Why Nate Silver Can Save Math Education in America

| December 14, 2012 | 44 Comments
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Ian Hill/Thinkstock/Penguin

By Nikhil Goyal

Call it “The Triumph of Nerds.” Poll statisticians have risen to rock star status. One of the most famous is New York Times’ wunderkind Nate Silver — or as Jon Stewart put it, “Lord and god of the algorithm.” He may be best known for predicting the 44th president, but Silver could be the one man who can save mathematics education in America.

Silver, who first gained notoriety for forecasting the performance of Major League Baseball players and for correctly predicted the winner of 49 of 50 states in the 2008 election, can save the tattered reputation of math subjects.

For students across the country, there’s clearly an engagement deficit in the subject. Paul Lockhart, a math teacher in New York, writes in A Mathematician’s Lament [PDF] that if he had to design a system for the express purpose of destroying a child’s natural curiosity and love of pattern-making, he couldn’t possible do a better job than is currently being done. He explains that he simply wouldn’t have the “imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.”

He has the potential to telegraph an important message to kids: It’s O.K. to be a math nerd.

Across the land, kids hate math. You can hear it in their constant groans and see it in their deranged faces. They ask their teachers, “When am I ever going to use this in life?” On most occasions, they never will. Even President Obama agrees. He recently said on the Tonight Show, “The math stuff I was fine with until seventh grade. Malia is now a freshmen in high school and I’m pretty lost. It’s tough.” And no wonder — the system is suffering from a tragic case of nostalgia. The origins of the current curriculum draw back to 1892 when the Committee of Ten hashed out a standard curriculum, which would eventually be adopted almost unanimously by schools.

As a result, the potential to love and embrace math is being squandered — perhaps even the future of potential Nate Silvers and Nobel Laureates. As students progress from grade to grade, many start losing interest in math.

There are lots of reasons for this. In the current system, students’ confidence in their math abilities becomes undermined, according to a Duke University study. Math is taught as computation rather than a means of exploration and discovery. Instead of engaging in meaningful problems and learning in depth rather than breadth, kids are assigned frivolous, repetitive problems. And finally, the way math is generally taught has no relevance to real life. School has become a practice of learning tricks for the test one week and forgetting the next. In elementary schools, kids come to understand that they’re expected to follow directions, fill out worksheets, and master a set of concepts.

Our process of transferring from subject to subject in math is also broken. The curriculum pyramid is founded on arithmetic and algebra, all building up to one subject — at the top of the pyramid is calculus. While mathematicians, engineers, physicists, and particular scientists use calculus in meaningful ways, in their day-to-day lives, most people do not. Ironically, M.I.T. graduates, who are trained in science and mathematics, said in a survey regarding their daily use of math that most use nothing more than arithmetic, statistics, and probability.

Sol Garfunkel and David Mumford in a New York Times Op-Ed summed it up nicely: “Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering. In the data course, students would gather their own data sets and learn how, in fields as diverse as sports and medicine, larger samples give better estimates of averages.” Clifford Konold, a professor at the University of Massachusetts, counted data displays in The New York Times and found that in 1972, there were four graphs or tables in 10 consecutive weekday editions, excluding the sports and business sections. There were eight in 1982 and 44 in 1992. Next year, he could find more than 100. His conclusion: statistical reasoning is an indispensable skill.

Fortunately, many universities are scrambling to teach statistics and probability, especially through sports. In one class at James Madison University, students used the example of Steve Nash of the Phoenix Suns and free throws to learn the probability of coin tosses. Last year’s hit film Moneyball popularized the power of probability from predicting division standings to on-base percentages.

Just weeks after the election, Nate Silver’s Triumph of the Nerds, his renowned legacy and dedication to numbers, has the potential to telegraph an important message to kids: It’s O.K. to be a math nerd. Numbers can actually mean something in the grand scheme of things. We need more people who can number crunch and predict and prize math.

If parents and teachers use Silver’s groundbreaking work to talk to young people about civics, polls, statistics, and numbers, the power and beauty of mathematics, kids can experience this fascinating subject could be experienced in a whole new way.

Nikhil Goyal is a senior at Syosset High School in Woodbury, New York, and the author of One Size Does Not Fit All: A Student’s Assessment of School.

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  • OlympusMath

    Great article. Nate makes all of us math nerds proud.

    So our viewpoint is that children get dejected when they are never really taught math fundamentals. They’re advanced in classes without being proficient. Some kids might understand one concept versus another but the teacher is responsible for the other 20+ kids staying on pace. Personalization is the key to education.

    If companies like Amazon/Netflix are so good are personalizing our experience online why can’t education do the same?

    We’re doing that for math! We are able to tailor curriculum to each student. Adaptive Math is the way to go. We’ve worked with over 10K students grade 6-12 who have had marked improvement.

    http://olympusmath.com

  • quintopia

    I don’t get why the blackboard contains mostly physical laws, but this article says nothing about physics classes…

    • SecularPatriot

      Blackboard stock photo.

      • Mike Darin

        It must be, but whoever wrote it screwed up the Pythagorean theorem. yeesh.

        • qpwoe

          Are you referring to the a^2 = b^2 + c^2? It’s still the Pythagorean theorem. Just swap ‘a’ and ‘c’, which you can do because they are variable names. Once real-life data are input, the names of the variables are unimportant.

          So, this unconventional rendition of the equation may have been an oversight; or, it may have been quite brilliant, given the article’s content.

  • Deb Carr

    Where are the jobs for mathematicians? My son has a BS in physics and math from a big ten university and is struggling to find a job. People ask him if he plans to teach. Until there is a known career path for math majors students will not see the value in studying math and science.

    • OkayThen

      This. If we really want more scientists and mathematicians, why have salaries been stagnant or declining?

      • IanDakar

        They haven’t for higher end salaries, just lower end ones that don’t need science/math.

        Trick is that majors that require math, like computer science, have more practical elements than theory subjects. It’s the difference between someone who paints using colors and someone who wants to study colors themselves.

    • IanDakar

      The issue is that there’s a difference between a major that uses a concept, and studying the concept itself.

      High concept majors are used to study and dive deeper into the subject so that the more practical majors can use it to better their fields. For example, your son’s Math major would have him studying on theories that will eventually be used by Accountants. Consider such subjects “research and development”.

      Thus the places he’ll be wanted in are areas that aren’t producing items, but are researching. Companies getting into aerospace may want physics majors in their R&D. Colleges will tend to have math majors as, not only do they teach, but they also are the R&Ds for math, especially since they can quickly fold into the lessons for those accountants and financial majors.

      Now if your son wanted a more typical career path, then he needed a practical major rather than a high concept one. You don’t take a math major to learn accounting, you take an accounting major. Accountants don’t research no theories on math: they take the theories made by Math majors in research centers and colleges and apply them into their jobs.

  • Jason Osborne

    Excellent point about the formulas on the photo of the blackboard in the article. I noticed the same myself. Just on a quick glance at the board shown in the article and off of the top of my head

    *T= period formula for a mass (m) on a spring of stiffness (k),
    *e_c= kinetic energy of point mass (m) with velocity (v),
    * F_n=centrifugal force of mass particle m traveling in a circle of radius (r) with velocity (v),
    * v_f=an unfinished formula for final velocity given initial velocity v_0+ a*t where a is acceleration (units perhaps m/s^2),
    * L=circumference of circle=2*Pi * radius of circle (r).

    Where are the formulas for

    *for a gaussian function 1/2sigma^{2}exp(-(x-mu)^2) (the bread and butter and foundation of statistics and probability)?
    *or the formulas (Partial Differential Equation, PDE) for the Black-Scholes pricing model for options (Finance) an equation related to the Heat-Equation from physics?,
    *or at least a small data set for goodness sake?

    Oh yeah…right (insert sarcasm for those that, like me, sometime fail to recognize it) those ideas/equations/data sets above take algebra (and eventually linear algebra) to deal with and understand, and of course calculus (how can you study a PDE, like those from finance, without derivatives (calculus), not to mention geometry (there are three formulas, at least, on the board related to circles.

    Of course, I agree that physics/engineering will be helpful for students. The practical question to me is “when and how”. These are long and difficult conversation those of us in education (and parents and students) need to be having.

    As a step 0, I would opt for giving teachers more flexibility to teach those subjects they are passionate about. Let the teachers be excited about their subjects and that enthusiasm should transfer to the students. This is the main theme in the comments I receive from my own college students, “you seem excited so I get excited”. But by the time students get to college the “I hate math” damage has been done (for 12yrs) and may not be reversible in 4-5 yrs. I suppose all of us in education will try nonetheless.

    But please, everyone try to realize the interconnectedness of all the ideas being discussed. Math is presented today as a series of known facts that need to be memorized and plugged through and into to get a final answer. This was not the way many branches of mathematics developed. I am no math historian, but I know enough to know that scientists of all stripes needed to invent mathematical tools to help them solve the problems/phenomenon that captured their interest (Google/Wikipedia Gauss, Bernoulli, Newton, Rayleigh, Ritz, Lagrange, Poincare, Maxwell, Einstein, and countless others of course not mentioned, see the biographies of many, many scientists, physicists, and mathematicians at http://www-history.mcs.st-and.ac.uk/BiogIndex.html)

    Best,

    Jason Osborne
    Professor of Mathematics at Boston University

    • VasyaPupkinsan

      “Let the teachers be excited about their subjects and that enthusiasm should transfer to the students.”

      Then it will become a problem for faculties to “excite” teachers. Start at the beginning – dumb parents demonstrate by example “real life” to their kids.
      Instead kids must be taugh by stick at schools rather than by carrot.
      Society is flawed, evolves back to stupid monkeys.. with all the “technology”.

      • IndeedNot

        If an art teacher were not interested and excited by the wonders that have been created over human history, would you hire them? The only reason that “exciting teachers” would be a problem is that math education has been in such a sorry state for so long

  • Plebus

    I believe much of the hatred for math exists in the way it is currently taught (no disrespect meant towards math teachers–they have my sympathies).

    Mathematics is currently taught in the same fashion that one teaches English Grammar. Students are frequently taught to memorize forms, not reasonable explanations. Example: every student is taught the f(x)= form in basic algebra without understanding why it is put that way. Further, mathematical concepts are frequently glossed-over in many textbooks and lessons with many students being given the explanation, “just do it this way, you will figure out later why.”

    Mathematics needs to be taught more for what it is: a language. It is a very precise technical language. Understanding it requires using it–even using it wrongly as children wrongly use words/phrases, and then being shown how to correctly use those words and phrases. Instead, in the current method students are often given math exercises but are not taught to play with mathematical concepts. Emphasis is placed on memorization and calculation, rather than conceptual play, understanding, and applied problem solving using mathematics.

    This is why most people first learn to love mathematics when they have their first physics class. Applying the concepts makes all the difference in the world.

    • IanDakar

      funny thing about your example of f(x)=form, I had a teacher that did offer the explanation.

      I remember looking at X +1 = 6 and wondering ‘what’s Y, what’s X.. why Y and not Z or T?” It wasn’t explained in high school. In college though, I had a teacher who said basically:

      X is just there to stand in place for something. The fact that it’s ‘X’ doesn’t matter. It just means ‘the number we don’t know’. I could say “dumptruck’ and it means the same thing.

      She then spent the rest of the day doing just that. Dumptruck + 5 = 9. Dumptruck +4 = Dumptruck – 4

      The rest was just branching from there. X is always the same number. If the problem has two different numbers, we use another letter.. Y typically. That we ‘solve for Y’ is just us being unimaginative. We could ‘solve for firetruck’. but we’re boring so we use the letter X, and we tend to put Y for the number we want to learn. Don’t remember how f(x) was taught but I learned it as a very fancy version of Y with a touch more meaning.

      I had a similar experience far earlier with learning multiplication, using egg cartons to show what multiplying actually does. Division then became “subtract is reverse add, divide is reverse multiply”

      Just an example that, sometimes, just explaining WHY you do it is enough to keep interest.

  • gmh

    Even mathematics professors argue about this. Jo Boaler’s book “What’s Math Got To Do With It?: Helping children learn to love their least favorite subject – and why it’s important for America” caused quite a stir. She was bullied while at Stanford by other staff for proposing what’s at the core of this article.

  • hbar

    So, the author argues that the problem is with the fundamentals of the system which apparently worked pretty well for over a century without adverse effect to society. It seems to me that what has changed is not those fundamentals’ ability to “destroy a child’s natural curiosity and love of pattern-making”, but rather the children, their parents, and teachers.

    I would submit that the very idea that ‘everything one learns has to have a direct practical application later in life’ is far more related to the above mentioned destruction. With such attitude why would anybody explore anything that doesn’t translate into a job or money making advantage in an obvious manner?

    From what I have seen from the students at a top tier university, their main problem is not the lack of math skills (those can be gained), it is attitude. They do not want to ‘waste their time’ with thinking or understanding concepts. They want A+ so that they can get into med school, and their main interest is what would be on the test. Interestingly enough even when I’ve solved for them in class the exact same problem that is later showing up on the test (just slight variation of the numbers) they still fail.

    • Mike Darin

      “Math is taught as computation rather than a means of exploration and
      discovery…Instead of engaging in meaningful problems and learning in
      depth rather than breadth…School has become a practice of learning
      tricks for the test one week and forgetting the next.”

      hbar- It’s no surprise students aren’t engaged by math the way it’s taught
      today, since no student wants to be a machine when they grow up. I agree with your point about attitudes and that students are typically only concerned with a letter grade, but the more fundamental problem is that math courses are not designed to inspire a transformation of those ‘attitudes’. The author argues that an overhaul of the curriculum to make the subject more relevant and applied would reveal the incredible ways in which math is intricately woven into the fabric of our daily experience, and cause more to embrace math rather than ‘just get through it’.

      • hbar

        I understand that point, but I have not seen any evidence that it works. For example when we teach electrostatics to pre-meds we look at a simple model of a neuron – does not shift their interest from ‘would it be on the test?’ to ‘is this how it really works?’. The situation is the same with engineers, or with humanities where we look at say paramagnetic resonance and dating archeological artifacts.

        Usually, once a semester I tempt my students with a very practical problem which involves the concepts they are supposed to understand and a little bit of thinking, but it is not in any textbook. It is a ‘bonus problem’ on a quiz and if they solve it they get A+ no matter what. For example if it is engineering students and they are learning the Ohm’s law and power dissipation, I may propose the burning out of an incandescent bulb with a varying thickness of the wire and ask in which section will it ‘burn’.

        So far nobody has managed to make any progress on these problems. And this is at a top Ivy League school, at least 20% of the class is bright enough to do it, if they look at the world differently.

        May be, as prof. Osborne posted, by the time they are in college the damage is already too big to undo.

        However, this being said, I think the outreach programs that most universities have are generally quite successful at generating interest in science.

        Many of the best scientists I know look at their job as basically toys for grown-ups (including the math part). Exposing children to this kind of attitude seems like a good way to stimulate their curiosity.

        • Patrick

          The way to enliven these kids’ interest in mathematics is to throw away the textbook and merely focus on problem solving. Give them a problem and the resources to solve it and let them connect the dots.

          Computer based math emphasizes concepts instead of calculation. For most people, the rigorous method of proofing something isn’t feasible if we want children to be interested in mathematics. For this reason I think we need to use computers more in doing mathematics so that children can learn the concepts rather than the routines.
          http://www.computerbasedmath.org/

        • IanDakar

          Once interest in a concept is raised then it is perfect time to ‘break it down to basics. I suggest that higher education students have already demonstrated that interest by not only choosing that voluntary extra education but also by choosing your subject (even if it’s a disliked subject, they chose the Major and, at worst, are willing to accept that they need the subject for what they want to do)

          That interest isn’t there yet in K-12. As such, ‘break it down’ may help them learn, but it won’t help them want to learn, and once they stop wanting to learn, everything else is a waste of time.

          When students see that 50 set of multiplication problems, for the third time this week, they need to feel a desire to want to do it, that they need this in order to obtain what they desire (and it has to be more than just ‘a good grade’). Schools, at least at my time, never supplied that.

          You said that the old system worked in the past. The past, however, never demanded that students learned much more than arithmetic for their daily lives. Higher order math and science could safely be reserved for ‘elites’ in particular high demand fields while the rest stuck to work that had low math/science demands.

          The system worked for the demands of the time. The demands have changed and,as it has shown, the system can’t adapt for the new requirements. The issue is mostly at the K-12 level. Colleges don’t have so much of this issue (which helps explain why those in other countries come here to learn) but, as you say, the damage is done.

  • http://www.facebook.com/profile.php?id=12332741 Aaron Cranford

    Yeah… good luck with that

  • http://www.facebook.com/jwcrissman James W. Crissman

    Gerrymandering is a good practical math problem. President Obama talks about how Republican math doesn’t add up, but they did a brilliant job of drawing district lines to allow them to control the U.S. House and a number of state governments in spite of their minority. In Michigan, Republicans got almost a quarter of a million fewer votes in state races, but still they control both chambers of the state government and most of our U.S. reps are Republican. There was some sharp math going on in the redistricting process. I wonder if a law limiting the ratio of the perimeter to the area of districts might not limit the effectiveness of self-serving map makers in a non-partisan way.

  • Bob

    To take some issue with the article I maintain that the problem is that math and science is exact – the answer is either right or wrong. We have been living in an age where everything is under some sort of dispute and people have a hard time dealing with absolutes.

    Perhaps it is because I’m an engineer and computer programmer I have had to draw on all those math skills learned at school at one point or another both professionally and at home from finance to woodworking. As an example you can’t do complex woodworking without having to apply basic math and at times geometry and trig.

    • IanDakar

      I’m not sure it’s just that. Myself, I remember having a strong ability to read and do math. The reading stayed with me, boosted by video game manuals (cat in the hat? I wanted to know the story behind Hyrule) and just finding the stories interesting at school.

      Math, I remember around early middle school when I would complete the first ten multiplication problems perfectly,only to see the other 40 problems of the same thing and get utterly bored. Eventually, I just stopped doing them, until I fell behind, then REALLY stopped doing them.

      A love for math never picked up until many years later, when I was literally running a shop in a multiplayer game for other players and spending more time crunching numbers on spreadsheets than the typical “fight monsters” elements the game was originally designed to do. A quick run of Khan’s Acad to catch up, then I took the concept to Accounting courses and still ‘in’ it.

      Meanwhile, I’m seeing kids half my age working trigonometry problems…because it the coding to run ‘robots’ in a combat game. A few weeks ago i saw a card game that had people in it debating the detail of random theories.

      Right and Wrong is part of it. The fact that K-12 math has had any semblance of relevance or interests.

      Try it yourself. Would a child, or even you, be more interesting in reading this:

      http://zs.ffshrine.org/album/legend-of-zelda/english-instruction-manual-scans/z1manual-05-06.jpg

      (I would’ve chosen a more ‘schoolish’ example, but I can’t find an example page of Stone soup with proper images)

      or complete these problems.

      http://re-downloads.com/wallpapers/multiplication-worksheets-1-12

      Note that math doesn’t HAVE to look like that. It can be engaging and interesting. I’ve seen it in classrooms. It wasn’t in MY classroom, however, and I bet it’s not in most.

  • lenny

    If math education needs to be saved, so does English, evidently: the word “notoriety” appears to be misused here, and one cannot write “a freshmen.”

    • IanDakar

      Meanwhile, the sentence you wrote was a run on sentence, you need a ‘then’ before ‘so’, and that’s not how you use a colon.

      Yes, I’m sure there’s mistakes in mine as well. The point isn’t to be snarky over minor details in writing.

    • Mark Krebs

      Oh, sure, capitalize “English” but not “math” won’t you? Ooh, what a give-away. Now we see the bias inherent in the system! Help, I’m bein’ repressed!

      • Nigel Nisbet

        Nice one brother – sorry sister

  • secondlaws

    I think there are a host of reasons why mathematics suffers such indignity at the hands of Americans. But to me one of the core and often overlooked reasons is the
    antipathetic relationship Americans have with abstraction (exhibited, for instance, in tendencies toward biblical literalism, our dominant entertainment choices, constitutional originalism, strong anti-intellectual cultural currents,and, I would argue, even our particular brand of capitalism). And there’s the rub, as mathematics, real mathematics, is the queen mother of abstraction. In its pure form mathematics is an exploration of an abstract world utterly indifferent to our reality.

    Inasmuch as Nate Silver is successful, it is because he is able to “translate” abstract (and, I would point out, exquisitely beautiful) mathematical ideas into a particular (and, I would further point out, somewhat mundane) context. Those same ideas might
    be “translated” into determining if a particular stock is a bargain right now, an estimation of the lifetime of a Higgs boson, how much an insurance policy will cost, the safety margin to build into the thickness of a bridge girder, or deciding whether a new idea for a reality television program is likely to turn a profit.

    Because of all this, I have very little confidence that Nate Silver, or card games, or robotics, or any of the other “hooks” (and believe me they have been tried ad infinitum, ad nauseum) for mathematics education in this country can have a lasting and meaningful effect on attitudes toward mathematics. Much like imagining that opening a copper mine in a beautiful mountain setting will generate a love of wilderness among mining executives and miners, as soon as the “concrete” rewards have been extracted from applying mathematics in a particular context, we are likely to find that the American psyche will move on leaving behind nothing but a landscape of slag heaps if it remains incapable of embracing the beautiful and transcendent abstractions of mathematics.

    • Nigel Nisbet

      Little more pessimism at the end than I normally like to indulge in, but this is absolutely spot on – that’s exactly what math is. And of course apart from being the Queen Mother of abstraction, it’s full of incredible inherent beauty.

  • RDM

    It is refreshing to see this discussion finally start within the math teaching community. High school math is designed more or less to prepare students for calculus, something that perhaps 5% will ever need beyond the first year of their post-secondary studies. Meanwhile, there is little or poor preparation for statistics, a topic that a large proportion of, if not most, students will need in their post-secondary studies. Why is this?

    High school math teachers themselves, by definition, were successful in a calculus-focused math education. They are part of a culture. As a result they are often poorly educated in statistics and not much interested in it. (This is also in part because until relatively recently the computing horsepower was not available in school classrooms. But it also remains a cultural issue nonetheless.) High school math teachers, and therefore the standards they ultimately collectively control, continue to see calculus at the pinnacle of a high school mathematics education for everyone. They mistake what is appropriate for their most able students, (those most like themselves, future mathematicians, engineers and scientists,) for what would best serve the majority of the student population.

    Statistics is considered a poor cousin in the world of academic mathematics. “Real mathematicians” don’t do statistics. Good mathematicians manage to see the natural beauty in mathematics and can’t relate to students, or a curriculum, that view mathematics in more utilitarian terms. These people often control the mathematics curriculum across all departments in a university, particularly the first year foundation and prerequisite courses.

    Calculus is often used as a proxy for intellectual ability more generally, even for arts, business and social science students. Universities often use calculus as a hurdle for first year students to jump, a means of weeding out the less able students, regardless of whether further study actually requires calculus as a real foundation (v.s. prerequisite) course.

    Calculus is a deeply ingrained part of the culture of mathematics education, 9-16. Sadly it is the default choice for most post-secondary bound students trying to keep their options open. Yet statistics can be equally intellectually challenging, and has the added bonus of real usefulness for most students, regardless of their path beyond high school. Only by addressing the need to change the culture at the post-secondary level will any lasting progress be made in mathematics education reform at the high school level. And even then there will be a calculus-oriented legacy in the high schools that will take a generation or more to overcome.

    This is not to say that calculus should be banished from high school, only that it should be offered more selectively.

    One final note to those that this post has no doubt inflamed. Think about what this “misuse” of calculus has done to the image of mathematics more generally as a worthwhile pursuit. By trying to force almost all students over the hurdle we have contributed to a deep animosity toward or fear of mathematics in the culture beyond school or university. No wonder STEM education is in crisis. It is socially acceptable to say, “I can’t do math,” even though the same person would never say “I can’t read.” The situation has arguably also contributed to the anti-intellectual bias of political discourse across our society.

    • secondlaws

      The scenario you paint – that statistics,
      because it’s applied, not abstract, will allay the animosity toward, and
      fear of math – is certainly not consistent in any way with my anecdotal
      experiences. My partner, E, was preparing for examinations in a graduate
      program that required statistics. E had taken no math other than a number
      of applied statistics courses since high school and E’s relationship with
      math was one of hatred and revulsion. After avoiding it for as long as possible
      – math was delicate turf for us: I am fluent in calculus and higher math -
      E finally asked me to explain standard deviation. Drawing on my
      abstract background and understanding, I explained it in quite a bit of
      detail, a sort of conceptual calculus approach (which, of course, was
      precisely what E had hoped to avoid), whereupon E exclaimed that in all of
      the many applied exposures the concept had never been understood – it had
      simply been given as an algorithm for calculation accompanied by
      an essentially meaningless definition, and apparently arbitrary criteria –
      and that if only teachers had taught for a deeper more abstract
      understanding perhaps math would not have been as unpleasant. That
      experience has now been borne out again and again and again as I have
      dealt with many, many math averse students – learning applied math in its
      own way generates animosity and fear. I have found for most students that
      comfort and fluency with abstract mathematical ideas, once they get over (or
      are forced over) that hurdle, renders applications much less intimidating and
      much more meaningful. I have a comment below that elaborates a bit on
      my own hypothesis that the aversion is really more generally to
      abstraction than simply to math.

  • SteveH

    Don’t let reality get in the way of a really great idea. Maybe it would be “engaging” to see what Feynman says about being a good scientist.

    First, “traditional” math has not been taught in most places for a couple of decades. When my son started school over ten years ago, the school had been using MathLand for many years. It was about as untraditional as you could get. It was so bad that it was erased from the web. All that remains are the bad reviews. It was replaced by Everyday Math, a curriculum that tells teachers to keep moving and to “trust the spiral”. Bright kids get to fifth grade not knowing the times table. I saw it happen. I had to use Singapore Math at home with my son. Everyday Math is just repeated partial learning.

    “The origins of the current curriculum draw back to 1892…”

    This is false. It’s clear that the author has not looked at Everyday Math and TERC, two of the most popular K-6 curricula.

    Second, the engagement meme has been around for some time and it’s just a way to blame the student. It’s a way to avoid looking at competence and curriculum issues. Schools spend about an hour a day on math and most of this this time is not used for drill and kill. It’s spent on mixed-ability, group learning using real world (engaging) problems. Schools send home notes telling parents to work on math facts with their kids. I got some of those.

    Why don’t students like math? Engagement is not the issue. Students don’t like math because they can’t do it. Many current very non-traditional curricula do not ensure mastery of basic skills. They spiral through the material with the hope that kids will “learn when they are ready”. Engagement is like eating mathematical Twinkies. It might be fun in class, but it disappears when students have to prove their knowledge with homework problem sets. Kids get lost and no amount of engagement will fix their gaps in knowledge and skills.

    “Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering. In the data course, students would gather their own data sets and learn how, in fields as diverse as sports and medicine, larger samples give better estimates of averages.”

    Has the author checked to see if MIT will accept this anytime in the future? Education is not about averages. It’s about INDIVIDUAL doors of opportunity, and all college engineering doors require students to get through at least differential equations. Unfortunately, many educators are willing to slam doors of opportunity closed in K-6 because of ideas like:

    “Ironically, M.I.T. graduates, who are trained in science and mathematics, said in a survey regarding their daily use of math that most use nothing more than arithmetic, statistics, and probability.”

    This just guarantees that students will NEVER get accepted into a school of engineering. Who will get in? Those students who get the required mastery of the basics at home or with tutors.

    Why is it that STEM career parents are often the ones who complain the most? Is it because we just want what we had when we were growing up? Yup, No. That isn’t it.

    • VasyaPupkinsan

      I agree with what you wrote.
      Duration of math classes is not enough. Teachers need to use sticks to teach
      kids, the way it used to be in nature – learn by making mistakes.
      Schools breed idiots with the stupid tolerance and “engagement”.

  • Nigel Nisbet

    Would agree entirely that the way math is taught often makes it a fairly pointless exercise. Far too frequently, students are taught procedural tricks in lieu of actual understanding. For example, learning to add fractions by the “smile” or “butterfly” methods (or whatever you want to call it: drawing a criss-cross and a lower line and multiplying along the lines to produce the numerator addends and a common denominator). This may temporarily produce some students who can perform a procedure, but… so what? These same students for the most part have no idea what a fraction is – they’re unlikely to be able to correctly place 4/3 on a number line for example.

    And this is a problem. Currently, the US has an Algebra proficiency among high school students (when tested on an exam – not by classroom grade) at under 40%, which is pretty much a disaster. So, that things need to change is not really up for debate. However, how they should change is of course the big question. I would agree with many of the comments here that all to often math curricula designed for “increased engagement” can be poor substitutes for good teaching, and the focus on “real-world” (which this article does lean towards) can be equally damaging. It is surprisingly hard to actually incorporate real world math into the classroom and still effectively target the actual mathematics in question.

    Math courses are arranged in the current sequence not as some kind of sadistic torture mechanism, but because, if taught well, this learning path becomes a vehicle for building a student’s capacity for abstract thought (which is applicable in every job, and practically every walk of life). Sadly however, most math teaching, curricula, and standards sets seem to have lost sight of this, and the focus is on what skills, by which age – and because many of those skills (say the ability to factor quadratic equations) don’t have much relevance to day-to-day life it’s not surprising that no-one sees the point and we have an engagement issue!

    [FYI, personally I do think an integrated math sequence would be an improvement, adding a little more stats wouldn't hurt either, but only because you can make more of the connectedness of the actual underlying math - ultimately you'll end up doing much the same math at around the same time]

    The trick here is to teach math in a way that makes the struggle of learning it fun from the very beginning. Kids need to be solving puzzles, building their spatial reasoning abilities, playing with the conceptual underpinnings of the mathematical world, and learning that they in fact can figure stuff out for themselves. The fact (as one other comment mentioned) that most students end up only interested in “is it on the test?” and “how can I get an A+?” speaks volumes about the fact that almost no-one is learning this because they love it – which again is a disaster.

    It doesn’t have to be like this. Math can be taught in a very different way. As a former high school math teacher this is something I did, with, I believe, some success – here’s my TEDx talk on the Geometry of Chocolate http://bit.ly/YtLCy8 which documents some of that journey.

    Additionally here are a couple of free spatial temporal apps (they start deceptively easy – but you try getting past about level 6):

    Big Seed https://itunes.apple.com/us/app/bigseed/id482245645?mt=8

    Kick Box https://itunes.apple.com/us/app/kickbox/id438373028?mt=8

    The key is that all students can learn, but they need to learn by doing, through experiences, and develop intrinsic motivation – that’s where real engagement comes from.

    And if this sounds like a fabulous pipe dream, realize that over 500,000 students are successfully using such a game-based learning system throughout the US. Go JiJi!!
    http://www.mindresearch.net/

  • secondlaws

    I just read this review
    http://www.nakedcapitalism.com/2012/12/cathy-oneil-why-nate-silver-is-not-just-wrong-but-maliciously-wrong.html#9TL1oviJOY5mQ3r4.99
    of Nate Silver’s book and I think it reveals some of the chinks in his armor. Hero worship is almost certainly a losing proposition as a path to math literacy.

  • CK

    Nikhil Goyal uses some unreliable sources. Here are two examples.

    If what’s meant by “the current curriculum” is a curriculum that leads to the achievement of the Common Core State Standards, then the “current curriculum” includes a hefty chunk of statistics. See the Progressions for the CCSS at http://ime.math.arizona.edu/progressions/.

    The account of the MIT graduates’ use of mathematics comes from Tony Wagner’s book. Wagner says: “Graduates from the Massachusetts Institute of Technology were recently surveyed regarding the math that this very technically trained group used most frequently in their work. The assumption was that if any adults use higher-level math, it would be MIT grads. And while a few did, the overwhelming majority reported using nothing more than arithmetic, statistics, and probability.” In the book (published in 2008, so “recently” is not so recent any more), there is a reference for this survey: http://www.hightechhigh.org/resource-center/Curriculum/Curric-HTH%20Math.pdf

    Findings from the survey do not support Wagner’s statement very well. See pages 9-10 which consist of quotes from 17 people. Of these, 3 said that they didn’t use much math or stat in their jobs (doctor, med student, software developer) and 3 mentioned only statistics (e.g., the medical researcher quoted below) or statistics and probability.

    My guess is that Wagner is not aware that things like statistics and fourier analysis require abilities to use symbolic representations and graphs that build on high school algebra and other high school mathematics. For example, one of the survey respondents mentions Kaplan-Meier survival curves, which are pretty sophisticated objects: http://en.wikipedia.org/wiki/Kaplan–Meier_estimator

  • SR

    I have so many problems with this article, but my main Question of the Week is this: does every adult in the US really NEED to “love and embrace” math? Many of us responding here (myself included) have math backgrounds. I certainly do love my subject; it’s what entertains me on a Saturday night which, I suppose, makes me a math nerd. However, I work with many intelligent, passionate people who don’t enjoy math – but they love Shakespeare or the history of the MIddle East or chemistry. Sure, I have some rudimentary knowledge of those things, but for me, they were subjects to get through, and if you asked me today to discuss the theme of King Lear and write a paper on it, I’d moan and groan but good. My top students do love math, and if they don’t have a solid foundation in algebra – and by that I mean the symbolic manipulation that is taught in high school – they’ll be at a real disadvantage in college.

  • milkyway way

    I would like to think that his style of delivering of knowledge is different. A little eccentric way to those who only knows the tradition system.

    _______________________

    Bright Heritage Engineering Consulting

  • beautiful wallpapers

    this http://blogs.kqed.org site is so beautiful.this site depend on about education.Silver, who first gained notoriety for forecasting the performance of
    Major League Baseball players and for correctly predicted the winner of
    49 of 50 states in the 2008 election, can save the tattered reputation
    of math subjects.

  • UncleB

    Wages still better on the Football Fields of America?

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