Children's Arithmetic Skills Do Not Transfer Between Applied and Academic Mathematics (nature.com) 74
Children working in India's fruit and vegetable markets can perform complex mental calculations with ease, yet struggle with basic written math tests that determine their academic future, according to new research that raises troubling questions about mathematics education worldwide.
The study, published in Nature, reveals how traditional education systems are failing to tap into the mathematical talents of students who develop practical skills outside the classroom, particularly those from lower-income families. MIT economist Abhijit Banerjee, who grew up watching young market vendors deftly handle complicated transactions, led the research. His team found that while these children could rapidly perform mental arithmetic, they performed poorly on standard written assessments like long division problems.
The findings come at a critical moment when mathematics education must evolve to meet modern demands, incorporating data literacy and computational skills alongside traditional mathematics. The research points to systemic issues, including a global shortage of trained mathematics teachers and assessment systems that reward memorization over reasoning. Without addressing these challenges, researchers warn, naturally talented students from disadvantaged backgrounds may never reach their potential in fields like research, entrepreneurship, or teaching.
The study, published in Nature, reveals how traditional education systems are failing to tap into the mathematical talents of students who develop practical skills outside the classroom, particularly those from lower-income families. MIT economist Abhijit Banerjee, who grew up watching young market vendors deftly handle complicated transactions, led the research. His team found that while these children could rapidly perform mental arithmetic, they performed poorly on standard written assessments like long division problems.
The findings come at a critical moment when mathematics education must evolve to meet modern demands, incorporating data literacy and computational skills alongside traditional mathematics. The research points to systemic issues, including a global shortage of trained mathematics teachers and assessment systems that reward memorization over reasoning. Without addressing these challenges, researchers warn, naturally talented students from disadvantaged backgrounds may never reach their potential in fields like research, entrepreneurship, or teaching.
Algorithms (Score:5, Informative)
Re:Algorithms (Score:4, Interesting)
Mathematicians are rare and tend not to think like other people do. Traditional approaches may not work as well for them, but an approach tailored to them wouldn't work at all for everyone else. Hence the problem with Common Core/Singapore math. The tried-and-true works-for-almost-all approach should not be abandoned.
Re:Algorithms (Score:4, Insightful)
And since the overwhelming majority of humans have no need, desire, or talent for pure mathematics, we should just stick with the approach that has over the centuries been proven to be the most effective.
What nonsense. Math is as essential a skill a reading: being innumerate is as bad in life as being illiterate, and a school system that isn't able to teach math to pretty much every student is failing horribly.
What is even this "traditional" approach that supposedly has "proven effective over the centuries?". Math teaching does not change fast but it certainly has not stayed the same "over the centuries", or across countries for that matter. So this "traditional approach" is that just whatever they happened to do in the good old days when you were in school: this is just another thinly disguised "why are they changing things?". Don't know what approach that was, but in many countries (including the US and, clearly from this paper, India, the "traditional" approach to math was not very successful, and left many students feeling they were "bad at math" instead of unblocking mathematical thinking for them.
I'm not a teacher, but I've spent a few hundred hours in recent years in elementary and middle school math classrooms, and my experience is that most children can do math at a much higher level than they're given credit for if they're given the right kind of teaching and attention. Being "good at math" isn't innate: I'm not denying there's a genetic component (as there is to almost everything in human nature), but to a large extent it's a skill that can be unlocked, when math starts to "click" for you.
So let's drop the condescension about most people being too dumb for math. Common Core may not be perfect but it's definitely a step in the right direction for math education because it focuses on having students understand why a solution is in a certain way instead of mindlessly memorizing procedures (is that your "traditional way"?), which doesn't work for any practical purpose (because those memorized procedures will be forgotten as soon as students have passed the test).
Re:Algorithms (Score:5, Interesting)
I'm 45. I struggled with math in school until my Dad, a mechanic, taught me 'tricks' to do math. Those tricks are pretty much the basics of Common Core today. My grandfather worked for the railroad. I used to test him with my calculator, asking him 'crazy' (to a 4th/5th grader) math questions. He was always right. His explainations were also similar to what we call Common Core math today.
The skill seems silly when we use it on math we already have memorized, but really, when we approach math for which we have not yet memorized and answer (and are lacking a cell phone to ask), we all have learned to leverage parts, if not all, Common Core math skills today. The most important being Step-Based Decomposition, and Leveraging Multiple Strategies.
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It was the other way around for me. I was taught the old traditional way and found for myself a few 'tricks' that are similar to but not necessarily the same as common core in able to be able to do it faster without pencil and paper.
Those are good to know, and might be better taught in 4th grade after learning the conventional way in 1st-3rd grade.
Notably, that would also be the order you learned in and it seems to have worked out for you.
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There were some clever ideas about thinking about math in Common Core (all fundamentally pretty obvious, but novel perhaps for young children) but it had some serious implementation problems. For starters, to use an exercise analogy, those, "clever ideas" were like advanced techniques in exercise disciplines where the attitude by bad instructors is that anyone can do it because they can, but that completely ignores that many people do not have the physical conditioning to remotely attempt those advanced tec
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And since the overwhelming majority of humans have no need, desire, or talent for pure mathematics, we should just stick with the approach that has over the centuries been proven to be the most effective.
What nonsense. Math is as essential a skill a reading: being innumerate is as bad in life as being illiterate, and a school system that isn't able to teach math to pretty much every student is failing horribly.
If you can do arithmetic, then you are by definition not innumerate. The very notion of numeracy is grounded in the practical, not in understanding abstract theory.
Memorization can Promote Understanding (Score:2)
Common Core may not be perfect but it's definitely a step in the right direction for math education because it focuses on having students understand why a solution is in a certain way instead of mindlessly memorizing procedures
I've no idea what this "Common core" is but frankly there does need to be some memorization early on - such as memorizing times tables - so you have an established knowledge base to build on. Those with less interest in maths find this useful knowledge and those who are interested in mathematical subjects use this to spot patterns and shortcuts that start them down the road towards more interesting things. That memorized base knowledge does not get forgotten - I still know my times tables today - because i
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Ah yes. It's not like the world has changed in the last few centuries.
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Majority of humans don't use pure mathematics, but that doesn't mean that they shouldn't. Few examples:
- Lottery
- Investing
- Should I rent or buy a house
- Finding marriage partner
- Deciding where to eat
- Deciding favorite chips flavor
All of these are math problems that have pretty easy to calculate answers. Yet hardly anyone actually uses math to make those decisions.
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On the arithmetic and algebra side of things, there's also: ...
- Household budget
- Compound interest
- Sales tax
- Lazy way to calculate tips
On the logic and formalism side, it's a little more difficult to find something universal. But there are a lot of trades where it really helps to know some geometry theorems and proofs. Such the inscribed angle theorem when surveying.
Because we don't necessarily know what trade a 10th grade might end up in. We should probably make their education broad enough to prepare
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OK, I'll bite. I was a math major in college. How does Math help with the last three items on your list?
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The much-maligned Common Core attempted to teach math how mathemeticians think
No. That is the opposite of what Common Core does. Common Core observed that there are many way that people think about math, and it tries to introduce each of those different ways, so that the student can find the way of thinking that works best for them. Some learners went their entire lives not knowing the way that works for them, so they were constantly frustrated by math. What you are descriving is the old way, which was teaching math the way mathematicians think of it.
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The much-maligned Common Core attempted to teach math how mathemeticians think
No. That is the opposite of what Common Core does. Common Core observed that there are many way that people think about math, and it tries to introduce each of those different ways, so that the student can find the way of thinking that works best for them. Some learners went their entire lives not knowing the way that works for them, so they were constantly frustrated by math. What you are descriving is the old way, which was teaching math the way mathematicians think of it.
So all the people frustrated with common core math - usually parents who know the answer to a problem instantly, but find the CC math ridiculouse - they are what - stupid, lying, old school far right, or just wrong because reasons?
Apparently I do not think about math correctly. I wasn't good at it in school, but I was lucky to be in the last class that learned how to use slide rules in tech class. The moment I did simple multiplication, something clicked. Grades shot up, and I'd do most of the work in my
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As some folks may recall (I haven't been active much in years), I'm a retired mathematician. I even have some experience teaching.
The whole Common Core thing is generally a good thing, at least as far as I can tell. It's just a set of standards, really. Little Timmy in Bumfuck, Maine, should have learned the same things as Little Jenny in Burbank, CA. I've never really understood the complaints. There's still plenty of room for people who exceed those standards. It's not like they're a limiting factor.
Anyho
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Many students don't learn anything more than arithmatics.
Are algebra and geometry no longer required classes? Back in the early 70s those were mandatory in grades 6-9. Not advanced, but you learned the basics, including sets, roots, how to derive things like a quadratic equation, and graphs. (In terms of learning anything beyond grade-school math, they were useless. Mainly because they were poorly motivated, and the teachers themselves couldn't do much beyond 7th grade math. I remember a math teacher in high school referring to calculus as "advanced mathmatics" t
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AFAIK, they're optional but algebra might be required - but only an intro type of class, like Algebra I back when we were kids.
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In theory, yes. In practice, it seems to lead to teachers marking kids wrong when they use the method that works best for them rather than the one the teacher wanted, in spite of a correct answer. What's this 5x3 = 5+5+5=15? WRONG!!! The one true way is 5x3 = 3+3+3+3+3 = 15! And none of this 3+3+3+3+2 = 6+6+3 business!
You could say that's on the teachers not grasping the common core, but it seems to be a common problem. And I have no earthly idea what these 'ribbon things' are that a poster above was talkin
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Yeah, we really need to revamp how math is taught.
The sharp end of that will, of course, rely on teaching the teachers better ways to teach math.
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Memorizing multiplication tables exercises language cognitive capability more than it exercises spatial capability, which is key to understanding pure mathematics.
Why do all kids need to understand "pure mathematics"? Why do all kids need to "think like mathematicians"? We've been trying to impose this in schools for years. It's a failure, and it'll always be a failure, because most people have neither the talent nor the desire to be mathematicians or ponder abstract math. The vast majority of people learn best by seeing and doing in the real world ( "Example is the School of Man, and he will learn at no other" - attributed to Edmund Burke ). This fruitless quest for
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The problem with common core is it wants to teach the kids to fly when they haven't even learned to walk yet. Based on comments in r/mathtechers, it also seems to produce teachers who hold a particular method to be the one true way and forget that ultimately arithmetic has a correct answer and that it's value is in the ability to get to it.
That's how kids end up told that 5x3 = 5+5+5 = 15 is WRONG and made to feel like they're bad at math. The kid that learned 3x5=15 by memory last year can just forget abo
Real World Examples (Score:4, Interesting)
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This. PhD in physics here. Trust me, I had to learn a lot of math to get there.
Concepts are powerful and important, for summarizing what a body of knowledge entails. However, to absorb these concepts, you need to work on problems. That is what builds the pathways in your brain, and allows you to utilize the concepts flexibly.
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Practice makes perfect! You must *try* many many times before the learning happens, before you see the patterns. Trial and error.
One of the big problems is that people give up before trying. They look at a problem and say I can't do it before any exploration. One time, I asked my girlfriend if she wanted to play frisbee. She said "no, I'm not very good at it." I asked her "have you ever played before?". She said "no".
What did Edison say? "I have not fail
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However, to absorb these concepts, you need to work on problems.
That's definitely true but, I think for most people, there's working on problems, then there's pointless chores. For example, for some people the mantelpiece getting dusty is a problem that needs to be solved and so it needs dusting every day, whereas for others, who cares if there's some dust on the mantelpiece unless it has actually built up into a solid layer. Once a month, or two months... twice a year... Meh. So, some people will see a raw math problem and be inspired to solve the problem of getting to
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The nature of word problems is a bit of an issue here of course Bob having 6 apples and Ellen having 38 raspberries might work pretty well for a young kid who can really relate to friends sharing fruit, but the same kinds of word problem themes get pretty stale as you get older.
Oh, c'mon. Fruit never gets old!
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I've found things in the back of my fridge that would beg to disagree with you... if I hadn't buried them at a crossroads in the dark of night with a stake through them so they would stop talking.
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Thanks for the reply. Responding to one thing:
[...] I think for most people, there's working on problems, then there's pointless chores.
As you go on to say (or at least infer) these chores may seem "pointless" until you view their broader context.
Consider the movie The Karate Kid in which the master has his student paint fences with attention to the up-down motion of the brush, and polish his many cars with attention to the "wax-on, wax-off" rotary-motion of his hands. It certainly seems pointless, until there is a scene that reveals all of it was to train his muscle-memory to react defensively
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This! When I taught game programming to high school students you should have seen their eyes light up when I showed them how Pythagoras is used for distance calculation and SOHCAHTOA used for trajectory. Once the students had real world examples they wanted more mathematics. Many of them had to be retaught these basics because they dismissed it as not needed any longer once their math course was finished.
Arithmetic is not math (Score:4, Insightful)
Yes, math uses numbers, but memorizing arithmetic rules and tables is a different skill than learning math
I suspect that many students who claim to "hate math", actually hate arithmetic and have poor memorization skills
Re:Arithmetic is not math (Score:4, Insightful)
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You missed MpVpRb's point: arithmetic != mathematics. You may need the former to have facility in the latter, but that doesn't mean they're the same. Nor does it mean that mathematicians are savants when it comes to mental arithmetic. Many aren't.
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Nor does it mean that mathematicians are savants when it comes to mental arithmetic. Many aren't.
I can do quite a bit of math in my head, even if it's just to sanity check something with an approximation. However, those skills have diminished in time as I no longer have much of a reason to use them. I'll say that my ability to do math in my head is better than average but I've never been at the 'savant' level.
Re:Arithmetic is not math (Score:5, Insightful)
I've thought about this a lot.
You have a narrow window when you are young. During this time, you must do rote memorization of your addition and multiplication tables - hundreds of times until you can do single digit problems in your sleep. If you don't, you will be fucked for life, finding it nearly impossible to do any further math.
Whatever mumbo jumbo is taught to kids outside of this window can be fixed later, but do not fuck around during this critical period because when it is closed, it is closed forever, and virtually no one who doesn't learn a good foundation at this time will ever overcome that disability and go on to become comfortable with math.
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I've thought about this a lot.
You have a narrow window when you are young. During this time, you must do rote memorization of your addition and multiplication tables - hundreds of times until you can do single digit problems in your sleep. If you don't, you will be fucked for life, finding it nearly impossible to do any further math.
Whatever mumbo jumbo is taught to kids outside of this window can be fixed later, but do not fuck around during this critical period because when it is closed, it is closed forever, and virtually no one who doesn't learn a good foundation at this time will ever overcome that disability and go on to become comfortable with math.
I think the point is that the "foundation" of memorizing a bunch of addition and multiplication tables isn't much of a foundation for anything.
The real foundation you need is figuring out how to but together those more abstract complex bits.
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I was always bad at my times tables. Even now I'm probably somewhat slower than I should be at dingle digit multiplication, and lean quite a lot on deduction not regurgitating.
But I'm good at order of magnitude estimation, and either way mental arithmetic comes up remarkably rarely in linear algebra, which I'm not too bad at. OK at projective geometry too, dabble a bit in exponential maps. Fourier stuff and differential equations, yep, ok, can cope. Probability and stats (I'm a dyed in the wool Bayesian) ar
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I was always bad at my times tables. [...] But if you ask me 7*9 yeah I have to think a moment.
The way I figured it out, when it started to fade, was to memorize the special table entries. Of course 10x and 11x are no-brainers to remember. But I reasoned that 7x9 must be (special entry) 7x7 + 2x7 (or even 7+7). And oh duh 7x10 - 1x7 but it's longer to subtract all those ones.
My earliest rules for some of the entries remind me of something an LLM might say. But everyone laughed when one day the teacher asked me 11x11 and my answer was "eleventy-leven?" Hmm, better use the factoring for those numbers
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I really disagree with this, but my perspective may be biased by my own experience. I found it easier to calculate the times tables from other principles rather than memorize them. I think what I actually did was memorize some basic ones like, for example, 5X5 is 25, from there it's easy to get 5X7 is 35 because 5+5 is 25 and 5X2 is 10 and 25+10 is 35, etc. Along the way of course, you inevitably do memorize all the stuff on the times table anyway, but I think my way ended up imparting greater understanding
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If only we switched to binary. We could help so many children. Think of the children.
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Well, memorizing those basic rules and tables is necessary
Meh on the tables. The basic rules, sure, but the tables derive from the basic rules. Maybe instead of memorizing the tables, children should learn to create the tables from scratch using the basic rules. As I said in another post, you do have to learn the basics before you can move on to advanced concepts, but that does not necessarily mean memorizing tables first. Kids are going to be doing math for at least a decade around the time they try to teach multiplication tables. They're going to memorize what t
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People say that a lot. The tables are not "rules" and they become remarkably less useful when you stop doing arithmetic. I used to joke that we weren't allowed to use numbers at all in my honors undergrad math classes. Joke as in "funny" not as in "not actually true." I think there's a good argument for learning what addition and multiplication actually *are* rather than what they do in a particular narrowly defined domain is a better way to learn artihmetic.
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Real math is about applying logic and solving new problems with those skills. While being able to add and multiply quickly and accurately in your head makes things easier, it is a basic skill that's needed, but speed is not essential, its not what math is really about. Its what I think people who don't understand math think its about.
I remember reading Roald Dahl's Matilda and how he showed how she was brilliant at math, but stating something like the number just appeared in her head, well if you don't know
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My father was a high school math teacher. I hated math in both elementary and high school. He assured me that what I actually hated was arithmetic, it was the least interesting part of math (he was also the computer teacher), and that I'd really like proper math when I eventually got to it.
He was right.
Many students, like me, dislike pre-university math because it's mostly arithmetic. But there are other reasons. Some of my cousins all liked math until they had a particular junior high teacher who insisted
They Might Transfer (Score:2)
They might transfer.
But I wouldn't count on it.
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I see pun skills don't transfer either.
Does India have Math (singular) or Maths (plural) (Score:2)
I was born and raised in a commonwealth country, and we had Maths (short for Mathematics)
I thought that Math (singular) was an american invention.
Of course we memorized the 12 times table as kids because calculators hadn't been invented yet.
I guess western kids these days have cellphones so don't need to memorize tables or learn long division.
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I assume that you mean 'solid state' calculators?
Mechanical calculators have been around for a long time.
Even solid state calculators have been around since the early 1960s. You weren't going to stick it in your pocket, but it was a solid state calculator. The first calculator I used was a fancy computer in the late 1960s or early 1970s. (I don't recall exactly which year it was). That would have been the HP 9100A, which I'd like to have one for my collection.
Calculus (Score:2)
This is probably related to the well-known phenomenon where some kids coast through math with mostly 'A' grades, maybe an occasional 'B+', without much effort... then stumble a bit in Calculus I, and totally crash & burn in Calculus II. And likewise, it's the inflection point where many kids who struggled with (and often, hated) "math" while growing up suddenly have their epiphany, do spectacularly well, and decide to become math majors halfway through college.
"inflection point" (Score:1)
I see what you did there :)
Re: Calculus (Score:2)
From my recollection, Calculus II was way heavier on rote memorization than anything before it in math education.
Critical moment my smelly rear-end. (Score:3)
No. That's dumb. Traditional mathematics hasn't changed, and the need for computer literacy is an entirely separate issue despite the traditional connection. That's the CS course, not the math class.
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What you propose doesn't seem to work for people who aren't proto-mathematicians, and since there aren't many of those and most people don't ever need more than basic algebra, we should stick with tried-and-true methods. Not everyone is capable of "understanding and generating maths", and fewer need to. Everyone needs to come up with the correct answer quickly. The students who will "unders
how do some people become calculators (Score:2)
How do some people become human calculators? It know some people who are basically inept at most things, but they can multiply pairs of 4+ digit numbers accurately without having to really think about it. They're really good at card games, but don't ask them to do anything academic with math.
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How do some people become human calculators?
You drink the juice of Sapho
Re: how do some people become calculators (Score:2)
Working memory + pattern recognition - rigor.
Examples Please (Score:2)
Can we get examples of these complex mathematics that the rural children are so good at? Because if it's all just spacial reasoning stuff that may be truly helpful in their personal lives but as far as I know doesn't have much applicability to frontier mathematics. Just because a kid can glance at a couple of baskets and tell you exactly how many times the capacity of the small one can fit in the big one does not mean they can solve hodge conjecture or that they would derive any benefit from training in s
Math in college (Score:3, Interesting)
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I struggled with some math in college that was "on paper". Meaning that I know it would take me 15 seconds to write a script to solve the math problem, but struggled to do it by hand on paper. I even remember asking the 70-ish year old instructor why do math symbols and programming symbols have to be different. Especially for boolean operations, I realized that it was pointless arguing but I at least wanted to say it out loud. In my university physics course I had my laptop out and would write little scripts for solving different problems where I could just plug in the numbers that the professor wrote on the board and immediately get an answer. She seemed impressed that I came up with that way for a solution.
This exactly. Different people have different minds, and your writing a script to answer the problem is really cool. What is important is that it solves the problem, not you following some arcane method that someone thinks is how all minds operate.
Like me first using a slide ruler was an ephipany. I can do math in my head now by imagining a mechanical model. I don't know how many people operate the same. But it solves the problem.
And when my son brought home the common core math, I looked at the prob
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It amuses me that we've heard all the exact same disparaging of math instruction before. Since you're talking about slide rules you might be old enough to remember the 1960s when "new math" was introduced. Parents hated it, thought it was unintuitive, added a lot of extra steps, and focused on
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You seem to be forgetting that the "New Math" curriculum lasted only a decade in most school districts, lingering on for another decade in a few. It had one of the same major complaints as Common Core math: it tried to teach more abstract, complex topics before students had a grasp of the basics. Not that I think rote memorization of times tables is great, but it's hard to teach children to think about math in deep ways if they do not understand the simple ways yet. I mean, asking a student why in 5X + 3X =
Not hard to see why (Score:2)
why do math symbols and programming symbols have to be different. Especially for boolean operations,
It's not that hard to see the reason why this is the case. Most maths notation predates computers and even typewriters. Go look at a PhD thesis from the mid 1980's or earlier and you'll see that while it is typewritten the maths symbols are usually added by hand. This left programming language developers the task of mapping maths notation into characters that could be typed on one line using a standard keyboard.
I had my laptop out and would write little scripts for solving different problems where I could just plug in the numbers that the professor wrote on the board and immediately get an answer.
That's great for basic, introductory physics courses but unless you learn how to handle the not
Sexagesimal (Score:2)
We need to go back to Ancient Babylonian methods and rebuild all of our education on Base-60 math [wikipedia.org]! Only then can we plow our fields and properly determine the angle of a triangle.
Missing the point entirely (Score:2)
Re: Missing the point entirely (Score:2)
I challenge you to non-numerically integrate a hyperbolic trigonometric function without memorizing anything.
Not surprising (Score:2)
Algebra (Score:3)
I always thought it was interesting how many people claim that "you'll never use algebra in real life"......but they (generally) have no problem figuring out how much additional money they need if something costs "Y", but they only have "X".
international studies determining standards (Score:2)
As it seems the US Department of Education will no longer be allowed to fund research in cognitive development methodologies, we can expect to see an increase in studies like this providing acknowledgments to non-US institutions. As the focus of these non-domestic studies will be on context affecting students outside the US, their results will be of increasingly less relevance to US educato
The soft bigotry of low expectations (Score:3)
“Now some say it is unfair to hold disadvantaged children to rigorous standards,” Bush remarked. “I say it is discrimination to require anything less — the soft bigotry of low expectations [carolinajournal.com].”
Call it for what it is (Score:2)
"particularly those from lower-income families"
You mean those from lower-caste families.
This is the country that has oppressed its own people so hard BY BELIEF that one of the rich fuckers insists the lower castes need to work 70 hours a week minimum so they can 'catch up.'