The Problem With Math Problems: We’re Solving Them Wrong

Originally posted in the NYTimes

Credit Illustration by Jessica Lahey

The following question, from a mother concerned about her daughter’s math education, landed in my email box recently:

My husband and I talked to our daughter’s pre-calculus teacher about her poor grades. He said that many students hit a wall at this point in math, moving from memorization — apply this theorem to this problem — to more abstract how-can-I-solve-this-problem thinking. I accepted that because that’s what is happening for her. What I thought later was that why can’t we find a way to help these many students get over that wall, instead of using it as a tool to weed out less developed brains? I really feel I have no way to have an impact on this teacher’s blind spot since it is shared by all math teachers and so many other teachers: If you don’t understand, it’s your fault.

As I’m not a math teacher, I asked three experts on mathematics instruction to weigh in. They told me that this question perfectly illustrates what’s wrong with math education and why we need to change it. Much of what we teach kids during their first decade of math education relies on students’ blind compliance and memorization of rules and facts. We reward correct answers, but we do not not encourage students to think independently about what these rules and facts might mean in the bigger mathematical picture.

Tracy Zager, a math-education specialist and the author of the forthcoming book “Becoming the Math Teacher You Wish You’d Had,” explained in an email why this kind of math education fails students: “It was never a sensible idea to try to have students memorize first and understand later; this approach to mathematics instruction is structurally flawed. I really feel for these parents and this kid, but the frustration they face is inevitable. If we teach kids math without understanding, we build on a house of cards.”

That house of cards will be fragile, and liable to collapse, when students move from elementary mathematics to complex problem-solving, said Steven Strogatz, an author and a professor of applied mathematics at Cornell University.

“If you follow the rules, you can do pretty much everything that’s expected of you without ever having to think imaginatively,” Mr. Strogatz said in an email. “This is not the way math should be taught, even at an elementary level. There really ought to be problem solving and imaginative thinking all the way through while kids master the basics. If you’ve never been asked to struggle with open-ended, non-cookbook problems, your command of math will always be shaky and shallow.”

Mr. Strogatz suggested, however, that this math teacher isn’t wholly to blame for her students’ frustration. “This teacher may have been brought up in a culture in which skill at problem solving is seen as a matter of talent; either you have it or you don’t,” he said. “Everyone can be taught techniques and strategies for better problem solving, and can be taught to feel pleasure in the struggles that make us smarter. With practice, all of us can get much better at it.”

While avoiding the kind of frustration this mother describes in her letter will require a larger shift in mathematics education, there are some things this parent can do now to help her daughter.

Mr. Strogatz suggested playing with age-appropriate puzzles. “Kids love puzzles, and wrestling with good ones can help them fall in love with math and get stronger at it,” he said.

After playing around on a couple of recommended websites, I fell in love with with Steve Miller’s Math Riddles. Mr. Miller, a mathematics professor at Williams College, has amassed a wonderful collection of puzzles, ranging from easy to very challenging, and even I, an admitted math phobic, had a lot of fun playing on the site.

For teachers and parents looking to improve their own problem-solving abilities, Mr. Strogatz recommended George Polya’s book “How to Solve It.” While it’s not exactly light reading, it introduces new ways to approach problems, and is a classic in the field.

Purchase two copies of Carol Dweck’s Mindset, one for you and one for your child’s teacher. Ms. Dweck’s book is already required reading in many school districts because it articulates the difference between a fixed mindset (either you have it or you don’t) and a growth mindset (everyone can be taught to feel pleasure in the struggles that make us smarter). A growth mindset is a powerful thing and is an essential first step toward more effective teaching and learning (and parenting).

If you are frustrated by your child’s math homework and want to improve your capacity to help, read Christopher Danielson’s “Common Core Math for Parents for Dummies,” which will be published this month. Mr. Danielson’s book can help parents reorient their thinking about mathematics so that they can begin to help their children more effectively.

And check out Mr. Strogatz’s New York Times series, on the “Elements of Math.” It begins with a preschooler’s understanding of numeracy and progresses all the way through to an examination of infinity. Tellingly, the most advanced topic discussed in the series was inspired by a 6-year-old’s question.

Above all, Mr. Strogatz concluded: “It’s crucial to help our students realize that it’s fine to get stuck – after all, the life of a professional mathematician (or any other creative person) is about being stuck nearly all the time! It’s how you get past being stuck that matters. And that’s one of the most valuable lessons that math has to offer.”

Schools Use Student Data to Find Signs of Trouble, Help Struggling Kids

Student Mack Godbee and mentor Natasha Santana-Viera go over Godbee's report card. Godbee's performance has improved since a data monitoring program identified him as a dropout risk.
Student Mack Godbee and mentor Natasha Santana-Viera go over Godbee’s report card. Godbee’s performance has improved since a data monitoring program identified him as a dropout risk.

By Sammy Mack

At Miami Carol City Senior High in Florida, a handful of teachers, administrators and coaches are gathered around a heavy wooden table in a conference room dubbed the “War Room,” looking through packets of information about several students.

There are others at the table, too: analysts from the group Talent Development Secondary, which monitors student data; City Year, a nonprofit that provides mentors; and Communities in Schools, which connects kids with health care and social services.

It’s a lot of cooks in the kitchen, but they’re all here to help students who are just starting to show signs of trouble.

The process works like this: analyst Jennifer Savino gathers information on attendance, behavior and performance in math and English. Then, based on some dropout risk studies from Johns Hopkins University, she flags kids who are on a downward trend. Those names show up on PowerPoint slides at these weekly War Room meetings.

Today, there are three kids on the list. A projector beams one student’s image on a screen, accompanied by a spreadsheet of his grades so far this year. His most recent report card shows a lot more D’s and F’s than in the first part of the year.

“He came to me last week and he said, ‘I’m hungry. I haven’t had anything to eat all day,’ ” says one teacher. “I had a bag of chips and I gave them to him.”

“If that happens again … we keep snacks in the office,” offers another.

A third person points out something not everyone knows about this student: Turns out, he’s spent more than a week this semester living in a car.

The team then discusses some potential options, like strategies for helping the student manage his time and putting him in touch with homeless services. A sports coach volunteers to coordinate everything.

This kind of interaction between different school departments didn’t happen before.

“If we don’t get to the core of the problem, we can’t teach them,” says Tracy Troy, who teaches math and special education.


When these meetings were first introduced three years ago, Troy, who has been on staff at Carol City for 14 years, was apprehensive about getting involved with students’ problems outside her classroom.

“Not that I don’t care, but I care too much,” she says. “And sometimes, it weighs on you. Because those are your children while you’re here.”

Now, she says, the War Room meetings help her help the kids.

Godbee has begun setting goals for each quarter, part of a strategic plan to help keep him on track at school.
Godbee has begun setting goals for each quarter, part of a strategic plan to help keep him on track at school.

The program, called Diplomas Now, identifies 150 to 200 students a year at Carol City. It costs about $600 per student annually to run.

Last school year, one-third of students flagged for missing school got back on track to graduation. Two-thirds of the students who were having behavioral problems made a turnaround.

“The point of all this isn’t to collect data. It’s to change what’s happening for individual kids,” says Paige Kowalski, a state policy director for the Data Quality Campaign, a group that advocates for better use of all that student information the states collect.

Kowalski says about 20 states have developed early warning systems like the one here at Carol City. Schools, she says, can learn a lot from the medical field, in particular.

“[They] don’t just put out reports saying, ‘The hospital lost all these patients and saved these people,’ ” she says. “They actually look at it and say, ‘What can we do better?’ ”


Earlier this year, Mack Godbee, a soft-spoken Carol City High 10th-grader, was the subject of a War Room meeting. The first quarter of the school year, Godbee’s report card was littered with D’s and F’s.

Today, it’s report card time again, and Godbee is going over his most recent grades with his mentor, Natasha Santana-Viera. Now, there are more C’s and B’s, and he got an A in English.

Godbee says his life would be very different if he had not participated in the Diplomas Now program. “No lie — I think I would have ended up dead,” he says.

That’s because he was spending a lot of time on the street. When his dad left home, he explains, he wanted to show his mom that they didn’t need him. So Godbee started selling drugs. He was 6.

By the time he got to high school, Godbee says, he was affiliated with a gang. He skipped classes, didn’t study and was angry all the time.

That might have been easy for teachers and administrators to miss. But earlier this school year, after looking at Godbee’s data, Santana-Viera sat him down and asked, “Are you OK?”

“I sat right there and thought about it. Like, am I really OK?” Godbee recalls.

And for the first time in his life, he said no.

Even with his improvements this year, Godbee doesn’t want to be the person he is now. “I want to be a different person. I want to be that kid that makes straight A’s and B’s on his report card,” he says. “Be in school every day on time. Be on that honor roll list. Go on field trips.”

Godbee has a lot to work on, but according to the data, he’s on an upward trend.


Isle Firm Accuses Oculus of Stealing VR Tech

Orlovsky and Oculus Rift by Sergey Galyonkin on Flickr

by · May 23, 2015

A Hawaii-based company this week accused Oculus Rift and its founder Palmer Luckey of building its virtual reality hardware company with information stolen from its own research and development.

The lawsuit, filed on Wednesday, says that Ron Igra and Thomas Seidl partnered to form Total Recall Development in Hawaii in 2010, with the aim of “developing immersive 3D technology, including cameras and head mounted displays.” The pair says they met Luckey in December of that year, and by the summer of 2011, engaged him to build a prototype for them.

Luckey delivered the prototype hardware to Total Recall Development in August 2011, having agreed to a “nondisclosure, exclusivity and payments agreement,” according to the suit. But in 2012, they said, “Luckey took the information he learned from the partnership, as well as the prototype that he built for the TRT using design features and other confidential information and materials supplied by the partnership, and passed it off to others as his own.”

Specifically, Luckey launched a Kickstarter campaign to crowdfund a “highly immersive, wide field of view, stereoscopic headmounted display at an affordable price,” which he called Ocolus Rift.

As the tech world knows, that Kickstarter campaign raised over $2.4 million from 9,522 backers, nearly ten times its goal. The startup only got as far as releasing advance versions of its hardware for developers before being acquired by Facebook for $2 billion.

This lawsuit comes two weeks after Oculus finally announced the release date of its consumer hardware. Total Recall Development isn’t the first to accuse Oculus of stealing ideas: Texas-based Zenimax filed suit last May. Interestingly, the Zenimax lawsuit covers the period between Luckey’s alleged work with the Hawaii partnership and the launch of the Kickstarter campaign.

“In April 2012, Carmack began corresponding with Palmer Luckey, a college-agedvideo game enthusiast living in southern California,” reads the Zenimax filing. “Luckey was working on a primitive virtualreality headset that he called the ‘Rift’ […] a crude prototype that lacked a head mount, virtualreality-specific software, integrated motion sensors, and other critical features and capabilities needed to create a viable product.”

Zenimax said it saw the ‘Rift’ as something that might work with Doom, a video game developed by its parent company, id Software. So, its employees “literally transformed the Rift by adding physical hardware components and developing specialized software for its operation.”

It would be interesting to compare the prototype Total Recall Development says Luckey built for them and the prototype Zenimax said he showed them.

I couldn’t find an entry for Total Recall Development in the state business registration system, but the pair do have a pretty compelling piece of evidence in a 2013 patent filing. Seidl and Ron, listed as being based in Haiku on Maui, were ultimately granted patent 9,007,430 for a “System and method for creating a navigable, three-dimensional virtual reality environment having ultra-wide field of view.”

There has been virtual reality research and development taking place in Hawaii for some time. In 2009, I visited the Virtual Reality Center, which helped people cope with anxiety with a combination of traditional therapy and virtual environments.

And the technology has its local fans, for sure. Last year brought the Hawaii Virtual Reality Club, and founder Ka’i Ka’u has since launched VRCHIVE, a startup focused on hosting VR content.

Photo: Orlovsky and Oculus Rift by Sergey Galyonkin/Flickr.

Internet Searches May Make You Think You’re Smarter Than You Are

Using the Internet is an easy way to feel omniscient. Enter a search term and the answers appear before your eyes.

But at any moment you’re also just a few taps away from becoming an insufferable know-it-all. Searching for answers online gives people an inflated sense of their own knowledge, according to a study. It makes people think they know more than they actually do.

“We think the information is leaking into our head, but really the information is stored somewhere else entirely,” Matthew Fisher, a doctoral student in cognitive psychology at Yale University, tells Shots. Fisher surveyed hundreds of people to get a sense of how searching the Internet affected how they rate their knowledge. His study was published Tuesday in the Journal of Experimental Psychology: General.

Fisher began with a simple survey: he asked questions such as “How does a zipper work?” or “Why are there leap years?” He allowed just half of his subjects to use the Internet to answer the questions.

Then he asked the subjects to rate how well they thought they could answer a question unrelated to the first question, such as “Why does Swiss cheese have holes?” or “How do tornadoes form?” People who had been allowed to search online tended to rate their knowledge higher than people who answered without any outside sources.

To reveal factors that might explain why the Internet group rated their knowledge higher, he designed follow-up experiments using different groups of people. First, he asked people to rate their knowledge before the test; there was no difference between subjects’ ratings. But afterwards, the Internet-enabled subjects again rated their knowledge better than the others.

Next, Fisher tried to make sure that people saw the exact same information. He told the Internet-enabled group, “Please search for the page with this information.” The non-search group was sent directly to the page. Fisher checked that the two groups used the same URL. Still, the people who could actively search rated their knowledge higher than those who simply saw the information.

And this is just a taste of the experiments Fisher ran. He also:

  • Compared different search engines.
  • Reworded his questions to make it clear that he was asking for only the subjects’ knowledge, not the Internet’s.
  • Made the online searchers use filters that would keep any relevant results from showing up.
  • Asked questions for which there were no answers online, such as “How do wheat fields affect the weather?”
  • Asked people to choose one of seven brain scans that most resembled their brain. The people who had been searching online picked the image with the most activity.

The results kept coming back the same: searching online led to knowledge inflation.

There are practical consequences to this little exercise. If we can’t accurately judge what we know, then who’s to say whether any of the decisions we make are well-informed?

“People are unlikely to be able to explain their own shortcomings,” says Fisher. “People aren’t aware of the quality of explanation or the quality of arguments they can produce, and they don’t realize it until they encounter the gaps.”

The more we rely on the Internet, Fisher says, the harder it will be to draw a line between where our knowledge ends and the web begins. And unlike poring through books or debating peers, asking the Internet is unique because it’s so effortless.

“We are not forced to face our own ignorance and ask for help; we can just look up the answer immediately,” Fisher writes in an email. “We think these features make it more likely for people to consider knowledge stored online as their own.”

Copyright 2015 NPR. To see more, visit

Why Kids Need to Move, Touch and Experience to Learn

When students use their bodies in the learning process, it can have a big effect, even if it seems silly or unconnected to the learning goal at hand. Researchers have found that when students use their bodies while doing mathematical storytelling (like with word problems, for example), it changes the way they think about math. “We understand language in a richer, fuller way if we can connect it to the actions we perform,” said Sian Beilock, professor of psychology at the University of Chicago.

Consider this word problem:

Two hippos and two alligators are at the zoo. Pete the zookeeper feeds them at the same time. Pete gives each hippo seven fish. He gives four to the alligators.

In an experiment on third graders, students were divided into two groups. One group read through the problem twice. The other group acted out the story as they read it, physically pretending to feed fish to the hippos and alligators as they read the problem. Both groups of students were asked how many fish the zookeeper fed to the animals.

The answer:

“Kids who acted out the story did better on this problem,” Beilock said. The kids who read the problem often got “eleven” as a solution. They had missed the word “each” in the problem. But because the acting kids had physically mimed giving each hippo seven fish before moving on, the difference was ingrained.

“What was important was matching the words with specific action; that led to enhanced learning,” Beilock said. “And after they’d acted it out they could actually do it in their head and get some of the same benefits.”


Scholarly study goes back a long time in history, but in terms of human evolution, many of the academic skills now required for successful functioning in the world are fairly new to the human brain. As neuroscientists investigate how humans learn, they often find that newer skills and aptitudes are mapped onto areas of the brain that also control basic body functions. Increasingly, this work is helping to illuminate neurological connections between the human body, its environment and the process of learning.

“In order to really engage our students and help them perform at their best we have to move beyond what’s happening in the head,” said Beilock at a Learning and the Brain conference. “We have to go beyond that.”

This area of study, called “embodied learning,” is not new to many educators. Maria Montessori highlighted the connection between minds and bodies in her 1936 book The Secret of Childhood: “Movement, or physical activity, is thus an essential factor in intellectual growth, which depends upon the impressions received from outside. Through movement we come in contact with external reality, and it is through these contacts that we eventually acquire even abstract ideas.”

Increasingly scientists are proving Montessori right. Researchers are studying the body movements of children as young as four-to-six months old and have found earlier and more frequent movement correlates with academic learning down the road. Kids who could sit up, sustain “tummy time” longer and walk were all correlated with future academic success, even when researchers controlled for socioeconomics, family education and type of future education, among other mitigating factors.

“A very strong predictor of academic achievement was how early kids were moving, exploring their world,” Beilock said. “When kids can explore their surroundings, all of a sudden, things change.” Once kids are on the move the adults in their lives use directives and other more complicated language forms. As kids are coached by their parents, they begin to understand the directions and change behaviors. And once a child can do something on her own, she’s more likely to internalize what’s happening with others. “There is evidence that our ability to use our hands affects the structure and functioning of the brain,” Beilock said.

As young children move and explore their worlds, they are learning through touch. Early bimanual training correlates with the robustness of the corpus callosum, a part of the brain that facilitates quick communication between the left and right brain hemispheres, Beilock said. This connection between using ones hands and swift communication in the brain may be part of the reason learning to play music is often correlated with math ability.

“Math is a very recent cultural invention,” Beilock said. The part of the brain responsible for numerical representation also controls finger motion. Many children first learn to count on their fingers, a physical manifestation of the connection. The studies of very young learners have solidified Beilock’s conviction that academic learning is inherently connected to the body.


A colleague of Beilock’s at the University of Chicago, Susan Goldin-Meadow has done extensive research into how student gestures can indicate a more nuanced understanding of math than students are often able to articulate verbally. Goldin-Meadow did a lot of work around problems of equivalence, which children often struggle to understand. She found that often students gesture in ways that indicate they understand how to solve the problem even if they are simultaneously describing an incorrect solution.

“It’s particularly helpful for teachers because it may give you insight into things students may not be able to express,” said Goldin-Meadow at the same conference. Not only could gestures be a good clue for teachers, but when students produce what Goldin-Meadow calls “mismatches,” meaning they are saying one thing and gesturing a different understanding, it indicates they are primed to learn. And, when teachers produce “mismatches” in their own speech and gestures, it helps students already in that primed state to learn by offering several strategies.

“Encouraging kids to use their hands brings out unsaid, and often correct ideas, which then makes them more open to instruction and more likely to learn,” Goldin-Meadow said. She also found that showing two ways of doing a problem with speech had very little effect on learning, but showing two methods when one was in gesture helped learners.

And the connection between bodies and learning doesn’t stop with the younger grades. Beilock studies how well students comprehend abstract concepts in high school physics. Many classes focus on listening to lecture, reading a textbook and doing physics problems. Beilock hypothesized that if students could feel an abstract concept like angular momentum on their bodies, they would both understand and remember it better.

She and her colleagues used a rod with two bicycle wheels attached to test their ideas. Students spun the wheels and then tilted the rod in different directions. As they changed the angle, the force they felt changed dramatically. In her experiment, one set of students got to hold and experience the wheel. Another group just watched the first group and observed the effects they were feeling. They were all quizzed on the material a week later.

“Those students who had more motor activation did better on the test,” Beilock said. “And those students were the ones who got the experience.” But what if one set of students was just better at physics? Researchers at DePaul University have replicated this experiment, strengthening the scientific link between hands-on experimentation and powerful learning.


Just as body movement and involvement can have a huge impact on learning, so too can the spaces where we learn. While neuroscientists are starting to be able to prove this link with their experiments, this concept is nothing new. Philosophers, writers and practitioners of Eastern religions have long made the same connection between the power of nature to relax the mind and readiness to take on the world.

“When we are in nature, our directed attention has time to rest and replenish,” Beilock said. That’s important because focus is like a muscle that gets tired. One researcher asked students to take a walk through the downtown of a college town. They weren’t asked to do anything in particular, but they naturally encountered a lot of stimuli. The other group took a walk in a natural setting. The nature walkers were better able to focus when they returned.

Visual distractions apply to the classroom as well. Carnegie Mellon researchers recently found that when students learn in highly decorated classrooms, their gazes tend to wander, they get off task and their test scores suffer. Limiting visual stimulus is particularly important for very young learners who are still learning how to focus, and yet kindergarten classrooms are often the most brightly and densely decorated in an effort to make institutional buildings feel more cheerful.


One way to help students reduce test anxiety is to let them work it out through their bodies beforehand. Beilock did an experiment with freshmen high school students before their first final. She asked them to write down concerns about the test and connect to other times when they felt similar. They were told to be as open as they wanted and that their writing would be confidential. A control group of kids were told to think about what wouldn’t be on the test.

This activity had little effect on kids who didn’t experience much test anxiety. But students experiencing high levels of anxiety saw a six percentage point gain on their test scores. And, when Beilock analyzed those students’ writing, she found the strategy was particularly effective for students whose writing revealed an eventual acceptance that the test was a minor hurdle, not the big scary all-consuming event they’d been worried about.

“We can start leveraging the power of our bodies to help us learn, think and perform at our best,” Beilock said. Too often students are cooped up inside for six or more hours, sometimes without an adequate recess ,and more likely than not, with little attention paid to how their bodies could be powerful learning tools in the classroom.

Rethinking the Role of Educator as Facilitator Amidst Tech Transformation

Thanks to the rapid developments in education technology, there is an abundance of teaching tools available to educators: videos students can watch at home, lesson plans that can be easily downloaded (and for free), courses that can be completed at one’s own pace. With so much information available, much of it on platforms developed by private companies, high school English teacher Michael Godsey asks what this all means for the future of the teaching profession in this post in The Atlantic, and what the role of “facilitator” could mean in the future classroom that’s closer to five years away instead of 20.

In the Atlantic:

“I don’t have many answers in this brave new world, but I feel like I can draw one firm line. There is a profound difference between a local expert teacher using the Internet and all its resources to supplement and improve his or her lessons, and a teacher facilitating the educational plans of massive organizations. Why isn’t this line being publicly and sharply delineated, or even generally discussed? This line should be rigorously guarded by those who want to keep education professionals in the center of each classroom. Those calling for teachers to “transform their roles,” regardless of motive or intentionality, are quietly erasing this line—effectively deconstructing the role of the teacher as it’s always been known.”

How Should Learning Be Assessed?


This is the second of a two-part conversation with Yong Zhao about standards, testing and other core elements of the modern system of education, and the assumptions that may be standing in the way of meeting the real learning needs of all children. He is a professor in the college of education at the University of Oregon and author of Who’s Afraid of the Big Bad Dragon: Why China Has the Best (and Worst) Education System in the World and World Class Learners: Educating Creative and Entrepreneurial Students.

There is already a strong backlash against politicians and school administrators because of high-stakes standardized tests, and the way results are used to justify school closures. Some parents and educators have encouraged families to “opt out” of tests, such as those related to the Common Core State Standards, as a way to protest these practices and the effects they are having on children, families and communities. However, Yong Zhao, education professor at the University of Oregon, recommends that parents, educators and policymakers go a step further, and use the moment to re-examine the role of testing—and the issue of accountability—more broadly.

Tests are just one form of assessment, he points out, and limited in what they can accurately measure. Important qualities such as creativity, persistence and collaboration, for example, are tricky to measure, because they are individualized and situation- or task-specific (someone may collaborate well in one group setting but not in another). And no test can measure whether children are receiving “a quality learning experience that meets the needs of individual students.”

High-stakes tests concern Zhao the most, because he says they represent more than misspent time and money. He faults them for suppressing creativity and innovation, and creating narrowed educational experiences, because everything that is not measured becomes secondary or is dismissed entirely. Moreover, “constant ranking and sorting” creates stress and makes students less confident.

Parents seeking assurance that their children are learning can look at their children’s engagement level, and notice if they’re exploring topics or pursuits that interest them, and improving in their areas of interest.

Steps for Identifying Needs

As for how to evaluate schools, he recommends that parents and community members ponder some key questions. “First of all, ask if the school is really personalizing learning to meet individual needs, with a broad and flexible curriculum,” he says. Children interested in music, for example, should have equal opportunities to develop that skill as to develop literacy.

The next question he would ask: “Is school an engaging place—do students want to go to school? If the more they go to school, the more they hate it, that would be a horrible place,” he says. Analogies with taking bad-tasting medicine fail, he adds, because there’s no disease involved, and “children don’t need to be fixed.”

And finally, “Do the teachers care about the development of the whole child?” he asks. “If a teacher just helped a student who had lost hope because of a personal problem, that should count for something. Teachers should be human mentors. Children can take ownership of their learning, but inevitably they will encounter setbacks. Do teachers help develop their social, emotional and physical well being, and challenge them and push them forward?”

On a broader societal level, educational equity can be gauged by whether schools in low-income jurisdictions receive comparable resources to invest in good teachers, professional development, materials, facilities, field trips and other enrichment activities.

Who Should be Accountable for What?

Teaching can be mandated, but learning can’t, Zhao points out; what adults can do is provide opportunities and offer guidance when needed. That’s what we should be tracking, he says—“accountability should shift back to what we do for kids, rather than what they’ve done for us.”

In other words, each person should be held accountable only for what he or she can control—the educators for providing an environment that stimulates and supports individual learning, and the community and government for providing sufficient funding to enable them to carry this out equitably.

Even if funding levels are modest (in the first article in this series, Zhao explained how quality can be achieved economically), the best way to ensure that the funds are well spent is to have greater local autonomy. “Locally controlled entities are much closer to their constituents,” Zhao says, and more responsive to pressure to cater to their needs. Those most invested in the schools’ learning environments—the children and their parents—then wouldn’t have to work as hard to get their schools to change direction.


Standards: Why Realizing the Full Promise of Education Requires a Fresh Approach

Spyros Papaspyropoulos/FlickrSpyros Papaspyropoulos/Flickr

This is the first of a two-part conversation with Yong Zhao about standards, testing and other core elements of the modern system of education, and the assumptions that may be standing in the way of meeting the real learning needs of all children. He is a professor in the college of education at the University of Oregon and author of Who’s Afraid of the Big Bad Dragon: Why China Has the Best (and Worst) Education System in the World and World Class Learners: Educating Creative and Entrepreneurial Students.

Education is not “omnipotent,” says Yong Zhao, education professor at the University of Oregon, but it can change the trajectory of people’s lives. Most recent education policies, such as No Child Left Behind and Common Core, have sought to better realize this potential by aiming for parity in outcomes, as indicated by standardized test scores. Proponents, including many civil rights groups, see such initiatives as a way to shine a light on inequality in education and pressure schools to help disadvantaged students graduate with the same knowledge and skills as their more advantaged peers, with the goal of better preparing them for colleges and careers.

Zhao says he embraces the underlying goal—to even the playing field for all children—but notes that inequities have been apparent for a long time. Furthermore, he believes that serving the best interest of all students requires a very different approach that starts with a paradigm shift in how we view education. Attempts to standardize individual student outcomes are an unhelpful, if not downright harmful, way to promote the development of human beings, he says. Instead, “we need to start with the individual child, instead of what others think [that child] should become.”

After researching different educational approaches over the years (his findings aresummarized in several books) Zhao has concluded that the most fruitful form of education—and the one with the best chance of empowering children to overcome poverty and other disadvantages—offers each child the opportunity to pursue his or her own goals, in a stimulating and supportive environment. Unfortunately, low-income students are least likely to have any of these elements in their schools. It’s this “opportunity gap,” rather than any “achievement gap,” that characterizes unequal education and is fully within the power of schools (and their funders) to remedy, Zhao says.

In the alternate vision, individual differences are not flaws to be fixed; the emphasis instead is on helping all students to identify and develop their areas of interest, and to build on their strengths. Standards, curricula and tests would play a very minor role, as tools to be deployed only when they can help a particular student to progress. Learning would be organized around individuals, instead of classes and grades. And rather than looking to schools and teachers to manage students’ learning, we should “give children autonomy, trust that they want to learn, and let them become owners of their learning enterprise.”

This also means redefining excellence to focus on how well educators support individual pursuits. “Look at what children are interested in or can do, and plan education with that in mind, rather than trying to fix them,” Zhao writes in his book, “Who’s Afraid of the Big Bad Dragon: Why China Has the Best (and Worst) Education System in the World.” “Expect everyone to be great, and start educating from that angle, and things can be very different.”

Whose Standards, and to What End?

Academic standards—whether part of Common Core or not—are subjective, Zhao says, and don’t account for the fact that children naturally develop at different rates, or that learning is more haphazard than linear. He also doesn’t buy the argument that they benefit disadvantaged children by setting a high bar. “Being able to pass a prescribed test is not a high expectation,” Zhao says. “To become exceptional in an area that you want to pursue—that is a high expectation, and it is about having dreams. By imposing standards, we are not elevating expectations, but perhaps driving down expectations, especially for poor communities. … We are depriving them of the chance to dream.”

Even worse, standards can “cause psychological damage to those not judged as good,” Zhao says. This can set off a vicious cycle, creating feelings of low self-efficacy and disengagement that undermine further learning, because “few people want to stick to a place where they are constantly told that they are not good.” A system based on punitive consequences for not meeting expectations can also backfire: If it gets children decoding letters or adding numbers sooner rather than later, but diminishes their interest in reading and leads them to hate math, Zhao asks, “is it worth it?”

Last but not least, “standards describe the past, not the future,” and reflect the notion that children must “fit into the world as it is,” he says. “We forget that our children are the creators and owners of the future.”

That said, certain types of standards (used with caveats) can be helpful in two ways, Zhao says. They can guide learners, by suggesting a sequence to follow, and describing the knowledge and skills needed in a given field. Such information is dynamic, subjective and personal—those interested in becoming mathematicians might benefit from different math standards than their otherwise inclined peers, for instance. Each individual should therefore be free to decide which standard he or she wants to pursue, whether that means using an established math program such as Singapore math, or the Common Core standards, or developing their own set of standards, Zhao says.

The other useful application of standards is broader, but it is for schools rather than learners, Zhao says: Standards can be developed to define the educational opportunities schools should provide to all students.

Does a Mandated Curriculum Help or Hinder Learning?

Standards (and their associated tests) often drive the design of a curriculum. Placing a lot of weight on test scores in a few subjects has led to “curriculum narrowing,” especially in schools that are under pressure to boost their aggregate scores or else lose funding or face closure. These are usually schools serving low-income students, meaning that “disadvantaged children experience a much less rich education than their advantaged counterparts,” Zhao says, and are therefore less likely to feel a connection to what they’re learning or to view it as relevant to their lives.

But there’s an even deeper problem, he adds: Any set curriculum is counterproductive and also discriminatory, along a dimension that affects people of all incomes and races.

It is counterproductive because the notion that following a set curriculum will make students “college and career ready” is misguided, he says. Not only is college acceptance “an artificial goal, as if life ends at college,” but there are many types of colleges and majors, requiring different sets of knowledge and skills. That is even more true of careers, especially in a rapidly changing world in which many professions will soon become obsolete and others have yet to be invented. “It is very difficult, if not impossible, to predict which course of study will give one a better chance of employment,” Zhao says. “If you want to be ready for a career, you’d better be the one to create that career yourself.” The best preparation for that, he adds, is for students to develop an entrepreneurial mindset and chart their own educational paths.

The second issue is that schools that are only oriented toward strengthening students in certain academic areas are imposing subjective and narrow definitions of success on all students and effectively discriminating against those whose interests and strengths lie in other areas, such as music, art, sports and crafts, Zhao says.

Even the basics—the knowledge that everyone needs in order to function in our society—don’t justify a mandated curriculum, he contends. A broad, flexible curriculum that supports children’s individual interests and strengths is more likely to engage them and promote learning, so that truly essential knowledge becomes “difficult to escape—when individuals want to pursue anything, they must learn the basics, so the basics are sought after, instead of imposed.”

A Different Mindset

What all this adds up to is a need to “re-imagine education,” Zhao says. His ideal educational environment (detailed here) would combine the essential elements of democratic schools and certain types of project-based learning programs. This can be accomplished even on modest budgets, he notes; what matters more is mindset.

He recommends questioning all basic assumptions. For example: “Is the teacher the only instructor, or can students help? How about using resources beyond the school, like the community or parents?” (A recent article shows how one school is leveraging such resources.) Technology can also expand access to resources within the wider community.

Another thing to bear in mind, Zhao says, is that schools that provide a learning environment that supports individual needs benefit greatly from harnessing their students’ intrinsic motivation, because they don’t have to work hard to try to overcome resistance to learning. All human beings are born with the capacity and desire to learn, he says, but their environment can either suppress or encourage that drive. “If people are driven by their own goals, that are meaningful to them, and feel a sense of accomplishment and self efficacy, then they really want to learn.”



Why We Need Learning Engineers

Recently I wandered around the South by Southwest ed-tech conference, listening to excited chatter about how digital technology would revolutionize learning. I think valuable change is coming, but I was struck by the lack of discussion about what I see as a key problem: Almost no one who is involved in creating learning materials or large-scale educational experiences relies on the evidence from learning science.

We are missing a job category: Where are our talented, creative, user-­centric “learning engineers” — professionals who understand the research about learning, test it, and apply it to help more students learn more effectively?

Jobs are becoming more and more cognitively complex, while simpler work is disappearing. (Even that old standby, cab driving, may one day be at risk from driverless cars from Google!) Our learning environments need to do a better job of helping more people of all ages master the complex skills now needed in many occupations.

I am not suggesting that all subject-matter experts (meaning faculty members) need to become learning engineers, although some might. However, students and faculty members alike would benefit from increased collaboration between faculty members and learning experts — specialists who would respect each other’s expertise — rather than relying on a single craftsman in the classroom, which is often the case in higher education today.

Education technology has enormous potential to help. While often expensive upfront, it has the chance to make learning more affordable, reliable, available, data-rich, and personalized. The technology within new learning environments — for example, an interactive simulation offered as part of a well-designed MOOC — is available 24/7, and can provide patient, repeated, and varied practice with supportive feedback that does not embarrass learners.

In the future, these environments may follow learners across their life spans, filling gaps from their past while allowing faculty members to provide the coaching, feedback, and motivation that is possible only with human interaction.

Unfortunately, technology has only a chance to help — there is no guarantee. While we hope that only the best instructors are engaged with technology, imagine your worst college professor. In the old days, that person damaged just a few hundred students per year. Thanks to video on demand and other wonders of technology, today that person might damage a few hundred thousand students — a weapon of mass destruction. Not exactly a win for technology and learning.

Technology is not the problem. As Richard E. Clark suggested in his book Learning From Media: Arguments, Analysis, and Evidence, education technology serves only as a delivery vehicle. All technologies can deliver effective or ineffective instruction. The key question is what you ask students to do and how you help them do it, not what tools you use.

After decades of experimental work by cognitive scientists and others, we now know a lot about how people learn. Neurons do not follow Moore’s law, the prediction by Gordon Moore in the 1960s that semiconductors would double in capacity every two years. Since our brains’ cognitive machinery does not change year after year, the good news is that investing in learning science will have long-lasting benefits.

Science, however, is not enough. It’s never enough for real-world problems.

Consider the tens of thousands of chemical engineers working in the United States. Anyone building a modern pharmaceutical factory needs them. You trust them to get the safety and regulatory issues right, and to use modern chemistry.

Indeed, most of the design processes leading to the conveniences of modern life benefit deeply from mediation between science and its application to real-world problems. Physicians, too, can be seen as “engineers” who use their knowledge of human biological science to tackle various medical problems within the constraints of medical care, economics, regulations, and other factors.

So where are the learning engineers? The sad truth is, we don’t have an equivalent corps of professionals who are applying learning science at our colleges, schools, and other institutions of learning. There are plenty of hard-working, well-meaning professionals out there, but most of them are essentially using their intuition and personal experience with learning rather than applying existing science and generating data to help more students and professors succeed.

Not applying learning science leads us into trouble:

We make assumptions about learning that don’t match the facts. For example, we talk about the need to understand various “learning styles,” yet meta-analyses over decades show no practical benefits from bucketing minds into style categories, compared with well-designed single instruction.
Students, faculty members, and administrators seem reluctant to question educational suppliers (of software, textbooks, and other materials) who do not deliver good evidence that their products or services solve learning problems.
Colleges rarely run controlled trials, commonly used in medicine, to compare one approach to learning with another. Sometimes there are ethical concerns with such an approach: If you think a particular teaching method is good, it would be wrong to withhold it, and if it’s not good, it would be wrong to use it widely. Yet many other fields recognize that a promising discovery does not necessarily lead to large-scale benefits — you need to test assumptions. Oddly, in higher education it is unremarkable to change a course with no evidence (by adding a new reading list or teaching practice, for example), while experimenting with a group of courses to test an idea seems controversial. Kaplan University, where I work, runs dozens of controlled trials to make sure we know if an approach or intervention makes a difference before we adopt it.

We don’t do a good job measuring what students learn. For example, a chemistry professor creating a test problem about Boyle’s law (the mathematical connection between pressure, volume, and temperature for gases) may, without realizing it, formulate an item that tests reading ability more than comprehension of the concept.

So what are we to do? To get started, several recent books provide very approachable syntheses of learning science: E-Learning and the Science of Instruction, by Ruth C. Clark and Richard E. Mayer; Why Don’t Students Like School?, by Daniel T. Willingham; and Talent Is Overrated: What Really Separates World-Class Performers From Everybody Else, by Geoff Colvin. I’ll add to the list a volume that I wrote with Frederick M. Hess, Breakthrough Leadership in the Digital Age: Using Learning Science to Reboot Schooling.

Just being exposed to information is never enough. To learn, instructional-­design and teaching professionals need the same things their students do: We have to provide explicit practice and coaching on applying the science about learning for everyone involved in instruction. At Kaplan Inc., we have developed a training program for our more than 100 instructional designers, to help them apply learning science to solve practical learning problems. They might, for example, decide against using a fancy 3-D video game to teach a particular concept once they see research that found that a simpler tool makes the point more effectively.

It is not simple to go from reading the science to putting it to work, day in and day out.

We also need decision makers in higher education — especially those who buy learning materials and educational-technology offerings — to ask harder questions. For example: What learning science underpins this offering? Is there learning science behind a particular professional-development activity as well? Do you have valid and reliable data showing that a new product works better than what we’re using? Will you conduct a pilot program to demonstrate that it works better? How are you using data to improve the learner and staff experience?

New technologies offer a real opportunity to revolutionize learning. The capacity for efficient, accessible, reliable delivery of learning and the generation of more data about learning than we’ve ever had before are huge assets. However, the challenge is to use these technologies correctly.

Whether in the classroom, at home, or at work, we owe it to learners, employers, and families to do a better job at “learning engineering” than we’ve done so far.

By Bror Saxberg APRIL 20, 2015 Pete Ryan for The Chronicle

Bror Saxberg is chief learning officer at Kaplan Inc.


How to Grow a Classroom Culture That Supports Blended Learning


The excerpt below is from the book “Moonshots in Education: Launching Blended Learning in the Classroom,” by Esther Wojcicki, Lance Izumi and Alicia Chang. This excerpt is from the chapter entitled “Trick in the Blended Classroom,” written by Wojcicki.

It all started in 1987, when I got a grant from the State of California. The state sent me eight Macintosh computers, never asking if I knew how to use them, and when they arrived I had no idea how to even turn them on. I realized then that I was going to fail if I didn’t get some help quickly. I looked around for colleagues who could help, but none of them had any idea. Our school had no IT department. So I took a leap of faith and confessed to my students that I had no idea how to use the new computers and that I needed help. This turned out to be a stroke of good luck, even though I did not see it that way at the time. It was the beginning of my new teaching methodology.

The students were absolutely thrilled to help me (can you imagine being asked to help a teacher?!), and that was the beginning of my collaborative teaching model. Only, at that point, it did not have a name, and in fact I had to hide it from other teachers who might have frowned on what I was doing. The students and I ended up spending hours after school and on weekends figuring out the computers and how to network them. I had never even heard the word “network” in a computer context. I was one of the first teachers in California to use computers in the classroom, and possibly the first in the nation to use computers in a journalism classroom.

I was soon sold on the idea of collaboration, respect, and trust in the classroom. And it turns out that building a culture of collaboration, respect, and trust is key to a successful blended classroom. The first action a teacher needs to take in the fall when school starts is to set up the culture. On the surface, this may sound like a waste of time, but in fact its importance cannot be overemphasized. Part of such a culture is understanding that the teacher is not the only expert in the room; in fact, students can know more than the teacher about some aspects of what they will be doing together.

Computers, tablets, and other electronic devices alone are not going to change the classroom. It is the change in culture that will make the difference.

To help everyone remember what it takes to set up a culture that works, I have come up with an acronym, TRICK. Each letter stands for an important part of the culture.

T = trust
 R = respect 
I = independence C = collaboration K = kindness

Trust The first thing to establish in the classroom is a culture of trust. That does not mean the students are given complete freedom to run wild and do what they want; it means the students trust each other to help in the learning process and the teacher trusts the students. The boundaries need to be established early in the semester. There are a variety of exercises to build trust that a teacher can use, ranging from the blind man’s game to walking into walls.

Since the teacher is the one in control, it is he or she who must take the initiative. Teachers need to put themselves into situations that require students to be trustworthy. Opportunities arise every day. For example, having students work in teams and be responsible to the team teaches trust. Creating a group blog or website gives students a natural way to develop trust in the team, and, if the teacher trusts the team, it builds a community of trust in the classroom.

However, the key to building trust is to actually trust the students. While that may seem counterintuitive to many teachers, it is really the only way to effectively build trust. For example, in my advanced journalism class, the students each have an individual story assignment, so no two students are doing the same thing. Some of the stories are particularly sensitive about issues in the school, the district, or the city. It takes a leap of faith on my part to trust students to get the information right and to write it up in an objective way. We publish the results online— typically garnering thousands of views—and in hard copy for three thousand local residents. Students have told me that trusting them to write the stories is significant in building their self-esteem.

The students also put out a newspaper or magazine. The newspaper class has an enrollment of seventy students, who work in teams on the paper. Six editors-in-chief are in charge of the class, giving the students critical leadership experience and a sense of control over the publication. The magazine classes have an enrollment of thirty-five and an editorial board of three editors. Each student in each class has a title that correlates to his or her responsibilities. Examples are news editor, editorial-page editor, feature-page editor, or reporter.

Besides having the students produce actual publications, a second suggestion is to allow the students to teach the class on a regular basis. For example, the teacher can designate one day a week when the kids take over the class for an hour or so. Having kids teach each other in small groups on a regular basis also creates a sense of trust in the class.

I also encourage the students to help with the technological side of the program. I use Google Docs to create documents and Adobe software to publish. New products come out daily, and many of those might be useful for me, but I have little time to investigate them. Thus, I ask my students to watch out for new software that might be useful for the program, tell me about it, and, if it seems appropriate, learn how to use it. They then share it with the rest of the class.

A third suggestion to enhance trust is to give students your home phone number, cell number, and e-mail and tell them to contact you when they have problems, but not later than a specified time in the evening. Just giving out that information provides for a culture of trust and caring. All students also have the same contact information for all other students including home phones, cell phones and addresses as well as my contact information.

A fourth suggestion is for the teacher to laugh at his or her own mistakes on a regular basis. We all make mistakes, and teaching students that mistakes are part of life is an important lesson in helping them accept themselves. I do that every day in class, and the mistakes are not difficult to find: Every day there is something that does not go as planned. Teachers who are willing to show that they are not perfect, don’t know everything, and can laugh at themselves can more easily develop trust.

Finally, and perhaps most important, is to put students in situations requiring them to think for themselves. They may stumble and have difficulties, but the key is to support them in their efforts while letting them solve the problem themselves. This builds trust in themselves, in the class as a whole, and between teacher and students.

Respect Teachers need to have sincere respect for their students, especially in today’s world, where the members of a class may come from very different backgrounds and experiences. But each one has unique gifts even if he or she also has unique problems. As a teacher I know how difficult it can be to respect students who create problems in the classroom, but it is up to the teacher to show respect. It goes a long way in making the student feel better about themselves.

Respect is part of trust. I trust the kids and respect them, and in turn they trust and respect me. Someone has to start the process, and it cannot be the students, since the teacher is in charge.

Giving students respect does not mean letting go of expectations. In fact, it means the opposite.

Esther Wojcicki (Credit: Joi Ito/Flickr)
Esther Wojcicki (Credit: Joi Ito/Flickr)

Teachers need to respect them as individuals and expect them to achieve at a high level. My expectations are high and I encourage my students to reach those standards by giving them the opportunity to revise their work on a regular basis. I use the mastery system model (which means students work on a skill until they master it) and grade only when students have finally mastered the standard. An innovative internet company called has software that sup- ports this pedagogy. Grades can be very discouraging for kids but if teachers return an assignment with suggestions on how to improve or correct the errors and kids understand it is part of the process of learning, they will still be excited to learn.

Famed psychologists Albert Bandura talks about the power of self-efficacy and how a student’s self image determines how they feel about themselves. He defines self-efficacy as a person’s belief in their ability to succeed in specific situations and says that self efficacy plays a major role in how people (especially students) approaches goals, tasks, and challenges. According to Bandura’s theory, people with high self-efficacy—that is, those who believe they can perform well—are more likely to view difficult tasks as something to be mastered rather than something to be avoided.

Albert Bandura – Wikipedia, the free encyclopedia

David Kelley, CEO of IDEO and head of Stanford University’s, has a similar philosophy which he calls Creative Confidence. He says the key to being creative and achieving is “believing in your ability to create change in the world around you. It is the conviction that you can achieve what you set out to do. We think this self-assurance, this belief in your creative capacity, lies at the heart of innovation. Creative confidence is like a muscle–it can be strengthened and nurtured through effort and experience.”

David M. Kelley

Carol Dweck, social psychologist from Stanford University, talks about the power of “mindset” and how if people think their intelligence is flexible and can grow, they will achieve, but if they think it is fixed and there is nothing they can do about it, they tend to be afraid to try. People with a growth mindset understand that their talents and abilities can be developed through effort, good teaching and persistence. They think that if they persevere, (mastery learning concept) they will succeed.

Carol Dweck

This is nothing new, but it is harder to do than to say. Students will rise to meet the expectations of their teachers and parents. By giving students the respect and having the expectation, teachers will be empowering kids. In my experience, students will achieve at levels far beyond what is expected if you give them the opportunity. Just believing in them helps them believe in themselves.


We all like independence; it is the foundation of our nation. For most children it starts when they are two years old and want to do everything themselves—to the chagrin of their parents. In elementary school, students want to be independent too, but as they progress through the system, they become more dependent on the teacher. By the time they are in high school—if they have been taught according to the old model—they are waiting to be told what to do. However, high school is a time when the students’ drive for independence should be at its peak. One way teachers can encourage this drive is to give students an opportunity to come up with their own projects within defined guidelines. For example, students could have a writing assignment, but one in which they pick the topic. It could be a restaurant review, with each student reviewing a restaurant of his or her choice.

moonshots coverCollaboration

Collaboration is an important part of the culture of the blended classroom. Students love to work with their peers, especially if they are working on a project they selected themselves. In fact, the main attraction of school for most students is being with their peers. So if teachers can make the environment a friendly, collaborative work space in which students feel comfortable, more learning will take place.

This type of learning is important for several reasons: 1) most workplaces today require collaboration and students need to practice those skills at school 2) students learn more when they are responsible for another students work 3) collaboration increases student interest in learning especially if it is on a common project such as a newspaper, magazine, video, or website.


Kindness is self-evident. If students feel that the teacher is kind, they want to learn. I can remember many instances of being kind to students who had made mistakes. It paid off a hundred times, because the students were so grateful, it made them feel relaxed and accepted. Being kind not only in school, but in life in general, makes the difference. As the American religious leader William J. H. Boetcker (1873–1962) put it: “Your greatness is measured by your kindness; your education and intellect by your modesty; your ignorance is betrayed by your suspicions and prejudices, and your real caliber is measured by the consideration and tolerance you have for others.”

Esther Wojcicki teaches journalism and English at Palo Alto High School in California. She served as Chair of Creative Commons and is currently a vice-chair of Creative Commons and an advisor to The University of the People, a global online non-profit free university. You can follower her on Twitter @EstherWojcicki.