The importance today, of "Times-Tables" ???

[Macbeth]

To this day it has always annoyed me that we had to go through the times tables by rote with "one's one is one, one's two is two, one's three is..." and then the same once we hit ten.

Two totally redundant tables there.

The eleven times table was out of bounds for a year or so. 

[IanB]

To this day it has always annoyed me that we had to go through the times tables by rote with "one's one is one, one's two is two, one's three is..." and then the same once we hit ten.

I'm sure I used to tune out and daydream during that stuff...

[TimNJ]

While I believe knowing times-tables up to about 12x12 is useful in both everyday life and engineering, I think the point of recent changes is to de-emphasize the memorization aspect of learning and to encourage other ways of approaching the problem.

I've been out of school for a little while now and learned via a mostly traditional education, but many times when I hear older folks talk about state of education, it's the same shit every time. Maybe, just maybe, the way you learned wasn't the best way ever. (Imagine that!) And even if YOU made it out okay, consider that other kids may have poor experiences.

I'm not here to completely defend removing times-tables (or similar) from the curriculum, but I just ask you to open your mind to new methods.

[Brumby]

Personally, I have nothing against new approaches - but to use something new just because it is new is not a justification for doing so.  Somebody's proposition that a new method has merit is NOT proof that it does.

Also, I find the argument that helping kids understand why 6 x 9 = 54 and being able to arrive at that answer via alternative methods is more of a waste of time these days.  This argument would have been far more significant 50 years ago.

Why do I say this?  Simple.  These days, the kids who will go on to use their skills in more advanced mathematical skills will likely find these excursions rather boring - and those that won't will just pull out a calculator ... which will likely be on their phone.

For those who find themselves having to do a real world exercise in arithmetic by hand, knowing your times tables off by heart allows the process to be more efficient and far quicker.

JMHO

[mtdoc]

While I believe knowing times-tables up to about 12x12 is useful in both everyday life and engineering, I think the point of recent changes is to de-emphasize the memorization aspect of learning and to encourage other ways of approaching the problem.

I'm not here to completely defend removing times-tables (or similar) from the curriculum, but I just ask you to open your mind to new methods.

Yes, I agree but just to be clear, here in the US, the new “common core” curriculum does NOT eliminare memorization of multiplication (aka “times”) tables. In fact, as I referenced earlier in this thread, it explicitly states knowing them by memory as an early (3rd grade) goal.

[Distelzombie]

Personally, I have nothing against new approaches - but to use something new just because it is new is not a justification for doing so.  Somebody's proposition that a new method has merit is NOT proof that it does.

Why do you assume they don't have a good reason to switch teaching methods? They're Scientists, after all. Also, someone has to test new methods that look promising theoretically. Some methods are inevitably getting scrapped. That's normal and good.
That shouldn't make anyone assume the scientists don't know what they are doing. (Not that I think you are)

[Brumby]

Also, someone has to test new methods that look promising theoretically. Some methods are inevitably getting scrapped. That's normal and good.

I wouldn't like to have been in that class.

[Cerebus]

Also, someone has to test new methods that look promising theoretically. Some methods are inevitably getting scrapped. That's normal and good.

I wouldn't like to have been in that class.

How do you know you weren't?

The scene: 1974. A young boy with scabby knees and short trousers stands next to an elderly man who has wild hair, a central bald patch, horn rimmed glasses, and a tweed jacket with leather elbow patches.

Man: [Cod Viennese accent] "Zo, zis young boy looks like an ideal subject for an ... [orchestra sting] ... educational psychology experiment." [crackle of distant lightning]

[Brumby]

I wouldn't like to have been in that class.

How do you know you weren't?

I had the times tables drilled into me in primary school ... actually the whole class did.

[rstofer]

Personally, I have nothing against new approaches - but to use something new just because it is new is not a justification for doing so.  Somebody's proposition that a new method has merit is NOT proof that it does.

Why do you assume they don't have a good reason to switch teaching methods? They're Scientists, after all. Also, someone has to test new methods that look promising theoretically. Some methods are inevitably getting scrapped. That's normal and good.
That shouldn't make anyone assume the scientists don't know what they are doing. (Not that I think you are)

Educational science is to science as sewer maintenance is to hydrodynamics.

How do we know?  Look around!  Achievement levels upon HS graduation are at all time lows (specifically in the US).  Sure, there are many who succeed in spite of the system but the vast majority graduate dumber than a box of rocks.

I prefer to think that the teachers want an elitist system whereby they seem to be the smartest person in the room.  Big words, complex ideas (badly explained), parents unable to help with homework...  Yup!  The teacher likely is the smartest person in the room.  At explaining some convoluted approach to mathematics.

Teachers, typically, make squat money.  Society doesn't value them, just ask.  We don't value them (and I'm talking at teachers less than full-blown professors at prestigious universities) because their performance (teaching kids to enumerate) sucks.

Did I mention that they don't want to have their salary tied to performance?  I realize how complex performance measurement can be when they inherit a class full of kids who don't want to learn.  I don't know how to deal with that.  We have kids whose attitude is "Nobody in my family ever got an education and I'm not going to get one either!".  But they are required by law to plug up the system.  That I don't now how to deal with it doesn't mean there isn't a solution.  In terms of percent improvement, it's easier to show this when the average is quite low.  What you don't want to be measured on is a bunch of AP students already at some 90+% level.  Percent improvement is hard to get!

You might notice that I don't hold our educational system in high regard.

New methods?  Why not use the same methods that created the greatest achievement in the history of mankind, landing a man on the moon and returning (landed July 20, 1969, almost 50 years ago).  We did that with conventional methods and extraordinary people but we did it with slide rules and times tables.  Does everybody remember that we made 6 landings and 12 astronauts have walked on the moon's surface?  Keep that in mind when comparing methodology.

It's a lot like the Calculus course my grandson is taking.  A very small percentage of the material will ever be applied outside of a math department.  Limits aren't a big deal, finding concavity is just about useless and proofs of L'Hopital's rule just never came up in my corner of engineering.  What did come up was related rates and optimization - the word problems.  Sure, the subjects are taught but only as a side issue to the 'elegance' of math.  Who cares?  If it doesn't solve a real-world engineering problem, skip it and move on!  Have a second track for math majors.  I understand (from a video course) that the University of Florida does indeed have two tracks through math - one for math majors and another for engineering majors.  Good for them!

At the end of my rant, I guess I just don't consider those people tinkering with teaching math as scientists.  More important, I don't want my grandson to become a lab rat.

[rstofer]

On the subject of achievement look at Singapore's educational system.  Their college graduates are very well educated.

Go to a McDonalds mid-afternoon and you will see all the tables in the back filled with teenage students doing homework.  No grab assing, just diligent effort.  I was amazed!  It's like a giant study hall!  And quiet, like a library!

Singapore takes education seriously.  And, no, I don't know if they are teaching 'times tables' but I'll bet they are!

[Distelzombie]

Dude. There would be no Smartphones if everyone would have sticked to what they always did, only following traditions. And don't say: "We would be better off without these anyway" That's not the point and is irrelevant.
We wouldn't even be gone out of the Ocean in prehistoric times, if not for some creatures who decided there could be something tasty up there to eat. Those you weren't following the new trend are still swimming in the ocean, btw. They're fish. Aren't you happy they decided to try something new for once?

Why do you all fear change so much? Change is in our nature.

Apparently they learn them in Singapore.
And, that someone else uses a technique for something doesn't justify using it to,o and it doesn't mean that it is the best or a better technique. That will be decided by the outcome.

[CatalinaWOW]

It's a lot like the Calculus course my grandson is taking.  A very small percentage of the material will ever be applied outside of a math department.  Limits aren't a big deal, finding concavity is just about useless and proofs of L'Hopital's rule just never came up in my corner of engineering.  What did come up was related rates and optimization - the word problems.  Sure, the subjects are taught but only as a side issue to the 'elegance' of math.  Who cares?  If it doesn't solve a real-world engineering problem, skip it and move on!  Have a second track for math majors.  I understand (from a video course) that the University of Florida does indeed have two tracks through math - one for math majors and another for engineering majors.  Good for them!

Different parts of engineering will require different elements of math.  One of the most obvious examples-- I can think of no use whatsoever for tensors in electronics engineering.  But mechanical engineers do find them useful from time to time as do solid state physicists (the guys who design the elements of our chips).  My particular path through engineering did involve the application of L'Hopital on a couple of occasions.  I wouldn't have known to Google it if I hadn't already had it in my toolbox.  Much of Electrical Engineering uses limits implicitly, particularly in the application of steps and impulse functions in transfer function analysis.  While many get away with assuming all of this just works it really is useful to know where the math works out, and where it has limitations.  It is also good to understand some of the implications to the results.  Many are not aware of Gibb's phenomenon in approximation of a square wave with a series of sinusoids.

I agree with much of your rant against US education, but I suspect that much of it is the result of trying to set inappropriate goals and trying to fit pegs of many shapes into a hole of one shape (with that shape not necessarily desirable.)  Silly goals, like sending everyone to college without understanding that there is not and cannot be a market for that many graduates.  Silly goals like trying to assure that everyone has a desk job.  Other goals, while laudable, may also turn out to be silly.  The common core attempt to get a higher degree of numeracy may be such.  The shortcuts and tricks taught in common core are obvious to those comfortable with numbers and may be of little use to those who are not.  In any case the broadening of the syllabus, with little extra time to teach it seems to insure that few will actually have these tools at their fingertips where they can be used.

[coppice]

It's a lot like the Calculus course my grandson is taking.  A very small percentage of the material will ever be applied outside of a math department.  Limits aren't a big deal, finding concavity is just about useless and proofs of L'Hopital's rule just never came up in my corner of engineering.  What did come up was related rates and optimization - the word problems.  Sure, the subjects are taught but only as a side issue to the 'elegance' of math.  Who cares?  If it doesn't solve a real-world engineering problem, skip it and move on!  Have a second track for math majors.  I understand (from a video course) that the University of Florida does indeed have two tracks through math - one for math majors and another for engineering majors.  Good for them!

Limits are a big deal in real world engineering. Concavity analysis is a big deal in engineering. L'Hopital pops up frequently in engineering. Maybe you shouldn't judge the whole field of engineering from your own experience. Try asking, say, a serious DSP engineer (i.e. one who does more than plug off the shelf modules together) if they've used this kind of maths in their day to day work.

[georges80]

Today. Cut/Paste from some texts with my son. ME prefix are my responses:

Yay, I missed 10 percent on my econ midterm because apparently arithmetic and simple algebra with 1 variable is impossible to do in your head
14:15
Like who can solve for P when given the equation 32-P=3P
14:16
How do you do .5*8*24 and then instead just write 4*24 = 96 to get rid of the half instantly
14:17
He literally said that the 96 I wrote down had no correlation to any of my answers even though one of my answers was 96,000 and I had just multiplied by a 1000 after since the 24 was in thousands of taxi rides and I just made the math simpler
14:19
ME: Talk to the idiot and explain you are good at mental arithmetic versus the moronic system where people question the need for knowing the times table
14:23
ME: Ask him to explain how did you get the correct answer and not get full marks
14:23
ME: This is bullshit
14:23
I did
14:27
This was during my talk with him
14:27
ME: Ask him if you are in college or still in elementary school?
14:29
ME: And did he request every arithmetic step be shown?
14:30
ME: Like in elementary school
14:31
ME: Was your final answer correct?
14:31
Of course it was
14:36
And sort of yeah
14:37
ME: Up to you, but I would escalate it through the department
14:50
ME: This is University and simplistic arithmetic steps are not showing your work, showing your work is equation or formula steps and only if requested in the exam paper
14:51
ME: Did the exam paper ask for all steps to be shown?
14:52
If you want partial credit yes
14:54
ME: Partial credit for a wrong final answer though I assume
14:55
Yeah
14:55
ME: Dispute it if I was you since you got the correct answer
14:55

So, this is 1st year Econ class at the university my son is going to (a UC, in California), he is studying Mechanical Eng. He took Ap Cal A/B in high school. Has completed 2 terms of higher calc in the first 2 quarters and now is taking a linear algebra class. A's in all the math classes. But Econ he is docked for a correct answer (with some partial result steps shown) for not showing each arithmetic step that was 'expected' - seriously?? This a kid for the 1st posted qtr was on the deans list at that UC.

I guess mental arithmetic and simple equation re-ordering in one's head is definitely frowned upon now...

cheers,
george.

[T3sl4co1l]

Well, it would be econ.

Tim

[rstofer]

Limits are a big deal in real world engineering. Concavity analysis is a big deal in engineering. L'Hopital pops up frequently in engineering. Maybe you shouldn't judge the whole field of engineering from your own experience. Try asking, say, a serious DSP engineer (i.e. one who does more than plug off the shelf modules together) if they've used this kind of maths in their day to day work.

I guess I would want to see an example.  I can be talked out of my position but in 30 years of engineering (not electronics), I never ran into an application.  I'll take you word for it but I would still like an example.  One where the ONLY solution is limits.  And then I would just plug it into Symbolab...

[TheN00b]

Today. Cut/Paste from some texts with my son. ME prefix are my responses:...


...cheers,
george.

That's quite moronic. Even in my high school, teachers skip basic arithmetic steps in example problems because its mental math. I can't bring myself to do it in physics at least (gotta keep that B by any means of partial credit possible!) but in calculus, I "skip" writing basic math on the paper. Same goes for our economics class. You know, even a basic microeconomics class.

[coppice]

Limits are a big deal in real world engineering. Concavity analysis is a big deal in engineering. L'Hopital pops up frequently in engineering. Maybe you shouldn't judge the whole field of engineering from your own experience. Try asking, say, a serious DSP engineer (i.e. one who does more than plug off the shelf modules together) if they've used this kind of maths in their day to day work.

I guess I would want to see an example.  I can be talked out of my position but in 30 years of engineering (not electronics), I never ran into an application.  I'll take you word for it but I would still like an example.  One where the ONLY solution is limits.  And then I would just plug it into Symbolab...

OK, lets take concavity, and related curve analysis. A lot of adaptive processes use an S like cost function. If there are local minima or maxima in that cost function you can't guarantee the system will adapt to the globally optimal position. If you want a robust system you'd better look carefully into the detailed character of that cost function.

[IanB]

I guess I would want to see an example.  I can be talked out of my position but in 30 years of engineering (not electronics), I never ran into an application.  I'll take you word for it but I would still like an example.  One where the ONLY solution is limits.  And then I would just plug it into Symbolab...

In thermodynamics, for example. The function \$x\ln{x}\$ often crops up, and \$x\$ may be zero. So you need the limit. Trivial perhaps, but needed. Symbolic differentiation and integration is often required to find analytical forms for frequently evaluated functions. If you are using an iterative root finder like Newton, then concavity or otherwise of a function is important to know if you are interested in stability and guaranteed convergence.

Then you have Maxwell relations, and homogeneous functions, and all sorts of other interesting analysis.

There are always tools to help of course, and symbolic algebra packages are invaluable, but still the need to understand the underlying theory exists. Some people being introduced to thermodynamics have been heard to say, "This is just applied mathematics!".

[GlennSprigg]

I always rather liked word problems, usually the actual math involved is a bit simpler and they almost always throw in some extraneous information. Half the problem is extracting the data from the sentences and I've always been good at that part.

Learning how to actually use math in the real world is at least as important as learning the math itself.

that seems to be the only way I CAN learn any math(s), if it's purely abstract, or even too generally applied, I find it much harder to retain the interactions. I swear there is a numerical version of dyslexia and I have it. I can remember lines from books that I read thirty years and more ago, or song lyrics, but unless Toots & The Maytalls made a song about it (54-46, that's my number) I ain't remembering your phone number.

Thank you (GerryBags) for your intelligent observations mate !
For some 'unknown' reason, I can remember long ago such things as all the vehicle rego plates of all the company vehicles
and remember ALL the 'necessary' formulas in maths/physics etc,... I can even quote the vast majority of 'Periodic Table' off
by heart etc. etc.   However...  I am SHOCKING for remembering 'Dates'    I couldn't remember even an approximate 'year'
that I completed my initial 'apprenticeship', let alone Company 'xyz' commencement withing say 5 years (Now in my 60's).
But I know my times tables.....  I started with a 'Slide-Rule' in school !!! draughting. Then calculators !!!

Though retired, I still know how to 'calculate' anything as a backup, while 'coding' xx
What more needs to be said?  If your school is better... GREAT!!!! xxx... bring the others up to grade....

[GerryBags]

Dave made a great point in passing on his live TTL computer build when asked in the chat to recommend a book for a beginner. To paraphrase, he said something like "I don't like to do that, as everybody's brain is wired up differently, and what works for one person doesn't necessarily work for someone else.".

That, I think, is the nub of it, and why no system of formal education is going to fit every member of the population, unless the single system is made to be adaptable from the outset and is actually constituted of many different educational systems (traditional rote-learning, vocational, whatever can be shown to work for a useful number of people) with each student being able to access any of them, regardless of demographic. How you'd actually go about that is far harder to say.

[CatalinaWOW]

Different folks do do and value things differently.  One of the most excruciating courses I ever took was Accounting.  The particular class I took was populated largely by engineers and other mathematically literate people.  But the professor was clearly used to a different group of people, or else had personal issues.  Every lecture spent a lot of time adding columns of numbers, detailing how you summed the rightmost digit, generating a carry element (carefully written in a smaller distinct font), which was then added to the next most significant digit column.   Step and repeat through each of the usually eight digit numbers.

While I and most of my fellows were not fascinated by the joys of double entry bookkeeping and classification of expenses we would have dearly looked forward to more of that and less of the endless repetition of early grade school arithmetic.

[bitseeker]

Wow, classic case of "know thy audience."

[james_s]

Thank you (GerryBags) for your intelligent observations mate !
For some 'unknown' reason, I can remember long ago such things as all the vehicle rego plates of all the company vehicles
and remember ALL the 'necessary' formulas in maths/physics etc,... I can even quote the vast majority of 'Periodic Table' off
by heart etc. etc.   However...  I am SHOCKING for remembering 'Dates'    I couldn't remember even an approximate 'year'
that I completed my initial 'apprenticeship', let alone Company 'xyz' commencement withing say 5 years (Now in my 60's).
But I know my times tables.....  I started with a 'Slide-Rule' in school !!! draughting. Then calculators !!!

Though retired, I still know how to 'calculate' anything as a backup, while 'coding' xx
What more needs to be said?  If your school is better... GREAT!!!! xxx... bring the others up to grade....

I've always been lousy at remembering dates, I remember history classes in Jr. High and High school tended to focus a lot on remembering specific dates on which notable events occurred and I tended to do rather poorly on those exams. It was all rather pointless too, if I need to know the date an event occurred I can easily look that up. What is much more important is learning about the causes and effects of an event, why it's historically significant and how it fits into other parts of history. It's good to know the general era when something occurred but I see almost no value in memorizing the date.