to understand this message. Yet. 

Jerry, the messenger, reveals that he'd be sunk if "RECALLED TO LIFE" were to come into fashion. This will be important later. I get kind of tired repeating "Trust me, this will be important later," but trust me. This will be important later. 

NB to teachers and frustrated readers: Adolescents are not used to waiting for information. YA fiction and television tend to give the plot away on an as-needed basis, and as today's adolescents NEED stuff IMMEDIATELY, they are not used to waiting. I like to assign a book like Skellig as a way of getting used to the idea of waiting for information. It's short, but doesn't give it all up in the first chapter. 

Chapter 3: The Night Shadows 

"A wonderful fact to reflect upon, that every human creature is constituted to be that profound secret and mystery to every other." (10) This, and "He was on his way to dig someone out of a grave" (12) are the main points of this chapter. 

People in England are so freaked out by each other, that even among those three passengers in the Dover Mail, "they were mysteries to one another, as complete as if each had been in his own coach and six, or his own coach and sixty, with the breadth of a county between him and the next." (10) Those passengers are so distrustful, and the people of England, by extension, are so distrustful of each other, that even when they are sitting next to each other in a coach, they may as well have the distance of an entire county between them. 

This whole first paragraph is about mood. Well, tone and mood. Okay, well tone and mood and the theme of imprisonment

Jarvis Lorry is on his way to Dover to meet someone and then head to France, where he will "dig someone out of a grave." (12) Not literally, of course. Jarvis Lorry is no grave-digger; he's a man of business. His digging will be metaphorical. Trust me, it's okay that you don't understand what his musings/delusions/nightmares mean yet. 

Know that the subject of this chapter, even with the switches between "he" and "I" is Jarvis Lorry. Jerry Cruncher, the messenger, makes some appearances to wonder about that RECALLED TO LIFE message, but the main focus of this chapter is Lorry. 

All of that confusing "dialogue" between Lorry and someone else is imagined. He's dreaming, hallucinating, fearing, whatever...he's worried about his coming meeting with the person who has been RECALLED TO LIFE and it haunts him. All that dig - dig - dig, is figurative, not literal digging, as I mentioned before. 

And in the final paragraph, we find out that whomever has been buried, has been buried for eighteen years. 

But the lovely part of this chapter is the change in tone between the meat of the chapter and this final paragraph. Dark, mist, hallucinatory nighttime images morph into, "He lowered the window, and looked out into the rising sun. There was a ridge of plowed land, with a plow upon it where it has been left last night when the horses were unyoked; beyond, a quiet coppice wood, in which many leaves of burning red and golden yellow still remained upon the trees. Though the earth was cold and wet, the sky was clear, and the sun rose bright, placid and beautiful." (14)

Can you see it? The beautiful scene indicating a change in tone from hopeless to hopeful, all "placid and beautiful"?

And with that new sense of hope, I call it a night. Even the dog is having nightmares as Ben watches the British version of The Office, which means it's time to go to bed. Please forgive the insane commentary behind the twitching paws. It's not me, it's Ricky Gervais. 

Tomorrow, chapters 4-6.

video



Tuesday, November 6, 2012

Election Day!


Tonight, my time will be dedicated to the Twitter hashtag #EduElection, a joint New York Times Learning Network and Edutopia education-o-rama. Teachers tweeting about the election. How fun is that??

Join us!

Tuesday, October 23, 2012

Hanging Out Under the Sword of Damocles


Interesting experience today. I received an email from one of my son's teachers, a very personable woman who was contacting me out of concern for a particular aspect of my son's learning. You would think that as a teacher, a teacher who composes at least a couple emails just like the one I received from this teacher every day, that I could maintain some perspective.

But I didn't. I got a little sick to my stomach, a little lightheaded. I worried about my child's ability to make it in high school, whether or not he'd get into college, if he'd ever be able to get a job that paid at - let alone above - the poverty line...

In other words, I may have overreacted, and I may have required a medicinal glass of wine. I just might have had one or two bitter thoughts about this teacher I otherwise adore and believe to be a great educator. How dare she question my child's competence? How dare she think my child is anything less than adorable and wonderful?

Yeah, I went there, and I could very easily have flipped out on that teacher. But I didn't. At least not outside the confines of my addled brain, because I logged off and closed the lid on my irrationality. Crazy, protective mom mode was not going to do anyone any good, and flipping out on my son's teacher would be the worst possible reaction, a surefire way to destroy my (and my son's) relationship with this teacher.

An couple of hours later, after that glass of wine, some dinner, an hour of helping my boys with their homework, and bedtime reading and snuggle, I had gained a wee bit of perspective. I thought about all those emails I write from my desk at school. All those emails I bang out when I simply intend to deliver the news that a quiz score was unexpectedly low or a homework assignment was forgotten. I certainly don't mean to send the message that those students are in trouble, out of their depth, or beyond help; I am simply keeping in touch. I only intend to convey the message that their children need support and a solid, open partnership between their parents and their teacher.

I have written about the importance of preserving the parent-teacher partnership for the New York Times but I did not totally understand what it means to receive disturbing news from a teacher when I wrote that piece. I'd been on parental easy street, twirling my umbrella and singing about blue skies.

I did not fully understand what it meant to be on the receiving end of an "I am just writing to let you know..." email until today.

However, no matter how much I'd love to avoid it, I will still have to deliver bad news, because that's my job. Believe me, it's always easier to keep bad news inside the confines of my classroom, because the minute an email leaves my out box, all hell can break loose. It has, and it likely will again. I hold my breath and hit 'send' on those emails, knowing that some parents will flip out on me.

But at least I understand now, in my gut, where it's coming from. Even my most challenging students are someone's kids. And if they were my kids, I would want to know what's happening at school, to have the opportunity to work together with their teacher to find a solution.

That said, I have an email to write to one of my students' parents, as well as a parent-teacher conference about my own son to prepare for. Here's hoping that sanity prevails on both fronts, because both the education of my students and of my children depends on it.









Wednesday, October 17, 2012

The Art and Science of Asking Questions


The response to "Against Accelerating the Gifted Child" in the New York Times' Motherlode blog has been overwhelming and gratifying, and I feel the need to write about to some of the main points that have come up in the comments section. There are over 200 comments at this writing, and while many have been quite supportive, many have been angry and critical, as they should be. If there were easy answers to the question of how to best educate gifted students, there would have been about 12 lukewarm comments responding to my post. The emails and comments I have received may have been contradictory, but at least they highlight the issues we must address in order to advance the cause of education for gifted kids. However, as Motherlode is not my personal forum, I have had to retreat here, to my turf, in order to adequately respond.

1. I am not actually against accelerating the gifted child. I teach many gifted students who have been accelerated, and many of them are quite happy and fulfilled. However, some are not, so what I am against is accelerating a child because the parents are so wrapped up in the mystique of having a gifted child that they never take the eventual emotional and social fallout into account. I have received quite a few emails from people who have thanked me for bringing up this aforementioned emotional fallout, and I stand by my thesis. While academic acceleration may be a good - nay, ideal - solution for some gifted children, parents may want to think ahead to middle school and beyond when making the decision to skip a child ahead in first or second grade.

2. Of course I am aware of the Iowa Acceleration Scale. I have experience with it; my current school uses it as a resource. I have been in on meetings where we have used it in order to decide whether or not to accelerate students. I have also read just about everything published on the subject of academic acceleration since 1972. What kind of idiot woud publish in the New York Times without reading every scrap of research on a given topic? I specifically stated that the research does not indicate that academic acceleration causes negative social or emotional fallout, but I confirmed with a statistician my sense that the subjective, retrospective reporting used in most research studies on accelerated students is a blunt research tool. So is anecdotal evidence, but when it comes to my own observations gathered over a decade of teaching, that's what I've got to fall back on. After reading reams of studies, I could have stated that the existing data are the gold standard, the be-all, end-all of the discussion on the state of grade acceleration, but instead, I found intriguing but imperfect data that begs further discussion and further inquiry.

3. "The gift of time." Okay, it may be trite, but it's a real factor. "Time" is a metaphor, an umbrella concept that stands in for so much more than chronological time. It represents time for emotional development, social development, physical growth, and about a hundred other factors that are conducive to happiness. The ability to control one's emotions. The ability to organize one's materials for class. The ability to defer gratification. The ability to filter information. The ability to filter out ambient distraction. These skills get developed during middle and high school, and the difference between a sixth grader and an eighth grader is about as vast as the difference between a pink marshmallow Peep and a well-tempered piece of dark chocolate.

4. I actually enjoy teaching way more than seeing my name in print. It has always been thus, and will always be so.

I'd keep going, but I have papers to grade and algebra homework to complete. I appreciate each and every one of the nearly 200 comments on my post, as it ensures that I will be invited back in order to write about some other topic that at least fifty people will assert I am completely unqualified to write about.

Friday, October 5, 2012

Distribution and Association


This has been a heady week. I had two very important moments this week, and both had to do with math. One was a matter of distribution, the other, association.


The Distributive Axiom
x(y+z) = xy + xz

It's been challenging to keep up with all of my homework. There's the grading homework I have do to every night - the compositions to be evaluated, the vocabulary to be graded, the Latin translations to be picked apart - and then there's my Algebra homework. I used to leave Algebra for last, as I had stressed to my students that I don't do my Algebra work until I have completed all of my teaching work. Last week, however, I came home, changed out of my teaching clothes into my comfy jeans, and dove straight into Algebra before I dealt with the grading. For once, I knew I had time to do both because my kids had requested what we call "scavenging night" for dinner and I would not be called into cooking duty, but I was actually...wait for it...excited to do my Algebra homework. I didn't even run outside into the yard to obsessively weed the garden, roll the compost barrel around the yard, and deadhead the flowers. Bonus Jess Lahey Axiom: hyperactivity + a hint of a hint of a hint of ADD = fun-filled afternoons of disorganized odd-job hilarity.

But back to my newfound enthusiasm for Algebra homework. Has the Earth experienced a geomagnetic polarity reversal? (I read on PBS.org that it happens every 250,000 years or so and now I'm worried.) I don't know what else could account for the crazy shift in my priorities. 

But here it is: I love distributing. It's almost as satisfying as simplifying. Maybe more. I can't decide. Changing 3(x+5) into 3x+15 is fun, and watch: I can even go in the other direction. 10x+20 can just as easily be transformed into 10(x+2). Is it just the imposition of order? I am a fan of organizing. Give me a label maker and five cases of wide-mouthed mason jars, and I can turn a disorganized pantry into the very model of a modern major-miracle. I love the purging of excess clutter, so the removal of factors in an expression is akin to taking truckloads of refuse from my basement to the dump. Satisfying. Cleansing. Where I was faced with a messy 10 and x and a 20 cluttering up the place, I can create order through 10(x+2). Clean. Neat. Minimalist. And gosh darn it, I love it. 


The Associative Axiom for Multiplication
(xy)z = x(yz)


In the midst of this shocking revelation, I attended the Dartmouth Writing Summit. In years past, I would have fallen all over myself to attend every second of this writing geek-fest, but this year, THIS year, was a challenge. I was only able to arrange coverage for a couple of my classes, so I had to choose carefully. I was only going to be able to attend one session. One. 

From Dartmouth Now:

"Pulitzer Prize-winning author and noted historian David McCullough is one of several scholars who will lecture at Dartmouth October 2 and 3 as part of 'Writing Summit 2012: The Power of Writing in the Contemporary World.'"

David McCullough?!?!? David McCullough??!!? Seriously? Holy Crap! I love David McCullough; he's one of my writing heroes. I would do just about anything to meet David McCullough.

But then I was faced with the following associative quandry: 


"The Writing Summit 2012 will feature 12 speakers, including keynote addresses by McCullough, Katherine Bergeron, professor of music at Brown University, Hortense Spillers, professor of English at Vanderbilt University, and Steven Strogatz, professor of applied mathematics at Cornell University."
Hold on...forget that McCullough guy...what's a Pulitzer-Prize winning author and noted historian when real pearls, math pearls, are being offered up by my newfound Algebra guru, Steven Strogatz?
And so, for the first time in my life, I have willingly chose to associate with math over...over...well, over just about anything else on the planet. Even this new crazy, upside-down planet where apparently, compasses point south. 
This reversal of polarities paid off, though, because Steven Strogatz was fantastic. He talked about 1) his work at the New York Times, 2) how he first scored his gig at the Times, and 3) his writing process. Spoilers: 1) He doesn't write about teaching math, but about teaching people to love math, 2) he first met his editor at the Oyster Bar in Grand Central Station, and 3) he employs a combination of longhand and dictation software. 
He even answered my question about how he handles the instant (and aggressive) feedback of Times commenters (his first piece currently has 546 comments) without resorting to a strategy of defensive writing. His answer? He doesn't read them.
And with that, Professor Strogatz taught me his most valuable lesson thus far: 
The Axiom of Successful Writing over Narcissism

Monday, September 17, 2012

Yearning for Some Joy of X


Last year, I decided to take Algebra I in order to get over my math anxiety. I wrote about it a couple of times here and at in the New York Times. In what anyone but myself could have predicted to be a critical error on my part, I began attending class halfway through the year. I missed the first half of the textbook, never learned how to sing the quadratic equation to the tune of some Christmas carol, and I could only attend class three days out of five because of my teaching schedule, so I was doomed to failure. This year, I have no such excuses. I am all in, from day one, four out of five classes a week.

If I was anxious about my performance in math the first time around, imagine the added pressure I am under now. My students are all aware that I am re-taking the class, and while they finished Pre-Algebra last June, I finished it in June of 1982. My teacher, Alison Gorman, calls on me in class, I do the homework every night at the dining room table while my sons do their homework, I hand in review sheets, and I just took my first test. I planned to take the test along with the rest of the class, but an emergency parent meeting took precedence, so I took my test at home. My sons were fighting over some thing or other at the time, so my test-taking environment was not what you might call calm and stress-free.

That said, things are going really well. Alison allows us to hand our review sheets in early for corrections, and I was the first student to earn a perfect score on the first one. Definitely a new Jess Lahey moment, and the review sheet has a place of honor on our refrigerator. I have been doing well on my homework, and was feeling confident going into my first chapter test. I will hand that in tomorrow, with all fingers crossed.

In the meantime, I've been trying to work out precisely what it is about math that freaks me out. Part of it is certainly the habit I've gotten into, the automatic assumption that I can't execute simple math without using my finger to draw the math problem in the air so I can remember to carry the one. Part of it has to do with my frustration that when when my husband or son multiplies 26 * 4, they simplify the whole endeavor to 25 * 4 for an easy 100, then remember to add on those extra four, for 104. I don't naturally think that way.

Then, last week, I isolated the real source of my frustration. I was doing the following problem:

30 - 5 * 3.

Simple, right? Well, here's what irks me. You have to do the multiplication first, because that's the rule according to the order of operations (PEMDAS - parenthesis, exponents, multiplication/division, addition/subtraction). So...do you do 5*3, which equals 15, then remember that the negative sign is there and take 15 away from 30? Or do you multiply a -5 by 3, which automatically gives you a -15, which you then add (or, as it's negative, take away) the 15 from 30?

Turns out, it works either way. Which is my problem. Alison claims that it doesn't matter. Rules are rules.

Rules. Tricky things, those rules. In Latin and English, rules are slippery creatures, best banned from my classroom. As soon as I tell a student they can rely on a grammatical rule, an exception sneaks out of the recesses of the English language to bite me on the butt and prove me wrong. So this whole trusting of rules thing does not lie within my comfort zone. I brought this up with Alison, and she smiled at my discomfort, reassuring me that I can relax. Rules are the rules, and that's the nice thing about math. Certainty.

My certainty lasted until second period Algebra class. Alison was explaining why numbers to the exponent of zero always equal one - it's a rule I did not understand last year, even after a very sweet student explained it to me repeatedly (see her explanation here). This year, I finally got it. In the middle of the explanation, Alison stopped, got a strange look on her face, and looked at me. She sheepishly apologized to me as she began to write the exception to the rule she had articulated not an hour before. Zero to the exponent of zero is not, in fact, one, but...drumroll...undefined. Not definable. Ahem. An exception. See? Bitten right there in the butt.

And then, an angel appeared. My personal math angel, who, as angels are wont to do, managed to make my life simultaneously simpler and much, much more complicated.

My math angel? Steven Strogatz - sorry, Professor Strogatz. He's a kick-ass teacher, bard of all things mathematical, and a lovely person, as I found out last week. He wrote a series of articles a while back for the New York Times that were amazing, and in advance of the release of his new book, The Joy of X (yeah, I know...so great, you know he did a fist-bump with his agent when he came up with that title), he's doing a new series for the Times. The first piece, on singularities, appeared last week, and I wrote to compliment him on it.

I wrote him an email, he wrote me and email, and we got to chatting about math. I explained my whole distrust of rules issue, especially in light of the zero to the zero debacle, and he replied to that email with his thoughts on the subject. My original email is in black, his are in red (I edited out some of his non-math comments):

Steven,


Sorry to bother you again, but there's a major issue of math you should be made aware of. 

I'm writing right now about the fact that math "rules" make me nervous. [They should make you nervous. There's a beautiful book called John Stillwell called "Yearning for the Impossible" on this very point.   http://www.amazon.com/Yearning-Impossible-Surprising-Truths-Mathematics/dp/156881254X   It argues that the great advances in math come when people break the rules. Two simple examples: (1) Rule: you can't divide 5 things evenly among 3 people, because 3 doesn't go into 5. True in the world of whole numbers. But if you "yearn for the impossible" and open your mind, break the rule, and invent fractions, suddenly your system of math becomes more free AND more powerful. (2) Rule: You can't take 6 away from 5. True, in the world of positive numbers. But if you yearn for the impossible and enlarge your concept of number and invent negative numbers, you can now work the math of of debts, which you couldn't even conceive of before. I discuss this sort of thing in the beginning of The Joy of x. It's the great narrative arc that runs through all of early math (and later math too, as Stillwell explains).]    I teach grammar and languages and there, "rules" are always in quotations - they are subject to the inevitable exceptions. So, when I come across the homework problem:

30-5*3

I get nervous. Is that -5*3 which is -15 [yes] that I take away [no. You don't take it away. If you're regarding it as -15, you need to add it, not take it away, from 30. You already used the negative sign to make the 15 into negative 15. You don't get to use it a second time to do a subtraction. I'll avoid the temptation to make a bad linguistic joke here about double negatives. Boo!]  from 30, or is that 5*3, and the negative is a subtraction symbol rather than a negative symbol - I mean heck, I don't know enough to know the difference, I managed to take linguistics as a substitute for college math…

Anyway, the fact that the answer is the same either way, and the fact that my Algebra I teacher can explain that it will always work out the same way, no matter what, does not ease my worry. 

There are always exceptions. My husband explained that this is what is lovely and amazing about math, that there are not exceptions. 

Alison Gorman, my lovely Algebra I teacher, explained that this is what is lovely and amazing about math, that there are not exceptions. 

Except…

Except…

I went in to math class the next day and learned why 3^0 is 1. Last year, I wrote about this, about how I had to just accept it as a RULE because I could not SEE it, and math people offered some lovely comments that went over my head. 

But Alison explained it so I understood this year, and I was happy. 

Except…

She then gasped and realized that she was about to make me very unhappy. Just when I had been mollified, when I realized that I could take solace in the rules of math, I could TRUST the rules of math, she offered up the one exception to that rule. 

Damn that 0^0 and its exceptive qualities. [yes, 0^0 is worthy of a column. Very tricky.]

Back to square one and my distrust of math rules. 

This is what I am writing about this evening. Although, as a side note, I did get an A on my first Algebra I chapter review, and I have decided that my new favorite thing to do is simplify. It's quite satisfying. Although when I was just asking my otherwise brilliant husband what the word I was looking for, "What am I trying to say…I simplify like…terms? variables?" he said, absentmindedly, "You simplify like a 'muthah'" which I assume he meant as some sort of compliment. 

Anyway. That's what I'm writing about, and I expect you to fix that whole "exception" issue in math as it appears to be my main stumbling block and source of distrust and unease. [Hope my comments above help. The biggie, which I did not talk about yet, is infinity. The Greeks after Aristotle said the rule is, you can't think about infinity. Not allowed. Too many paradoxes. Math was stuck with that rule for thousands of years, till the 1600s, when the yearning for the impossible got too overwhelming, and the need too great. And the result was calculus, which tamed the infinite and harnessed it to solve all kinds of problems that ultimately made modernity possible.You'll see what I mean when you read the book...]


Jess [Steven]

So you would think that Algebra I would be a breeze, what with Professor Steven Strogatz willing to personally explain the subtleties of my Algebra homework, but I guess not. And now that my teacher, my students, my students' parents, my blog readers and math stud Steven Strogatz are aware of my adventures in Algebra I, the stakes have been raised. Good lord, I hope I did well on my Chapter One test.

P.S. Professor Strogatz's Radiolab segments are some of their best, and they generally produce the best stuff on the radio. His TED lecture on synchronicity in the natural world rocks, too.

P.P.S. After reading this post, he recommended this page, for its discussion of 0^0.

UPDATE: I just got my test back from Alison, and I got a 97/102! Some stupid addition errors and not fully understanding how to simplify some fractions lost me a couple of points, but I'm pretty darn proud of myself today.

Sunday, August 5, 2012


Wow. I am so honored to be in such august company. The New York Times has named me one of the "33 Educators We Admire," and I could not be more humbled, excited, and eager to get back in to my classroom.  Three weeks left!


Friday, November 11, 2011

Fortes Fortuna Iuvat



I just found out that there's an "Elizabethan proverb commentary" website out there. I discovered this while perusing the weekly Bestiaria Latina digest. Oh, shut up. I fully understand that the sentence I just wrote puts me in a difficult position, high horse-wise. I had planned to poke fun at the aforesaid community of Elizabethan proverbists, but isn't mocking the Elizabethan proverb commentary while admitting that I receive weekly email digests from an organization called Bestiaria Latina just a wee bit of situational irony?

Oh! Oh! Teachable moment! Situational Irony: Miss Havisham is all in a lather because her daughter Estella won't show her love, but Miss Havisham is the very person who raised her to have no heart. Doh. 

In case you feel less than educationally topped off today, the featured proverb at the Elizabethan proverb commentary is fortes fortuna iuvat, which translates as either "fortune favors the brave," or "Fortune favoreth bolde adventurers, nothinge venture, nothing to have: spare to speake, spare to spede," depending on your era of origin. Me, I prefer the modern version, but it's nice to know that if I land in 1564, I will have a couple of proverbs at the ready.

Fortes fortuna iuvat. Teaching isn't usually the sort of job that results in publicity, let alone a shout-out in the New York Times, but it's been a great ride. The combination of that piece and my new blogging gig over at the Core Knowledge Foundation leads me to believe in the power of the Betsy bracelet. As a new friend noted, it's a good week to be Jess Lahey.

K.J. Dell'Antonia wrote a really nice piece about my blog and my teaching, and response has been overwhelming and quite varied. She linked to my blog, so a huge number of readers went there and emailed to tell me what they thought of me and my teaching style.

I'm a lumper, so let's do some lumping. Most readers were supportive and believe I made the right move, allowing my kids to go back and deal with their failures. However, some thought I humiliated my students by "punishing" them for failing to learn the material the first time. Some got bored of criticizing stuff in the New York Times and moved on over to my blog for fresh fodder. As there are pieces on rabbit pee and I swear once or twice on that blog, they found concerning things to email me about. Yes, that's right, I ended that sentence with a preposition on purpose, deal with it. A couple even linked over to my Core Knowledge blog post and sent me messages about my irresponsibility in allowing students to read Catch-22 (relax, my students know that the more mature books on the top shelf of the independent reading bookcase have been a wee bit excised by yours truly in order to allow them to read great literature while not being subjected to R-rated sex and violence) and questioned a whole host of other issues I won't bother to go into.

My assessment? People have a lot of opinions.

My answer to all of these readers? My students trust me. I work very hard to make sure that they know I care about them, they are secure in the fact that I have created a safe and constructive classroom environment, and they understand why I am challenging them rather than simply that I am challenging them. And if they are a little embarrassed by their failure to prepare, well, that's good. They should be. How they react to that embarrassment is what matters. I came oh-so-close to failing Civil Procedure in my first semester of law school and I was completely humiliated. I may have cried in bathroom and I may have eaten my body weight in chinese pork dumplings, but I also confronted my failure. I asked the professor to show me precisely what I'd messed up on my exam (in law school, one three-hour exam decides the grade for the entire semester) and I never made those same mistakes again. I made plenty of other ones, but I never made those particular mistakes again. I also never ate those particular pork dumplings again.

It's part of my job to teach my students to be brave and view their failures as learning opportunities. To buck up and return to the place of their defeat and ask for help.

I'm just grateful I get to be in that place when they show up.