Posted in Educational Reform, Math

Research Shows Timed Testing Causes Math Anxiety – DUH!

I recently came across an article in Education Week where Stanford mathematics education professor Jo Boaler highlights a number of research studies that establish something those of us who pay attention have known for a long time: timed testing causes math anxiety. Can you say “Duh!”

The article and its sources describe the results of various studies of the cognitive, behavioral, emotional, and neurological effects of timed testing, which I will summarize below. Not to scare you or anything, but

  • Timed testing creates math anxiety that disproportionately affects the highest and lowest performing students
  • Math anxiety tends to persist and grow over time with repeated exposure to negative stimuli, leading to lasting consequences, including limitation of career options
  • Math anxiety actually has measurable neurological effects that inhibit the recall of known facts as well as the acquisition of new knowledge – that’s right, sending your kids to school can actually prevent them from learning and lead to lasting brain damage
  • Math anxiety causes emotional distress that can contribute to self-image issues that persist throughout adult life
  • Math anxiety is on the rise and is directly correlated with common public school teaching policies
  • Timed testing kills curiosity and enthusiasm and leads students to see math as a matter of performance and competition rather than as a fascinating subject with intrinsic value, which corresponds to am immense loss of value for society
  • Timed testing leads students to equate effectiveness and achievement with rapidity, which is so far from the truth it’s not even funny

This article just goes to highlight two things I have always said, that more fear = less learning, and that the public school system is accomplishing the exact opposite of what it should be doing, at an alarming rate. It just adds more evidence to the pile that for many students, school actually does more harm than good, and sane alternatives are needed, like, yesterday.

So what is the solution? The article and its references also highlight the positive changes that need to happen, specifically that learning needs to take place in an emotionally uplifting, stress-free environment that uses positive reinforcement and encourages exploration, imagination, and creativity, and that develops divergent thinking skills alongside convergent thinking skills.

For kids who are suffering under the yoke of public schooling, I always do my best to control and counteract the psychological damage caused by such practices as timed testing, and empower them to discover and use their innate mental superpowers.

Posted in Educational Reform, Math

Does Being Good At Math Make You “Smart”?

It continues to confound and amaze me how often I have the following type of exchange:

Person: “What do you do?”

Me: “I teach math.”

Person: “Oh my god, you must be so smart! I hated/was terrible at math!”

My experience learning and teaching math has shown me that not only is math just another subject that anyone who desires can learn and become skilled at, what’s more it is an innate human ability that everyone has, just like the ability to use language, recognize faces, run, swim, or climb trees. Along with math, all of these are activities that we recognize as skills that can be developed and improved, yet still innately human and instinctive for us as a species. All humans can do math, just like all birds can fly and all cats can hunt.

So, why is math considered to be a measure of “smartness” rather than an innate ability that anybody can develop? I speculate there are at least two factors feeding into the persistence of this pattern:

One is that the Newtonian-Cartesian scientific paradigm, which emphasizes the supremacy and superiority of rational, quantitative, and convergent modes of thought over and above the workings of insight, intuition, divergent thought, and artistic perception, has been supremely successful in the areas of science to which it readily applies, which has led to a kind of arrogant intellectual monism in which rational, linear, convergent thinking is seen as superior to nonrational, nonlinear, or divergent thinking.

The other is that math is generally taught in primary school in ways that are demonstrably inefficient and counterproductive, and that lead to disempowerment and sap intellectual curiosity, so only people with exceptional talent or exceptional immunity to cultural conditioning tend to thrive intellectually in such an environment. In an ideal learning environment, different people would pursue different subjects to different degrees determined by their interest and motivation, but nobody would come away with a phobia of any particular subject, or of learning in general, as is far too often the case in traditional public schools.  This is why much of the work I do as a tutor and academic coach consists of what is essentially PTSD rehabilitation therapy for math-related social anxiety.

Posted in Books, Educational Reform, Teaching & Learning, Tips for Students, Tips for Teachers

The Role of Neural Associations in Learning

Excerpted from Triggers, by Stanley Mann:

“Multisensory imagination is the world’s finest teaching machine, and we all possess it.  We simply need to learn how to use it.”

I just came across this great quote in a book I’m reading. The book is about using triggers, or neural associations, to direct one’s attention in constructive ways. The quote comes from a chapter on using triggers to enhance learning ability. It resonates with me on a number of levels.

First of all, the idea of multisensory imagination is a little-known but extremely powerful learning enhancement tool, and is the sort of thing that we should be teaching kids about in school instead of pumping them full of facts and figures. To truly learn anything you have to make it real in your mind, fully engaging with it in your imagination with as many sensory channels as possible; both sight and sound at the very least, and ideally touch, smell, and taste if possible. Conversely, teaching can’t work unless it engages the imagination and the emotions through multiple sensory channels. Educators and curriculum designers need to be mindful of this principle in order to be effective.

Secondly, triggers in general, and learning triggers in particular, rely on the principle of association. Our brains are constantly making associations among various environments, stimuli, and emotional states based on our experience. Neurons that fire together wire together, so when two experiences are repeatedly juxtaposed, they tend to become linked. This means that to optimize your learning process, you need to create a positive physical and mental learning environment for yourself, so that you are comfortable and feeling good while you are learning. Conversely, if the learning environment is physically or mentally uncomfortable, such as by feeling coercive and emotionally unsafe, then the negative feelings it evokes will come to be associated with the process of learning itself, causing them to be re-experienced whenever future learning endeavors are undertaken. This is another principle of human psychology that educators and legislators need to take heed of.

Posted in Educational Reform, Gamification, Inspiration

Gamification: The Coming Wave Of Education

Tech blogger and serial entrepreneur Peter Diamandis, famous for opening up the space frontier with the original Ansari X-Prize for commercialized spaceflight, recently wrote

“In the traditional education system, you start at an ‘A,’ and every time you get something wrong, your score gets lower and lower. At best it’s demotivating, and at worst it has nothing to do with the world you occupy as an adult. In the gaming world (e.g. Angry Birds), it’s just the opposite. You start with zero and every time you come up with something right, your score gets higher and higher.”

This quote gets to the heart of why I think gamification is the coming wave of education. Gamified learning is not only more relevant and efficient than traditional learning, it is inherently exciting and motivating. Long recognized as a powerful productivity tool in the business and sales realms, gamification is just now starting to make headway in education. One of the most popular language-learning apps, Duolingo, gamifies the process of learning a new language. Even more exciting, to my mind, is that what started as a commercial app like any other is now making its way into classrooms, helping to transform the school experience into something more fun and empowering.

The implications of this to me seem staggering. Imagine a world where “education” and “school” aren’t things that we have to make kids do, but that all kids want to do. Where there are no deadlines or barriers to learning anything, and any person of any age can begin to learn any subject at any time, as easily as getting addicted to the latest mobile game. How will this affect social mobility and intellectual freedom? How will it affect governments and corporations? How will it affect communities, families, and individuals? One thing I’m sure of is that I’m excited to see!

Posted in Educational Reform, Math, Teaching & Learning

The Moore Method

“I hear, I forget. I see, I remember. I do, I understand.” — Chinese proverb

The Moore Method is a little-known method for teaching advanced math that gets great results. In essence, it sacrifices breadth of coverage for depth of understanding, i.e. it prioritizes quality over quantity when it comes to learning a subject.

In essence the Moore Method works by having the students present the course content themselves. In higher math, the semester starts with a list of definitions and theorems to prove from them, with new theorems being introduced as students progress through the material. However, I believe that this approach could (and should) be adapted to other topics and levels of study and scaled up. This type of participatory/active, rather than receptive/passive, classroom experience is a fundamental feature of the educational revolution that is sweeping the planet.

“That student is taught the best who is told the least.” Robert Lee Moore, inventor of The Moore Method

Posted in Educational Reform, Tips for Students

Don’t Borrow Money For College

The college debt crisis is one of the greatest injustices in American history, ranking right up there with the Native American genocide, slavery, and the Vietnam war.  The best thing that you can do is refuse to participate, and stand up for your right to an education AND a livelihood by refusing to take loans for college.



FACT: The easy availability of college loans drives up tuition prices.

Just like housing bubbles are perennially fueled by decreasing federal interest rates, an increase in the availability of credit in any market drives prices up. Why are more students taking bigger loans to go to college? Because prices are increasing. Why are prices increasing? Because more students are taking bigger loans.

FACT: College cost increases have exceeded cost-of-living increases and median wage increases.

Why do colleges charge more for tuition? For the same reason that oil cartels continuously raise prices and gas stations gouge consumers at the pump. Because they can.


While college costs have gone up, value has decreased

A college degree is not a shoo-in for a job. At the same time that college costs have been skyrocketing, the number of jobs available has been shrinking, and the number of opportunities to create a rewarding career from scratch has been increasing. The go-to-college-get-a-job career plan isn’t the only game in town, even when it is possible.

Well-intentioned advice can still be misguided

Parents of high school age kids today grew up in a world where having a college degree meant having a better-than-average shot at a high-paying job, and not having one meant a lifetime toiling at a payscale tied to the minimum wage. Parents don’t always realize that times have changed, and may think that because going to college, and taking loans if necessary, made sense for them, it makes sense for their kids too. But the future does not equal the past.



Education should be a right, not a luxury. Education is the foundation of an economy, and the basis of the pursuit of happiness.

Make no mistake – debt is indentured servitude. It means that the money you earn does not belong to you. The looming college debt crisis threatens to create an entire generation of debt-locked peasants.



Let’s face it: the United States spends more money on weapons of mass destruction than any country in the world, and more money on surveiling and incarcerating its citizens than it does on educating and caring for them. Increasing militarization and decreasing education does not a recipe for a bright and prosperous future make.

If the United States wants to avoid obliterating itself back to the dark ages, it needs to recognize these truths as self-evident.

Beyond resisting the pressure to take college loans, what can you do? You can figure out how to pay for college without taking loans. Or, you can skip college altogether and get right down to creating the life of your dreams.

Posted in Educational Reform, Independent Education, Inspiration, Tips for Students

That’s Just The Way It Is…NOT, Part 3

So many aspects of our modern lives and the way society is structured are taken for granted, and we just assume things are the way they are because they have to be that way. This series of posts looks at a few of the hidden assumptions we commonly make about education.

You Have To Go To College If You Want A Good Job

This conventional wisdom of the baby boom era is erroneous in two ways:

1. It is no longer true that you have to go to college to get a “good job”


2. It is no longer true that you have to get a “good job” to have a successful, exciting, satisfying, or rewarding career.

“What do you want to do?” is no longer synonymous with “What job do you want to have?”, but can more and more be answered quite literally:

“I want to go on adventures”

“I want to write”

“I want to make art”

“I want to help people discover themselves”

“I want to photograph wildlife”

“I want to heal people”

“I want to make people laugh”

“I want to create companies”

“I want to teach”

Any of these or countless similar aspirations can indeed form the foundation of a successful career.  Just as the huge lumbering dinosaurs were replaced by small, nimble, and adaptable mammals as environmental conditions changed, the changing technological environment and the resultant diffusion of the means of economic productivity is causing the huge, monolithic organization to become extinct, quickly to be replaced by tiny start-ups and independent solo operators.

These days you can be a freelance just-about-anything, and the opportunities to create a totally new career from scratch are only limited by the restrictions on the human imagination.  From 16-year-old sailors circumnavigating the globe, to 17-year-old nuclear physicists, to whole families bicycling around the world, more and more lifestyle pioneers are showing us all that life can be about so much more than getting a “good job” – if you want it to be.