Sunday, April 20, 2014

The best book written on education in the late 20th century

is The Phantom Tollbooth, by Norton Juster. It describes deep issues that thoughtful educators wrestle with daily: wisdom, friendship, trust, relationships between children and adults, and most importantly, knowledge.

I remember it as one of my favorite books growing up, but I hadn't reread it in years. Lately, I've taken to reading to my daughter again before her bedtime, and I decided that I would read her books I thought she should know about but might not pick up on her own. I started with Alice in Wonderland and Through The Looking-Glass, and then began on Phantom Tollbooth. As I've been reading it to her, I've found myself fighting the temptation to stop and underline everywhere. It's that good.

Let me just quote you a part, at length, from the latter part of the book. The protagonist, Milo, and his companions, Tock the watchdog and the Humbug, have just arrived at the Castle in the Air to rescue the princesses, Rhyme and Reason:
"It has been a long trip," said Milo, climbing onto the couch where the princesses sat; "but we would have been here much sooner if I hadn't made so many mistakes. I'm afraid it's all my fault."
"You must never feel badly about making mistakes," explained Reason quietly, "as long as you take the trouble to learn from them. For you often learn more by being wrong for the right reasons than you do by being right for the wrong reasons."
"But there's so much to learn," he said, with a thoughtful frown.
"Yes, that's true," admitted Rhyme; "but it's not just learning things that's important. It's learning what do do with what you learn and learning why you learn things at all that matters."
"That's just what I mean," explained Milo as Tock and the exhausted bug drifted quietly off to sleep. "Many of the things I'm supposed to know seem so useless that I can't see the purpose in learning them at all."
"You may not see it now," said the Princess of Pure Reason, looking knowingly at Milo's puzzled face, "but whatever we learn has a purpose and whatever we do affects everything and everyone else, if even in the tiniest way. Why, when a housefly flaps its wings, a breeze goes round the world; when a speck of dust falls to the ground, the entire planet weighs a little more; and when you stamp your foot, the earth moves slightly off its course. Whenever you laugh, gladness spreads like the ripples in a pond; and whenever your sad, no one anywhere can be really happy. And it's much the same thing with knowledge, for whenever you learn something new, the whole world becomes that much richer."
"And remember, also," added the Princess of Sweet Rhyme,"that many places you would like to see are just off the map and many things you want to know are just out of sight or a little beyond your reach. But someday you'll reach them all, for what you learn today, for no reason at all, will help you discover all the wonderful secrets of tomorrow."
The Phantom Tollbooth, chapter 18

That's pretty much it, isn't it? The answer to "why do you teach?" A partial answer to "why should I learn this?" Partial, because specifics do matter, but a partial answer is better than what we often have now.

I think, if I were interviewing teachers for a new school, I'd ask what 3 books influenced them the most as a young person. I'd hire anyone listing this book in a heartbeat. It is a humane plea for the centrality of both knowledge AND wisdom in a life of meaning. It is a work of depth disguised as a children's book. It is a book that cries out to be reread. And I am truly grateful that Norton Juster chose to write it more than 50 years ago.

Saturday, March 29, 2014

To Whom It May Concern

After 15 years as a public school mathematics teacher, I am leaving.

This kind of thing happens every year, every spring. Teachers leave, others come in; students graduate, students enter. Schools continue.

I am grateful for many things:
  • The amazing colleagues I had at my first school (The Beacon School) during my first 4 years as a teacher. I learned much of what I know about kids and schools from them.
  • The unbelievable colleagues I have at my current school (Summit High School). We are a merry band, we are damn good, and we care for kids. I'm proud to have had the opportunity to work for so long with such a professional, dedicated group.
  • The educators I have gotten to know better over the last decade-and-a-half outside my own schools. Many I only "know" through social media such as Twitter, but I have had the great good fortune to meet several in person. Their knowledge, passion, and wisdom are an inspiration.
I am going to be teaching mathematics at Newark Academy starting in September. It will be a huge change. Much will be different. But in the end, everything that mattered before still matters now: I want kids to have a chance to experience what math can be like. I want them to know that it's not just formulas, homework problems, and tests.

I'm looking forward to the challenge.

Monday, February 17, 2014

Jordan Davis

By now, the message that the jury trial of the killer of Jordan Davis ended with a mistrial has gone out. 
There are a host of other related messages that have long since been received by the African-American community throughout the history of this country; this is yet another page in that thick book.

In the middle of thinking about this, I had a telephone conversation with a very wise friend last night. He reminded me that the most important thing about someone is not what they are against, but what they are for. What one is willing to build, not what one wishes to see destroyed.

Me: I want to build.

Very fortunately, I was asked by Chris Lehmann of the Science Leadership Academy in Philadelphia to help a group of educators come up with a lesson plan to use in class - TOMORROW - with their students to talk about the Jordan Davis case and the larger issues surrounding the case. TOMORROW, so the story just doesn't disappear. TOMORROW, so that the memory of what happened remains.

It has been a miracle of crowdsourced educational thought. The product that resulted from the efforts of Chris, Jose Vilson, Melinda Anderson, Alexa Dunn, Joshua Block, Zac Chase, Diana Laufenberg, John Spencer, Matt Kay, Luz Maria Rojas, Audrey Watters, Bill Fitzgerald, and me (to a VERY VERY SMALL EXTENT) is one that I'd like to see teachers across the country spend time with tomorrow.

We are trying to build something out of a tragedy. We are trying to figure out how to turn a too-common occurrence - a murder racially motivated - that too often gets taken for granted and make it have some amount of meaning. To create a lever that, perhaps with the right fulcrum, could move the world just a bit in a positive direction.

I am proud and gratified to have played my tiny role, but prouder still of the people who stepped up and created and organized this. Please follow the link below if you are interested in seeing what is possible. Education can move mountains. It must.

Sunday, February 9, 2014

On Analogies, Bad Uses Of

Many years ago, before the Earth had finished cooling, there was a test called the Scholastic Aptitude Test. (Actually, it was called the Scholastic Achievement Test at first, then the Scholastic Aptitude Test, then the Scholastic Assessment Test, and now just goes by SAT. Anyway.)

On this test were questions on something known as analogies. You might have heard of them. They looked like this*:

(Think over your answer. I'll wait.)

I absolutely HATED analogy questions. It was rare that I'd find an answer that I felt conveyed the same  relationship as the original; more commonly, I'd find that there was more than one I could equate to the original.

In any event, my experience with them led me to be skeptical about their use as a rhetorical device, because they could be deployed with such ease that often the deployer wouldn't realize they were inapt. They would be used to draw comparisons between events or situations that just were not equivalent in any meaningful way.**

I've not had to think about analogies for years, which has been nice. However, over the last month or so they've reared their (IMO) ugly heads. I'm not going to go into details, except to say that one of them involved apartheid, and the other involved the Tuskegee experiment. Both of them were used as analogies to situations going on in public education right now - by people presumably defending public education.

Here's my problem with that.

Folks who defend public education need to make their case to the public not only with clarity and with purpose, but with accuracy. And using analogies that are inflammatory, that are unkind, that open unhealed historical wounds does not help.

It's on us to be the ones that are above board and clear and accurate. We can be righteous in our rage - we can be strong and unwavering in our voices - but we cannot become like those we disagree with. We have to be better.

And some may say that this is unfair, and this is not right, and this puts us at a disadvantage. And they'd be right. But, while I'm normally known as a Bible-quoter, this passage sticks with me in response: "For what will it profit a man if he gains the whole world and forfeits his soul?" (Matthew 16:26).

Education isn't a contest to be "won". (Bad analogy!) Education is about helping students and families and communities. And if we are going to help make education better for students and families and communities we have to be thoughtful in our language, consistent in our voices, and above all, fair in our comparisons.

*Here's the answer to the analogy. I'll let you draw your own conclusions.
**Godwin's Law is the canonical example of inapt comparisons on the Internet. We really, really don't want to go down that kind of road, do we?

Monday, January 27, 2014

What I'm not writing about Educon. Because anything specific I'd have to say about it has been said repeatedly. The only thing I could possibly add is that I continue to be gratified, humbled, and enlightened by the people I meet, hear, watch, Tweet with, and am challenged by when I am there. I'm privileged in more ways than I know.


So what I am writing about is not writing.

I note that I haven't blogged since November (hey, all, thanks for noticing!), and that's totally fine. Because my voice isn't the one that needs to be heard in and amidst all of the education chatter that goes on out here on the Interwebz. In my 15th year of teaching, I'm feeling pretty good about the things I know, the things I don't know, what I can learn, and what I still need to (which is endless, but that's OK, because that's life).

There's one little thing that nags me though: student voice. Or the lack thereof. As a math teacher, I've not ever given a lot of thought to student voice. Even when I have tried to make things more engaging, change things, do more activities or less, it's still been (for the students) that my class is more a case of done TO, and less a case of done WITH.

And that's a problem. Because there's CONTENT that needs to be covered, dammit! Who's got time to hear from students? And in the world we're in, with tests and SGOs and college acceptances and midterms and so on, I'm acutely aware that teacher voice is becoming ever quieter. We're being heard less and less.

We're getting so quiet, in fact, that we're reaching the level of quietness that formerly was reserved for the STUDENTS we teach.

Isn't it funny? I worry so much that teachers aren't being heard, that I'm coming face-to-face with the fact that students NEVER have been heard, and that we're approaching them in lack of influence over the national educational conversation. Ha ha ha.

Friday, November 8, 2013

Hippies, physics, and math ed

I just borrowed David Kaiser's "How the Hippies Saved Physics", and am really enjoying it. It's providing a weird trip down memory lane for me, especially as the physicist Jack Sarfatti plays a major role. In the early days of the Internet, when I was a grad student in the early 1990s, I spent far too much time on interesting newsgroups such as sci.physics and alt.physics; Jack was one of those who was really pushing the boundaries of what was considered "real physics" and alternative perspectives. I enjoyed his commentary, and it really made me think. As it happened, when I was in high school I had also read three of the other seminal books on "hippie physics", Gary Zukav's "The Dancing Wu Li Masters", Heinz Pagels' "The Cosmic Code", and Fritjof Capra's "The Tao of Physics". I was in waters deeper than I could understand then, and I only read them on the surface ("Wow, man! ESP and quantum mechanics! Cool!"). I put those speculations and interpretations away for quite a while, but they've started to creep back into my awareness of late.

But what is striking me right now as a math teacher is a passage from Kaiser's book, describing how the teaching of quantum mechanics in 1950s America had changed from pre-World War II era pedagogy. Prior to the dispersal of the European founders of quantum mechanics across the globe, they had had ample opportunities to argue, debate, discuss, and wonder about the philosophical implications of what they had invented-slash-discovered. Textbooks written in the 1930s included long philosophical asides on the interpretation of quantum mechanics. Famously weird phenomena such as Schrödinger's cat and the double-slit experiment became commonplace topics of conversation.

That all changed after the war, because physics was perceived as an applied field; it had helped win the war for the Allies, and as the Cold War became more heated, physics became more important. In order to keep up the supply of physicists, the style of teaching and the topics taught changed. From Kaiser:
Faced with such runaway growth, physics professors across the country revamped their teaching style. They began to accentuate those elements that could lend themselves to high-throughput pedagogy, pumping record numbers of students through their courses. First to go was the discussion-based, qualitative, philosophical inquiry into what quantum mechanics meant... A few years later, another critic [the physicist George Uhlenbeck] weighed in... he accused his American colleagues of confusing what was "easy to teach" - the "technical mathematical aspects" of quantum mechanics, which could be chopped up and parceled out on problem sets and exams - with the conceptual, interpretive material that students needed most. (pp. 17-18)
In short, the larger the class, the less time spent talking through the big issues at the heart of quantum mechanics... The quarter century during which this Cold War style reigned witnessed an extraordinary buildup of calculating skill. All the same, an intellectual trade-off slipped by unnoticed, with wide-ranging implications... The fundamental strangeness of quantum reality had been leeched out. (pp. 19-20)
To my mind, this parallel is occurring right now in mathematics education. With more and more students taking more and more mathematics, we are devoting less and less time to investigating the strangeness within it alongside our students. We confuse what is "easy to teach" (that is, "easy to assess") with conceptual, interpretive material.

It required a bunch of frustrated young physicists in the 1970s to change the perspective of the larger physics community to any degree. And arguably, that philosophical way of thinking still has not re-entered the physics world, much to its loss. Calculation still rules physics, and it still rules math education. And when we lose math students because we've spent too much time on the "how" and not enough on the "why/what happened", that's an even greater loss.

Friday, August 30, 2013

Nicholson Baker, algebra 2, and equity

Like many other folks, I've read Nicholson Baker's article on Algebra 2 in the September 2013 issue of Harper's. And I think many of the comments that have been written on it are interesting, thoughtful, and useful for the discussion. Some of these include comments by Jose Vilson, Michael Doyle, and Jason Dyer. The most useful ones for me to think about are the first two, because they clearly set upon something that we often (choose to?) ignore in these conversations about "reforming" math education, which is the socioeconomics of it.

Before I start offering my own perspective in that line, I want to state clearly and for the record: I did NOT read Baker's article in the same way that I read Andrew Hacker's article of a year ago in the New York Times.

I will state that, for the record, I agree with the vast bulk of what Baker says in his article, and that to do otherwise is to ignore the realities of what actually happens in real classrooms to real students.

Maybe it's that I'm a year older, maybe it's that I'm just not going to get riled up any more by someone claiming that math education is irreformable, and so therefore should be tossed out and replaced with...'a one-year "teaser course" in mathematics for ninth graders. A one-year course in all of the "big ideas in mathematics". Hm. Sounds familiar. (Believe me, I don't think Baker knows me from Adam, and he certainly didn't read my EduCon 2.5 proposal, but still...something in the aether, apparently.) And Baker writes with much more sympathy and understanding of the struggles of a typical mathematics student than Hacker did, in my opinion. He also did a much better job of bringing in big guns to support his position (e.g., Underwood Dudley, Steven Strogatz, Paul Burke, Michael Wiener). He also, and most importantly in my mind, reminded everyone of the history of math education in the 20th century, and how right up to Sputnik only a small cadre of students took advanced mathematics of any type, not just algebra 2.

Baker's complaint about math education (NOT MATH!), as I read the article, is that it lacks a fundamental narrative. That is, we expose our students to "hairy, square-rooted, polynomialed horseradish clumps of mute symbology that irritate them, that stop them in their tracks, that they can't understand." We do this for a variety of reasons: it's on the test, it's the next unit in the (Common Core) curriculum, it's what they need to take the next course, etc. We spend no time at all on the great story, which is of math itself and the power we humans have gained by its use. As a result, we produce large numbers of students who (mostly) think of math as that disconnected, irrelevant, annoying, frustrating subject. If you believe Baker's numbers from the Amplicate survey, 86% of respondents HATED algebra. Which is a smaller percentage than the number of respondents who HATED geometry. This is success? If you are going to complain about Baker's article, then I think you need to start there. It does no good to criticize Baker's rational functions example by drawing from other references defining rational functions, and then complaining that Baker's example is merely one of not finding a student-friendly definition. It's the CONCEPT that is the problem for students, not the wording.

Baker's take on the "robotic gecko" Algebra 2 book is priceless, and precise:
It's a highly efficient engine for the creation of math rage: a dead scrap heap of repellent terminology, a collection of spiky, decontextualized, multistep mathematical black-box techniques that you must practice over and over and get by heart in order to be ready to do something interesting later on, when the time comes. (p. 33)
(By the way, this also offers something different from Hacker's complaints, and perhaps also why Baker's article made more sense to me than Hacker's. Hacker's article: math is too hard for kids, so we shouldn't teach it. Baker's article: math-as-taught lacks a compelling story, so we need to think about how to teach math so that its story can be told.)

From my colleagues, many of whom are feverishly working on new and better ways to teach rational functions, I can already hear the complaints: "Not in my classroom! In my classroom students learn to THINK!" "We do projects where students demonstrate their understanding (sic) of the material!" "I have a really good way to teach topic X, and my students Really Get It!" Is that so? Are you sure? Are your students so different from Amplicate's anonymous respondents? English has a narrative. History has a narrative. Learning a foreign language is a tangible goal, if no narrative. What is the story of mathematics? Do you talk about it? Do your students see the grand sweep? Or is it logarithms last week, and trig identities tomorrow?

So I'm on board with Baker's points, and his general plea for something different in math. And I'm feeling pretty good because for a magazine like Harper's to publish something like this is, honestly, nice to see.

But there's this little nagging voice in my head. Which says: what happens to those kids next? They've taken that "first year"/9th grade course; what now?

And then I read Jose Vilson's and Michael Doyle's posts on Baker's article, and they poke huge holes in my good feelings (deservedly so) and make that little nagging voice a loud screaming. Vilson puts it bluntly, and Doyle quotes it in big letters:
If someone said, “Let’s end compulsory higher-order math tomorrow,” and the fallout happens across racial, gender, class lines, then I could be convinced that this was a step towards reform.
Jose Vilson
And that's really the heart of all of this, isn't it? We can't do what we need to do with mathematics education, which is reformulate it to make the required-for-everyone-part meaningful, and leave the higher-order stuff for those for whom, as Baker says, "Fourier analysis is a joy and a marvel, a way of hearing celestial music". We can't do it because, as Doyle puts it so well:
Algebra II has become a badge, one of many, that pretends to separate middle class white boys from, well, everybody else.

You can pass A2 without understanding a whole lot about mathematics, or even numbers, but the vast majority of careers that "require" A2 do not actually require that you actually use it--they just require that you have some kind of certificate saying you passed a course labeled Algebra II.

Michael Doyle
Now, as a teacher in a suburban district, I feel this argument. In my bones I know this is right. In my bones, and as I've experienced, I know that students in the upper/upper-middle socioeconomic classes go to Kumon and Sylvan and Huntington Learning centers. They get all of that individual, expensive (I know because I've done it) tutoring. They meet with some kind soul once, twice, or more every week to go over homework, to prepare for tests, to have that someone explain - patiently, over and over and over again if needed - how one does X. How one factors quadratics, simplifies rational expressions, or whatever.

If your family has the cash, your family gets you the tutoring you "need". If not, good luck. Anyone wonder why the number of students from less privileged backgrounds drops as the math level goes up? I don't.

And let's not forget that college entrance requirements generally won't allow students to NOT take algebra 2 in all of its spiky decontextualized-ness. Or to not take the SATs/ACTs, which are (of course) exemplary assessments of critical thinking and creativity (with bubble-forms).

So here's what I predict would occur from an implementation of Baker's proposal. Almost every kid takes his 9th grade class. Gets a great overview of mathematics. Some, who are intrinsically interested in the subject, go on to the "college track" sequence, starting (perhaps) from a reformulated "algebra 2/precalculus"-type class, then calculus. Some, who have found other interests in mathematics this way, take a different path; perhaps through statistics, probability, or discrete math. And some have taken all of the math they're going to take. Great!

In an ideal world, kids would sort themselves in this way based on their interests.

Kids in track #1 ("calculus track"): These are the kids who love math, who love the challenge of it, and who see the abstractions of algebra and analysis as pursuits worthy of study.
Kids in track #2 ("statistics track"): These are the kids who recognize the importance and practicality of math, and who see utility for it in their futures.
Kids in track #3 ("one and done"): These are the kids who have had a good experience with math, who have seen the forest for the trees, but do not wish to go deeper as their interests lie elsewhere.

In the real world, though, college pressures, parental pressures, "Race to Nowhere"-type stuff, become issues. Here's my prediction for what would really happen:

Kids in track #1 ("calculus track"): Based on current college policies, this track would still have the leg up on college admissions. Parents of kids in upper socioeconomic strata would make sure (spend whatever $ necessary) that their kids were in this track and that they stayed there.
Kids in track #2 ("stats track"): may still get tutors for assistance. Not nearly as advantaged for college admission, but because they are taking meaningful mathematics all the way through high school, may be at less of a disadvantage.
Kids in track #3 ("one and done"): Any guesses about college for those kids?

Now of course, if this proposal REALLY were implemented, my other prediction is that the top-end (socioeconomically) kids who otherwise would have been in a public school will quickly bail for a traditional private school, offering "real math" and that all-important college advantage.

In either case, kids on track #3 - how do you ensure they have access to quality educational opportunities post-high school? And I'm not interested in hearing "Well, they only took 1 year of MATH, so they shouldn't." If you really believe that for a student to do well at "good university X" they have to pound their heads through at least precalculus, you'd be wrong. I will assert (without evidence) that student success in college is more about a student's work habits, overall knowledge base, and interpersonal and time management skills than whether or not they got a B in precalculus or an A- in algebra 2. Don't believe me? Ask yourself: how many math courses do students have to take to get a degree from a "prestigious" comprehensive university?

And now I feel rotten, because I'm back to the beginning. This is as far as I can think through it: Math education needs work, as Baker says. His proposed changes would alter student attitudes towards mathematics, which in my head is terribly important. But I believe he is naive to imagine that this reform would really change anything meaningful in terms of equity.

What I need to work on answering: where is the lever for change that I have control over? Where's the big red button I can push to help make things for EVERYONE better? Because I can't control issues of equity, which are ultimately preventing any meaningful changes from happening.

Actually, maybe I can. Maybe I can tend my own garden and do what I can do in my own school to make things more equitable. Hm.....