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I have to ask, do those "tricks" represent the way math is usually taught in America? It looks like a bad joke to me.

by Camillo 11y ago

nmrm2 11y ago
> do those "tricks" represent the way math is usually taught in America? Anecdotally, yes -- and damn proud of it! A lot of the backlash against Common Core Mathematics is from people who want Mathematics education to stay that way. The reason is that a huge amount of mathematics educators in American secondary schools aren't properly trained in even elementary Mathematics. At the lower grades (ages < 15 or 16) it's mostly because you can go through all of high school and university in America without understanding anything about Mathematics. For example, most people at the university I attended never took a Calculus course. Everyone was required to take a Mathematics course, but there are math courses that are essentially repeats of what you would expect a non-exceptional sixth grader to understand -- matching linear functions to their graphs and the like. These courses even get recommended by teaching colleges because even Calculus I was perceived as "hard" or "advanced" "math". And Calculus I itself was entirely superficial and mostly trick-based (because calculus isn't proof based except at a tiny handful of elite universities). Result: most Mathematics educators a typical student encounters before the age of 15 have never written a proof (with practical consequences; e.g., they don't know what induction is). Even worse, these educators would probably have a hard time defining a function in terms that a working mathematician would find meaningful (educators now have their own cutesy but non-rigorous definitions for things like "number" and "function"). At the upper ages (~15 until university), I'm convinced it's because teachers are not properly compensated and so teaching doesn't appeal to the best students. Many high school teachers that teach math at least complete an undergraduate degree in Mathematics, although even that is not actually required in many states. However, based upon my anecdotal experience tutoring and interacting with peers while in university, Education students are typically in the bottom half of Mathematics students and often rely on (and prefer :-( ) "trick"-based "mathematics", even in proof-based courses (memorizing formats of theorems and corresponding proofs, then figuring out what symbols/numbers to plug in. But with zero understanding of the underlying argument).
- acheron 11y ago
  A lot of the backlash against Common Core Mathematics is from people who want Mathematics education to stay that way. You've got it backwards here; the Common Core curriculum is basically all "tricks" without understanding.
  - plonh 11y ago
    This is an utter myth promoted by Glen Beck fanbloggers. Every time one of these attempted potshots goes viral, a sane person like Friendly Atheist patiently explains how ignorant the ranter is.
  - 21echoes 11y ago
    The explicit, stated strategy of Common Core Mathematics is to emphasize understanding and conceptual learning over rote execution. And it does this, in practice, by teaching multiple different strategies for solving the same problem, and teaching why they all work the same. This, of course, leads to the hyperbolic frothing at the mouth on mommy-blogs and the like when a take-home sheet featuring just one of the many strategies taught is not the vaunted One True Trick that the parent in question learned as a child. Cue blogs titled "I'm a certified public accountant and even I can't do math this way!", which of course proves the very point Common Core is trying to make -- that older generations don't actually even know Math at all, but rather a bag full of tricks without a hint of understanding.
iheartmemcache 11y ago
I'm in my late 20s. I think a lot of these tricks were a result of George Bush II's "No Child Left Behind" testing mandate (2002? around there), where test results directly correlated to the amount of federal funding you'd receive. In response, teachers adopted quick tricks in order to optimize for test performance (i.e. 'teach for the test'). I'd wager these "tricks" are what teachers are forced to use to cater to effectively get the average student to perform optimally on those standardized tests. People just now entering their undergraduate programs, I speculate, will be familiar with these shortcuts. Math is taught in a wide variety of ways, depending on where you live, what type of schools you're going to (private east-coast Andover/Exeter vs inner-city Chicago), how rich your city is (higher taxes => more money for schools => safer/better environments => fosters a better learning experience & a life at home that values rigorous grasp of academic concepts), etc. I was one of those lucky guys to grow up in an environment that had a heavy emphasis on academia at the 'publish or perish (then tenure)' level and my school systems emphasized concepts over rote memorization (i.e., a course on geometric proof formulation where you are given a set of axioms from which you must derive all consequential Lemmas, which is basically the opposite of 'heres a few tricks'), If your class size is 35, and you have even one or two disruptive kids in class I'd imagine even the most dedicated teachers would start 'teaching by the tricks, for the test'. To answer your question: America is a big place. The difference between most Euro countries is culturally less than the difference between NYC and Harlan, Kentucky. An interesting corollary of this is (let's choose to ignore ethical implications here -- I believe everyone has the right to free, high quality education, housing, and food), but purely from the POV of workplace-competition-over-jobs, the more schools continue to teach poor analytic skills, the less competent my competitors are. I'm no Perelman or Feynman, but I do pretty fine
- Decade 11y ago
  OMG. Bush has been out of office for 6 years already. “It’s Bush’s fault” is not a legitimate response, and almost never was. I’m not saying he was good for the country, oh no not at all, but you can’t blame this on him. This partisanship is a disease on the nation. Many of the tricks are there because math in the US has traditionally been taught for repetitive manual use. You need your accounts calculated, you get somebody to add all those numbers and put the result on paper. I was just looking at a math book from the 1940s, and the first couple chapters are all shortcuts to doing multi-digit multiplication and stuff. Math education has not caught up to a reality filled with abundant accurate computing power. This horrible way of teaching math really is the most common way it is taught in America, and it has been so ever since schools were started in America. Not all those tricks are common, especially things like horses and Jesus fish. Those stupid drawings are only a desperate attempt to use a mnemonic to memorize a rote procedure. Every previous effort I’ve noticed has tried to eliminate this problem and failed. New Math in the 1960s. Reform Math in the 1990s. Everyday Math in the 2000s. The problem is not in the exact curriculum used. A good teacher with enough autonomy can teach well with any of these curricula. Obviously, there is a problem somewhere between concept and implementation.
pflats 11y ago
Just for clarity on all my responses in these threads, I'm a (minor) contributor to Nix the Tricks and a personal friend and research partner of the author. Yes, all of the tricks were submitted by math teachers that we have seen used in practice. I don't think that we are all Americans, but a most of us are. I personally haven't seen too many of them, especially the weirder ones, but I know they were not invented whole-cloth for the book.

I have to ask, do those "tricks" represent the way math is usually taught in America? It looks like a bad joke to me.

by Camillo 11y ago

I have to ask, do those "tricks" represent the way math is usually taught in America? It looks like a bad joke to me.

nmrm2 11y ago

> do those "tricks" represent the way math is usually taught in America? Anecdotally, yes -- and damn proud of it! A lot of the backlash against Common Core Mathematics is from people who want Mathematics education to stay that way. The reason is that a huge amount of mathematics educators in American secondary schools aren't properly trained in even elementary Mathematics. At the lower grades (ages < 15 or 16) it's mostly because you can go through all of high school and university in America without understanding anything about Mathematics. For example, most people at the university I attended never took a Calculus course. Everyone was required to take a Mathematics course, but there are math courses that are essentially repeats of what you would expect a non-exceptional sixth grader to understand -- matching linear functions to their graphs and the like. These courses even get recommended by teaching colleges because even Calculus I was perceived as "hard" or "advanced" "math". And Calculus I itself was entirely superficial and mostly trick-based (because calculus isn't proof based except at a tiny handful of elite universities). Result: most Mathematics educators a typical student encounters before the age of 15 have never written a proof (with practical consequences; e.g., they don't know what induction is). Even worse, these educators would probably have a hard time defining a function in terms that a working mathematician would find meaningful (educators now have their own cutesy but non-rigorous definitions for things like "number" and "function"). At the upper ages (~15 until university), I'm convinced it's because teachers are not properly compensated and so teaching doesn't appeal to the best students. Many high school teachers that teach math at least complete an undergraduate degree in Mathematics, although even that is not actually required in many states. However, based upon my anecdotal experience tutoring and interacting with peers while in university, Education students are typically in the bottom half of Mathematics students and often rely on (and prefer :-( ) "trick"-based "mathematics", even in proof-based courses (memorizing formats of theorems and corresponding proofs, then figuring out what symbols/numbers to plug in. But with zero understanding of the underlying argument).

acheron 11y ago
A lot of the backlash against Common Core Mathematics is from people who want Mathematics education to stay that way. You've got it backwards here; the Common Core curriculum is basically all "tricks" without understanding.
- plonh 11y ago
  This is an utter myth promoted by Glen Beck fanbloggers. Every time one of these attempted potshots goes viral, a sane person like Friendly Atheist patiently explains how ignorant the ranter is.
- 21echoes 11y ago
  The explicit, stated strategy of Common Core Mathematics is to emphasize understanding and conceptual learning over rote execution. And it does this, in practice, by teaching multiple different strategies for solving the same problem, and teaching why they all work the same. This, of course, leads to the hyperbolic frothing at the mouth on mommy-blogs and the like when a take-home sheet featuring just one of the many strategies taught is not the vaunted One True Trick that the parent in question learned as a child. Cue blogs titled "I'm a certified public accountant and even I can't do math this way!", which of course proves the very point Common Core is trying to make -- that older generations don't actually even know Math at all, but rather a bag full of tricks without a hint of understanding.

iheartmemcache 11y ago

I'm in my late 20s. I think a lot of these tricks were a result of George Bush II's "No Child Left Behind" testing mandate (2002? around there), where test results directly correlated to the amount of federal funding you'd receive. In response, teachers adopted quick tricks in order to optimize for test performance (i.e. 'teach for the test'). I'd wager these "tricks" are what teachers are forced to use to cater to effectively get the average student to perform optimally on those standardized tests. People just now entering their undergraduate programs, I speculate, will be familiar with these shortcuts. Math is taught in a wide variety of ways, depending on where you live, what type of schools you're going to (private east-coast Andover/Exeter vs inner-city Chicago), how rich your city is (higher taxes => more money for schools => safer/better environments => fosters a better learning experience & a life at home that values rigorous grasp of academic concepts), etc. I was one of those lucky guys to grow up in an environment that had a heavy emphasis on academia at the 'publish or perish (then tenure)' level and my school systems emphasized concepts over rote memorization (i.e., a course on geometric proof formulation where you are given a set of axioms from which you must derive all consequential Lemmas, which is basically the opposite of 'heres a few tricks'), If your class size is 35, and you have even one or two disruptive kids in class I'd imagine even the most dedicated teachers would start 'teaching by the tricks, for the test'. To answer your question: America is a big place. The difference between most Euro countries is culturally less than the difference between NYC and Harlan, Kentucky. An interesting corollary of this is (let's choose to ignore ethical implications here -- I believe everyone has the right to free, high quality education, housing, and food), but purely from the POV of workplace-competition-over-jobs, the more schools continue to teach poor analytic skills, the less competent my competitors are. I'm no Perelman or Feynman, but I do pretty fine

Decade 11y ago
OMG. Bush has been out of office for 6 years already. “It’s Bush’s fault” is not a legitimate response, and almost never was. I’m not saying he was good for the country, oh no not at all, but you can’t blame this on him. This partisanship is a disease on the nation. Many of the tricks are there because math in the US has traditionally been taught for repetitive manual use. You need your accounts calculated, you get somebody to add all those numbers and put the result on paper. I was just looking at a math book from the 1940s, and the first couple chapters are all shortcuts to doing multi-digit multiplication and stuff. Math education has not caught up to a reality filled with abundant accurate computing power. This horrible way of teaching math really is the most common way it is taught in America, and it has been so ever since schools were started in America. Not all those tricks are common, especially things like horses and Jesus fish. Those stupid drawings are only a desperate attempt to use a mnemonic to memorize a rote procedure. Every previous effort I’ve noticed has tried to eliminate this problem and failed. New Math in the 1960s. Reform Math in the 1990s. Everyday Math in the 2000s. The problem is not in the exact curriculum used. A good teacher with enough autonomy can teach well with any of these curricula. Obviously, there is a problem somewhere between concept and implementation.

pflats 11y ago

Just for clarity on all my responses in these threads, I'm a (minor) contributor to Nix the Tricks and a personal friend and research partner of the author. Yes, all of the tricks were submitted by math teachers that we have seen used in practice. I don't think that we are all Americans, but a most of us are. I personally haven't seen too many of them, especially the weirder ones, but I know they were not invented whole-cloth for the book.