Why Bill Gates Loves Sal Khan….

Posted on July 27, 2012 by rmberkman

If you’ve been reading all the hoopla and criticisms of Khan Academy, you’ll know that Bill Gates referred to Khan as “the best teacher he’s ever seen.” This quote can be interpreted a couple of ways. Perhaps, it is a “dis” on the teaching he experienced at the prestigious Lakeside School in Seattle as a teenager. At the same time, we should remember that Gates did drop out of Harvard during his sophomore year, so perhaps he was not working with a very large sample size. In my view, Gates’ admiration for Khan can be understood by understanding their similarities.

  • The Hobbyist As Professional: Both Gates and Khan started out as amateurs who were hacking around in their respective fields. When Gates started out playing with a computer bought by funds from his private school’s “Mothers Club,” he had little idea that this might turn into a profession, and to this day, almost all his knowledge is self-taught. Similarly, Sal Kahn never imagined his videos would become a worldwide phenomena; his understanding of teaching is based on his own experiences, with almost no attention paid to what is going on in the actual profession of education.
  • Quantity, Quantity, Quantity: As any user of Microsoft’s products knows, Gates’ products have a tendency to skew towards the side of “feature bloat.” That is, a word processor is more than just a word processor: the current version of Word does everything from twisting type in all sorts of amateurish ways to reprogramming your toaster oven to poach an egg (okay, maybe not….) Similarly, Khan Academy offers over 3,000 videos which cover everything from how to multiply positive and negative numbers to the causes of the French Revolution. This is reminiscent of the Woody Allen joke about two Jewish women discussing the food at their Catskill resort: “Oh, the food here is so bad…” “Yes, and the portions are so small!” Sure, Word is a terrible word processor, and Khan Academy is boring and full of errors: but look at how much you get for your money!
  • Lack of Elegance: The most prominent feature that both Gates and Khan share is the utter lack of interest in any kind of design appeal in their respective products. Anybody who has worked with both Windows and Macintosh agree that there is no comparison: Apple pays almost manic attention to even the finest details of the interface, from the fonts used in the file names to the organization of its icons. Windows, by comparison, is a melange of garish colors and hideous fonts that does nothing more than reinforce the notion that computer programmers are immune to something known as “esthetics.” Khan’s videos make Windows look like the work of the Frank Lloyd Wright: the narration is halting, filled with “ums” and “ahs,” which disrupt the coherence of thought. His handwriting is barely legible, and what he writes is often disorganized and incoherent. Nobody will ever confuse a Khan lesson with the one that was crafted especially for him at this 2011 TED presentation.
  • Lack of Originality: We all know that Gates’s flagship product, Windows, was a blatant ripoff of Apple’s Macintosh operating system ( and whether Apples GUI was original is a subject of dispute, but let’s not get into that.) Khan is in the same boat: he is not the first to put lessons on the web; ever since the debut of YouTube, anybody with a video camera and an internet connection has been able to put up a “how to” video on the web, whether it is tuning a bassoon to brushing your dog’s teeth. There is nothing “innovative” about what Khan has done; Marc Chagall was innovative, and Sal Khan is no Marc Chagall.
  • Reliance on Brute Force: In the same way that Windows become the dominant operating system by loading it onto any computer which had a hard drive capacious enough to withstand the bloat, so has Khan become the leader in online education by creating thousands of low-quality videos on things about which he has not much more than a glancing knowledge. Khan has triumphed by taking meaty subjects like mathematics and chopping up into tasteless nuggets that are easy to eat but ultimately have no intellectually nutritive value.
  • Reinforcing Stale Paradigms: Both Gates and Khan share the distinction of reinforcers of current paradigms. Gates’ business model forced users to buy into his vision of what computing should be; that is, it came from a centralized power who called the shots about how a computer should look and feel. Khan also buys into an old paradigm, one of teaching as emanating from a central authority: his videos tell you what to think and do, without demanding that you actually question why things are the way they are. This critique of Khan’s lesson on multiplying and dividing positive and negative numbers is a devastating dissection of Khan’s tired old methodology.

In summary, it’s not hard to see why Bill Gates and Sal Khan are a match made in heaven; with Microsoft quietly slipping into irrelevance after 25 years, people who have actual concerns about the state of education in the United States can only hope that the Khan Academy fad will have a much shorter half-life. Of course, it will then be time for yet another educational fad.

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“You’re too young to be bad at this….”

Posted on May 17, 2012 by rmberkman

A teacher asked me to bring pentominoes to her class, for they were reading a book that involved a character who walked around with pentominoes in his pocket. As one of the students was working on arranging the 12 pentominoes into the shape of a rectangle, he sighed under his breath and commented, “man, I really stink at this….”

Whenever students tell me they are not good at something, I immediately remind them that while a lot of mathematics is tricky and challenging, it can also be mastered through practice. This has led me to change my language: I never tell them they don’t understand something; it is always, “you don’t understand this yet.” I find the power of “yet” to be immediate and optimistic: it conveys the idea that they will eventually understand, and just because it is not immediate does not mean it will never arrive.

To this student, I replied, “You just started working on this like, what, 5 minutes ago? How can you tell whether you’re no good at this?”

The student shook his shoulders, and his frustration continued.

“I am really no good at this!” he complained.

“You can’t tell yet whether you’re not good at this. Give it a lot more time.”

“How long?”

“Well, to really know if you’re not good at something takes a long time. Usually 10 or 20 years…”

“What? How can that be?”

“Because, the real test of whether you’re no good at something is to work at it for years and years and to see no improvement. That’s the only way to know that you’re no good at something.”

“So…?”

“Basically, you’re too young to stink at something. You’ll need to spend a lot more time on this to really know if you’re no good at it.”

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Math, Art, West Coast: Brilliant!

Posted on March 27, 2012 by rmberkman

During my travels, I love to take in the local art scene (no matter if it isn’t quite local….) Many people ask why art, if my work is in mathematics. Well, the truth is that before I was in mathematics, I was in visual arts: I was trained as a calligrapher, studied photography, printmaking, filmmaking, industrial arts and, to round it all out, mechanical drawing and architecture. With this kind of background, I developed all kinds of mathematical expertise, including an intuitive understanding of ratio and proportion from mixing chemicals in my darkroom and enlarging photos. I learned to measure precisely as well as how to work in scale through my years of mechanical drawing and architecture, and developed an eye for expressing mathematical relationships through my work in graphic design.

Here’s one of the examples of “art & math” I saw during my travels:

Where's the art?

This is a piece by Bonnie Bronson entitled JAS #1. it’s a trio of metal plates attached to the wall. To me, it is a intricate juxtaposition of shape and space, which is what a lot of these artists are dong in their work.

Here are a few things I want to point out as you look at this:

  • Where do you “begin” looking at this? Does it “read” from right to left, left to right, front to back or back to front? Should we look a the largest object first and then move to the smaller ones?
  • Is there a predominant “shape?” How do the shapes “fit” together? They all seem to share a common height (the trapezoid in the front may be taller, or is that a trick of perspective?), and the back trapezoid seems to be the same as the one in the front, save it has been “complete” on the right side. Or is the smaller trapezoid a truncated version of the one in the back?
  • The rhombus which separates the two shapes does so in many ways: besides separating them by space horizontally, it also creates a layer between them. Why is Kelly keeping the two related shapes away from one another?
  • The smaller trapezoid has another function, besides being a part of the larger one; it also splits up the rhombus behind it, yet also completes it as rough approximation of the trapezoid that is on the end. What kinds of tricks is Kelly playing with us? And what about that trapezoid on the viewer’s right: it is partially obstructed by that rhombus. Is the rest of it there, or not? We assume these shapes are “filled,” but are they really?

So, what do you think? Is it just a couple of plates screwed into the wall, or is there really an “art” behind that “art?”

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Math Anxiety in Seattle

Posted on March 21, 2012 by rmberkman

I’m back in Seattle for year 3 of my annual West Coast tour, which consists of visiting my sister and her brood in Seattle, and giving a workshop at Pacific Science Center (note there is no “The” at the beginning of the label, which I find kind of odd.) Last year my “tour” was Seattle & Portland for the workshop “Wiring the Brain for Mathematics: Neuroscience & Numeracy,” and I so much positive feedback that I thought I should surely return with a workshop on Math Anxiety, which is a kind of sequel, in that it focuses squarely on the connections between math and the emotions. As I stated in the workshop, mathematics is the most emotional subject taught in school, because it is the one that makes us question our “intelligence” each day.

There was a smaller group this year, about 30 teachers from as far away as Orcas Island and Bridgeport, out on the Eastern Plains; many of them were veterans of the “Wiring the Brain” workshop in 2010 and ’11, so it was comforting to see some familiar faces.

Highlights of Seattle’s “Math Anxiety” Workshop

Of course, the wonderful energy, humor and thoughtfulness that the participants bring. I was really taken by the kindess and respect shown to one of our members who had a hearing deficit and asked people to stand while asking questions and adding comments.

At one point during the workshop, we discussed the idea of math having lots of “rules,” and I brought up the change I made to my practice recently to eliminate the use of the word “rule” when describing a process in mathematics. I asked why I would eschew the term “rule” in mathematics, and we discussed the idea that rules often seem authoritarian and arbitrary, as well as emanating from a “higher power.” Instead I suggested that we use the word “property” in place, in order to emphasize that mathematics is a system, and that as this system developed, it was found to have certain characteristics that are known as “properties.” For example, the number 6 has certain properties: it is even, it is divisible by 1, 2 and 3, and it is the first perfect square number.

During lunch I happened to sit with Cheryl for a bit, and we examined  some of her students’ papers and discussed the idea of how her third graders understood the process of creating equivalent fractions through the use of a “rule.” Clearly, the word “property” would not be a good term to replace this; we agreed that thinking about this as a “method” would be more appropriate, in the same way we would teach any other process, like baking a cherry pie or cleaning a bassoon.

All of which brings to mind a way to sum up this idea of replacing authoritarian language with more descriptive language: There are no “rules” in mathematics: there are properties and methods. Perhaps we need to put this idea front and center by titling our courses and textbooks that way:  Mathematics: Properties & Methods.”

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Cheap Ways To Improve Girls’ Achievement in Mathematics

Posted on April 22, 2011 by rmberkman

New readers will see that out of my first 3 posts, 2 of them have been harrangues about the current state of mathematics education, where people will flail around for anything ANYTHING to improve their child’s improvement. I’m a research kinda guy, which is why these programs drive me crazy: there’s either no research to back up their long-term effectiveness (and two to take him) or the research itself is rather suspect (Even The Times Can’t Get The Math Right.) So let’s look at the opposite side of the coin: what research is both provocative, relevant and useful, and has been conducted by a company that is not going to benefit from the results.

Slate, an online magazine, published a wonderful summary of research called “An Easy Way to Boost Women’s Score’s in Physics,” which would seem to apply to mathematics at well. Researchers at the University of Colorado (who have no way to benefit monetarily from the results, a sure sign that this will be unbiased), asked female undergraduates enrolled in physics classes to undertake a 15 minute writing exercise about things that mattered most to them, first at the beginning of the semester, then just before the mid-term exam. Women who underwent this task averaged a B in class, while those who wrote about what mattered to them least averaged a grade of C. There were no changes for women who averaged an “A”, or for men.

The authors of the study were interested in something called “stereotype threat,” that is, the concept that members of an underperforming group can be influenced by biases against them. This has also been demonstrated on women’s performance on math tests back in, are you ready for it, 1999! So, if we’ve known about this for over a decade, how come the research hasn’t been put into action?

I see three reasons for the failure of putting the results of these studies into action. The first is, the studies seem to fly in the face of common sense. Both of these studies identify psychological reasons for the underperformance of women in the sciences, and if there’s anything people distrust, it is psychological research, no matter how rigorously it is performed. Perhaps it has to do with the fact that we associate psychology with someone sitting on a couch in a room complaining about his/her mother. The fact is, psychology is a rigorous science that relies on the same tools as physics, biology and chemistry; the only difference is the research subjects. A wonderful book that demystifies psychology can be picked up for a penny on Amazon: it’s called “How to Think Straight About Psychology” and it truly will.

The second reason I think that these results have not been implemented is that they don’t seem to be related to the actual teaching of mathematics. That is, many teachers, especially in high school and college, are not interested in the actual “craft’ of teaching. There was a saying I remember from my early days in the classroom: in the elementary school, teachers teach students; in the high school, teachers teach subjects. The focus of improving teaching seems to rely on changing the tools and curriculum, without changing the actual environment in the classroom. Joe Boaler wrote a wonderful book on this subject entitled “What’s Math Got To Do With It?” in which she implemented a math curriculum that radically re-designed the classroom environment. Instead of sitting in a seat following instructions by the teacher, students were given difficult problems to solve and were free to create techniques that would develop their mathematical reasoning. The results were compelling: the students not only performed better in mathematics, but also fully intended to continue their studies of “maths” through college.

The final reason that these findings don’t get implemented has to do with economics: they don’t cost anything! If you’ll compare them to other “solutions,” you’ll see that these findings are very cheap to implement. Unfortunately, our society only values those things which have a price on them, so we feel compelled to purchase new textbooks, more computers, “improved” curricula and all sorts of colorful manipulatives, most of which are untested or of dubious value. Nobody stands to profit from asking girls to write about what matters to them; you can’t shrink-wrap and market techniques for reducing stereotype threat, so there’s little interest in “buy in.”

It’s unfortunate that there is so much good research out there on “what works,” and so little of it actually makes it into the classroom. It’s very reminiscent of the old joke about the man who lost his keys and looks under and streetlamp in a different location, even though his keys are a block away. “Oh, I know they’re not here, but the light is so much better!” he informs us. Sure, it looks good every time we adopt a “new and improved’ curriculum, but is that really where the lost keys to better mathematics education can be found?

Have a good piece of research that can be implemented in your classroom? Why not share it with the community; post it below, or email it to me and I’ll write about it!

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Even the Times can’t get the math right….

Posted on April 20, 2011 by rmberkman

You can bet that whenever there is a slow news week, an article will turn up in the New York Times on some new educational “breakthrough” that will finally help all children learn math. This week’s entry into the “miraculous math” derby is…. drumroll please! A Better Way to Teach Math by David Bornstein.  It alway helps to look at the credentials of the author of an article like this: Bornstein is one of the Times third-string writers: he covers everything from health care to bullying to how you can turn your rice husks into electrical power. Here he wears the hat of an expert on mathematics education.

Anybody who has seen the materials published by JumpMath will not see anything unfamiliar: it’s the same tired old stuff, repackaged into teenie-tiny units that are easily taught by teachers, and quickly and forgettably digested by curious children. You can download the fraction materials and see that there is nothing magical to this method: it uses the same models we’ve all seen before, including the ubiquitous pie divided into equal pieces. It re-hashes the same old rule-based procedural drill & kills, and carries on the passive math tradition that has not led to widespread numeracy since it was introduced a century ago. So why is it “working?”

There are several explanations for the so-called “improvements” that children make using JumpMath, which goes back to the old adage, “correlation does not imply causation.” The first is that any program which has a reputation that precede itself suffers from something called the “Hawthorne Effect.” That is, the program worked because the teachers were told it would work, and the children were no doubt aware that they were doing something that is supposed to be “different,” so they just worked harder. In essence, it wasn’t the program itself that caused the jump in improvement; it was the fact that the class was using any new program. A one year jump in test scores is not a “trend” by any means, just like a one day jump in the stock market is not a rally.

Second, this program requires teachers to undergo quite a bit of training to implement. They have to read the materials carefully, and no doubt undergo hours of outside training to implement it properly. If these teachers are getting ongoing support to make this program work, then the success of the program is more than likely due to the teachers getting support. Again, any program whose implementation includes extensive teacher training is bound to improve scores in the short run.

Finally, the study does not take into account any of the confounding variables. Perhaps this program requires more time on instruction in school? Maybe  the homework assignments require longer periods of time than the old program? If a teacher spent 2 hours per week on math suddenly spent twice that amount of time on instruction, we should expect to see scores rise. The same is true of homework: perhaps this program demands more time, so that instead of doing 20 minutes of homework each night, students are doing more like 40 minutes or more? Thus, it wasn’t the methodology of the program or the uniqueness of the materials, it was merely students spending more time on instruction and practice.

Now, there is no doubt that some of the things mentioned in the article are true: math anxiety is truly an issue that holds children back from high levels of achievement, and practice definitely boosts performance. Having teachers who are more confident of their mathematics ability will certainly help the students with whom they work. But is this curriculum in and of itself a miracle? Sadly, no, because those of us who have been involved in math education know the simple truth: there is no such thing as a “miracle curriculum.”. Teachers teach students, not curriculum; a great teacher can easily overcome a lousy curriculum, and a lousy teacher can easily foul up a brilliant curriculum.

So let’s just get a grip. Oh, and let’s see how many days it will be before the Times runs yet another “math miracle” article.

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What Would Mario Say?

Posted on April 18, 2011 by rmberkman

Mario Salvadori: 1907 – 1997

The late Mario Salvadori was an engineer, educator, and (I use this word rarely) visionary, who lived what most of us would consider a very colorful life: born in Rome, Italy, Salvadori earned doctoral degrees in civil engineering and mathematics, and served as an instructor at the University of Rome. A critic of Benito Mussolini, he followed the recommendation of his friend and teacher, Enrico Fermi, emigrating to the United States around 1938.

Salvadori worked for the Lionel Train Company until 1940, and then, unbeknownst to himself, became a consultant on the Manhattan Project. After WW II, he took up teaching at Columbia University, where he became a professor at the School of Architecture, Planning and Preservation. Nearing retirement, Mario turned his attention to working with underprivileged youth in under-served schools in New York City. He created a hands-on curriculum to teach children about engineering and architecture, and was an inspiration to teachers (including myself) for many years. I first met Dr Salvadori at a workshop he gave at Brooklyn College in 1988 where he discussed the principles of structural engineering and its applications to mathematics.

I later hired Mario to give a presentation to parents and children at a full-day math and science event I organized at the Bank Street College of Education in 1991. My fondest memory was discussing the workshop with Mario on the phone, when he inquired how many people might be in attendance. When I said there would probably be about 15 parent-child dyads, he asked, “oh, so few? Why can’t we have more?” I eventually arranged for him and his crew to use a space that accommodated over 60 people.

While perusing back issues of Harper’s Magazine, I discovered a charming article which Salvadori authored on the state of mathematics education in the United States.   The article, entitled “Math’s a Pleasure,” described Salvadori’s own unhappy memories of learning mathematics, the boredom and frustration he felt throughout his education, and how the current state of mathematics education drives out curiosity and excitement. What is most fascinating about this article is that it was not published in the 60’s, 70’s, 80’s or 90’s, but back in 1958. To read it more than a half-century later is to experience, as Yogi Berra would describe it, “deja vu all over again.”

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….and two to take him.

Posted on April 14, 2011 by rmberkman

Wasn’t it P.T. Barnum who stated that there was a sucker born every minute, and two to part him with his money? The latest iteration of this comes from Body & Mind Builders, a company in Manhattan that provides yoga, pilates and music programs to adults and children. Somehow these well meaning folks got hoodwinked by an outfit called “Abacus After School.” Kudos to whomever is behind this for merging every buzzword and cultural stereotype we associate with high achievement in mathematics: it’s old, it’s Asian, it’s multi-cultural, it’s multi-sensory. While I don’t doubt that using an abacus is fun and somewhat useful in teaching children about base 10 thinking, the notion that a parent should subject their child to hundreds of hours of instruction (and thousands of dollars in payments) in the hopes of transforming their child into a calculating powerhouse is just a little bit, how should we say, “19th century?” Once we again we get embroiled in the old misconception that confounds calculating with mathematics. Once again we are frightened into believing that there are hordes of Asian kiddies pushing themselves ahead of our bonehead sons and daughters, leaving us at the bottom of the mathematical barrel. Once again we are left with the impression that a typical Japanese kid spends his time in a stuffy classroom moving beads along metal rods back and forth (or, even more embarrassingly, spasmodically tapping his fingers on a table) calculating America’s interest on its debt payments to China, while our children loaf around at home playing video games and eating fatty foods. Very impressive stuff indeed.

So let’s be a little realistic here: the only people who benefit from teaching children how to use an abacus are the people who build, market and sell them. What this video proves is that Japanese parents suffer from the same math anxiety as their American counterparts and are foolish enough to send their children to a program that has no known educational benefits (other than making for excellent YouTube footage.)

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