I don't know whether multiplication tables are required in elementary school - but I do know that a vast majority of my former students could not multiply two numbers mentally and come up with even a rough, order-of-magnitude approximate answer.
For instance, if asked to estimate 33 x 4.9, you might quickly estimate that the answer would be between 150 and 165, because you know that 3 x 5 is 15, and that 30 is 10 times 3, and that 10 x 3 x 5 is 150, and that 33 is about 10% bigger than 30, and 10% bigger than 150 will get you to 165. Finally, you know 4.9 is a wee bit less than 5, so the correct answer must be a bit less than 165.
You would probably go through that thought-process almost subconsciously, and just guess that the answer would be, very roughly, around 160 or thereabouts.
For most younger people, that ability is completely gone. Most of the students I've had in the last ten years wouldn't have any idea if the answer was going to be 1, 50, 900, 22000, or three million.
Along similar lines, have you ever had an experience like this: you buy something at the corner store for, say, $6:45. Not wanting to get a handful of coins and small bills in change, you hand over a $10 bill, a $1 bill, and fifty cents in change.
The young person on the other side of the counter looks baffled, then slightly amused, and gently offers you your $1.50 back, trying to explain to the obviously senile old fool she's dealing with that $10 is more than enough to cover the cost of the purchase.
You then explain that you gave her the additional $1.50 because she can then give you a single $5 bill in change, rather than having to give you three $1 bills or coins plus 55 cents in change.
She looks nonplussed, enters the amounts into her cash register, and is utterly baffled when the machine tells her to give you $5 in change (and five cents in coin). Then she asks you "How did you know that was going to happen?"
Slight variants on this have happened to me many times during the last twenty-odd years. Anyone else?
Obviously this isn't an issue of intelligence, per se, but rather has to do with how a person has internalized the value of numbers. I think the lack of this ability is also the reason why so many students were willing to believe that a 0.4" diameter metal rod actually measured 4 inches in diameter, and why teachers are so often faced with a ludicrously absurd answer along with an indignant "But the calculator said so!"
I'm hoping that the day never comes when I read about the bridge that collapsed because it was constructed from girders with 1 centimetre wall thickness, rather than the intended 10 centimetre wall thickness, because the engineering team had no clear internal idea of the difference between 1 and 10, and the construction crew never noticed the error because they didn't know roughly how big 10 centimetres is, visually.
-Gnobuddy
> they didn't know roughly how big 10 centimetres is, visually.
We should go back to rods, cubits, hands, and fingers.
_I_ can't picture "10cm" on sight. But if it was specced "hand wide" I'd know instantly if they delivered the wrong stuff.
We should go back to rods, cubits, hands, and fingers.
_I_ can't picture "10cm" on sight. But if it was specced "hand wide" I'd know instantly if they delivered the wrong stuff.
Something I haven't seen brought up yet on this thread: the loss of cursive writing, and the consequences of that seemingly trivial change.
I have zero qualifications as a brain researcher myself, but I've read lay articles and books by a number of researchers that suggest that small things we do very frequently have a bigger impact on our brains, than big things that we do rarely.
One example is walking barefoot, which constantly re-builds the neural connections in your brain that process the signals from the nerves in the soles of your feet; the end result is keeping your brain tuned to recognize and maintain your balance as you walk.
If you never walk around barefoot, but instead walk only when wearing shoes for several decades, the nerves in the soles of your feet send fewer and less sensitive information to the brain. As a result, it's now thought that these neural connections weaken over that time, and the end result is that more elderly people lose their balance, fall and injure themselves.
As many of us know, a fall involving a senior citizen can be catastrophic, and for many of them, it signals the beginning of the end of their lives, as a fall frequently results in broken bones and a steep nose-dive in overall health that continues until death.
In the same way as walking barefoot is good for your brain, it turns out that handwriting is good for the brain also; planning out the shapes and sizes and intersections needed to form legible block lettering engages many parts of your brain, including areas responsible for processing vision, language, motor control, logistic, and so on.
However, while block lettering provides some brain exercise, it turns out that the much more complex curves of cursive writing give your brain much more of a workout than block lettering does. This has a number of surprising effects on people who write frequently, including speeding up the learning of new material, increasing the number of new ideas generated, and improving retention of material you'd written. There is even evidence that writing in cursive increases attention span and may make people calmer.
Some of this information came from the book "The Brain That Changes Itself" ( The Brain That Changes Itself: Stories of Personal Triumph from the Frontiers of Brain Science: Norman Doidge: 0000143113100: Books - Amazon.ca ), but I've also read similar things from several other sources; one was an article on the New York Times called "What's Lost As Handwriting Fades", an article which is now behind a paywall.
However, I found a copy here (there is also a second article about teenage anxiety, unrelated to the first article about cursive handwriting's effects):
https://www.lachsa.net/ourpages/auto/2017/2/6/35994471/2 AP articles on psychology 2017.pdf
In English and related languages using the same alphabet there is both block lettering and cursive writing, but there are many other world languages in which there is no equivalent to block lettering. One presumes that children (and adults) writing in those languages will continue to benefit their brains.
-Gnobuddy
I have zero qualifications as a brain researcher myself, but I've read lay articles and books by a number of researchers that suggest that small things we do very frequently have a bigger impact on our brains, than big things that we do rarely.
One example is walking barefoot, which constantly re-builds the neural connections in your brain that process the signals from the nerves in the soles of your feet; the end result is keeping your brain tuned to recognize and maintain your balance as you walk.
If you never walk around barefoot, but instead walk only when wearing shoes for several decades, the nerves in the soles of your feet send fewer and less sensitive information to the brain. As a result, it's now thought that these neural connections weaken over that time, and the end result is that more elderly people lose their balance, fall and injure themselves.
As many of us know, a fall involving a senior citizen can be catastrophic, and for many of them, it signals the beginning of the end of their lives, as a fall frequently results in broken bones and a steep nose-dive in overall health that continues until death.
In the same way as walking barefoot is good for your brain, it turns out that handwriting is good for the brain also; planning out the shapes and sizes and intersections needed to form legible block lettering engages many parts of your brain, including areas responsible for processing vision, language, motor control, logistic, and so on.
However, while block lettering provides some brain exercise, it turns out that the much more complex curves of cursive writing give your brain much more of a workout than block lettering does. This has a number of surprising effects on people who write frequently, including speeding up the learning of new material, increasing the number of new ideas generated, and improving retention of material you'd written. There is even evidence that writing in cursive increases attention span and may make people calmer.
Some of this information came from the book "The Brain That Changes Itself" ( The Brain That Changes Itself: Stories of Personal Triumph from the Frontiers of Brain Science: Norman Doidge: 0000143113100: Books - Amazon.ca ), but I've also read similar things from several other sources; one was an article on the New York Times called "What's Lost As Handwriting Fades", an article which is now behind a paywall.
However, I found a copy here (there is also a second article about teenage anxiety, unrelated to the first article about cursive handwriting's effects):
https://www.lachsa.net/ourpages/auto/2017/2/6/35994471/2 AP articles on psychology 2017.pdf
In English and related languages using the same alphabet there is both block lettering and cursive writing, but there are many other world languages in which there is no equivalent to block lettering. One presumes that children (and adults) writing in those languages will continue to benefit their brains.
-Gnobuddy
I talked about this a bit in an earlier post - when I taught in the USA, eventually approximately 40% - 50% of my students would measure the diameter of a finger-sized rod and tell me confidently that it was four inches, when it was actually 0.4 inches. What concerned me most about this development was exactly what you said, that they had no clue that 4 inches is about the width of your hand, and not the width of your finger.
When I began teaching in Canada, it was, of course, in metric units, and so I expected my students to know that, for instance, a human finger is about a centimetre wide, and that you can more or less hug a tree with a 1-metre diameter trunk, but not one with a 2-metre trunk. 🙂
I'm okay with American students not being familiar with metric units (though very necessary for those who go on to become scientists, for instance). And the same in reverse in Canada, I really don't expect any Canadian student to have a clue how many kilogrammes correspond to 1 slug.
While Canada is nominally metric, I found out when I moved here that we're actually entirely schizophrenic about units. My car speedometer is marked in both mph and km/hr, I buy gasoline in litres, but inflate my tyres to a specified pressure in pounds per square inch. If I walk into Home Depot here, probably 90% of everything inside is in imperial dimensions, except for those things (lumber, piping) which is in even more bizarre units specific to that trade (board feet, 2x4s that are actually 1.5" x 3", et cetera.)
At least we don't measure our weight in stones. I'm thankful for that small mercy. 😀
-Gnobuddy
@billshurv
Small cars aren’t so small anymore either, is why they need that extra power.
While I have lived in the US all my life, I was raised with nearly all European cars in our family from birth. Had (4) Opels, before I had a driver’s license, parents had several Volkswagens, Rover, Triumph TR2.
I’m well aware of the bouncy, heavy sleds that everyone else was driving. I can only figure they were designed by drunks for the purpose of driving drunk perhaps(?) They certainly weren’t the way of the future, that’s for sure.
A lot of kids don’t have any interest in driving these days, different times. I’ve tried to get my daughter to the go-cart track, but no interest.
Small cars aren’t so small anymore either, is why they need that extra power.
While I have lived in the US all my life, I was raised with nearly all European cars in our family from birth. Had (4) Opels, before I had a driver’s license, parents had several Volkswagens, Rover, Triumph TR2.
I’m well aware of the bouncy, heavy sleds that everyone else was driving. I can only figure they were designed by drunks for the purpose of driving drunk perhaps(?) They certainly weren’t the way of the future, that’s for sure.
A lot of kids don’t have any interest in driving these days, different times. I’ve tried to get my daughter to the go-cart track, but no interest.
Many of the gargantuan SUVs and pickup trucks on the roads in North America today, weigh about twice as much as an original 1960s/70s Volkswagen Beetle - a four door family car - did.
Based on the trend over the last twenty years, apparently the wave of the future is "irresistible force meets immovable object". Two and a half tonne vehicles crammed with several hundred horsepower. The stupidest possible approach, in a world strangling on petroleum emissions.
Kids - particularly those exposed to TV, tablets, and smartphones early - don't even have much interest in playing outdoors now. "Outdoor play has been steadily decreasing for North American children": What's Causing the Decline in Children's Play | Fix.com
A brain researcher I spoke with told me that extensive TV watching makes children physically passive, teaching them to sit motionless and inactive for long periods of time, rather than being up on their feet and moving around. There is also evidence that it makes them mentally passive, slowing down active thought processes and replacing them with the trance-like receptive state many of us have seen or experienced ourselves when binge-watching TV / NetFlix.
That conversation happened in the early 2000s, before the advent of the iPhone and Android. But clearly, putting a smartphone in a child's hands doesn't exactly encourage him/her to get up and play actively. 🙄
-Gnobuddy
Even a Prius is absolutely huge. I think some amount of it is that Americans are getting increasingly large and need more space so the door can close.
Now we're talking!
I hope more people see the benefits of barefoot walking, it's great. If you're not used to it there is a big benefit (absolute must!) of doing a slow transition to begin with. But it's much better for the knees and lower back.
I made a cheap setup with steeringwheel + pedals set in the cellar, the kids practically live there despite the low temps.
And I did promise them to go to the local go kart track in when spring comes, they're very excited about it.
Not exactly the point, but one thing I never understood is why would anyone want to wear shoes indoors unless it's really cold. You just walk around in the streets over all the dirt and muck, dog crap and spit and then you just happily walk into your living room wearing the same shoes. Nice.
Even "completely" metric countries use some old units. Go ahead and try to buy car wheels using metric units in Europe for example. Even though the official timber sizes are metric, we still colloquially talk about 2x4's and 4 inch nails and whatnot. Threaded water pipe fittings are all imperial sizes while copper pipes are metric. So you basically have an imperial size at one end and metric in the other. Yet, copper pipes used in AC systems are imperial.
Attachments
In the late 90's the State of Florida implemented the mother of all standardized tests, the FCAT, or Florida Comprehensive Assessment Test. It, in various forms was used to measure the "quality of education" and was used to grade students and well as schools. In 1999 when my daughter was in school, a student was given 4 chances to pass that test before being allowed to graduate, or participate in school sports.
Another of my daughter's friends had done poorly on test #3, AND he wad a decent player on the football team, so magically he shows up at our house with an old copy of the test. We had a couple months to prepare him for the "last chance." I remember spending several sessions with him pondering the same question, and how to best approach it. I don't remember the exact numbers, so I'm making them up.....
Johnny goes to McDonalds and buys a burger for $1.98, Fries for $1.19, and a Coke for $0.99. He hands over a $5 bill, how much change should he get back?
Calculators were not allowed, and smart phones did not yet exist.
I give the state props for using real world examples that this kid should have been able to handle at age 18 or 19. After a couple of months of pounding this, and other stuff into his head, he did pass test #4 by one or two points.
There were 4 "multiple guess" answer choices, two of which were easily eliminated. In the real world you need to know how to do this. Faced with a test, you work these questions backwards. Take your best guess at the answer, add it to all the prices and see if you get 5, Yes, that's right answer, no, choose the other possible answer.
He played football through high school, but wasn't recruited by any college. We helped him with applications to several sports oriented colleges. He heard back from one or two small schools, but couldn't pass their entrance exams.
Mentally rounding off it adds up to "about" $4.20, so "about 80 cents change back.
That takes about 5 seconds, the point being to decide whether a $5 bill is enough and you will get "some" change or you need to add more money.
You say average "yung´unes´" can´t do that?
Maybe, will check next time I am waiting at a supermarket line to pay.
One BIG problem against everyday "math practice" is that hardly anyone pays with bills any more, which have fixed values and usually generate cash returns, also in bills and coins, while sweeping a plastic card extracts the *exact* amount, period.
Unused muscles=atrophied muscles.
It also applies to "brain muscles" .
That takes about 5 seconds, the point being to decide whether a $5 bill is enough and you will get "some" change or you need to add more money.
You say average "yung´unes´" can´t do that?
Maybe, will check next time I am waiting at a supermarket line to pay.
One BIG problem against everyday "math practice" is that hardly anyone pays with bills any more, which have fixed values and usually generate cash returns, also in bills and coins, while sweeping a plastic card extracts the *exact* amount, period.
Unused muscles=atrophied muscles.
It also applies to "brain muscles" .
I have two grand-kids from my second marriage.
The older learned multiplication, fractions, etc the way I did.
The younger was not required to learn them, instead they were taught how to use a calculator.
I have heard a young person state that 1/3 is bigger than 1/2 because 3 is bigger than 2.😱
If you really want to confuse a clerk at a checkout line, give them change such that they will give you back a quarter.
The older learned multiplication, fractions, etc the way I did.
The younger was not required to learn them, instead they were taught how to use a calculator.
I have heard a young person state that 1/3 is bigger than 1/2 because 3 is bigger than 2.😱
If you really want to confuse a clerk at a checkout line, give them change such that they will give you back a quarter.
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Our youngest was taught math by some ‘new math’ technique....of course in having to help him with his homework my way of showing your work did not align with whatever nonsense they were trying to teach him. This resulted in F’s on his homework even though it was done 100% correct, and me coming really close to going to jail when voicing my displeasure at the school....we ended up homeschooling him from grade 5-8, he passed all qualifiers with upper 90% scores and did very well in math all through high school.
Problem may be in how they’re teaching elementary math these days.......it was some of the most convoluted BS I’ve ever seen.
Problem may be in how they’re teaching elementary math these days.......it was some of the most convoluted BS I’ve ever seen.
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Exactly, and thereby arriving at the only possible correct answer on that test in little time. This is often the case with many tests that have only 4 or 5 answer choices.
Tests where you must write in the correct answer, or even show how you got it requires actually doing the requested calculation, but these kinds of tests do not allow for rapid grading via an optical scanner, or a card with a hole punched over the correct responses.
I'm too old to know what an "average young person" is today. I know that a good portion of my daughter's friends could not handle those simple skills.
Nor could any of my grandkids today.... They can all outplay me at any video game, but none can beat me at one lap around the paved track at the park without cheating (about 1 mile).
Try this test, walk into a fast food restaurant and ask the cashier for an item that's from their competitor's menu (IE, ask for a Big Mac at Burger King) and see how long they will stare at that machine looking for the proper button to push. It works better with lesser know items. Try the breakfast menu.
For 41 years I worked in a high technology facility. Once the factory was gone, taking all "labor" jobs with it, I constantly had to remind my coworkers that the establishment was NOT a normal cross section of society. Want real world opinions on our phone products, go to the shopping mall, and not the fancy upscale mall either.
Bicycle parts are often specified in odd metric sizes that correspond to nice round Imperial units, e.g. 28.6 mm instead of 1-1/8". 26 mm was common for an aluminum road bike handlebar clamp diameter, that's metric, but some bars were 25.4 mm (1"), and carbon fiber handlebars drove a change to a larger diameter, so they use 31.8 mm (aka 1-1/4").
The bicycle parts like so many other things are built with machines that use imperial units, then sent to a metric country. Happens here in the great white north a lot, and I assume a number of other countries as well.