Classroom Math Quotes

An eternal question about children is, how should we educate them? Politicians and educators consider more school days in a year, more science and math, the use of computers and other technology in the classroom, more exams and tests, more certification for teachers, and less money for art. All of these responses come from the place where we want to make the child into the best adult possible, not in the ancient Greek sense of virtuous and wise, but in the sense of one who is an efficient part of the machinery of society. But on all these counts, soul is neglected.

Everyday we have to go to classroom 107A, where portions of English, math and social studies are meted out like different nutrients of a hospital diet.

Education makes your maths better, not necessarily your manners.

Ode to Algebra Thrust into this dingy classroom we die like lampless moths locked into the desolation of fluorescent lights and metal desks. Ten minutes until the bell rings. What use is the quadratic formula in our daily lives? Can we use it to unlock the secrets in the hearts of those we love? Five minutes until the bell rings. Cruel Algebra teacher, won't you let us go?

I have an English degree, which has as much value as The Papiermark in The Weimar Republic in 1923. It's worthless, and why I'm now a duck farmer. Plus, what could I do with English but be a classroom colonialist? If I wanted to teach something racist, I'd be a math professor.

unsolicited advice to adolescent girls with crooked teeth and pink hair When your mother hits you, do not strike back. When the boys call asking your cup size, say A, hang up. When he says you gave him blue balls, say you’re welcome. When a girl with thick black curls who smells like bubble gum stops you in a stairwell to ask if you’re a boy, explain that you keep your hair short so she won’t have anything to grab when you head-butt her. Then head-butt her. When a guidance counselor teases you for handed-down jeans, do not turn red. When you have sex for the second time and there is no condom, do not convince yourself that screwing between layers of underwear will soak up the semen. When your geometry teacher posts a banner reading: “Learn math or go home and learn how to be a Momma,” do not take your first feminist stand by leaving the classroom. When the boy you have a crush on is sent to detention, go home. When your mother hits you, do not strike back. When the boy with the blue mohawk swallows your heart and opens his wrists, hide the knives, bleach the bathtub, pour out the vodka. Every time. When the skinhead girls jump you in a bathroom stall, swing, curse, kick, do not turn red. When a boy you think you love delivers the first black eye, use a screw driver, a beer bottle, your two good hands. When your father locks the door, break the window. When a college professor writes you poetry and whispers about your tight little ass, do not take it as a compliment, do not wait, call the Dean, call his wife. When a boy with good manners and a thirst for Budweiser proposes, say no. When your mother hits you, do not strike back. When the boys tell you how good you smell, do not doubt them, do not turn red. When your brother tells you he is gay, pretend you already know. When the girl on the subway curses you because your tee shirt reads: “I fucked your boyfriend,” assure her that it is not true. When your dog pees the rug, kiss her, apologize for being late. When he refuses to stay the night because you live in Jersey City, do not move. When he refuses to stay the night because you live in Harlem, do not move. When he refuses to stay the night because your air conditioner is broken, leave him. When he refuses to keep a toothbrush at your apartment, leave him. When you find the toothbrush you keep at his apartment hidden in the closet, leave him. Do not regret this. Do not turn red. When your mother hits you, do not strike back.

The New Groupthink is also practiced in our schools, via an increasingly popular method of instruction called “cooperative” or “small group” learning. In many elementary schools, the traditional rows of seats facing the teacher have been replaced with “pods” of four or more desks pushed together to facilitate countless group learning activities. Even subjects like math and creative writing, which would seem to depend on solo flights of thought, are often taught as group projects. In one fourth-grade classroom I visited, a big sign announced the “Rules for Group Work,” including, YOU CAN’T ASK A TEACHER FOR HELP UNLESS EVERYONE IN YOUR GROUP HAS THE SAME QUESTION.

the ability to attend to a task and stick to long-term goals is the greatest predictor of success, greater than academic achievement, extracurricular involvement, test scores, and IQ. She calls this grit, and first discovered its power in the classroom, while teaching seventh-grade math. She left teaching to pursue research on her hunch, and her findings have changed the way educators perceive student potential. Gritty students succeed, and failure strengthens grit like no other crucible.

The reality is that most of us grow up strapped in an educational system that favors obedience over independent thinking. We’re rewarded for trusting authority, and punished for challenging it. We focus on memorizing the stuff other people came up with—formulas in math, grammar rules in English, theories in physics, cell functions in biology—rather than grasping the logic behind our most important breakthroughs and tracing the footsteps of their discovery. We answer test questions with what we think our teacher wants to hear. We chase grades instead of knowledge. And worst of all, we leave the classroom woefully unequipped with the thinking skills that matter most: how to balance open-mindedness with skepticism, how to identify bias, and how to challenge assumptions—including our own—in a way that’s truly objective.

model’s blind spots reflect the judgments and priorities of its creators. While the choices in Google Maps and avionics software appear cut and dried, others are far more problematic. The value-added model in Washington, D.C., schools, to return to that example, evaluates teachers largely on the basis of students’ test scores, while ignoring how much the teachers engage the students, work on specific skills, deal with classroom management, or help students with personal and family problems. It’s overly simple, sacrificing accuracy and insight for efficiency.

But the “jobs of the future” do not need scientists who have memorized the periodic table. In fact, business leaders say they are looking for creative, independent problem solvers in every field, not just math and science. Yet in most schools, STEM subjects are taught as a series of memorized procedures and vocabulary words, when they are taught at all. In 2009, only 3% of high school graduates had any credits in an engineering course. (National Science Board, 2012) Technology is increasingly being relegated to using computers for Internet research and test taking.

desirable difficulties,” obstacles that make learning more challenging, slower, and more frustrating in the short term, but better in the long term. Excessive hint-giving, like in the eighth-grade math classroom, does the opposite; it bolsters immediate performance, but undermines progress in the long run.

I'll be taking a two-hour after-school class twice a week for seven and a half weeks. After those thirty hours of classroom time, which will bring me to the end of March, I'll need six hours behind the wheel. And then and only then will I be able to drive. I do the math in my mind as I speed home on my motorcycle from the firdt class.

Terrible as this is, there’s worse news. An article in the New York Times points out a statistic that should make our nation’s leaders tremble… suspension rates, kindergarten through high school, have nearly doubled from the early 1970s through 2006. Whatever is happening with our test scores, something else, something catastrophic, is going on in our schools. As countless teachers across America can testify, disruptive kids are hijacking our classrooms.

This kind of parenting was typical in much of Asia—and among Asian immigrant parents living in the United States. Contrary to the stereotype, it did not necessarily make children miserable. In fact, children raised in this way in the United States tended not only to do better in school but to actually enjoy reading and school more than their Caucasian peers enrolled in the same schools. While American parents gave their kids placemats with numbers on them and called it a day, Asian parents taught their children to add before they could read. They did it systematically and directly, say, from six-thirty to seven each night, with a workbook—not organically, the way many American parents preferred their children to learn math. The coach parent did not necessarily have to earn a lot of money or be highly educated. Nor did a coach parent have to be Asian, needless to say. The research showed that European-American parents who acted more like coaches tended to raise smarter kids, too. Parents who read to their children weekly or daily when they were young raised children who scored twenty-five points higher on PISA by the time they were fifteen years old. That was almost a full year of learning. More affluent parents were more likely to read to their children almost everywhere, but even among families within the same socioeconomic group, parents who read to their children tended to raise kids who scored fourteen points higher on PISA. By contrast, parents who regularly played with alphabet toys with their young children saw no such benefit. And at least one high-impact form of parental involvement did not actually involve kids or schools at all: If parents simply read for pleasure at home on their own, their children were more likely to enjoy reading, too. That pattern held fast across very different countries and different levels of family income. Kids could see what parents valued, and it mattered more than what parents said. Only four in ten parents in the PISA survey regularly read at home for enjoyment. What if they knew that this one change—which they might even vaguely enjoy—would help their children become better readers themselves? What if schools, instead of pleading with parents to donate time, muffins, or money, loaned books and magazines to parents and urged them to read on their own and talk about what they’d read in order to help their kids? The evidence suggested that every parent could do things that helped create strong readers and thinkers, once they knew what those things were. Parents could go too far with the drills and practice in academics, just as they could in sports, and many, many Korean parents did go too far. The opposite was also true. A coddled, moon bounce of a childhood could lead to young adults who had never experienced failure or developed self-control or endurance—experiences that mattered as much or more than academic skills. The evidence suggested that many American parents treated their children as if they were delicate flowers. In one Columbia University study, 85 percent of American parents surveyed said that they thought they needed to praise their children’s intelligence in order to assure them they were smart. However, the actual research on praise suggested the opposite was true. Praise that was vague, insincere, or excessive tended to discourage kids from working hard and trying new things. It had a toxic effect, the opposite of what parents intended. To work, praise had to be specific, authentic, and rare. Yet the same culture of self-esteem boosting extended to many U.S. classrooms.

Montessori believed that if children were exposed to a safe, experiential learning environment (as opposed to a structured classroom), with access to specific learning materials and supplies, and if they were supervised by a gentle and attentive teacher, they would become self-motivated to learn. She discovered that, in this environment, older children readily worked with younger children, helping them to learn from, and cooperate with, each other. Montessori advocated teaching practical skills, like cooking, carpentry, and domestic arts, as an integrated part of a classical education in literature, science, and math. To her surprise, teenagers seemed to benefit from this approach the most; it built confidence, and the students became less resistant to traditional educational goals. Through this method, each child could reach his or her potential, regardless of age and intellectual ability.

When they enter the classroom, however, they may well discover that the algorithms have got there first. Companies such as Mindojo are developing interactive algorithms that will not only teach me maths, physics and history, but will also simultaneously study me and get to know exactly who I am. Digital teachers will closely monitor every answer I give, and how long it took me to give it. Over time, they will discern my unique weaknesses as well as my strengths and will identify what gets me excited, and what makes my eyelids droop. They could teach me thermodynamics or geometry in a way that suits my personality type, even if that particular method doesn’t suit 99 per cent of the other pupils. And these digital teachers will never lose their patience, never shout at me, and never go on strike. It remains unclear, however, why on earth I would need to know thermodynamics or geometry in a world containing such intelligent computer programs.

When they enter the classroom, however, they may well discover that the algorithms have got there first. Companies such as Mindojo are developing interactive algorithms that will not only teach me maths, physics and history, but will also simultaneously study me and get to know exactly who I am. Digital teachers will closely monitor every answer I give, and how long it took me to give it. Over time, they will discern my unique weaknesses as well as my strengths and will identify what gets me excited, and what makes my eyelids droop. They could teach me thermodynamics or geometry in a way that suits my personality type, even if that particular method doesn’t suit 99 per cent of the other pupils. And these digital teachers will never lose their patience, never shout at me, and never go on strike. It remains unclear, however, why on earth I would need to know thermodynamics or geometry in a world containing such intelligent computer programs.7

You whom I could not save, Listen to me. Can we agree Kevlar backpacks shouldn’t be needed for children walking to school? Those same children also shouldn’t require a suit of armor when standing on their front lawns, or snipers to watch their backs as they eat at McDonalds. They shouldn’t have to stop to consider the speed of a bullet or how it might reshape their bodies. But one winter, back in Detroit, I had one student who opened a door and died. It was the front door to his house, but it could have been any door, and the bullet could have written any name. The shooter was thirteen years old and was aiming at someone else. But a bullet doesn’t care about “aim,” it doesn’t distinguish between the innocent and the innocent, and how was the bullet supposed to know this child would open the door at the exact wrong moment because his friend was outside and screaming for help. Did I say I had “one” student who opened a door and died? That’s wrong. There were many. The classroom of grief had far more seats than the classroom for math though every student in the classroom for math could count the names of the dead. A kid opens a door. The bullet couldn’t possibly know, nor could the gun, because “guns don’t kill people,” they don’t have minds to decide such things, they don’t choose or have a conscience, and when a man doesn’t have a conscience, we call him a psychopath. This is how we know what type of assault rifle a man can be, and how we discover the hell that thrums inside each of them. Today, there’s another shooting with dead kids everywhere. It was a school, a movie theater, a parking lot. The world is full of doors. And you, whom I cannot save, you may open a door and enter a meadow, or a eulogy. And if the latter, you will be mourned, then buried in rhetoric. There will be monuments of legislation, little flowers made from red tape. What should we do? we’ll ask again. The earth will close like a door above you. What should we do? And that click you hear? That’s just our voices, the deadbolt of discourse sliding into place.

Reader's Digest (Reader's Digest USA) - Clip This Article on Location 56 | Added on Friday, May 16, 2014 12:06:55 AM Words of Lasting Interest Looking Out for The Lonely One teacher’s strategy to stop violence at its root BY GLENNON DOYLE MELTON  FROM MOMASTERY.COM PHOTOGRAPH BY DAN WINTERS A few weeks ago, I went into my son Chase’s class for tutoring. I’d e-mailed Chase’s teacher one evening and said, “Chase keeps telling me that this stuff you’re sending home is math—but I’m not sure I believe him. Help, please.” She e-mailed right back and said, “No problem! I can tutor Chase after school anytime.” And I said, “No, not him. Me. He gets it. Help me.” And that’s how I ended up standing at a chalkboard in an empty fifth-grade classroom while Chase’s teacher sat behind me, using a soothing voice to try to help me understand the “new way we teach long division.” Luckily for me, I didn’t have to unlearn much because I’d never really understood the “old way we taught long division.” It took me a solid hour to complete one problem, but I could tell that Chase’s teacher liked me anyway. She used to work with NASA, so obviously we have a whole lot in common. Afterward, we sat for a few minutes and talked about teaching children and what a sacred trust and responsibility it is. We agreed that subjects like math and reading are not the most important things that are learned in a classroom. We talked about shaping little hearts to become contributors to a larger community—and we discussed our mutual dream that those communities might be made up of individuals who are kind and brave above all. And then she told me this. Every Friday afternoon, she asks her students to take out a piece of paper and write down the names of four children with whom they’d like to sit the following week. The children know that these requests may or may not be honored. She also asks the students to nominate one student who they believe has been an exceptional classroom citizen that week. All ballots are privately submitted to her. And every single Friday afternoon, after the students go home, she takes out those slips of paper, places them in front of her, and studies them. She looks for patterns. Who is not getting requested by anyone else? Who can’t think of anyone to request? Who never gets noticed enough to be nominated? Who had a million friends last week and none this week? You see, Chase’s teacher is not looking for a new seating chart or “exceptional citizens.” Chase’s teacher is looking for lonely children. She’s looking for children who are struggling to connect with other children. She’s identifying the little ones who are falling through the cracks of the class’s social life. She is discovering whose gifts are going unnoticed by their peers. And she’s pinning down—right away—who’s being bullied and who is doing the bullying. As a teacher, parent, and lover of all children, I think this is the most brilliant Love Ninja strategy I have ever encountered. It’s like taking an X-ray of a classroom to see beneath the surface of things and into the hearts of students. It is like mining for gold—the gold being those children who need a little help, who need adults to step in and teach them how to make friends, how to ask others to play, how to join a group, or how to share their gifts. And it’s a bully deterrent because every teacher knows that bullying usually happens outside her eyeshot and that often kids being bullied are too intimidated to share. But, as she said, the truth comes out on those safe, private, little sheets of paper. As Chase’s teacher explained this simple, ingenious idea, I stared at her with my mouth hanging open. “How long have you been using this system?” I said. Ever since Columbine, she said. Every single Friday afternoon since Columbine. Good Lord. This brilliant woman watched Columbine knowing that all violence begins with disconnection. All

In the online math class, there was almost no meaningful student/teacher or student/student interaction. To equate this type of online learning with a real-world classroom experience is a major stretch.

Adam: Adam was a young man whose anxiety turned into a monster. Where Shelly had a very mild case of social anxiety, Adam’s case could only be called severe. Over a period of several years, his underlying social fears developed into a full-blown school phobia. A quiet, unassuming person, Adam had never stood out in the classroom. Through elementary school and on into high school, he neither excelled nor failed his subjects. By no means a discipline problem, the “shy” Adam kept to himself and seldom talked in class, whether to answer a teacher’s question or chat with his buddies. In fact, he really had no friends, and the only peers he socialized with were his cousins, whom he saw at weekly family gatherings. Though he watched the other kids working together on projects or playing sports together, Adam never approached them to join in. Maybe they wouldn’t let him, he thought. Maybe he wasn’t good enough. Being rejected was not a chance he was willing to take. Adam never tried hard in school either. If he didn’t understand something, he kept quiet, fearful that raising his hand would bring ridicule. When he did poorly on an exam or paper, it only confirmed to him what he was sure was true: He didn’t measure up. He became so apprehensive about his tests that he began to feel physically ill at the thought of each approaching reminder of his inadequacy. Even though he had studied hard for a math test, for example, he could barely bring himself to get out of bed on the morning it was to take place. His parents, who thought of their child as a reserved but obedient boy who would eventually grow out of this awkward adolescent stage, did not pressure him. Adam was defensive and withdrawn, overwrought by the looming possibility that he would fail. For the two class periods preceding the math test, Adam’s mind was awash with geometry theorems, and his stomach churning. As waves of nausea washed over him, he began to salivate and swallowed hard. His eyes burned and he closed them, wishing he could block the test from his mind. When his head started to feel heavy and he became short of breath, he asked for a hall pass and headed for the bathroom. Alone, he let his anxiety overtake him as he stared into the mirror, letting the cool water flow from the faucet and onto his sweaty palms. He would feel better, he thought, if he could just throw up. But even when he forced his finger down his throat, there was no relief. His dry heaves made him feel even weaker. He slumped to the cold tile and began to cry. Adam never went back to math class that day; instead, he got a pass from the nurse and went straight home. Of course, the pressure Adam was feeling was not just related to the math test. The roots of his anxiety went much deeper. Still, the physical symptoms of anxiety became so debilitating that he eventually quit going to school altogether. Naturally, his parents were extremely concerned but also uncertain what to do. It took almost a year before Adam was sufficiently in control of his symptoms to return to school.

Why is such a wonderful school not the norm? Shouldn’t SVS already have been copied in a million different places? The answer isn’t so simple—or maybe it is. The idea of total freedom for children is very threatening to most people. The kinds of objections that are raised are these: “But there are some basics—how do you ensure that each child learns them?” We at Sudbury Valley are not so certain that there are any basics, but we are certain that our students are in an environment that is real, that is totally linked to the larger community, and that if there are things everyone should learn, the kids in the school surely know it as well as the adults, and it is up to them to ensure that they learn it. Often, people are angry when they learn that most students can learn all of basic math in just 20 hours of classroom work. They feel cheated because they spent years and years of doing repetitive mathematics either because they hated it and weren’t interested and were bad at it or because they learned it fast but were told they had to redrill, redrill and redrill some more or they would forget everything. Now I ask you, would you really forget it if it were truly basic? But

It’s not my fault.” For all those decades, she thought there was something wrong with her. She believed her father when he said she didn’t think right, and his words became part of her self-concept.

The other article was by Lois Weiner, a professor who prepared urban teachers at New Jersey City University. Weiner was a parent activist at P.S. 3 in District 2, which she described as a highly progressive alternative school with an unusual degree of parent involvement. She claims that district administrators were stifling teachers and parents at P.S.3 by mandating "constructivist" materials and specific instructional strategies ... She [Weiner] continued, "The degree of micromanagement is astounding." Those who challenged the district office's mandates, she said, risked getting an unsatisfactory rating or being fired. Weiner contended that "opposition from parents is building against the new math curriculum," which was supposed to be field-tested with control groups, but instead was mandated for every classroom." Teachers were expressly prohibited from using other math textbooks or materials, and some were clandestinely "photocopying pages of now-banned workbooks.

Weirdly, the more standard classroom math you’ve had, the harder it’s going to be to avoid answering in an impoverished way. Such as, e.g., validating a/(1-r) by observing, in the best Calc II tradition, that the relevant geometric series here is a particular subtype of convergent infinite series, and that the sum of such a series is defined as the limit of the sequence of its partial sums (that is, if the sequence s1, s2, s3, …, sn , … of a series’ partial sums tends to a limit S, then S is the sum of the series), and that sure enough, w/r/t the above series, Lim (sn) = 1 so a/(1-r) works just fine … in which case you will once again have answered Zeno’s Dichotomy in a way that is complex, formally sexy, technically correct, and deeply trivial. Along the lines of ‘Because it’s illegal’ as an answer to ‘Why is it wrong to kill?

I woke up every morning at six to study—because it was easier to focus in the mornings, before I was worn out from scrapping. Although I was still fearful of God’s wrath, I reasoned with myself that my passing the ACT was so unlikely, it would take an act of God. And if God acted, then surely my going to school was His will. The ACT was composed of four sections: math, English, science and reading. My math skills were improving but they were not strong. While I could answer most of the questions on the practice exam, I was slow, needing double or triple the allotted time. I lacked even a basic knowledge of grammar, though I was learning, beginning with nouns and moving on to prepositions and gerunds. Science was a mystery, perhaps because the only science book I’d ever read had had detachable pages for coloring. Of the four sections, reading was the only one about which I felt confident. BYU was a competitive school. I’d need a high score—a twenty-seven at least, which meant the top fifteen percent of my cohort. I was sixteen, had never taken an exam, and had only recently undertaken anything like a systematic education; still I registered for the test. It felt like throwing dice, like the roll was out of my hands. God would score the toss. I didn’t sleep the night before. My brain conjured so many scenes of disaster, it burned as if with a fever. At five I got out of bed, ate breakfast, and drove the forty miles to Utah State University. I was led into a white classroom with thirty other students, who took their seats and placed their pencils on their desks. A middle-aged woman handed out tests and strange pink sheets I’d never seen before. “Excuse me,” I said when she gave me mine. “What is this?” “It’s a bubble sheet. To mark your answers.” “How does it work?” I said. “It’s the same as any other bubble sheet.” She began to move away from me, visibly irritated, as if I were playing a prank. “I’ve never used one before.” She appraised me for a moment. “Fill in the bubble of the correct answer,” she said. “Blacken it completely. Understand?” The test began. I’d never sat at a desk for four hours in a room full of people. The noise was unbelievable, yet I seemed to be the only person who heard it, who couldn’t divert her attention from the rustle of turning pages and the scratch of pencils on paper. When it was over I suspected that I’d failed the math, and I was positive that I’d failed the science. My answers for the science portion couldn’t even be called guesses. They were random, just patterns of dots on that strange pink sheet. I drove home. I felt stupid, but more than stupid I felt ridiculous. Now that I’d seen the other students—watched them march into the classroom in neat rows, claim their seats and calmly fill in their answers, as if they were performing a practiced routine—it seemed absurd that I had thought I could score in the top fifteen percent. That was their world. I stepped into overalls and returned to mine.

I have dealt with killahs before." I study her face. She is not speaking figuratively. Her dark eyes hold mine. "I told you where I came from." I do some quick math. In the 90's, around the time my world was shattered by my father's death, Sierra Leone was brutalized by civil war. Mariama would have been a young adult, watching everything around her being blown to pieces. I learned it as a fact in a college classroom. Mariama lived it. How little thought I've given to the life of this woman I've come to depend on.

In summary, Culturally Relevant Teaching claims that the dominant culture uses schools to sustain and reproduce itself. The goal of the Culturally Relevant Teacher is to tailor her methods and practices to identify and deconstruct this dominant culture. She must determine how the dominant culture(s) marginalizes other cultures—other ways of reading, writing, doing math, practicing science, behaving, and “knowing the truth”—in her classroom. Likewise, the goal of the Culturally Relevant Teacher is to help students deconstruct their own culture(s) and determine how they specifically are oppressed by the dominant culture(s), or how their culture(s) oppress the marginalized culture(s). After modeling this deconstruction, the Culturally Relevant Teacher’s mission is to empower and inspire her students to change the dominant culture through social justice activism. Her job is to push her students to develop critical consciousness.

Some students think their role in math classrooms is to memorize all the steps and methods. Other students think their role is to connect ideas. These different strategies link, unsurprisingly, to achievement, and the students who memorize are the lowest achieving in the world.

Judith Richards (1993), a teacher in Cambridge, Massachusetts, recounts her experience in a third/fourth grade classroom of children of white and African-American professionals and working-class Haitian immigrants. When she structured a traditional math problem-solving activity, the children of professionals invariably took the lead. However, when she embedded the same type of math problem-solving activity in a traditional Haitian folk tale, the Haitian children took the lead. It seems reasonable that culturally responsive pedagogy would positively affect learning. In both instances, the cognitive task facing children from cultures that were different from mainstream culture was simplified when they did not have to deal with both an unfamiliar speech event and instructional content. Further, one can imagine that using a familiar communication style could possibly reduce cultural dissonance, create a sense of membership, and symbolically affirm children who are members of racial minority groups (Erickson 1987).

The teacher might be talking about history or math, but what the students in a traditional classroom are learning is how to be students in a classroom. And they are learning it very well. They are learning how to take notes. They are learning how to surreptitiously communicate with peers. They are learning how to ask questions to endear themselves to authority figures. It

It is certainly true that no child should be left behind. A greater truth is that no child should be permitted to hold other children behind. Our nation’s education experts are missing the point. Reading is not the problem. Math proficiency is not the problem. Test scores, which everyone obsesses over, are not the problem. The problem is that disruptive students are driving teachers batty. One third of all new teachers leave after three years; almost half bail out in five years. Every day, this should be the newspaper headline:

Furthermore, academic fads have been forced upon successive generations of elementary and secondary school students, including the “New Math,” the “Open Classroom,” “Values Clarification,” “Cooperative Learning,” “Outcome-Based Education,” “No Child Left Behind,” and more recently “Common Core” and “Race to the Top,” for which trillions of dollars have been and are being wasted on inferior educational outcomes. Even the once-heralded school lunch program is not safe from statist overreach, where billions of dollars are spent on federally mandated lunches that many students refuse to eat.23

One teacher in Montclair, California, Eric Marcos, started flipping his math classroom when his sixth graders decided it would be better if they did the flipping of the math concepts. They created hundreds of short tutorials themselves that are available online at MathTrain.tv.

Making is a way of bringing engineering to young learners. Such concrete experiences provide a meaningful context for understanding abstract science and math concepts. For older students, making combines disciplines in ways that enhance the learning process for diverse student populations and opens the doors to unforeseen career paths.

frustration has flared up over the Common Core initiative, involving the implementation of national reading and maths standards for primary and secondary school children. The Gates Foundation played a central role in bringing the standards to fruition. Spending over $233 million to back the standards, the foundation dispersed money liberally to both conservative and progressive interest groups. The two major teachers' unions, the National Education Association and the American Federation of Teachers, each received large donations, as did the US Chamber of Commerce. Gates himself suggested that a benefit of the standards is that they open avenues towards increasing digital learning. In 2014, Microsoft announced it was partnering with Pearson to load Pearson's Common Core classroom material onto Microsoft's Surface tablet. Previously, the iPad was the classroom frontrunner; the Pearson partnership helps to make Microsoft more competitive.

Teachers greatly influence how students perceive and approach struggle in the mathematics classroom. Even young students can learn to value struggle as an expected and natural part of learning, as demonstrated by the class motto of one first-grade math class: If you are not struggling, you are not learning. Teachers must accept that struggle is important to students' learning of mathematics, convey this message to students, and provide time for them to try to work through their uncertainties. Unfortunately, this may not be enough, since some students will still simply shut down in the face of frustration, proclaim, 'I don't know,' and give up. Dweck (2006) has shown that students with a fixed mindset--that is, those who believe that intelligence (especially math ability) is an innate trait--are more likely to give up when they encounter difficulties because they believe that learning mathematics should come naturally. By contrast, students with a growth mindset--that is, those who believe that intelligence can be developed through effort--are likely to persevere through a struggle because they see challenging work as an opportunity to learn and grow.

Many teachers felt that no matter how creative they were in the classroom, it wouldn’t make a difference anyway. They talked about a devastating erosion in standards, how the students of today bore no resemblance to the students of even ten or fifteen years ago, how their preoccupations were with anything but school. It was hard for teachers not to feel depressed by the lack of rudimentary knowledge, like in the history class in which students were asked to name the president after John F. Kennedy. Several students meekly raised their hands and proffered the name of Harry Truman. None gave the correct answer of Lyndon Johnson, who also happened to have been a native Texan. In 1975, the average SAT score on the combined math and verbal sections at Permian was 963. For the senior class of 1988–89, the average combined SAT score was 85 points lower, 878. During the seventies, it had been normal for Permian to have seven seniors qualify as National Merit semi-finalists. In the 1988–89 school year the number dropped to one, which the superintendent of schools, Hugh Hayes, acknowledged was inexcusable for a school the size of Permian with a student body that was rooted in the middle class. (A year later, with the help of $15,000 in consultant’s fees to identify those who might pass the required test, the number went up to five.)

Creating original mathematics requires a very high level of motivation, persistence, and reflection, all of which are considered indicators of creativity (Amabile, 1983; Policastro & Gardner, 2000; Gardner, 1993). The literature suggests that most creative individuals tend to be attracted to complexity, of which most school mathematics curricula has very little to offer. Classroom practices and math curricula rarely use problems with the sort of underlying mathematical structure that would necessitate students’ having a prolonged period of engagement and the independence to formulate solutions. It is my conjecture that in order for mathematical creativity to manifest itself in the classroom, students should be given the opportunity to tackle non-routine problems with complexity and structure - problems which require not only motivation and persistence but also considerable reflection.

The most important pillar behind innovation and opportunity—education—will see tremendous positive change in the coming decades as rising connectivity reshapes traditional routines and offers new paths for learning. Most students will be highly technologically literate, as schools continue to integrate technology into lesson plans and, in some cases, replace traditional lessons with more interactive workshops. Education will be a more flexible experience, adapting itself to children’s learning styles and pace instead of the other way around. Kids will still go to physical schools, to socialize and be guided by teachers, but as much, if not more, learning will take place employing carefully designed educational tools in the spirit of today’s Khan Academy, a nonprofit organization that produces thousands of short videos (the majority in science and math) and shares them online for free. With hundreds of millions of views on the Khan Academy’s YouTube channel already, educators in the United States are increasingly adopting its materials and integrating the approach of its founder, Salman Khan—modular learning tailored to a student’s needs. Some are even “flipping” their classrooms, replacing lectures with videos watched at home (as homework) and using school time for traditional homework, such as filling out a problem set for math class. Critical thinking and problem-solving skills will become the focus in many school systems as ubiquitous digital-knowledge tools, like the more accurate sections of Wikipedia, reduce the importance of rote memorization. For children in poor countries, future connectivity promises new access to educational tools, though clearly not at the level described above. Physical classrooms will remain dilapidated; teachers will continue to take paychecks and not show up for class; and books and supplies will still be scarce. But what’s new in this equation—connectivity—promises that kids with access to mobile devices and the Internet will be able to experience school physically and virtually, even if the latter is informal and on their own time.

Making is a way of bringing engineering to young learners. Such concrete experiences provide a meaningful context for understanding abstract science and math concepts.

Many people believe overlearning means studying or practicing until mastery is achieved. However, in the research literature, overlearning refers to a learning strategy in which a student continues to study or practice immediately after some criterion has been achieved. An example might be correctly solving a certain kind of math problem and then immediately working several more problems of the same kind. Although working more problems of the same kind (rather than fewer) often boosts scores on a subsequent test, doing too many problems of the same kind in immediate succession provides diminishing returns. “In the classroom and elsewhere, students should maximize the amount they learn per unit time spent studying or practicing—that is, they should get the most bang for the buck. How can students do this? The scientific literature provides an unequivocal answer: Rather than devote a long session to the study or practice of the same skill or concept so that overlearning occurs, students should divide their effort across several shorter sessions. This doesn’t mean that long study sessions are necessarily a bad idea. Long sessions are fine as long as students don’t devote too much time to any one skill or concept. Once they understand ‘X,’ they should move on to something else and return to ‘X’ on another day.

teaching math was convoluted and confusing, his grammar lessons could bore a statue to tears, and when it came to Ethoen history and mythology, Jahrra often found herself tempted to launch her pen at him.  He never got anything right, often obscuring facts or making heroes out to be twisted or idiotic.  Jahrra usually went into daydream mode during his lectures, but one day his lesson was so outrageous she couldn’t even lose herself in her own thoughts. “I wish we didn’t have such an awful teacher,” Gieaun groaned as they streamed out of the stuffy classroom on their final day of school. “I

In math problem-solving, the constructivist approach shifts from rote memorization to active exploration, where students engage in collaborative sense-making, developing problem-solving skills and mathematical reasoning.

All of this told of harm done, of a drug that made a child depressed, lonely, and filled with a sense of inadequacy, and when researchers looked at whether Ritalin at least helped hyperactive children fare well academically, to get good grades and thus succeed as students, they found that it wasn’t so. Being able to focus intently on a math test, it turned out, didn’t translate into long-term academic achievement. This drug, Sroufe explained in 1973, enhances performance on “repetitive, routinized tasks that require sustained attention,” but “reasoning, problem solving and learning do not seem to be [positively] affected.”26 Five years later, Herbert Rie was much more negative. He reported that Ritalin did not produce any benefit on the students’ “vocabulary, reading, spelling, or math,” and hindered their ability to solve problems. “The reactions of the children strongly suggest a reduction in commitment of the sort that would seem critical for learning.”27 That same year, Russell Barkley at the Medical College of Wisconsin reviewed the relevant scientific literature and concluded “the major effect of stimulants appears to be an improvement in classroom manageability rather than academic performance.”28 Next it was James Swanson’s turn to weigh in. The fact that the drugs often left children “isolated, withdrawn and overfocused” could “impair rather than improve learning,” he said.29 Carol Whalen, a psychologist from the University of California at Irvine, noted in 1997 that “especially worrisome has been the suggestion that the unsalutary effects [of Ritalin] occur in the realm of complex, high-order cognitive functions such as flexible problem-solving or divergent thinking.”30 Finally, in 2002, Canadian investigators conducted a meta-analysis of the literature, reviewing fourteen studies involving 1,379 youths that had lasted at least three months, and they determined that there was “little evidence for improved academic performance.”31

Reading is the king of subjects. Math and science, writing and social studies -- they all depend on it. It's the most important thing children learn in school.

Many females have a problem not only with stereotypes, but with other people’s opinions of them in general. They trust them too much... This vulnerability afflicts many of the most able, high-achieving females. Why should this be? When they’re little, these girls are often so perfect, and they delight in everyone’s telling them so. They’re so well behaved, they’re so cute, they’re so helpful, and they’re so precocious. Girls learn to trust people’s estimates of them. “Gee, everyone’s so nice to me; if they criticize me, it must be true.” Even females at the top universities in the country say that other people’s opinions are a good way to know their abilities. Boys are constantly being scolded and punished. When we observed in grade school classrooms, we saw that boys got eight times more criticism than girls for their conduct. Boys are also constantly calling each other slobs and morons. The evaluations lose a lot of their power. Even when women reach the pinnacle of success, other people’s attitudes can get them... The fixed mindset, plus stereotyping, plus women’s trust in people’s assessments: I think we can begin to understand why there’s a gender gap in math and science. That gap is painfully evident in the world of high tech. Julie Lynch, a budding techie, was already writing computer code when she was in junior high school. Her father and two brothers worked in technology, and she loved it, too. Then her computer programming teacher criticized her. She had written a computer program and the program ran just fine, but he didn’t like a shortcut she had taken. Her interest evaporated. Instead, she went on to study recreation and public relations. Math and science need to be made more hospitable places for women. And women need all the growth mindset they can get to take their rightful places in these fields.

Maya’s face as though wondering what to tell her. ‘It’s just I know they weren’t always happy, and I did once wonder if they’d have stayed together… There was something my husband, George, said when you were first in my maths class. As you know, he taught the other year one class at your primary school and mentioned how once he’d had to break up an argument between your parents when they were waiting to pick you up from school. It must have been pretty heated for him to remember it after all that time – he wasn’t one to gossip. Apparently, Mrs Lyons wouldn’t let you out of your classroom until George had managed to calm them down.’ Maya feels her stomach clench. ‘All couples argue.’ ‘I know.’ Mrs Ellis pats her hand. ‘And that’s why you mustn’t worry about it. It was a long time ago, anyway.’ The bus is stopping. Bending to her bag, Mrs Ellis moves it so that it’s not in the way of the people getting on. ‘But if you ever feel you want to spread your wings, you mustn’t feel your dad would be on his own. He’s a grown man, and you can’t make him your responsibility. I’m sure he has friends, neighbours, even work colleagues who would keep an eye on him. Doesn’t he have his own private practice in Lyme Regis?’ ‘Yes, but it’s not the same. He needs me.’ Maya’s voice slips away, so it’s barely a whisper. ‘Yes, he needs me. It’s why I couldn’t go to university.’ She doesn’t want to talk about that time for, although her dad had been encouraging when she’d first told him she was applying, a week after the forms were filled in, a cloud had settled over him. One that was darker than previous ones. Maya had tempted him with his favourite food, enticed him out for healing walks along the clifftop, but nothing she’d done could lift it. Eventually, telling herself it was because of what she’d done, she’d deleted her application from the computer. When her dad had found out and asked why she’d done it, she’d told him it was because she couldn’t face more studying. Would rather earn a living. Whether he’d believed her or not, she couldn’t say. What she did know was that he’d never tried to change her mind. ‘Do you like your job, Maya?’ Maya lowers her eyes and studies her hands. It’s something she hasn’t given much thought to. Her job is just something she does to get through

Of course you know the answer. You Muslims are good at math because you need to know how to make bombs.” Reading this, and the rest of my son’s essay, tore my heart. Even at thirteen years old in a math classroom in one of the most diverse cities on earth, my son faced hostility simply because of the family into which he was born. So much of my life was spent working to combat Islamophobia and raise awareness about its impact on

Employees who sit near windows report higher energy levels and tend to be more physically active both in and out of the office. In a study of elementary schools, students in classrooms with the most daylight advanced as much as 26 percent faster in reading and 20 percent faster in math over the course of a year. Hospital patients assigned to sunnier rooms were discharged sooner and required less pain medication than those in rooms with less light.

From kindergarten through senior year of high school, Evan attended Crossroads, an elite, coed private school in Santa Monica known for its progressive attitudes. Tuition at Crossroads runs north of $ 22,000 a year, and seemingly rises annually. Students address teachers by their first names, and classrooms are named after important historical figures, like Albert Einstein and George Mead, rather than numbered. The school devotes as significant a chunk of time to math and history as to Human Development, a curriculum meant to teach students maturity, tolerance, and confidence. Crossroads emphasizes creativity, personal communication, well-being, mental health, and the liberal arts. The school focuses on the arts much more than athletics; some of the school’s varsity games have fewer than a dozen spectators. 2 In 2005, when Evan was a high school freshman, Vanity Fair ran an exhaustive feature about the school titled “School for Cool.” 3 The school, named for Robert Frost’s poem “The Road Not Taken,” unsurprisingly attracts a large contingent of Hollywood types, counting among its alumni Emily and Zooey Deschanel, Gwyneth Paltrow, Jack Black, Kate Hudson, Jonah Hill, Michael Bay, Maya Rudolph, and Spencer Pratt. And that’s just the alumni—the parents of students fill out another page or two of who’s who A-listers. Actor Denzel Washington once served as the assistant eighth grade basketball coach, screenwriter Robert Towne spoke in a film class, and cellist Yo-Yo Ma talked shop with the school’s chamber orchestra.

I know that the way he comes into a classroom, he wants the students to leave knowing math. This makes me open my mind to what he has to say and how he’s trying to say it.

We didn't want our children to waste their time in the same empty rituals of education that we did: passing tests only to forget the subject matter when the grades were given; spending years with passing grades in foreign-language instruction yet being unable to have even a rudimentary conversation in the language outside of the classroom; struggling to learn advanced math skills that were seldom used outside of class; doing lab experiments that were more rote exercises than scientific inquiries. Time and youth cannot be regained, so perhaps, ultimately, the real crisis in education may be one of disillusionment among graduates rather than poor performance among current students.

Innovations are happening in conventional schooling. Some people will read the chapters to come and respond that their own children’s schools are incorporating evidence-based changes, making them more like Montessori schools—eliminating grades, combining ages, using a lot of group work, and so on. One could take the view that over the years, conventional schooling has gradually been discovering and incorporating many of the principles that Dr. Montessori discovered in the first half of the 20th century. However, although schooling is changing, those changes are often relatively superficial. A professor of education might develop a new reading or math program that is then adopted with great fanfare by a few school systems, but the curricular change is minute relative to the entire curriculum, and the Lockean model of the child and the factory structure of the school environment still underlie most of the child’s school day and year. “Adding new ‘techniques’ to the classroom does not lead to the developmental of a coherent philosophy. For example, adding the technique of having children work in ‘co-operative learning’ teams is quite different than a system in which collaboration is inherent in the structure” (Rogoff, Turkanis, & Bartlett, 2001, p. 13). Although small changes are made reflecting newer research on how children learn, particularly in good neighborhood elementary schools, most of the time, in most U.S. schools, conventional structures predominate (Hiebert, 1999; McCaslin et al., 2006; NICHD, 2005; Stigler, Gallimore, & Hiebert, 2000), and observers rate most classes to be low in quality (Weiss, Pasley, Smith, Banilower, & Heck, 2003). Superficial insertions of research-supported methods do not penetrate the underlying models on which are schools are based. Deeper change, implementing more realistic models of the child and the school, is necessary to improve schooling. How can we know what those new models should be? As in medicine, where there have been increasing calls for using research results to inform patient treatments, education reform must more thoroughly and deeply implement what the evidence indicates will work best. This has been advocated repeatedly over the years, even by Thorndike. Certainly more and more researchers, educators, and policy makers are heeding the call to take an evidence-based stance on education. Yet the changes made thus far in response to these calls have not managed to address to the fundamental problems of the poor models. The time has come for rethinking education, making it evidence based from the ground up, beginning with the child and the conditions under which children thrive. Considered en masse, the evidence from psychological research suggests truly radical change is needed to provide children with a form of schooling that will optimize their social and cognitive development. A better form of schooling will change the Lockean model of the child and the factory structure on which our schools are built into something radically different and much better suited to how children actually learn.

The evidence suggested that many American parents treated their children as if they were delicate flowers. In one Columbia University study, 85 percent of American parents surveyed said that they thought they needed to praise their children’s intelligence in order to assure them they were smart. However, the actual research on praise suggested the opposite was true. Praise that was vague, insincere, or excessive tended to discourage kids from working hard and trying new things. It had a toxic effect, the opposite of what parents intended. To work, praise had to be specific, authentic, and rare. Yet the same culture of self-esteem boosting extended to many U.S. classrooms. In the survey of exchange students conducted for this book, about half of U.S. and international students said that American math teachers were more likely to praise their work than math teachers abroad. (Fewer than 10 percent said that their international teachers were more likely to praise.) That finding was particularly ironic, given that American students scored below average for the developed world in math. It also suggested that whatever the intent of American teachers, their praise was probably not always specific, authentic, and rare.

To cease as though one had never been, to exit life with no hope of living on in the memory of another, to be expunged from history’s record—that is a fate literally far worse than death.”23 Really? Literally far worse than death? That’s quite a statement. I turned to Jones. “What are some of the most common forms of symbolic immortality that people pursue?” “Having or adopting children is a big one—trying to live on through your kids,” he answered. “Nathan Heflick was explicit in Psychology Today: ‘So why do people have children? One reason is to transcend the great specter of death.’24 The great actor Sir Peter Ustinov said, ‘Children are the only form of immortality that we can be sure of.’”25 “Why doesn’t that work?” I asked. “Just do the math. Our genetics quickly get watered down. In twenty generations, your future offspring will only have 0.000004 percent of your genes. You couldn’t feed a mosquito with that. Actually, given the way genes are transferred in blocks, with some dominant and others recessive, it’s unlikely any of your genes will survive that long.” “What about memories that are carried on through families?” Jones smiled. “Do you know the first names of your great-great-grandparents?” I felt sheepish. “Uh, no, I guess I don’t.” He reassured me with a pat on my shoulder. “Don’t feel bad,” he said. “I’ll often ask classrooms full of students if they know the first names of their great-great-grandparents—

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