Those who know, teach!

What would it take to invest students deeply in helping each other really understand the material? After reading Dan Pink’s post on “flipping homework” (described here), one algebra teacher posted a fascinating comment describing his out-of-the-box approach.

Every class day, this teacher gives a one-problem quiz. Afterward, the teacher readies those students who correctly solved the problem to help those who didn’t solve it, on the board.

Next, each student who still didn’t solve it gets help from those who solved it (either on the quiz or on the board) until all students understand the problem.

Exams are taken by only one student of the teacher’s choice. All students get the grade attained by that student.

The result? “Learning and exam preparation become a group effort, and all win or lose together,” wrote this teacher, identified in the comments only as Durfa.

I want to know more about this strategy of coaching collaboration and academic material at the same time! Do you know someone who has tried it, in any subject? How did it work out? Send in your example, and I’ll send you a complimentary copy of Fires in the Mind. Those who know, teach!

Practice: We’re in it together

Most of what we know, remember, and use, we didn’t learn by teachers and textbooks filling our empty heads, Marion Brady reminds us in an excellent recent blog post confronting current education “reforms.” Instead, we came to learning with our own ideas, opinions, explanations, beliefs and values. And then “we discovered real-world patterns and relationships — new knowledge that caused us to constantly rethink, reorganize, reconstruct, and replace earlier knowledge.”

That’s a very serious intellectual practice, worthy of 10,000 hours. (Translate: eight years of school!) And it takes a coach — someone to watch closely, suggesting just the next stretch a learner needs, at just the right moment. It’s a delicate business, not simple transfer of information– and it has everything to do with the learner’s motivation. As Brady puts it,

As is true of adults, kids’ ideas and beliefs become part of who they are, so attempts to change them may come across as attacks on their identity and be resisted.

That’s why teaching is such a complex, multi-step process, he says in this wonderful summary of what the good teacher practices every day. (Reminder: 10,000 hours is at least five or six years of teaching!)

The teacher has to (a) “get inside” that head to figure out what’s thought to be true, right, or important, (b) understand the kid’s value system well enough to offer ideas sufficiently appealing to warrant taking them seriously and paying attention, (c) choose language or tasks that question old ideas and clarify new ones, (d) get feedback as necessary to decide how to proceed, (e) load the whole process up with enough emotion to carry it past short-term memory, and (f) do this for a roomful of kids, no two of whom are identical.

The faces of students in our Practice Project lit up when they told me of the learning experiences that really stuck with them. Above all, it was hands-on projects, internships, and apprenticeships that led them to ask better questions, explore their subjects more deeply, and rise to the challenge of producing new knowledge.

Along the way, their level of engagement with adults also shifted in crucial ways. Learner and teacher were in it together. And it showed.

Practice: We're in it together

Most of what we know, remember, and use, we didn’t learn by teachers and textbooks filling our empty heads, Marion Brady reminds us in an excellent recent blog post confronting current education “reforms.” Instead, we came to learning with our own ideas, opinions, explanations, beliefs and values. And then “we discovered real-world patterns and relationships — new knowledge that caused us to constantly rethink, reorganize, reconstruct, and replace earlier knowledge.”

That’s a very serious intellectual practice, worthy of 10,000 hours. (Translate: eight years of school!) And it takes a coach — someone to watch closely, suggesting just the next stretch a learner needs, at just the right moment. It’s a delicate business, not simple transfer of information– and it has everything to do with the learner’s motivation. As Brady puts it,

As is true of adults, kids’ ideas and beliefs become part of who they are, so attempts to change them may come across as attacks on their identity and be resisted.

That’s why teaching is such a complex, multi-step process, he says in this wonderful summary of what the good teacher practices every day. (Reminder: 10,000 hours is at least five or six years of teaching!)

The teacher has to (a) “get inside” that head to figure out what’s thought to be true, right, or important, (b) understand the kid’s value system well enough to offer ideas sufficiently appealing to warrant taking them seriously and paying attention, (c) choose language or tasks that question old ideas and clarify new ones, (d) get feedback as necessary to decide how to proceed, (e) load the whole process up with enough emotion to carry it past short-term memory, and (f) do this for a roomful of kids, no two of whom are identical.

The faces of students in our Practice Project lit up when they told me of the learning experiences that really stuck with them. Above all, it was hands-on projects, internships, and apprenticeships that led them to ask better questions, explore their subjects more deeply, and rise to the challenge of producing new knowledge.

Along the way, their level of engagement with adults also shifted in crucial ways. Learner and teacher were in it together. And it showed.

Two smart guys telling it how it is

Mike Rose in his new blog-post talking about where people like us stand in “the technocratic and structural approach to education” that “has become the coin of the realm”:

Without a deep and specific understanding of the way children learn and the skill and art of teaching and how that skill and art develop, all the structural/technical reform in the world won’t be effective. It’s like trying to cure cancer without knowledge of cell biology.

And Hayes Mizell in Ed Week pushing for professional development that helps teachers gain that understanding:

Meaningful change means professional development driven by teachers’ understanding of their students’ learning challenges. Once this understanding is gained, teachers must commit to learning whatever is necessary to address these challenges and to continually refine their skills to increase their students’ performance.

Where and how are you moving toward these outcomes in your teaching practice? Please share your experience with us. I’ll send a complimentary copy of Fires in the Mind to the best responses that come in.

Practice, performance, pride

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What a work of art these young performers have created on a street corner in Oakland! I can’t help but think of the hours they must have spent collaborating, breaking moves down, looking for patterns, using familiar moves in new ways, critiquing, revising, persisting, taking up new challenges . . . and a very public performance to take pride in at the end.

In short, they’ve been practicing an “expert process” that will serve them in many other contexts. Whatever it took to get it going, we should be studying it!

The ticket-roll as math practice

Once again today Dan Meyer’s terrific blog lends common sense and clarity to what it means to practice math at the high school level. “Mathematical notation isn’t a prerequisite for mathematical exploration,” he writes. “Mathematical notation can even deter mathematical exploration.” To illustrate, he uses a problem that starts by asking questions about a big roll of tickets:

When the textbook asks a student to “find the area of the annulus” in part (a) of the problem, there are at least two possible points of failure. One, the student doesn’t know what an “annulus” is. (Hand goes in the air.) Two, the student knows the term “annulus” but can’t connect it to its area formula. (Hand goes in the air.)

That’s the outcome of teaching the formula, notation, and vocabulary first: the sense that math is something to be remembered or forgotten but not created.

Meanwhile, let’s not kid ourselves. The area of an annulus isn’t difficult to derive. Let the student subtract the small circle from the big circle. Then mention, “by the way, this shape which you now feel like you own, mathematists call it an ‘annulus.’ Tuck that away.”

Similarly, if I give you this pattern, I know you can draw the next three pictures in the sequence. That’ll get old so I’ll ask you to describe the pattern in words. You’ll write out, “you add two tiles to the last picture every time to get the next picture.” I’ll show you how much easier it is to write out the recursive formula An+1 = An + 2. ¶ I’ll ask you to tell me how many tiles I’ll find on the 100th picture. You’ll get tired of adding two every time, and we’ll develop the explicit formula A = 2n + 3, which makes that task so much easier.

Terms like “explicit” and “recursive” and “annulus” can do one of two things to the exact same student: make the kid feel like a moron or make the kid feel like the master of the universe.

Planting the ‘habits of experts’

A teacher from Vermont wrote in about discovering our “Habits of Experts” list last June, and using them to prompt reflective writing exercises that wrapped up his students’ year. That worked so well that now he wants to start the year with such work. Here are John’s thoughts–what would you add to them?

Ever since I encountered a discussion of the importance of metacognition in Arthur Costa’s Teaching for Intelligent Behavior, I have tried to encourage students to think about how they learn and how they can get better at it. Each year I tried different approaches that both encouraged metacognition and introduced the students to new ideas: Plato’s idea of the Form of the student, Pirsig’s idea of quality, Crawford’s idea of practical progress in excellence. These met with mixed results; I would say usually the students were tolerant but not enthusiastic!

This last school year I decided to try something new. I was struck by the list of “habits of experts” presented in Fires in the Mind. Near the end of the year I explained to the students what the book was about and asked them to think about how they had become more expert as learners in this course (a senior-level honors course). I presented them with the following prompt:

Think about your work in this class over this last year. Look at this list of habits of experts. Pick one of the habits and one incident or action by you in this class this year that shows that you have begun to develop the habits of an expert learner. Describe that incident or action. Make the description as detailed as possible so that the reader will fully understand why you chose this episode to illustrate your growing expertise.

The results were exactly what I hoped for: insightful, honest, real, and demonstrative of a mature self-awareness. Sara, for instance, wrote about how she had volunteered to be the mediator when the students had role-played a negotiation between the humans and animals in Animal Farm as part of a unit on negotiations. She had consciously sought out new challenges. Ian discussed how had decided to welcome critiques of his papers, even though up until then he had resisted the process. Nick had considered other perspectives in our studies of various theories of human nature and had found himself much more open to alternative views of political, economic, and other realities.

I think this would be much more effective if I were to give the list of habits of experts to the students at the start of the year, explain to them the sort of topics and activities I envisioned in the course throughout the year, and then ask them to write about their goals for personal growth as learners. With periodic check-ins, this should result in even more development of metacognitive abilities and conscious practice of intellectual skills.

Planting the 'habits of experts'

A teacher from Vermont wrote in about discovering our “Habits of Experts” list last June, and using them to prompt reflective writing exercises that wrapped up his students’ year. That worked so well that now he wants to start the year with such work. Here are John’s thoughts–what would you add to them?

Ever since I encountered a discussion of the importance of metacognition in Arthur Costa’s Teaching for Intelligent Behavior, I have tried to encourage students to think about how they learn and how they can get better at it. Each year I tried different approaches that both encouraged metacognition and introduced the students to new ideas: Plato’s idea of the Form of the student, Pirsig’s idea of quality, Crawford’s idea of practical progress in excellence. These met with mixed results; I would say usually the students were tolerant but not enthusiastic!

This last school year I decided to try something new. I was struck by the list of “habits of experts” presented in Fires in the Mind. Near the end of the year I explained to the students what the book was about and asked them to think about how they had become more expert as learners in this course (a senior-level honors course). I presented them with the following prompt:

Think about your work in this class over this last year. Look at this list of habits of experts. Pick one of the habits and one incident or action by you in this class this year that shows that you have begun to develop the habits of an expert learner. Describe that incident or action. Make the description as detailed as possible so that the reader will fully understand why you chose this episode to illustrate your growing expertise.

The results were exactly what I hoped for: insightful, honest, real, and demonstrative of a mature self-awareness. Sara, for instance, wrote about how she had volunteered to be the mediator when the students had role-played a negotiation between the humans and animals in Animal Farm as part of a unit on negotiations. She had consciously sought out new challenges. Ian discussed how had decided to welcome critiques of his papers, even though up until then he had resisted the process. Nick had considered other perspectives in our studies of various theories of human nature and had found himself much more open to alternative views of political, economic, and other realities.

I think this would be much more effective if I were to give the list of habits of experts to the students at the start of the year, explain to them the sort of topics and activities I envisioned in the course throughout the year, and then ask them to write about their goals for personal growth as learners. With periodic check-ins, this should result in even more development of metacognitive abilities and conscious practice of intellectual skills.

Singing Pythagorus


Anyone who remembers the periodic table via Tom Lehrer’s wonderful song “The Elements” (below) will also appreciate this musical mnemonic ditty about the Pythagorean theorem, composed by a high school boy from Pendleton County (KY) High School. Does anyone else have a great one to contribute? (If you send yours in, we’ll send you a complimentary copy of Fires in the Mind.) And tell us: Does this kind of practice work for your students?

Fun as serious business

The elementary school teacher who calls for more fun in the classroom in a post on today’s Gotham Schools community blog is talking about serious business–math, reading, science, and history. When children are totally absorbed in their time outside schools–straining to reach the next rung on the jungle gym, or caught up in imaginative play–they may not have happy smiles on their faces, C. W. Arp notices, but they certainly report that they’ve been having fun. More fun than in the classroom, he says:

So here is my radical new way of thinking: The children in my elementary school need to be taught how to have fun. They have not had enough experience with fun. They are too often discouraged from having fun, or even chastised for having fun. I once said to a particularly active student, in my first year, “Do you just come to school to have fun? School is not a playground!” Frequent admonishments at my school: “You play too much,” or “All he/she does is play around.” But the students’ lack of focus is precisely because they are not having fun. Fun is engagement. Fun is interested activity. Fun is very serious business.

I’ll be watching for the suggestions Arp promises to make in future posts about how to help younger students find that sense of absorbed satisfaction as they master classroom learning. Send in yours, too!

Doing the math

Riley Lark is a high school math teacher, five years into the profession. He loves his job: teaching kids to “translate reality into math and back,” with “little tools like factoring, graphing, and logarithms.”

But his kids have even more important things to practice in the long hours they spend in school, Riley believes. It’s also his job to teach them responsibility, respect, curiosity, investigative skills, teamwork skills, and the attitude that their mistakes and lack of knowledge are actually key elements of learning.

Luckily, he says, “it turns out that math is a great medium through which to teach these things.”

So on Riley’s blog, he and a handful of math teachers are sharing their lesson plans, techniques, philosophies, exams, and project ideas with a self-reflective thoughtfulness and humor that makes you feel like you’ve made great new friends. His July “Virtual Conference on Soft Skills” is currently bringing their voices together in a grassroots PD that has the ambiance of a terrific conversation in the shade of a summer lawn.

For example, Dan Goldner tells what he’s learned from the times when, without warning, a class shuts down completely in a “soft mutiny” — silent, disengaged, blank, unwilling to say what’s going on.

“The non-communicative aspect of the soft mutiny makes it hard to know just what’s going on,” Goldner writes, as he describes how he works his way out of the quicksand, trying not to take it personally:

• Ask the students “What would be most helpful for you now?” This gives students input and control without forcing them to voice their own sense of being lost, or, if they’re mad at me or feel I’m doing poorly, without forcing them to say things they think might upset me or hurt me. This question got useful answers that moved the class forward about 50% of the times I asked it.

• If that question gets no response, then make a transition to another mode, activity, or task. Acknowledge that “This isn’t working. Let’s shift to a different approach altogether.” This gives everyone a way to leave behind the “stuck” feeling.

I love seeing these teachers work through the problems of effective teaching together. Completely committed to fostering quantitative reasoning, they dedicate themselves equally to building confidence and leadership in their students. On both sides of that equation, they give kids plenty of respect — and practice.

If you have great examples of that kind of teaching (whatever your subject area), send them in! I’ll send a complimentary copy of Fires in the Mind to the best replies we receive.

On cluelessness

“Tell me what you’re already really good at!” That’s the first thing I asked of the students in our Practice Project. It wasn’t just to make them feel good about themselves. Instead, it got us started talking about the process that goes into “getting good”—whether at baseball or cell biology.

Still, a lot of people ask me if my teenage collaborators weren’t exaggerating their own competence when they described how good they were. Given their youth, how could they really know where they stack up? They don’t even know what they don’t know!

Maybe so—but hey, aren’t we all that way?

I’ve been thinking about all this, while reading Errol Morris’s fascinating series of essays in the New York Times, on whether our incompetence actually makes it impossible for us to recognize our incompetence. (Speaking of which, the unpronounceable term for this “anasognosia” kept me away from the piece for days!)

Morris takes off from a scholarly paper by Justin Kruger and David Dunning, “Unskilled and Unaware of It: How Difficulties of Recognizing One’s Own Incompetence Lead to Inflated Self-assessments,” from a 1999 issue of the Journal of Personality and Social Psychology. He goes back and forth with Dunning, trying to make sense of it from several perspectives, including neurology, psychology, philosophy.

It’s a wonderful conversation from beginning to end (including footnotes and readers’ comments). But I kept wanting bring it down to the level of teacher and student, mentor and apprentice, school and community.

For example, Dunning could have been talking about my students—or about me!—when he told Morris:

People can be clueless in a million different ways, even though they are largely trying to get things right in an honest way. Deficits in knowledge, or in information the world is giving them, just leads people toward false beliefs and holes in their expertise.

College students with bad grammar, Dunning found, actually think their grammar is correct. In the same way,

The average detective does not realize the clues he or she neglects. The mediocre doctor is not aware of the diagnostic possibilities or treatments never considered. The run-of-the-mill lawyer fails to recognize the winning legal argument that is out there. People fail to reach their potential … simply because they are not aware of the possible. This is one of the reasons I often urge my student advisees to find out who the smart professors are, and to get themselves in front of those professors so they can see what smart looks like.

It’s an invitation to look at ourselves as well as at our students. For example, Morris muses:

Of course, I’d like to imagine myself near the top, planted firmly in the upper quartile. But upper quartile of what? I could devise a test that makes me look smart. But what would I have to exclude?

School is over for the summer, and now we have time to dream a little. Why not take a dip into the currents of these questions, and come up with your own?

How will we know what next year’s students really know and can do already? How can we point them to explore the territory they don’t even know exists? And who’s going to do that for us?

I’ll send a complimentary copy of Fires in the Mind to the most helpful comments that come in on this!

The refrigerator door

Gary Stager has a beautiful article in the current issue of Creative Educator, celebrating the “genius of print” and the “beauty and value of paper.” Especially as the year ends and kids take work home in bulging bagfuls, it gives me hope. The high-tech-heads in education are not forgetting the heirloom quality of student work–the kind children and families can hold in their hands, page through with grandparents or younger siblings, display on the refrigerator door.

Stager writes:

As teachers, we often promote the idea that process is more important than the end product, yet it is often the product itself that provides context and motivates students to learn.

And he emphasizes the quality of the work:

While every project may not generate an objet d’art, we should assume that every project we undertake has the potential to do so.

In a related earlier article, he advocates raising the bar for student projects, to include the highest standard of all: Does the project have a chance of enduring? Like Ron Berger in his classic An Ethic of Excellence, Stager wants a set of goals in which teachers and students embrace “the aesthetic of an artist or critic.”

It’s easy, Stager warns, to get distracted by the technology, forgetting about whether the work lives up to its larger purpose. His goal for a successful project: We just can’t bear to take it off the refrigerator door.

The rhythm of joint action

Sports teams that warm up together before a game usually do it to heighten camaraderie and spirit. But synchronous exercise of that kind also seems to increase not just their motivation but their ability to pursue joint goals successfully, says a new study in the Journal of Experimental Social Psychology.

This might mean, for example, that kids who practice Double-Dutch jump-rope, or ballroom dance, or playing in a band—anything that involves moving together in time—are actually getting sharper at accomplishing anything they try that involves cooperation, perception and reaction to a partner’s actions.

A little “action research” by teachers and students is worth a try! Science class after gym class, anyone?

Bait the hook for math thinking

In his wonderful TEDx talk, Dan Meyer, a high school math teacher in Santa Cruz, CA, explains how he gets students who are “mathematically and conversationally intimidated” to formulate math problems themselves — based on their genuine curiosity about the world.

Meyer presents kids with everyday phenomena (like a hose slowly filling a big container in the school courtyard) and asks them simple questions (“How long will it take to fill up?”). Instead of memorizing formulas (or copying them from already-solved examples), his students practice “patient problem-solving.” Slowly, steadily, in small groups, they check out their intuitions and formulate their own reasoning.

Meyer recommends five rules of thumb for math teachers, including “Ask the shortest question you can” and “Let students build the problem.” He asserts: “The math serves the conversation, the conversation doesn’t serve the math!”

It’s another way of saying that Motivation + Deliberate Practice = Mastery.

Constructing wings to fly with


“I can figure that out!” That’s the message that comes across in the how-to videos in the current online issue of Edutopia — showing how a challenging hands-on project can create a culture of steadily increasing motivation and mastery. My favorite shows ninth graders from Seattle whose science teacher drew them into a long term project to engineer from papier-mache a light-weight wing construction that works. I had to agree: “It’s hard–but once you’re on the inside, it’s fun!”

Spring practice

This is the time of year that kids hate homework most! The weather is warmer, and the clock is running down to the end of the school year. Teachers get mad at kids who blow off their homework . . . and kids get mad at teachers who assign it.

So why, in certain schools around the country, are kids working harder than ever on after-school academics right now?

We see them staying after to work in the computer labs. We see them collaring teachers in the halls for advice. We see them asking other students to read what they’ve written and give their opinions on making it better.

Where does all that motivation come from? Here’s the secret: One day in May or early June, these kids have to get up and present what they’ve learned in front of others whose opinions they value.

That one factor makes kids their “spring practice” in academics as seriously as any baseball player going into spring training. As Bridget, one of our student contributors to the book Fires in the Mind, noted:

With a presentation, it’s not just the teacher who’s gonna be disappointed in you, it’s gonna be a whole audience. You have your peers judging you, and outside people, so you want to present the best of yourself. And that pressure creates a better product.

Performance assessment like these require students to practice all kinds of things that don’t usually show up on tests. For example, Brooklyn Prep, a small New York City public school, assesses end-of-year roundtable presentations largely on the “habits of mind” students can demonstrate.

Roneesha, an eleventh grader, explained to her panel how those habits influenced her final paper in history. She said:

I think it was mainly the habits of mind of analysis and perspective that helped me most. I already had the background information . . . the only thing was how to get it down on paper and choose my position properly. Mainly, perspective helped me see what was the question, and what was it that I knew about the question, and how could I put that, so I could write an essay that fully answered that question.

“It’s amazing to us to see the tone shift when portfolio presentations are happening,” one New York teacher told me:

All of a sudden students take it more seriously. We all felt like students were like really learning, just from going through the process of the presentation. Even just having a voice on other students’ panels — really assessing another student based on a rubric — had an effect on kids. I am so excited to do it again this month.

Quite a few schools do this kind of performance assessment, often called exhibitions, though we don’t hear enough about it in this policy climate of high-stakes standardized testing. But May is a good time to go see for yourself what kids know and can do! The Coalition of Essential Schools has declared National Exhibition Month, and schools around the country are inviting the community in as guests and panel members.

What are YOU asking your students to practice this spring? How are you asking them to practice it? Who are you inviting in to see how they’re doing?

Share your experiences with practice! We’ll mail you a free copy of Fires in the Mind if your comment causes others to reply!