One day, Adam Holman decided he was fed up with trying to cram knowledge into the brains of the high school students he taught. They weren’t grasping the physics he was teaching at the level he knew they were capable of, so he decided to change up his teaching style. It wasn’t that his students didn’t care about achieving — he taught at high performing, affluent schools where students knew they needed high grades to get into good colleges. They argued for every point to make sure their grades were as high as possible, but were they learning?

“I felt I had to remove all the barriers I could on my end before I could ask my kids to meet me halfway,” Holman said. The first thing he did was move to standards-based grading. He told his students to show him they’d learned the material, it didn’t matter how long it took them.

“The kids realized this made sense,” Holman said. He taught physics and math at Anderson High School in Austin, before moving on to become a vice-principal. His students were mostly well-off, high achievers, and they knew how to play the game to get the grades they needed. But Holman found when he changed the grading policy, students worried about grades less and focused more on working together to understand the material.

“It turned my students into classmates and collaborators because I didn’t have a system in place to deny the collaboration,” Holman said. His students stopped copying homework. There was no curve that guaranteed some kids would be at the bottom. Instead, the class moved at its regular pace, but if a student persisted at a topic until they could show they understood it, Holman would give them credit. “It turned the kids on my side,” Holman said. “I was there to help them learn.”

**BUILDING TRUST**

Holman didn’t just change his grading policies. He also changed his teaching style to focus on inquiry, good questions and independent discovery. Starting off, he knew juniors and seniors weren’t used to learning that way, so first he had to build trust with them so they’d understand why he was asking so much of them.

At the start of each class period Holman and his students did icebreakers and read and discussed articles about how human brains learn best. Holman knew he was asking students to be vulnerable with one another–to share their misperceptions about math and physics–and so he spent precious class time working to make sure students trusted one another and him.

The class read Timothy Slater’s article, “When Is a Good Day Teaching a Bad Thing?” which discusses the unspoken contract that can exist between teachers and students by which a teacher will pass a student as long as he or she doesn’t make trouble. Students recognized their own experience of education in the article. “It wasn’t meant to be a bash on teachers, but just to say we are aware that teaching is really complex,” Holman said. “It’s really difficult and sometimes we don’t know how to handle kids.”

Holman also asked students to read “Sermons For Grumpy Campers,” by Richard Felder, a graduate level professor who never lectured. In it, Felder describes his students grumbling that they hated group work and that it was his job to teach them, not the other way around. Holman’s students said the complaints sounded like they came from kindergarteners or themselves and were amazed to find out the complainers were graduate level engineering students.

Talking about these issues openly validated the inevitable complaints of students and helped them buy into the new approach. If an article was a little harder, Holman would use it as differentiated instruction, asking his best readers to take it on and summarize it for the class.

“It wasn’t perfect and it didn’t turn my kids into all physics majors, but for the kids who were on the border, it made a difference,” Holman said. Discussing their learning with them, switching grading policies and assigning more inquiry-based, hands on lessons all helped Holman’s students feel he trusted and respected them. And they rose to the challenge. “I think the kids were just waiting to be let loose and to be treated like adults,” Holman said.

**STUDENT RESPONSES**

Most of the students responded well to the new teaching style, Holman said, but he was most touched by his struggling math class. “I saw that my kids had been told they were stupid and failures, but I saw so much potential in them,” Holman said. They’ve never been given the time to master a concept through multiple tries. So when Holman opened his door to help them after school and during lunch for as long as it took, many seized the opportunity.

Holman remember one struggling math student, Isabel, particularly well. She was taking algebra, convinced she was terrible at math. But when the grading policy was changed and she had a little more time to work on units that were difficult for her, she became a top student in the class. “She said, ‘for the first time in my life I’m trying to learn everything instead of just get a 70 [percent],’” Holman said.

“Students clearly learned in Mr. Holman’s class, and he never pushed fear,” wrote a former student, Kate Nunke, in an email. She described the rest of her high school experience as one long fear fest: “Fear of not getting into college, fear of not passing, fear of disappointing parents, fear of looking like a fool in front of your peers,” the list goes on. But Nunke says Holman’s teaching style jolted students into thinking about their learning in a new way.

“I think many students didn’t realize that they could learn without a textbook or without step by step instruction,” Nunke wrote. “At times I felt that Mr. Holman’s physics class was the hardest class ever because I didn’t get a step-by-step instruction. We are used to being handed the answer, thus not necessarily learning, just being told.”

Nunke said she’s been thinking a lot about Holman’s approach now that she has graduated and is taking a gap year in which she spent a semester at an outdoor education school focused entirely on experiential learning. “A lot of the teaching that Mr. Holman did, now that I think back to it, was teaching his students how to ask questions and investigate by themselves,” she wrote.

**TEACHERS RESIST WHAT WORKS**

Despite his success, Holman has had a hard time convincing other teachers to try some of his more progressive approaches. He became a vice-principal to spread and support the instructional practices he believes work, modeling lessons and pushing teachers to step out of their comfort zone.

“We know how kids learn; we know what classes should look like, and yet our classes look almost the opposite,” Holman said. He says there’s a particular deficit in math, where teachers and parents expect things to be taught the way they learned them. Not everyone has experienced good math instruction themselves, Holman said, so they can’t even begin to conceptualize a new way of doing it. “Imagine explaining color to someone who has never seen it,” Holman said. “You have to show them, you have to model it.”

But all of these approaches require taking a leap of faith and many teachers don’t feel they have that luxury. Teachers often complain that more progressive approaches like this suck up time and they can’t cover everything in the jam-packed curriculum. These arguments are excuses, Holman said. He said he never covered every single topic in the curriculum, but he did delve deeply into the ones he saw as most important.

**HOLMAN’S READING LIST**

For those interested in building metacognitive moments into the day, here are the articles Holman found to be useful and more or less reading-level appropriate for his high school students.

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**By Anya Kamenetz, NPR**

Little children are big news this week, as the White House holds a summit on early childhood education December 10. The President wants every four year old to go to preschool, but the new Congress is unlikely to foot that bill.

Since last year, more than 30 states have expanded access to preschool. But there’s still a lack of evidence about exactly what kinds of interventions are most effective in those crucial early years.

In New York City, an ambitious, $25 million dollar study is collecting evidence on the best way to raise outcomes for kids in poverty. Their hunch is that it may begin with math.

**Time That Counts**

“One! Two! Three! Four! Five!”

Gayle Conigliaro’s preschool class are jumping as they count, to get the feeling of the numbers into their bodies–a concept called “embodied cognition.”

P.S. 43 is located in Far Rockaway, Queens, just steps from the ocean. The area is still recovering from Hurricane Sandy. But now it’s been chosen as one of 69 high-poverty sites around New York City for a research study to test whether stronger math teaching can make all the difference for young kids. The study is funded by the Robin Hood Foundation, which is dedicated to ending poverty in New York. Pamela Morris, with research group MDRC, is lead investigator.

“MDRC and the Robin Hood Foundation developed a partnership really with a broad goal,” she says, “Which is, they want to change the trajectories of low income children. And to do so by focusing on preschool.”

There’s plenty of evidence on the long-term importance of preschool. But why math? Morris says that a 2013 study by Greg Duncan, at the University of California, Irvine, showed that math knowledge at the beginning of elementary school was the single most powerful predictor determining whether a student would graduate from high school and attend college. “We think math might be sort of a lever to improve outcomes for kids longer term,” Morris says.But there’s a real lack of math learning in pre-K. In one study, in fact, just 58 seconds out of a five-hour preschool day was spent on math activities. Part of the problem, says Doug Clements, at the University of Denver, is that “Most teachers, of course, have been through our United States mathematics education, so they tend to think of math as just skills. They tend to think of it as a quiet activity.”

Clements is the creator of Building Blocks, the math curriculum being tested in this new study. Building Blocks is designed to be just the opposite: engaging, exciting, and loud. “We want kids running around the classroom and bumping into mathematics at every turn.”

At P.S. 43, math games, toys, and activities are woven through the entire day. At transition time, the teacher asks the students to line up and touches their heads with the “counting wand.” At circle time, fittingly, the children talk about shapes. Just a few months into the school year, they observe correctly that a geometric shape must be a “closed figure” and that a square is “a special rectangle.”

“How do you know it’s a circle?” asks the teacher. “Because it goes round and round,” says one girl with a bear barrette in her hair.

When Ms. Conigliaro asks, “how do you know,” she’s asking the kids to think about their own thinking. That’s a skill called metacognition. Explaining your reasoning out loud also develops verbal ability.

At choice time, besides the play-dough and pattern blocks, there are computer games matched to Building Blocks that keep track of each student’s progress. And two children play a game called Number Match (“Is three more than two? How do you know?”) as a teacher watches. The teacher is keeping notes of each child’s level of understanding. The idea of developmental paths, or “trajectories of understanding,” is a core concept in Building Blocks.

“There are reliable levels of thinking through which kids pass on their way to achieving a certain understanding in mathematics,” Clements says. For example, children go from simply chanting “onetwothreefourfive,” to separating out each number word, to associating a number word with a given amount, to knowing that when you stop counting, the last number tells you “how many.”

Also in the classroom is a coach from Bank Street College of Education, who comes every other week to help the teacher put Building Blocks into practice. This is important to the study design. The coaches ensure that the curriculum is being implemented. Pamela Morris says, “Often we ask teachers what curriculum they’re delivering and we find it’s a book on their bookshelf collecting dust.”

The study will follow up with these students and a control group all the way through the third grade. They’ll be directly assessing their math and reading abilities and looking at their grades and test scores later on. Morris is curious whether working on math will enhance the children’s ability to self-regulate, inhibit impulses, pay attention appropriately and hold important concepts in working memory. This is a group of skills known as executive functioning. For example, if the teacher says “clap and count to five,” will you be able to stop clapping before you get to six?

But Conigliaro, a 24-year veteran teacher, is already convinced of the value of this curriculum.

“I just feel like the aha moment. This is what teaching should be. Where’s the literacy program?” she says. “We would just like it to be a research based program so we can give our kids the best.” She says the kids’ progress amazes her every day.

Copyright 2014 NPR. To see more, visit http://www.npr.org/.

]]>A good portion of the adult population hates math, and a lot of people believe they aren’t good at it so they avoid it completely. Those perceptions often come from their experiences learning math in school, which may not have been positive. In her Atlantic article Jessica Lahey writes about a Cornell professor who takes special pride in teaching non-math majors to appreciate numbers. He does it with an inquiry-based, hands-on approach that would likely work for kids learning math for the first time too. Lahey writes:

“Twelve years of compulsory education in mathematics leaves us with a populace that is proud to announce they cannot balance their checkbook, when they would never share that they were illiterate. What we are doing — the way we are doing it — results in an enormous sector of the population that hates mathematics. The current system disenfranchises so many students.”

]]>Many of us tend to align ourselves with either numbers or words. We’re either math brains or we’re reading brains.

In college, my fellow English majors joked about how none of us could long-divide to save our lives, while our friends in engineering groaned about the fact that Lit 101 was a graduation requirement.

But it turns out that about half the genes that influence a child’s math ability also seem to influence reading ability, according to a study published in the journal *Nature Communications*.

“You’d think that cognitively what’s going on with math and reading is very different,” says Robert Plomin, a behavioral geneticist at Kings College London, and one of the authors of the study. “Actually, people who are good at reading, you can bet, are pretty good at math too.”

The researchers looked at 2,800 pairs of 12-year-old British twins who were part of the larger Twins Early Development Study. Some pairs were very nearly genetically identical; the other pairs were fraternal twins, meaning they are the same age and shared a quite similar early environment, but are no more genetically similar than other siblings.

The scientists assessed each child’s math and reading skills based on standardized tests. To gauge how genes influenced the students’ aptitude, the researchers compared the test results of twin siblings as well as the results of unrelated children.

The researchers also analyzed the participants’ DNA, in hopes of turning up a particular gene or set of genes shared by people with high math or reading ability — genes that were, perhaps, missing in people with low abilities. (Some earlier, smaller studies had suggested such highly influential gene variants might exist). But no particular gene or sets of genes emerged. That may be because a lot — maybe thousands — of genes may be involved in helping to shape these abilities, Plomin says.

What the study did find was that children’s reading ability and math ability seem to be related — and much of that relationship can be explained by genetics.

The research also showed that genes can’t explain everything about our abilities, Plomin says. “These genetic propensities are like little nudges,” he says. Slight variations in your genes may nudge you to read more for pleasure. “And that can snowball,” Plomin says.

These kids who like reading may spend more time at the library or may ask their parents to buy them more books — and all of that practice reading will push their skills even further.

Other kids may find reading to be a bit harder due to genetics, Plomin says. “It’s not that the child just isn’t motivated, or that he’s just not trying hard enough.” But with some extra encouragement and support, these children can become good readers as well.

Environmental factors may also explain why, among genetically identical twins, one may prefer math while the other prefers reading, Plomin says. One twin may end up with a really good math teacher, while the other doesn’t. Or one may fall ill, and that may set her back.

Right now, we don’t have all the answers, Plomin says. “I wish I knew what some of the genes are,” he says. That would allow scientists to learn more about how we each learn best.

“What’s going to be needed is very large samples of people to be able to isolate these genes,” says Douglas Detterman, an emeritus professor of psychology at Case Western Reserve University and editor of the journal *Intelligence*. Detterman, who wasn’t involved in this study, says scientists would likely have to look at the DNA of millions of people in order to start figuring out which genes affect our academic aptitudes.

It’s a daunting task, he says, “but I think it’ll happen faster than we expect.” As we learn more about the influence of genetics on learning, we’ll be able to more easily figure out which learning environment works best for each child.

Here, teachers are a bit like farmers, Detterman says. And children are a bit like corn. “You have corn plants that do well in certain environments, and don’t in others. And the farmer’s job is to get the corn plants into the right soil.”

Educators have been talking about changing the traditional way of teaching math for a long time, but nothing seems to change. Elizabeth Green’s New York Times Magazine article digs into why it has been so hard for U.S schools to effectively implement changes to math pedagogy, and just how far American students have fallen behind as a result. A lot of it comes down to ensuring teachers are comfortable with the new methods, she writes:

“In fact, efforts to introduce a better way of teaching math stretch back to the 1800s. The story is the same every time: a big, excited push, followed by mass confusion and then a return to conventional practices. The trouble always starts when teachers are told to put innovative ideas into practice without much guidance on how to do it. In the hands of unprepared teachers, the reforms turn to nonsense, perplexing students more than helping them.”

]]>Prodigies in piano or dance can study at schools like Juilliard to develop their musical or performing arts talent. By contrast, nothing like Juilliard exists for children who show great promise at math. But an ambitious experiment will soon change that: In fall 2015, a small, independent school that’s exclusively tailored for math whizzes will open in downtown San Francisco.

Designers of the new, non-profit Proof School intend to provide mathematically gifted youth an intensive and complete education in grades 6-12 that typical schools can’t muster. The pupils will learn advanced areas of math, such as number theory topics that a university math major or graduate student might tackle. They’ll work on math research projects, and engage in community service through math tutoring.

“They’re going to be involved in math in a really different way, a really exciting and dynamic way,” said Sam Vandervelde, who is leaving his math professorship at St. Lawrence University in New York to become the new school’s dean of mathematical sciences.

Proof School will initially open with roughly 45 children in three grades, with plans to grow to around 250 students in a decade. Getting in won’t be easy, but the school’s mission is to serve the needs of “math kids” in the Bay Area — ranging from high-IQ wunderkind types to students who participate in math competitions or math circles, to children who love to play with numbers. “What we want is kids who are passionate about math,” said Paul Zeitz, school co-founder and chair of mathematics at the University of San Francisco.

The new school takes its inspiration from math circles, an Eastern European and Russian tradition that spread to the U.S. starting in the 1990s. These weekly extracurricular clubs bring youngsters together with a mathematician who guides them in exploring numerical ideas and concepts in depth. It’s often a highly interactive conversation, with the kids avidly chiming in with questions and thoughts.

For kids who live and breathe for numbers, the experience can be transformative, as Ian Brown of Marin County, Calif., can attest. In 2011, he began taking his 10-year-old son, Nico, to local math circles. Nico hadn’t been happy or thriving in his public elementary school, because “he wasn’t finding kids in his classes who understood what he was going on about when he was talking about higher mathematics,” Brown said. But math circle changed everything. “Not only did the lights go on, but the heart went on,” he said.

About a year later, Nico joined an advanced, invitation-only math circle for a half dozen students that was led by Zeitz. “Here they all are, for two hours once a week, joyful, joyful, joyful,” Brown recalled. One day in January 2013, as he watched the group animatedly discussing how many ways there are to color a cube with two colors, he turned to another student’s father, Dennis Leary, and marveled: “Look at these guys, they’re thrilled to be working together. Why don’t we do this all day long — and every day?”

Brown wanted to build a school for kids like his son “that they feel is really meant for them.” One conversation led to another and to the birth of Proof School, with him, Leary, and Zeitz as co-founders. To jumpstart it, Brown left his job as a language-arts teacher and dean at a private school for gifted and talented youth where his son, now 13, currently attends seventh grade.

While San Francisco has several high-caliber schools, including Lowell High School, it lacks specialized science schools such as Stuyvesant High School in New York City or the North Carolina School of Science and Mathematics in Durham. But Proof School won’t be like any school out there, anywhere, Zeitz said. Not only will its student body be different — they’ll all have exceptional math ability — but so will its teachers.

At a traditional school, a teacher in a top-notch math classroom might take students on the intellectual equivalent of a strenuous hike that brings them to top of the hill. But as Zeitz put it, “what they don’t realize is that they’re in this incredible mountain range, which they can’t see because their teacher doesn’t know how to get them to put on a hang glider and jump off the cliff and see the entire topography at once.” Proof School teachers will ideally have math Ph.D.s and the deep expertise to do that, he said.

As in math-circle style, the curriculum will emphasize working on and communicating about interesting math problems. Because one of Proof School’s guiding principles or “axioms” is not to waste their pupils’ time, the kids will be spared the unchallenging busy work or mind-numbing exercises that are common in standard schools, Zeitz said.

Every afternoon, students will spend two-and-a-half to three hours learning mathematical sciences, including computer science. Following an unconventional block curriculum structure, the academic year will be broken into six blocks of math instruction that each immerse the entire school in a single topic (such as problem solving or algebra) for five weeks straight. For each topic, kids will be placed into 10 to 12 different tiers by their skill level, Vandervelde said, which allows a lot of flexibility in meeting their individual needs.

“We’ll sort kids into groups based on what they’re ready for,” he said, not by age or grade. Some off-the-charts precocious students will be able to take on very advanced problems at the level of the U.S.A. Mathematical Olympiad, and “we’re going to be ready for them too,” said Vandervelde, who, like Zeitz, competed in the International Mathematical Olympiad as a teenager. “We want to develop and nurture every one of those kids and bring them along as far as they are capable of going.”

Recruiting girls to the school is a high priority, Zeitz said, noting that many young girls are enthusiastic about math but often drop out in their interest between sixth and ninth grades. “We would like to fight that trend as much as possible,” he said.

Beyond numbers, the school will offer a full education, with non-math courses in English, history, languages, and science all scheduled in the mornings in a traditional grade-level manner. Proof School’s teaching style will also draw upon blended learning methods that make use of technology in the classroom, as well as inquiry-based learning practices. Because classroom facility space will initially be limited, the founders plan to tap nearby educational resources: Students might go to the Exploratorium for hands-on science learning, to the Museum of the African Diaspora for history, and to TechShop for 21st century shop class.

Since some math kids are not exactly social butterflies when it comes to people skills, the school’s guiding axioms also make a point of teaching students how to engage with and navigate the world around them. “We will work as hard on social-emotional intelligence and communication skills — writing and public speaking — as we will on anything else,” Zeitz said.

Zeitz and his colleagues have much work ahead to make all the prime factors of their creative ideas, logistical plans, and hiring goals — which includes finding a charismatic humanities dean who “is able to stand up to math nerds,” he said — add up to an equation for success. They’re getting ready to launch an early admissions program and give “a day in the life” school preview this summer. Currently in fundraising mode, the founders hope to secure at least $1 million in order to keep the private tuition as low as possible and provide ample scholarships and financial aid.

To make the school accessible to math kids around the Bay Area, the campus will be located near public transit, most likely in San Francisco’s South Financial District area. The founders also plan to share their math curriculum and resources with the world in an open-source way, which will include hosting math talks and events for the public.

Many families in Silicon Valley have expressed strong interest in Proof School, but other reactions have ranged from initial skepticism to some concerns that the school will be elitist. “We’re not going to be elitist but we will be elite,” Brown said. “We’re not going to be snobby. We’re simply taking kids who operate at this [intellectual] level and putting them together with their peers, which they haven’t had in the past. And many have suffered for it.”

His own son, for example, is leaving his private middle school after this academic year because he has no math peers there, Brown said. If all goes well, after a gap year of homeschooling, the plan is to start Nico in ninth grade at Proof School in September 2015. “Oh, he can’t wait!” Brown said.

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