The Phrase “Growth Mindset” and Its Problems

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I have brought up growth mindset, skeptically, many times on this blog; in addition, I dedicated a chapter to it in my second book, Mind over Memes. My basic argument is that we both have and need a mixture of mindsets; while it can be damaging to believe that your abilities are absolutely fixed, there is no evidence that an unfettered belief in growth would benefit anyone. Beyond this, something about “growth mindset” bothers the ear. Conceptual problems aside, the phrase itself rings false.

My criticisms take nothing away from Carol Dweck’s and others’ research; they aren’t about the research. Nor do they disparage those who have been helped by the concept of growth mindset. Rather, I take up the matter from a linguistic and philosophical standpoint. Today I will focus on the linguistic.

I have already brought up the problem with each of the two words. Limitless growth is not always desirable; moreover, our attitudes about improvement may not constitute a “mindset.” Together, the two words ring with an importance that has not been earned. “Growth mindset” sounds like a life solution, an attitude that, once adopted, will open you up to happiness and success. As a result, anyone who questions “growth mindset” gets accused of negativity, even unhappiness. Unless you are a terrible, mean, frustrated person, how could you possibly criticize something that liberates people, that allows them to reach their true potential? If you oppose growth mindset in any way, aren’t you wishing stultification upon the world?

Dostoevsky’s Underground Man would have had a field day with this. But even a happy person, a person who does believe in certain kinds of improvement, can have serious qualms over “growth mindset” as a concept, without being mean or wishing anyone ill. Unfortunately, the very phrase “growth mindset” is constructed to imply otherwise. It’s like “cooperative learning” in that way. If you question or criticize anything about “cooperative learning,” you get written off as uncooperative.

A week ago, in a New York Times article, Alina Tugend wrote about making a mistake, long ago, in a New York Times column. After that mistake, she found herself wondering why people berate themselves so much for mistakes; later she wrote a book on the subject. One of her major sources of insight and inspiration was Carol Dweck’s Mindset: The New Psychology of Success and the accompanying research, which she summarized in the present article. The next part of the article described an interview with Dweck during the pandemic. Could growth mindset help people through the Covid crisis? Dweck replied with laudable caution, but Tugend offered reasons for optimism. She concluded the article by reflecting on the process of writing it. It had not been easy:

This article, the one you are reading, proved to be a mini-Mount Everest for me. Somehow I couldn’t get it right. My editor offered some helpful comments, but a second try also fell flat. My first thought was “Oh forget it — this just won’t work.” The second thought was an internal wry smile and an acknowledgment that I wasn’t demonstrating much of a growth mind-set. Back to the computer.

Now, scrapping a piece isn’t necessarily a sign of “fixed mindset,” but I’ll leave that aside for now. The point is that this article was more of a personal reflection than anything else. The comments varied widely–some enthusiastic, some critical or skeptical, but I didn’t see anything nasty. No putdowns, no ad hominem remarks. All in all, they were remarkably civil and thoughtful. Then I saw this:

Alina,
Thank you for the article and persevering through the challenges of putting it together. No quick and easy answers in psychology, and mindset only gives us a small part of the big picture, but a useful part. Try not to give these comments too much time, lots of stone throwing unhappy people reading the Times these days. Stay in the light.

I see the commenter’s point about not giving the comments too much time. But what was with those “stone throwing unhappy people”? If people had been hurling insults at her, or even at the article, that remark would have made sense. But if objecting to some aspect of “growth mindset” is tantamount to “stone throwing” or “unhappiness,” then there’s something manipulative about the phrase itself. It automatically casts aspersions on those who sidestep its temple.

Many fads and cults depend on phrases like this, phrases that sound so good on the surface that only a cruel, miserable person could question them. This does not mean that the researchers themselves have sought to create any kind of cult or fad–in fact, they have resisted this, from what I can tell–but the phrase lends itself to that kind of thinking. There are the Good and Enlightened who believe in Growth Mindset, even if their own growth mindset isn’t perfect. Then there are the Bad and Deluded who have reservations of one kind or another. The one group walks in the light, the other in confusion and brambles.

The Underground Man’s words (I decided to quote him after all) hit the mark. This is from Dostoevsky’s Notes from Underground, Part I, Chapter 10:

You believe in a palace of crystal that can never be destroyed—a palace at which one will not be able to put out one’s tongue or make a long nose on the sly. And perhaps that is just why I am afraid of this edifice, that it is of crystal and can never be destroyed and that one cannot put one’s tongue out at it even on the sly.

You see, if it were not a palace, but a hen-house, I might creep into it to avoid getting wet, and yet I would not call the hen-house a palace out of gratitude to it for keeping me dry. You laugh and say that in such circumstances a hen-house is as good as a mansion. Yes, I answer, if one had to live simply to keep out of the rain.

Exactly! The problem with “growth mindset” as a phrase is that “one will not be able to put out one’s tongue or make a long nose on the sly.” That, and it is more of a hen-house than a palace. It can help with certain things, up to a point, but it is not the answer to all of life, nor is anyone obligated to pursue its perfect, complete manifestation. In fact, there’s reason to think that that would be hell.

The organization MindsetWorks continues to promote the notion that everyone should be on a “journey” to more growth mindset.

Our mindsets exist on a continuum from fixed to growth, and although we’d like to always have a growth mindset, the reality is that we can only be on a journey to a growth mindset. The goal is to recognize fixed mindset elements in ourselves and then reflect on feedback and strategies for how to improve.

This is the “crystal palace” through and through; MindsetWorks not only puts growth mindset forth as an ideal but also leaves no room for the possibility that someone might “be on a journey” to a different destination. No, we are all supposed to examine ourselves for any remaining elements of “fixed mindset” and remove them, one by one, until we all embody perfect growth and eat each other up.

What would I offer instead of “growth mindset”? Well, I see no need for a catchy phrase at all. Instead, adopt a working principle that humans are capable of improvement and learning. Bring that principle into teaching, employment, and other areas of life–show it through your own attitudes and practices–and remember that it does not encompass the truth about a person, a subject, or the world.

I made a few edits to this piece after posting it.

In Person

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The coronavirus isolation is not all bad. It’s good for working on projects, sifting through thoughts, going on bike rides. Even on a short bike ride, I find all kinds of things to explore; I turn off onto dirt roads (which are dry, not muddy, right now), discover a bridge or path I didn’t know about before, take detours, cross meadows, peer into the river, and turn back when I think it’s time.

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So that’s isolation, on the one hand. At home, too, there’s a lot of exploring in it. Putting together the online journal Folyosó, which will appear on May 11, I have been editing pieces, experimenting with layouts, fixing this or that feature, and getting so absorbed in the whole thing that I stay up late.

But the pandemic is bringing out, in different ways, the necessity of doing certain things in person. Zoom and other online services are substitutes, and substitutes only. Sometimes a substitute will not do. For instance, we (the drama club, the drama teacher, and I) were going to take Kata Bajnai’s play Farkasok (Wolves) to the festival in Veszprém this June. The festival was cancelled; of course it was. First of all, if the drama troupes cannot rehearse, how can they prepare for a festival? Second, a festival of this kind cannot take place virtually. We were disappointed, but this just brings out how drama requires physical presence–of the actors among each other, of the stage and space, and of the audience along with the actors. The actor and director Joel Grey wrote about this in a memorable and treasurable New York Times piece.

With teaching, too, the best thing is to have classes in person. We work with the substitutes because we have to, and some good things come out of them. But there is nothing like being in the room together, seeing each other’s facial expressions and gestures, sensing the mood as the lesson progresses, picking up on understanding and uncertainty, and above all, living the lesson–be it grammar, literature, or something else–together. The substitutes–Discord, Zoom, Messenger, Google Classroom, and so on–are functional, but functionality is not everything. I think of Dostoevsky’s Underground Man:

You believe in the crystal palace, eternally indestructible, that is, one at which you can never stick out your tongue furtively nor make a rude gesture, even with your fist hidden away. Well, perhaps I’m so afraid of this building precisely because it’s made of crystal and it’s eternally indestructible, and because it won’t be possible to stick one’s tongue out even furtively.

Don’t you see: if it were a chicken coop instead of a palace, and if it should rain, then perhaps I could crawl into it so as not to get drenched; but I would still not mistake a chicken coop for a palace out of gratitude, just because it sheltered me from the rain. You’re laughing, you’re even saying that in this case there’s no difference between a chicken coop and a mansion. Yes, I reply, if the only reason for living is to keep from getting drenched.

–Fyodor Dostoevsky, Notes from Underground, translated by Michael Katz.

I don’t think anyone is mistaking Zoom, etc., for a palace. But it’s also good to see them for what they are: substitutes. Less than ideal. Not the ideal itself. Granted, they can do some things that in-person gatherings cannot (for instance, bring together people from all around the world). But that doesn’t make up for the losses.

A new video by the rock band Kiscsillag expresses this uproariously (and bawdily). The song itself, “Nem szégyellem,” precedes the pandemic–and appears on the band’s new album, Tompa késekbut the video itself was shot on mobile phones, just a few weeks ago, in the band members’ homes. (See a Music Backstage article on this.) A gem of quarantine rock and home filming–and you don’t need to know Hungarian to appreciate it, though each word raises the appreciation higher.

 

 

There you have the soul of it, ticklish but true. It isn’t just that certain things are best done in person. It’s that when all the things around you–the food in the fridge, the bathtub, the rocking horse, the vacuum cleaner, the chess board–start acting as substitutes for the world, then you know that you, too, have been substituted.

 

Knowledge vs. Nonsense

Rarely does an article make me cheer as did Shannon Rupp’s in Salon (about the benefits of studying philosophy). Here’s one of my favorite quotes:

I’ve long thought that the debate about whether universities should be offering trades training or educating citizens is something of a red herring — the discussion should be about whether to study knowledge or nonsense.

A treasure! Thanks to Joanne Jacobs for bringing it to my attention.

It brings me back to my first year of teaching, when I wrote a letter to the New York Times about the misguided focus on “strategies,” especially reading strategies.

“Strategies” of that kind make me queasy (unlike chess strategies, which I enjoy). Yet I fear that the “strategy” nonsense is now being supplanted by other kinds of nonsense (or even wrapped up inside it). At least there are people calling out the nonsense! Here’s another quote from Rupp’s article:

I spent a semester defining ordinary things. Hats. Chairs. It’s harder than it looks. And I remember a classmate’s resistance to it. He kept ranting that it was stupid — everyone knows what a chair is! — before dropping out.

Of course, everyone only thinks she knows what a chair is. Or social justice, for that matter. Politicians, CEOs of questionable ethics, and all PR people count on exactly that. They will say something vague — I find the buzzwords du jour all seem to have some reference to “social” in them — and leave us to fill in the blanks with whatever pleases us.

Voila: we hear whatever we want and they get away with whatever they want.

Yes, and the same can be said about “strategies.” What are they? In many cases, they are methods of evasion. When I taught elementary and middle school, I saw students dutifully look at the picture on the cover, read the blurbs, make predictions about the book’s contents–before even opening the book and reading. They had been taught to do this. Then, once they started reading, they continued dancing around the text–making “text-to-self connections,” using pictures to help with word meanings, and so on. I encouraged them to pay attention to what was actually there.

But now the focus is on “close reading,” and while that’s an improvement, it might get taken too far. For instance, you do need to understand certain things outside the text in order to grasp the text. Try a “close reading” of Aristophanes without any knowledge of mythology, ancient Greek literature, or ancient Greek history! You might as well try to boil a turnip without water (or other suitable liquid).

Also, reading is not always linear; the mind goes here and there, drawing connections and imagining things. When you read Crime and Punishment, for instance, you start to feel the presence of Svidrigailov and Porfiry Petrovich. You can cite textual evidence, of course, when describing these presences, but it’s also good to take them in less rationally, to imagine them in the room. This requires close reading, but not of a strictly analytical kind. Similarly, when reading a poem (such as Blake’s “Auguries of Innocence“), it’s as important to take in its mystery as it is to notice its structure, syntax, and tropes. (This goes for literary nonfiction as well; if you try to read Emerson’s “Experience” in a strictly analytical manner, your mind will end up in knots, and the text will fly away.)

How should one read, then? Well, the thing one reads will often lead the way. If it’s good literature, it calls for careful, thoughtful, imaginative reading. If it’s nonsense, well, then, it calls for the “spot-the-nonsense” strategy, which requires some background knowledge–of philosophy, literature, and other subjects–as well as a salutary allergy to buzzwords and overpuffed ideas.

Why Give Literature an Honored Place in School?

In education discussion and elsewhere, the terms “literature,” “fiction,” and “nonfiction” get jumbled up a bit. I jumble them too—I catch myself talking about “literature vs. nonfiction,” for instance, knowing that there’s overlap between the two. The term “literature” refers to works with lasting artistic merit (except when one is talking about the “literature” on a given topic). Artistic merit is difficult to define, but it involves a certain transcendence as well as mastery. A literary work goes beyond literal meaning; it has hints, metaphors, paradoxes, juxtapositions, ironies. It takes us a bit beyond the information that it presents. Moby-Dick may teach us a thing or two about whales, but that’s only part of what it does.

In that sense, the push for more and more “nonfiction” in classrooms (for instance, through the Common Core Standards) does threaten literature instruction. Those pushing for more “nonfiction” rarely have Emerson, Buber, or Kierkegaard in mind—works that tease us with possibilities. They want students to read argumentative pieces and informational reports: that is, works with a clear thesis supported by evidence. Of course it’s important for students to read such works; the problem lies in privileging them: in hinting, through one mandate after another, that informational text is more useful than literature (for college and career preparation) and therefore more valuable.

“But no one’s saying that!” some will protest. “No one said that informational text was to come at the expense of literature. The ELA standards apply to all of the subjects, not to English class alone.” Well, if this were so, English teachers would not be getting directives to include much more informational text in their curricula. New York State would not be considering a proposal to require high school students to write a research paper (for English class) that draws on at least four informational texts. Make no mistake: the push is for informational text. And it’s destructive as well as misguided.

Should students be reading informational nonfiction? Of course—but they don’t have to do this in English class. From elementary school onward, they should read on scientific, historical, and other topics. They should have a chance to read ancient mathematical proofs, musical scores, biographies, letters, historical documents, and more. Where should this take place? In the most appropriate classes. At times, students might read a work of fiction for history, or study a song for English. In the early elementary years, some of the courses may be combined into “literacy blocks”—so that students may find themselves reading poetry and historical narratives in the same class. But overall, each course should have readings for its domain—and English class should be the place for literary works.

An English course in expository writing might be an exception here. If a school’s English department offered a specific course in writing a research paper, then the other English courses wouldn’t have to be eroded. My high school had such a course—and many students reported years later that it was the most important course they took. Nonetheless, the other English courses were devoted to literature, excellent literature, and no one apologized for that. It was in middle and high school that I first read Sophocles, Euripides, Chaucer, Shakespeare, Milton, Hardy, Faulkner, O’Connor, T. S. Eliot, and others. No one doubted that such works were important; no one suggested that we were deficient in information. (We read a range of historical works and wrote research papers for history class.)

Now, there are big gaps in my education, including my literary education, but I found myself prepared not only for college, not only for a range of workplaces (even in the 21st century), but for a life that I want to lead, a life that involves pondering words, listening to music, and sifting through thoughts. I was not prepared in all ways, but who can be? Either one enters predictable situations with skills and knowledge to match them, or one enters the unknown, with the risk that one may not always know what to do. Who on earth would want the former? I’ll take the uncertainty and the risk any day, again and again. That said, one shouldn’t be foolhardy about risks; one shouldn’t enter the adult world defenseless. I have been foolhardy at times, defenseless at times, but not in relation to academic or vocational knowledge. I had what I needed in order to learn more; I had, moreover, a store of things to recall and reread.

Reminiscence aside, what is at stake here? Why stick one’s neck out for literature? It isn’t always beautiful (beauty is a complex topic), meaningful (try to find a stable meaning in Dostoevsky’s Notes from Underground), or even likable (I find 100 Years of Solitude irritating at times). It is easy to slip into sentimentality about literature, but sentimentality is not the point. Literature deserves an honored place in schools for many reasons, including its ability to open up areas of life that we might not otherwise face. There is room in it for bravery and uncertainty. When reading “The Love Song of J. Alfred Prufrock,” one does not have to be snappy and polished; one does not have to put on a good face or rattle off talking points. One can roam for a while in the lovely and perplexing mess. (It isn’t mess itself, by any means–but it allows for a bit of the messy, and takes us out of the realm of the pat.)

Today’s students learn skills like “speed networking”—making a quick, flawless impression. What they don’t learn, often, is the practice of mulling, of staying with something they don’t immediately understand, and of allowing themselves their own mysteries too, and allowing themselves time. Not all students have lost this; some know how to sit with uncertainty, difficulty, questions, pain. Sadly, these very students get faulted for being “off-task,” since the tasks have become quick and shallow. Our priorities have gone off kilter; things that can keep us mindful and soulful get shorter and shorter shrift.

 

Note: I made a few edits to this piece after its initial posting.

Teaching the Underground

undergroundOne aspect of teaching that rarely gets discussed (on blogs and in education news) is the intellectual and ethical challenge of taking students through a complex work like Dostoevsky’s Notes from Underground. I find myself turning lessons in my mind, asking myself what to bring out, what questions to ask, what background to provide, what comparisons to draw. This would be the case with just about any lesson—but with Notes from Underground it’s particularly important, as the work is easy to misunderstand in one way or another. Once the basic understanding is there, it’s possible to appreciate the work’s paradox and play on the one hand and its serious moral questions on the other.

Its narrator and protagonist, the “Underground Man,” lives alone in a dingy Petersburg apartment, from which he does not emerge. He writes and writes, in some sense baring his starkest truths, in some sense fooling the reader. He rails against the formulas that others embrace, formulas for a perfect society or even a reasonable one. No perfection, no happiness, he insists, matters as much to man as his own free will—and for that reason he will knock down any structure and deny any equation, even if in doing so he only harms himself. The Underground Man seems to rebel against formulas and final answers, yet he clings to his own formula, a formula of negation. In the second part, we learn how he landed there; we learn something about his life and actions before his retreat. (I won’t reveal what he tells—but it isn’t comforting.)

A reader of Notes from Underground can easily fall into one of two traps. One error is to judge him without any kind of compassion or identification—to say, “I’m not like that; that man is messed up” and be done with it. The other is to identify with him completely—to see him as a reflection of the hidden self. While this error is a bit more fruitful than the first, it’s still an error, if the reader does not recognize the Underground Man’s responsibility for his condition. To grasp the Underground Man, one must bring both compassion and judgment, both identification and distance. The proportions are difficult to determine (and will vary from person to person and from reading to reading), but both elements need to be there, if the work is to come through. (Other elements need to be there as well; one needs to be able to hear his tones, jokes, allusions, and much more.)

Isn’t that one of our ethical challenges in general—to determine the right mixture of judgment and compassion? Too much judgment without compassion, and you write the person (or work) off. Too much compassion (if that’s the word—I’m not quite satisfied) without judgment, and you neglect the person’s free will and choices. Yet there is no perfect ratio; it shifts from moment to moment and from situation to situation. Nor can it be calculated; one must find it through experience, teachers, and instinct.

From what I have seen, it is more common for students to write the Underground Man off than to see themselves in him. This is partly because introspection gets short shrift today. These kids have been brought up to think in terms of success and achievement, not in terms of understanding human nature. That’s an oversimplification, though; many do understand something of the Underground Man; many do see aspects of themselves, and a few have even found a combination of judgment and compassion. In any case, both extremes have dangers.

The first time I read Notes from Underground, at age eighteen, I couldn’t separate myself from him (until part 2). I thought I was him—and was horrified. Years later, I approached him from a distance and found him very funny. In between, I have had mixtures of responses. Today I see a great deal of the Underground Man in myself but understand, also, how important the differences are. I am not advocating “text-to-self connections”—but Dostoevsky clearly wants us to ask who this Underground Man is and how he might reflect us.

There’s a lot at stake in reading Notes from Underground properly, yet there is no “proper” reading. There is only alertness and avoidance of pitfalls. Or, rather, there’s much more, but it can’t be taught directly, just as one can’t be taught to understand another person.

These are the thoughts that occupy a good deal of my day, when I’m not scrambling to get things done. It matters to teach this work well; that, in turn, is not just a question of bringing out key themes, devices, etc., but involves careful reading, a good understanding of the students, an understanding (when possible) of the original Russian, and a strong ethical and aesthetic sense. It involves a great responsibility: you have to be a good guide to take students into the underground and out again. In short, it requires a good chunk of all that I have and am—including the ability to put myself aside as we focus on the work.

I wish policymakers (of various kinds) had an inkling of this aspect of teaching. It seems completely forgotten, except in nooks of the education world. It’s as though “content” didn’t demand one’s soul, intellect, and conscience, as though you could teach it “effectively” without vitality. No wonder so much work gets piled on teachers; few realize that to teach well, one must be willing to leave the busyness behind, to take a long walk, attend a concert*, or read a book slowly, in order to be shaken into life, the life inside and outside of books, the jumbled, mistake-ridden life that, even at its most perplexing, has room for courage and grace.

*Concert: On Friday I attended the Wingdale Community Singers’ record release show for their new album, Night Sleep Death. A gorgeous performance. The title(-ish) song brings together two Walt Whitman poems, A Clear Midnight” and “O Living Always–Always Dying.”

Neither Crystal Palace Nor Underground

Last week I had the joy of publishing an article featuring three students’ pieces. Each piece has distinct ideas, approach, and personality; none of the three would fit a rubric exactly. All deal with philosophical ideas and texts; whether witty, serious, or both, all grapple with something substantial.

Call it spark, verve, or individuality, I hope my students never lose this quality. Our schools and workplaces live by the rubric. Even when a school sees beyond the rubric, as mine does, it must prepare students for the rubrics of tests. Students know exactly what is expected of them and learn to fulfill it exactly. They know they will get five points for doing this, ten points for doing that.

What rubrics offer is predictability and fairness. A student who receives a B knows why, and knows what to do to get an A. (There should always be some degree of that; grading should not be haphazard.) Yet rubrics take a great deal away. They come across as supreme judges, when they are mediocre ones; they miss what really matters in a piece—the genuine grappling, among other things. I do not mean they should be abolished; of course they have a place, but they should not be ultimate arbiters.

I have scored tests and have seen how students who follow the directions exactly (but say very little) can score higher than students  who have a great deal to say but fail to follow all of the directions. Indeed, when one follows such rubrics, one is forced to disregard what a student says.

In many ways the world of rubrics is analogous to the very crystal palace that Dostoevsky’s Underground Man criticizes. Here is the telling passage (Fyodor Dostoevsky, Notes from Underground, translated by Michael Katz):

You believe in the crystal palace, eternally indestructible, that is, one at which you can never stick out your tongue furtively nor make a rude gesture, even with your fist hidden away. Well, perhaps I’m so afraid of this building precisely because it’s made of crystal and it’s eternally indestructible, and because it won’t be possible to stick one’s tongue out even furtively.

Don’t you see: if it were a chicken coop instead of a palace, and if it should rain, then perhaps I could crawl into it so as not to get drenched; but I would still not mistake a chicken coop for a palace out of gratitude, just because it sheltered me from the rain. You’re laughing, you’re even saying that in this case there’s no difference between a chicken coop and a mansion. Yes, I reply, if the only reason for living is to keep from getting drenched.

Today’s students live in a chicken coop of rubric after rubric. They learn to be well-rounded superstars—leaders, go-getters, initiators, networkers, and, sure, students with GPAs of 4.0. They build up digital portfolios and resumes. They know what the colleges want and plan years in advance to achieve it. A wise person remarked to me this week, “They not only have no room for eccentricity; they have no room to pause.”

You need to pause in order to write an interesting piece, to have a good friend, to understand a piece of music. You need it to find a way of living that is neither crystal palace nor underground, a chant or song with lilts and cracks and silences. Yes, you need to learn to survive and compete, but you need not bow to the terms of such demands.

My birthday is a week from Thursday. I dedicate it to such a way of living, and to the hope that my students will find it on their own terms or, having already found it, not lose sight of it.

The Deep Problem with the School of One

This morning, Rachel Monahan reported in the New York Daily News that two of the three New York City schools that piloted the “School of One” decided to drop the program. After a great deal of expenditure and hype, the School of One didn’t show better results on the state math tests than regular math classes.

I am not surprised by this report. The School of One (which I discuss in the eighth chapter of my book) assumes that mathematics consists of a progression of skills. Its proprietary software program generates a daily “playlist” for each student and lesson plans for the teachers. Students enter the classroom, view their playlist, and go to their appointed station. On a given day, a student might play a video game, work in a small group, receive direct instruction from a teacher, or engage in some combination of these activities. Teachers might spend fifteen minutes with one group, a few minutes here and there with individuals, and another fifteen minutes with another group. The students take frequent multiple-choice quizzes, which help to determine their activities and grouping. Supposedly, by working at their own pace in their own preferred style, students will make great progress.

But mathematics is not an amusement park. It is about recognizing patterns and seeing problems in more than one way. It requires imagination as well as precision. In the best math classes, students learn to struggle with problems that at first seem daunting (but for which they are adequately prepared). They try this and that, seeming to get nowhere, and then suddenly they see it. In a flash, it is all clear—and the solution sheds light on problems from earlier lessons and problems still to come.

Students cannot rely on such flashes of insight, of course. After solving a difficult problem, they must practice solving similar problems until they come easily. Then they continue on to the next challenge, which often arises out of the problems they have solved. A good math curriculum has a clear, logical progression but also moves back and forth and outward. Over time, as students advance and gain knowledge and experience, they develop what Alfred North Whitehead called “that eye for the whole chess-board, for the bearing of one set of ideas on another.”

Personalized, computerized instruction doesn’t do justice to such a curriculum; even precocious students need guidance through the challenges. It is the teacher who knows how to pose a problem in different ways and to draw more than the obvious conclusions from it. It is the teacher who can glean where a student is going wrong and guide him back on track. Such teaching takes time. A class can easily spend an entire lesson on a single theorem or concept, and the students learn from each other’s efforts.

What happens when the lesson is fragmented, when students go off into their various groups and corners to play a game or work on an activity? Well, in many cases both the students and the mathematics itself are shortchanged. The students may make progress with problems of a basic sort (like those that appear in summer math workbooks) but will need the teacher for the trickier and subtler points. Also, flitting from activity to activity isn’t always helpful; mathematics requires focus and doggedness. (Yes, sometimes the solution comes to you after you walk away—but those hours of puzzling and pondering help to bring this about.)

So why has the the School of One enjoyed such hype? Not only are there powerful political and commercial entities behind it, but it appears to address a real problem. Today’s classrooms have a wide range of levels; the advanced and struggling students study together. Since tracking is not an option (especially at the elementary and middle school levels), the teacher is expected to accommodate all levels at once. Given that state of things, a personalized learning system (aided by software) sounds like a crystal palace of sorts. To some, it is the future.

But to paraphrase Fyodor Dostoevsky’s Underground Man, if it is raining and I crawl into a hen-house in order to stay dry, I will not call it a palace out of gratitude. It is still a hen-house. Something analogous holds true for the School of One. It is a makeshift solution, and an expensive one at that.

What can we do instead of expanding the School of One? We could adopt strong math curricula that give students a foundation in the early grades. We could allow for certain kinds of flexible tracking—so that, for instance, a fifth-grade student could take math  with sixth graders if she were prepared (but would take other classes with her fifth-grade classmates). We could have public lectures, seminars, and workshops on mathematics, so that parents, teachers, and others could grapple with math problems together. We could identify first-rate math textbooks, possibly translating a few from other languages, so that teachers did not have to scramble for appropriate resources. All of this would be far less expensive—and far truer to the purpose of teaching math—than the School of One.

  • “To know that you can do better next time, unrecognizably better, and that there is no next time, and that it is a blessing there is not, there is a thought to be going on with.”

    —Samuel Beckett, Malone Dies

  • Always Different

  • ABOUT THE AUTHOR

     

    Diana Senechal is the author of Republic of Noise: The Loss of Solitude in Schools and Culture and the 2011 winner of the Hiett Prize in the Humanities, awarded by the Dallas Institute of Humanities and Culture. Her second book, Mind over Memes: Passive Listening, Toxic Talk, and Other Modern Language Follies, was published by Rowman & Littlefield in October 2018. In February 2022, Deep Vellum will publish her translation of Gyula Jenei's 2018 poetry collection Mindig Más.

    Since November 2017, she has been teaching English, American civilization, and British civilization at the Varga Katalin Gimnázium in Szolnok, Hungary. From 2011 to 2016, she helped shape and teach the philosophy program at Columbia Secondary School for Math, Science & Engineering in New York City. In 2014, she and her students founded the philosophy journal CONTRARIWISE, which now has international participation and readership. In 2020, at the Varga Katalin Gimnázium, she and her students released the first issue of the online literary journal Folyosó.

  • INTERVIEWS AND TALKS

    On April 26, 2016, Diana Senechal delivered her talk "Take Away the Takeaway (Including This One)" at TEDx Upper West Side.
     

    Here is a video from the Dallas Institute's 2015 Education Forum.  Also see the video "Hiett Prize Winners Discuss the Future of the Humanities." 

    On April 19–21, 2014, Diana Senechal took part in a discussion of solitude on BBC World Service's programme The Forum.  

    On February 22, 2013, Diana Senechal was interviewed by Leah Wescott, editor-in-chief of The Cronk of Higher Education. Here is the podcast.

  • ABOUT THIS BLOG

    All blog contents are copyright © Diana Senechal. Anything on this blog may be quoted with proper attribution. Comments are welcome.

    On this blog, Take Away the Takeaway, I discuss literature, music, education, and other things. Some of the pieces are satirical and assigned (for clarity) to the satire category.

    When I revise a piece substantially after posting it, I note this at the end. Minor corrections (e.g., of punctuation and spelling) may go unannounced.

    Speaking of imperfection, my other blog, Megfogalmazások, abounds with imperfect Hungarian.

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