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An Advanced Math Education Revolution Is Underway In the U.S. (theatlantic.com)

Posted by timothy on from the nerd-camp-is-the-best-camp dept.

AthanasiusKircher writes: The Atlantic has an >extended article on the recent surge in advanced math education at the primary and secondary levels in the U.S., arguing that last year's victory for the U.S. in the Math Olympiad was not a random anomaly. Participation in math camps, after-school or weekend math "academies," and math competitions has surged in recent years, with many programs having long wait lists. Inessa Rifkin, co-founder of one of these math academies, argues that the problems with math education begin in the 2nd and 3rd grades: ""The youngest ones, very naturally, their minds see math differently.... It is common that they can ask simple questions and then, in the next minute, a very complicated one. But if the teacher doesn't know enough mathematics, she will answer the simple question and shut down the other, more difficult one." These alternative math programs put a greater focus on problem-solving: "Unlike most math classes, where teachers struggle to impart knowledge to students—who must passively absorb it and then regurgitate it on a test—problem-solving classes demand that the pupils execute the cognitive bench press: investigating, conjecturing, predicting, analyzing, and finally verifying their own mathematical strategy. The point is not to accurately execute algorithms, although there is, of course, a right answer... Truly thinking the problem through—creatively applying what you know about math and puzzling out possible solutions—is more important."

The article concludes by noting that programs like No Child Left Behind have focused on minimal standards, rather than enrichment activities for advanced students. The result is a disparity in economic backgrounds for students in pricey math activities; many middle-class Americans investigate summer camps or sports programs for younger kids, but they don't realize how important a math program could be for a curious child. As Daniel Zaharopol, founder of a related non-profit initiative, noted in his searches to recruit low-income students: "Actually doing math should bring them joy."

28 of 218 comments (clear)

  1. drop coding, do math by sittingnut · · Score: 5, Insightful

    drop the silly coding classes that gives nothing ('nerds' will learn anyways, others never will), do maths!

    -
    but will americans ever be free of mind control to even ask,
    "I admit that twice two makes four is an excellent thing, but if we are to give everything its due, twice two makes five is sometimes a very charming thing too." - from 'notes from underground' by fyodor dostoyevsky

  2. Education is getting better by 110010001000 · · Score: 4, Interesting

    I have noticed that Public education is getting better in the US. They are now teaching Math much more effectively (at least at the elementary school level). At first I thought the Common Core was dumb after my elementary school child showed me what he was doing, but after researching the teaching methods I know understand the reasoning behind techniques they are using. Plus the efforts of Code.org to introduce our kids to logic and programming at an elementary school level is really helping with all of their studies. Amazingly teaching basic logic helps in all aspects of life. Kudos to the Common Core people and Code.org. Too frequently the teaching "experts" are teaching the wrong techniques. Anyone who grew up learning "new math" (Venn diagrams, etc) in the early and mid 1980s public schools knows what I mean by that!

    1. Re:Education is getting better by 110010001000 · · Score: 3, Informative

      It isn't a single point of data. I did research on Common Core. The teaching "experts" who came up with "New Math" were not seeing anyone. They were idiots and ruined math for decades. The Common Core people know what they are doing, because they are people who actually learned Math and Engineering at some point in their lives. The techniques are paying off. Go research to techniques if you are interested. My guess is you are too lazy to do it.

    2. Re:Education is getting better by 110010001000 · · Score: 2

      Actually I don't. This is the best place to devote my expert analysis on all topics.

    3. Re:Education is getting better by AthanasiusKircher · · Score: 2

      The teaching "experts" who came up with "New Math" were not seeing anyone. They were idiots and ruined math for decades.

      Um, no. Well, you can argue that they "ruined" math education, but they weren't "idiots." The New Math was developed in the 1960s mostly by college professors and advanced math people in reaction to the "Space Race." The idea was to introduce mathematical abstractions (set theory, formalizations of analysis, etc.) at lower levels in education, which might be beneficial to students who were heading toward engineering and science degrees.

      As you rightly point out, there were a number of problems with the execution here. First, not every middle-school student has the talent or interest in becoming an engineer or scientist, so the New Math came across as increasingly irrelevant and confusing. Second, teachers often weren't clear on the rationale for the methods either, which led to poor implementation. Third, the New Math took basic algorithms of computation (which would be useful to everyone, whether they were heading for college in science or not) and made them seem complex and arcane (e.g., doing arithmetic in other bases), thus alienating less-talented students even from basic math.

      I'm not sure what you were studying in the 1980s, but that was well past the heyday of the New Math.

      In any case, the goals of the New Math were very different from Common Core -- the New Math wanted to increase output of scientists and engineers from our schools (focusing on abstract math for talented kids), regardless of the negative impact it had on the rest of the population's education. The Common Core instead is trying to be about better math pedagogy and better understanding for kids in general. We can argue about the details of the implementation, but the aim is different.

      Bottom line: the New Math was developed by experts in math not pedagogy. They weren't idiots -- they just didn't care about teaching the masses how to compute a tip when paying for dinner. They were trying to win the Cold War. And while their efforts arguably screwed up primary math education for the majority, the New Math reforms to secondary education were largely successful in improving pre-college math training in American high schools.

    4. Re:Education is getting better by AthanasiusKircher · · Score: 3, Interesting

      I disagree. In fact had the opposite effect: New Math as taught in the late 1970s/early 1980s was unsuccessful in teaching pre-college math.

      Sorry, but I'm not sure we're talking about the same thing. The New Math in secondary education was developed in the 1950s and implemented in the 1960s. By the early 1970s, the New Math movement was largely dead.

      By replacing basic Math education like algebra/geometry with the screwed up "New Math" they ruined math for those of us who actually had to take it in college for engineering. You can't learn Calculus without a solid understanding of Algebra and Geometry.

      I'm not sure you know what you're talking about. In the mid-1950s, high school enrollment in Algebra was down to about 25% of all high students, and enrollment in Geometry was down to less than 12% of high school students. The New Math was about encouraging students to take such courses, by combatting an anti-intellectual populism in the previous generation of educational reformers. It also encouraged clarity in concepts and algorithms in these classes which would line up better with advanced math taught in college. Also, the very idea of teaching calculus in high school was a product of the New Math reform.

      New Math didn't teach what we needed to know to be successful in college math.

      Without the reform of New Math curricula in the 1950s and 1960s, you may not have even had the option of taking math like geometry or algebra in high school, let alone calculus. How would missing out on such things be better preparation for college math??

      I think you're focusing too much on the reforms to primary education, and you don't seem to know what secondary New Math curricular reform was about. It was mostly about emphasizing the math you think claim it was jettisoning from curricula.

      I'd suggest you read about what the New Math reform actually was about. Here's a short intro to curricular reforms over the 20th century, here's a longer history of the New Math movement, and here's an intro to the sorry state of secondary math education in the U.S. around 1950 -- which definitely included little decent prep in geometry or algebra. One of the main goals of the New Math reform was to incorporate "a solid understanding of Algebra and Geometry" into the U.S. high school. At times, the reformers did go too far into abstraction, but I'm really not sure what you're talking about.

    5. Re: Education is getting better by Bengie · · Score: 3, Interesting

      the common core scam (which is incompatible with logic-based mathematics), kids can no longer fail regardless of performance

      Common Core tests have a high failure rate because of the much higher goals. You're conflating so called "Common Core curriculum" which is sold by private companies with the standardized Common Core progression benchmarks. Any test can be "Common Core" as long as it closely aligns with the Common Core benchmarks. How the tests are done or how the curriculum is taught has nothing to do with "Common Core" except marketing.

    6. Re:Education is getting better by AthanasiusKircher · · Score: 2

      Sets. Venn Diagrams. We always called it "New Math" but maybe it had some other term at that point.

      Well, set theory and stuff like Venn diagrams were part of some New Math curricula beginning in the 1960s, but mostly at the primary (or maybe middle-school) level. They were intended to teach things like Boolean algebra, which would be relevant to new trends (at that time) in computer programming. Again, the emphasis was on getting students up-to-speed to participate in the Space Race, etc.

      And I also should note that Venn diagrams were in fact meant to be visual aids to support the new abstract concepts (like Boolean algebra and set theoretical relationships), kind of like the visualizations you're arguing for in Common Core.

      Anyhow, they certainly weren't supposed to displace algebra and geometry in high-school curricula. If your school did that, they were doing the "New Math" wrong.

  3. Math is a Chore by sycodon · · Score: 5, Insightful

    The way math is taught, Math is a chore. The way common core teaches it, it's a stupid, idiotic chore.

    There is never an example of the wonders of math. No examples of what can be accomplished and how you can actually benefit. It's just a series of numbered problems with the answers to the odd numbers in the back and precious little explanation. Something to finish before class is out and to remember just long enough to pass the next test.

    Math is a chore because it's taught like a chore.

    --
    When Fascism comes to America, it will call itself Anti-Fascism, and tell you to give up your guns.
    1. Re:Math is a Chore by 110010001000 · · Score: 2

      Math IS a chore. Learning IS a chore. People need to realize that not everything in life is "fun". You need to do the chores in order to get work done. Too many people don't want to put in the work.

    2. Re:Math is a Chore by sycodon · · Score: 3, Insightful

      Yes, but there needs to be a context and a purpose to that chore.

      When you are learning to read first grade books, the teacher is reading third grade level books to you. You see what's possible. YOU want to read that book. But you can't. So you work harder on the books you can read in order to be able to read the higher level books.

      It's like being taught to sculpt marble by MichaelAngelo, but he only lets you see the 6 square inches around the chisel.

      --
      When Fascism comes to America, it will call itself Anti-Fascism, and tell you to give up your guns.
    3. Re:Math is a Chore by Kwyj1b0 · · Score: 2

      Math IS a chore. Learning IS a chore. People need to realize that not everything in life is "fun". You need to do the chores in order to get work done. Too many people don't want to put in the work.

      While that might be partly true, it is also true that Math education is a chore because it was treated as a process of memorizing, not discovering - memorize process x,y,z so you can answer contrived questions a, b, and c. There is an excellent essay on this topic: A mathematician's lament.

    4. Re:Math is a Chore by bluefoxlucid · · Score: 2

      Learning is not hard; it is, however, *effort*.

      It's also technology. I've been collecting some of the high technology--spanning modern, classical, and *lost* technology--and trying to turn that into a primary education system. That's a complex feat of engineering *well* beyond my personal capability. I'm trying to put something together that adults can understand and which skilled teachers can stream in the same rough order and detail I provide to teach first-grade children; I can't create a viable classroom curriculum, but I can probably figure out what you'd need to put in one.

      I remember going through school with teacher telling me to study and take notes. That's where all this started for me: I was never taught how to study or take notes. Now I'm aware of SQ3R, SQW4R, OK5R, MURDER, OARWET, PQRST, and the other dozen or so nearly-identical study systems; I also know about Cornell Notes, three-column notes, and a few specialized concept maps. I've learned about Soroban mathematics and the transition from the Soroban to Anzan--arithmetic computed in your head faster than you can punch it into a calculator. I've learned about mnemonics fundamentals (visualization, organization, association), tools (rhythm, rhyme, acrostic, mnemonic numeracy), and systems (peg, link, PAO, mind palace). I've learned a lot about maximizing human efficiency in studying and learning--minimizing the time and sheer mental effort applied.

      I've taken this out pretty far. I know about the dorsolateral prefrontal cortex, the part of your brain that enforces your direct decisions on other parts of your brain. I know your brain tries to hum along doing what it *usually* does, and the dlPFC expends its ATP reserves forcing your brain to expend *more* energy in other places, what scientists call "willpower". I know all the things I listed above, all the strategies I've devised, serve to reduce that energy expenditure, increasing the amount of action you can take per day (less effort means more learning and more time spent on-task; more effort means you lose focus quickly). You need these things, and you need to drill them into your brain as basic processes so you don't expend much energy invoking them, thus ensuring a net-gain.

      Want to know where geniuses come from? They're made. They're the kids who happen to stumble across fancy mental tricks that reduce the amount of thinking they do. Those of us who were attentive enough to think about things, to reflect, learned to associate information to other information: I never had to memorize my math formulas because I would pick them apart to understand how they worked, and then *re-derive them* during every homework assignment and every test. I've seen people who are just incredible geniuses and people who are masterfully creative; they're doing better than I am, but we're all doing the *same* things with our brains: gluing bits of information together. It's the time I spend not putting in the effort that cuts me down.

      Of course it's not always fun. I spent 4 hours today thinking about how I should study on Duolingo, meanwhile staring at IRC scrolling by while not really reading it; I zoned out to avoid the labor of thinking, when I could have spent an hour learning and solidifying new information. The guy who's studiously pouring over his Japanese books and whining about how hard it is is learning Japanese faster than I'm learning Esperanto, and I can learn Esperanto 20 times faster than *anyone* can learn Japanese. Everyone is like this. We think some people are just dumb, but they're just not using their facilities effectively.

      --
      Support my political activism on Patreon.
    5. Re:Math is a Chore by bluefoxlucid · · Score: 3, Insightful

      Things you need to rote memorize in math: Complement sets {(1,4),(2,3)} and {(1,9),(2,8),(3,7),(4,6)}; Multiplication tables; Computational algorithms (addition and subtraction using the complement sets; multiplication and division using the multiplication tables; mental calculation for square roots, and the generalized nth root algorithm); Algebraic rules. Have these at your fingertips and a computation is equivalent to its result: glance at a page of numbers and recite the result immediately, without thinking.

      Things you *should* memorize in math by network: Algebraic formulas; Trigonometric identities; Geometric formulas; Methods of derivations of the prior. These are things which tell about each other. You'll remember how they work by working with them; you'll associate them together by how and why they function; and you'll begin recognizing that pieces of equations are related to pieces of other equations, allowing you to put them back together when you forget. That association will let you walk your memory back to any equation you need if it isn't immediately familiar; if you *do* forget something like the Law of Cosines, you can recreate it based on what you do remember.

      The set of required rote memory--stuff you're going to need to repeat to yourself again and again--is minimal. Even then, you'll likely memorize the compliments, the algorithms, and the algebraic rules by habit of doing; you'll need to memorize the multiplication table by brute force, since you're only ever going to focus on recalling a few elements here and there, instead of all elements *constantly*. Everything else fits into large, complex systems which you can map out in your mind to develop a broad field of organized, associated information, thus strengthening the links to all these facts by making them cognitive.

      When *I* was in school, they just made us memorize each new concept and equation. We had to recite equation when prompted, and were only given them in the form of "This equation solves this type of problem." Rote memorization in inappropriate places.

      --
      Support my political activism on Patreon.
  4. ask Shatner who gets credit by bill_mcgonigle · · Score: 4, Insightful

    From my experience with kids of this generation, there's one teacher who's responsible for most of the positive increase in mathematical competency in recent years: Salman Khan.

    I'm sure you'll find any number of politicians and their cronies at the textbook corporations who will claim credit, but when they mess everything up and the children find themselves mystified and befuddled, they turn to Khan for help.

    --
    My God, it's Full of Source!
    OUTSIDE_IP=$(dig +short my.ip @outsideip.net)
  5. Re:Math is fine! by Forgefather · · Score: 2

    Based on surveys conducted on graduated seniors at my University math majors were some of the most highly paid degrees in the entire place with starting salaries a year out in the six figures range. Most of them were people with advanced degrees in statistics and were employed creating models for investment on wall street.

    --
    "There are lies, there are damn lies, and there are statistics"
  6. Re:Its maths dammit by Pseudonymous+Powers · · Score: 2

    apparntly in America there is only one math.

    When you abbreviate a word you don't tack letters back on the end. We don't shorten Chemistry to Chemy, after all.

    Thank goodness. Until I saw this exchange, I thought I was the only one here who wanted to have a fruitless 30-minute argument about where exactly the letter u belongs or doesn't belong.

  7. Note by JWW · · Score: 2

    The kids winning these competitions today were not taught Common Core math in elementary school.

    Or to put it another way, these gains will not be long lived as the inadequately taught youth in elementary school today make their way into the secondary levels.

  8. Re:Math is fine! by EzInKy · · Score: 2

    Yes a very, very few do. And it would be wonderful if anyone could take from the commons and profit by adding value to what nature has provided. Unfortunately the one percent have laid claim to anything that should be available to be had for free. Such is life!

    --
    Time is what keeps everything from happening all at once.
  9. Re:Math is fine! by Impy+the+Impiuos+Imp · · Score: 2

    Well, it's a long term gripe that society as a whole would be much better served devoting to intellectually elite student's education just a fraction of the money spent making sure every last clown can calculate change by the time they graduate.

    But you know, political memes and "them elites don't need it! >:-( "

    And that was before all this privledge meme shit hit the fan. Try it today.

    --
    (-1: Post disagrees with my already-settled worldview) is not a valid mod option.
  10. Journey to the Center of Dearth by epine · · Score: 3, Interesting

    My father taught me binary in the early seventies when I was still in elementary school, with black marbles and a grey egg carton. I got it right away. Numbers were one thing, representations of numbers was another thing, and these could be whatever you found convenient, so long as you obeyed certain rules (I wasn't so accelerated that I immediately started banging out Euclid's Elements on the piano).

    Then I thought really hard one Saturday afternoon about fractions (on the unit interval, which I thought of as positive integers with the numerator greater than the denominator), and discovered that even though there are a lot of them, it is possible to enumerate them exhaustively, though not by the traditional "counting up" procedure, which got me hooked into the problem of the common divisor thing.

    The next project I recall was to exhaustive write out the Tic Tac Toe game tree. Since I was a lazy bastard (always have been) this involving thinking very hard about something somewhat like symmetry groups.

    Over the annual summer visit to my grandparents—small town prairie Badlands without the cool geography, though often we managed a trip to see the hoodoos—I played a lot of solitaire on the golden-green shag carpet which Puss Puss—the duodecarian house cat who lived in the shadows under my grandparent's bed (the short duration of our visits was probably for her sake)—sometimes preferred in her dotage over asking out into the Canadian winter. Quite undeterred by the sticky and/or stinky patches, I managed to clearly formulate the concept of a "decision procedure" and that such a thing could be unambiguously specified; furthermore, I worked out (at first empirically) that the greedy algorithm was provably not optimal for Klondike (for me at that time, all Solitaire was just "Solitaire", though I knew several).

    At age ten, the boundary between empiricism and proof is still a fuzzy one.

    In grade five, I spent a lot of time (by myself) trying to puzzle out the rate-limiting step in long-hand square root. I had by then also discovered E=IR and P=IE. Pretty soon I had determined that this generates 4 choose 1 times 4 choose 2 simple algebraic forms. But for an entire painful week, some kind of thick cloud entered my brain and I couldn't reliably write all the forms down without a lot of mucking around; this I knew to be completely bogus, and a permanent blot on my record. By the time the cloud passed, I was pretty good at substitution and gathering. Later, when I first encountered a matrix (don't recall), I immediately went to myself "oh, that's just algebra, better organized". At least something stuck.

    Now, during this entire period of my life, I was in a constant state of deeply repressed rage about this thing called "school", with all the inherent stimulation of Puss Puss waiting out the daily bedtime / ultimate final departure of the grandchildren (geriatric cat yay!) from the furthest dark remove under the master bed.

    Grade six came as a shock. For the first time I experienced a math teacher who believed in letting kids learn at their own natural rate. He quickly put four of us a private work program. We could go as fast as we wanted, but the rule was we had to do all of the tedious exercises at the end of every chapter. Many of these exercises were heavy on the pencil work, so I only made it through grades six, seven, eight, and nine. My fingers put in about 90% of the work (this is not actually a bad thing), and my brain put in the other 10% (this being 100 times more than 0.1%). Awesome!

    So I was armed, locked, and loaded for bear when I showed up at the beginning of grade seven. I figured I could knock off ten, eleven, twelve by Easter, and still have a month left over for real math at long last.

    Problem: my grade seven teacher thought my purpose in life was to sit enthralled by his boring lectures. Shields up! I don't recall a single thing he wrote on the board

    1. Re:Journey to the Center of Dearth by junkgoof · · Score: 2

      8 * 8 =64

      x * x =x ^2

      (x-1)(x+1)=x^2 +x -x -1 = x^2 -1



      Should work for any numbers...



      (x-2)(x+2)=x^2 - 4



      And so forth. Algebra...

      --
      You got me into this! You were the ideologue! I'm only a poor assassin! - Twenty evocations, Bruce Sterling
  11. Re:Math is fine! by DigiShaman · · Score: 2

    Well yeah, all the money is in analytics. Google, IBM, Political Science, basically anything involving statistics and analytics is going to be future-proof as far as jobs are concerned. It's one thing to crunch the data, but it's quite another to understand it well enough to do modeling.

    --
    Life is not for the lazy.
  12. Re:Ironically its because common core sucks by 110010001000 · · Score: 2

    Actually probably the issue is that Common Core is exposing that kids aren't learning it, so they need extra help. Nothing wrong with that. Previously you had no idea who was learning and who wasn't. Parents bitch because they don't understand it, and haven't bothered to research it.

  13. Re:Math is fine! by tnk1 · · Score: 3, Insightful

    He had a point. The register isn't for math, it is for *accounting*. He has to true up his drawer against the receipts for that shift. One loaf of bread isn't going to be a huge issue, but if loaves start walking out the door and the cameras pick up the cashier taking cash and not entering it, it is possible that the cashier gets in trouble at least for failing to account for things.

    Worse, if someone actually is stealing those loaves or cans of spaghetti (low amounts of shoplifting are common in stores) and the cashier is seen taking money for those things which is not accounted for, they assume he or she is running a side business and pocketing the cash.

    So yeah, he's probably not going to jail, but you were not entirely in the right there.

  14. Re:Math is fine! by Bengie · · Score: 2

    Businesses will send their employees to college

    No business will send their workers to college, they'll send them to a tech school for specific classes or to training seminars. None of which are a replacement for a good education. Technical knowledge expires quickly, education lasts a lifetime.

  15. Stop repeating what idiots say on Fox. by Hognoxious · · Score: 2

    At first I thought the Common Core was dumb after my elementary school child showed me what he was doing, but after researching the teaching methods I know understand the reasoning behind techniques they are using.

    Clearly you need to do a bit more research. Common core isn't about methods or techniques at all.

    https://en.wikipedia.org/wiki/...

    "The standards do not dictate any particular pedagogy or what order topics should be taught within a particular grade level."

    http://www.corestandards.org/a...

    "That is why these standards establish what students need to learn but do not dictate how teachers should teach. Instead, schools and teachers will decide how best to help students reach the standards."

    --
    Confucius say, "Find worm in apple - bad. Find half a worm - worse."
  16. Re:Math is fine! by ze_foster · · Score: 2

    I loved math until the 3rd grade (c. 1973); and between 3rd and 12th grades, I was a math failure. When I hit the age of 21, I decided to go to college, and that meant starting from scratch with remedial math at the local junior college, and the plan was to transfer to a 4-year university after that. Remedial math was wonderful: I had an instructor (Dr. Baum) who would keep explaining things until I could understood. This was very different from gradeschool where instructors would keep repeating the same thing that I didn't understand, but say it a bit louder each time they repeated it (as if that was supposed to help me understand). Five years later I was in my senior year after my transfer to UC Berkeley. I was an EECS major, and I had completed the Calculus (for engineers) and Math Analysis, and I was sailing toward my EECS degree. I decided to take a trip back to my original jr college, and look up Dr. Baum. To my extreme disappointment and sadness, I found out Dr. Baum had died. He never knew the door he had opened for me. Here we are, 30 years into my EECS career (more of a CS career, as it turns out; but I get to beat up on oscilloscopes and logic analysers once in a while), and it has been a lot of fun. Dr. Baum proved that it can come down to EXACTLY ONE instructor who reaches a student's mind, and without excellent instructors, we easily lose minds that could otherwise have been STEM participants. More's the pity. WE NEED MORE MATH TEACHER that aren't crappy.