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

[GlennSprigg]

I'm in my early-mid 60's now, and was recently 'Shocked' that the majority of
school kids these days, (I'm in Australia...), do NOT know the basic tables !!!!!!!
I know we have computers & tablets & phones & calculators, but when you
don't have that 'one' needs to still know the basics, today, tomorrow & ever.

Kids here, leave 'Primary' School, (Year 7), with no such enforced preparation.
Say one asks someone what is "36 x 46".... We write it one under the other, &
draws 2 lines..... (Hey we are working it out 'manually', ha... xxx).....   So...
The 1st step is "What is 6 x 6"..... No more short cuts here !, they don't know!
(6x6 = 36, write the 6, carry the 3....)  They have no idea
Something is WAY wrong with things these days........

My 'Niece' knew what '3 x 4' was....  (Wow.. advanced... that equals '12'... )
Next question....  "What's 30 x 40".......   Her answer......
"How the hell would you expect me to know that !!!!!", with much indignation.
I explained that it is '3x4' with two '0's after it, being 1200....   (oops, edited)
She looked at me as if I was from another Planet !!!!!  (And still didn't get it...)
(She is now 14 years old...........)

TELL ME I'm missing something    

[BradC]

I'm 44. I never learned my times tables (although the they tried very hard to make me). Instead I learned the mental arithmetic required to solve those questions and any others that could be asked that were outside the bounds of the tables being learned by rote. My maths teacher once said "you can't solve that problem using a logarithm".

When asked to clarify that he replied that indeed you could solve it that way, but that was unsupported by the current curriculum and therefore if I was to answer that way in an exam and my final answer wasn't correct I'd get no points for a partial or correct methodology. I casually remarked that wouldn't be a problem as I never needed to show working because I was always correct.

As they used to say in the Middle East : "same, same but different".

Incidentally that attitude (whilst entirely accurate in that particular class) did not serve me well later in life and took quite some years of hard adjusting.

[jpanhalt]

Ah, but think of the really important stuff they have learned....I'm still thinking.  Excellent preparation to work a cash register at McDonalds.   

[Cerebus]

Kids here, leave 'Primary' School, (Year 7), with no such enforced preparation.
Say one asks someone what is "36 x 46"....

You're going to have to put an actual age against that if you want to be understood by the multi-national audience here.

In what we call(ed) primary school here in the UK (ages 5-7) I wouldn't expect them to be able to do "36 x 46" off pat by the end of primary school. Basic times tables "3 x 6", "3 x 4" and "6 x 6", to some extent yes, but not long multiplication by that stage.

Just checked, the current UK curriculum doesn't expect them to know the full 12 x 12 times table until a year after that, and only then to start doing full long multiplication. The previous year includes 'short multiplication' which is XX x X, i.e. multiplying a 2 digit number by a one digit number.

[bitseeker]

TELL ME I'm missing something    

I don't think you're missing something. It's the kids who are missing out. But, I'm just an old guy now and probably don't "get it" anymore.

The other day I paid cash for something and while the cashier was working on collecting the change from the cash drawer, I said I had three pennies (you know, to make the coinage come out nicely) and she just looked at me funny.

[sleemanj]

I'm over 40 now, don't ask me what anything above a multiplier of 6 is unless it's a common pairing like 8x8, or a decimal multiplier of course.

If you are resorting to doing stuff long-hand, a few extra seconds to figure out what 7x9 is isn't going to hurt none.

The main thing is to understand how to work out what you don't know.  And preferably developing sufficient understanding to be able to find a sufficiently efficient route (ie, recognising that 7x9 is 7 times 10 minus 7, rather than 7 plus 7 plus...)

As for showing working, it's not about "salvaging marks", it's about showing you understand how to solve the problem and didn't just make a stab in the dark or arrive at a correct answer by some incorrect method out of sheer luck.

[Cerebus]

Meanwhile in China.

When I did grade school, we did first order equations with one unknown at grade 6, and quadratic at grade 7, then trigonometry at grade 9 and advanced trigonometry at grade 11, followed by entry level calculus at grade 12.

Which, if I understand the Chinese grade system translates to:

When I  did grade school, we did first order equations with one unknown at age 12, and quadratic at age 12/13, then trigonometry at age 15 and advanced trigonometry at age 15/16, followed by entry level calculus at age 18.

Which isn't far from the western norms in my time, except that we studied trig earlier (age 13/14) - which was a welcome relief from all the classical geometry that filled our notebooks at age 12 and made the algebra we did look like light relief - and were on to an introduction to calculus by age 15/16. My maths O-level examination papers (taken at age 16+) included basic calculus questions.

[Cerebus]

That looks right to me. Maybe nowadays the kids just spend too much time on social justice and political correctness.

Says the man who comes from a country where mandatory school classes include 'social studies', 'ideology and morality' and 'labor studies'. 

[IanB]

In what we call(ed) primary school here in the UK (ages 5-7)

The age range of primary school would depend on which county you live in and which LEA you come under. Where I grew up we had Primary school up to age 10, and Secondary school from age 11 onward. (Primary school was in two stages, Infant school and Junior school.)

Primary/Secondary is I think the most common system in England, but I believe some counties have or had Primary/Middle/Secondary school systems with different age ranges for each.

[Ampera]

>Entry level calculus at grade 12

Good to know I'm ahead of the Chinese punch. 

I'm a bit of a bad example here, as I knew pretty much my complete times tables by the time I was around 7ish, maybe 8. I then started on base level Algebra (unknowns etc.) when I was around 10. 4 years later was my first college course, College Algebra and Trigonometry, which was largely a review, with some more advanced Trig concepts thrown in. I'm 16 now and while I am taking a lull with college stats, my last class (when I was 15) that I would call advanced-ish maths was Calc 2.

I think, based on the American school system at least, it would be reasonable to expect most kids here to know the complete times tables and be able to do most long maths by around age 9-10. Then again, I've met 13 years olds who could barely read.

I honestly don't have too much of a benchmark, being an introverted homeschooled child (neither caused the other for those worried). I think kids age 7 should be capable of full basic arithmetic, but everybody picks things up at their own rate and own level of dedication.

I'd say the worry point is being 12 and not knowing total and full arithmetic, along with a few concepts of how equations work.

[T3sl4co1l]

That looks right to me. Maybe nowadays the kids just spend too much time on social justice and political correctness.

Says the man who comes from a country where mandatory school classes include 'social studies', 'ideology and morality' and 'labor studies'. 

Keep in mind, the state goal of education: to create citizens obedient to the party(ies).  That any real (intellectual) education occurs, is strictly coincidental.  It just so happens that, in advanced economies, the intellectual power of the people, is the economic power of the people, and therefore of the state -- democracy arises naturally as a consequence of personal power.  It is, of course, for this reason, we must assert ourselves, to the fullest extent of our positions in this vast economy -- including demanding that our children be taught useful, practical skills, like accounting and computer science.

Ahem, borderline-acceptable topics aside,

I've seen "time stables" more than a few times, and in accordance with the intentional typo, they stink about as bad.   I'm not one for wrote memorization, something that's never been particularly valuable to anyone, anyway.  (You can't beat understanding, or creativity, into students with a stick; no, it's a much bigger problem than that -- to get that outcome, you must reorganize "school" entirely.)  I was taught arithmetic in the traditional (what today's [US] parents remember) way, but over time I've forgotten much of the memorization that goes into it (like times tables) and drifted towards a more intuitive, decimal and factorization based method.

Which, it's encouraging to finally see this being implemented in today's curricula (related to "common core" I guess).  Practical arithmetic?  Who would've thought!

Which comes with all the noise of parents griping that "3 x 5 = 15 is wrong", because they don't understand the context of that question (a task of 'making tens' or whatever it's called).

Tim

[IanB]

I'm not one for wrote memorization, something that's never been particularly valuable to anyone, anyway.

I think that's the wrong way of looking at it. Many powerful computational algorithms contain lookup tables somewhere at their core. And that is to be expected: for some things it is faster to retrieve the result from memory than it is to compute it from scratch.

Thus it is with times tables.

If we look at the mind/brain as having an analytical and executive function, then the more basic facts it contains in its database for instant recall, the more powerful and capable will be at solving problems and making decisions.

[Cerebus]

In what we call(ed) primary school here in the UK (ages 5-7)

The age range of primary school would depend on which county you live in. Where I grew up we had Primary school up to age 10, and Secondary school from age 11 onward. (Primary school was in two stages, Infant school and Junior school.)

Primary/Secondary is I think the most common system, but I believe some counties have or had Primary/Middle/Secondary school systems with different age ranges for each.

That's kind of my point, if people refer to their education system by the local 'code name' we don't know what they're talking about, so please put ages.

[Cerebus]

I'm not one for wrote memorization, something that's never been particularly valuable to anyone, anyway.

I think that's the wrong way of looking at it. Many powerful computational algorithms contain lookup tables somewhere at their core. And that is to be expected: for some things it is faster to retrieve the result from memory than it is to compute it from scratch.

Thus it is with times tables.

If we look at the mind/brain as having an analytical and executive function, then the more basic facts it contains in its database for instant recall, the more powerful and capable will be at solving problems and making decisions.

The difference is, as I understand it, kids are nowadays taught to count in twos, count in threes and so on. It's the same data as the times tables but it's organized in a different fashion, a fashion that's better suited to the associative and sequential nature of human memory. For the rote learners: how many times did you have to mentally chant "five sevens are  ..." to trigger the associated memory when you were calculating something?

[Alex Eisenhut]

I'm not one for wrote memorization, something that's never been particularly valuable to anyone, anyway.

How did you know what those words mean? And how to write them?

[IanB]

The difference is, as I understand it, kids are nowadays taught to count in twos, count in threes and so on. It's the same data as the times tables but it's organized in a different fashion, a fashion that's better suited to the associative and sequential nature of human memory. For the rote learners: how many times did you have to mentally chant "five sevens are  ..." to trigger the associated memory when you were calculating something?

But at the end of the day, I want that instant recall for myself. I don't want to mentally have to go 7, 14, 21, 28, 35 when I need to know what five sevens are.

Personally, I never had much time for chanting. I think visually, so I worked from the multiplication square and concentrated on learning the relatively few "difficult" products in the middle, ignoring the easy ones around the edges. I also simplified my task by only learning half of the table. To this day, I recall six sevens rather than seven sixes, and seven eights rather than eight sevens.

[Cerebus]

But at the end of the day, I want that instant recall for myself. I don't want to mentally have to go 7, 14, 21, 28, 35 when I need to know what five sevens are.

What you have now is instant recall, what you had then was the ability to formulate "5 sevens are ... 35" where that "..." is your memory working.

I'm saying that kids ultimately remember the same stuff, they are just taught it differently from our generation. We learned times tables, they learn counting multiples - it is the same data, organized differently. I can't do it the way kids are taught now, precisely because I was taught differently, but I imagine their mental process is "what's the 5th entry in the list of counting by seven" - they don't have to actually mentally count up, just as you and I don't have to start from "1 seven is seven...".

[Cerebus]

I'm not one for wrote memorization, something that's never been particularly valuable to anyone, anyway.

How did you know what those words mean? And how to write them?

You know full well that he said "wrote [sic] memorization" not just "memorization" and you know the two things are not equivalent.

Rote learning is memorizing that "the Battle of Hastings was in 1066", learning why there was a battle and subsequently remembering that is not the same thing. Any idiot can regurgitate the facts of history, few, it seems, can understand them.

[NiHaoMike]

I'm not one for wrote memorization, something that's never been particularly valuable to anyone, anyway.

I think that's the wrong way of looking at it. Many powerful computational algorithms contain lookup tables somewhere at their core. And that is to be expected: for some things it is faster to retrieve the result from memory than it is to compute it from scratch.

Thus it is with times tables.

If we look at the mind/brain as having an analytical and executive function, then the more basic facts it contains in its database for instant recall, the more powerful and capable will be at solving problems and making decisions.

Why preload the cache when you can just let it load by itself? I remember all the common resistor color codes even though I never made the effort to study them.

And I'm sure any computer scientist will tell you that preloading the cache with data that is unlikely to be used is wasteful.

The difference is, as I understand it, kids are nowadays taught to count in twos, count in threes and so on. It's the same data as the times tables but it's organized in a different fashion, a fashion that's better suited to the associative and sequential nature of human memory. For the rote learners: how many times did you have to mentally chant "five sevens are  ..." to trigger the associated memory when you were calculating something?

Digital designers quickly learn to think in powers of two.

[coppice]

Seeing something in a supermarket, and struggling to figure out how much several of them will cost is a practical problem for people. Not being able to do fast rough estimates in their heads, makes it harder for people to relate to what's happening around them. Even though we all have a calculator in our pockets these days, they are a slow and clumsy way to deal with many simple tasks.

Its not the times tables in themselves that really matter. Its the impact on a person's ability to think and analyse their way through simple day to day tasks if they lack all capacity for simple mental arithmetic. Each time I see someone using a calculator in a supermarket to work out how much 3 loaves will be, I see someone as functionally handicapped as someone in a wheelchair.

[Zero999]

I've always thought learning times tables parrot fashion was pointless and still do. I did learn them, because I had to, but can no longer remember them. It's more important to understand the concept and be able to figure it out.

[helius]

I sometimes regret that I only learned the tables up to 10x10 (there are some times when knowing 13x12 would be useful without having to do long multiplication: measuring with yardsticks for instance). But there is a limited window for acquiring this skill and I am far beyond it.

[Gyro]

As someone who a Parietal lobe 'issue' and surgery have left with Acalcula, remembered times-tables etc. have been a lifesaver. Having such lookup tables 'hardwired' in memory makes all the difference in daily life - even if the process of hard-wiring them by repetition was a little painful on the way to school all those years ago!

It's always pays to have a backup for 'critical' functions.

[Rog520]

Public schools (at least West Coast US schools) are much different today in many respects, including how and what you're required to learn. Entry-level teachers are generally poorly paid, class sizes are large, children are hyper and easily distracted, and parental involvement is often inadequate and sometimes totally absent. A teacher considers it a successful day if they can keep the kids under control, nevermind having them memorize the multiplication tables. I blame a lot of this on the parental side of things. Schools are on pins and needles because they're afraid of getting sued if they manhandle Johnny because he's out of control, or if they commit some kind of unintentional non-politically-correct faux pas.

"When I was in school" we were required to learn the multiplication tables to 10x10 by 3rd grade (roughly 8 years old). I had a hell of a time with it. But I come from a family of teachers and there's no way that was going to be allowed to slide. So I memorized them and yeah, remember them all to this day. I even remember some other useful things that we were required to learn in school  . Kids today have access to instant information in the palms of their hands, and they're used to simply looking up stuff they don't know on the fly. While that makes finding answers to questions simple and fast (and actually takes some load off of teachers), it doesn't have the same effect on the brain as studying something. The Google generation has all of the answers and none of the substance.

[bitseeker]

"When I was in school" we were required to learn the multiplication tables to 10x10 by 3rd grade (roughly 8 years old). I had a hell of a time with it. But I come from a family of teachers and there's no way that was going to be allowed to slide. So I memorized them and yeah, remember them all to this day.

Similarly, I learned the tables to 12x12 and still have instant access to them. Is that simply because I still activate those memories?

Those who indicated that they no longer have direct recall of the tables they learned, is that because you (1) stopped using them on a regular basis, (2) switched to computing the results in lieu of the tables, or (3) something else?

I'm curious because I hadn't considered those memories going away before hearing folks here say that  they "lost" them.

[bd139]

Times tables are really important to learn. Only learn 12 if you're in an imperial country though. 10 is fine elsewhere.

Never lost them, use them daily. It's a form of memoization (not memorization - different thing!) i.e. caching regularly done mathematical operations so they are less expensive to do later on. When doing mental arithmetic, it speeds you up several orders of magnitude if you just know the answer to mul/div operations. I can crunch stuff most of the time in less time than finding the calculator, entering it and working out if I fudged the entry or not. The only reason I can do this is because I don't have to retain so much intermediate information when doing calculations because the answers to them are just there.

People who lost them didn't need them. The brain filed it away. It's in there somewhere. I can probably still ride a bike but I just can't be arsed these days

[chris_leyson]

On the flip side of the coin as it were, long division wouldn't be so easy if you didn't know your times tables. Of course it all depends on how many digits there are in the the divisor, for difficult or long divisors I would scibble down a look up table on the edge of the page. Many years ago, about 40, in a control lecture we had to do long division with polynomials, I remember thinking wow this is easy and when I had worked out the lecture example and looked up from my page of scribblings the lecturer was still explaining long division to most of the class. I guess that those who had been taught long division had forgotten.
Anyway, back to the subject, anyone who does low level programming knows their 16x table. 11x table is easy and 12x table is cool because of the relatively prime factors 3 and 4, 12 point FFT done using the prime factor algorithm is bloody fast.

[DimitriP]

TELL ME I'm missing something    

The quality of education is improving.
Older generations educated using lower standards are incapable of comprehending the improvement due to using outdated  methods when  benchmarking education quality.
Yeah, yeah, that's got to be it !

 We should start a flipgrid on this (  https://info.flipgrid.com/  )   

[LaserSteve]

I hated my Dad when he made me stay inside and study his huge pile of flashcards all the way to 13x13. The elementary school teachers actually asked him to stop with that in 6th grade as it was "too advanced" for some one with my issues.   Now at age 48,  I run rings around most of my  colleagues on quick approximations,  except for the Chinese-Americans.    Even with a really bad learning disability in math, those tables, plus considerable practice dealing with powers of ten, and a quick set of memorized  rules for dealing with  Decibels get me through the day. 


Dad passed away about ten years ago, but if I could thank him for one thing...  13x13 = 169 floating up in a few brain cycles is a very useful skill. 

Steve

 

[CatalinaWOW]

This is just a variant on the "Why learn anything when you can Google it" question.  My personal opinion is that cache memory in the sense of the recent posts is not terribly limited as it is in many computer architectures.  And certainly not saturated in a large majority of the population.  For one simple example of this, consider people who are well represented on this forum who are poly lingual who still show no limitations on learning more things.  Those who aren't poly lingual obviously have quite a lot of unused memory.

The reason you learn all of these maths and history and physics and so on is to come in ahead of the guys who have to look it up on their smartphone (assuming they have even memorized enough to generate a good search term) and then figure out the interactions and applications.  You are using that time to figure out the problems and potential solutions. 

Our education systems (worldwide apparently) seem to have overlooked this, which will generate real opportunities for a small number of people, and varying degrees of disappointment for most of the rest.

[Cerebus]

The quality of education is improving.

I know you're being semi-sarcastic, but I suspect it probably is improving.

My secondary school teachers where a mix of old-school amateurs with no formal training in education, and college of education graduates. Those with formal training in education were at least OK teachers, some were great, but only one of that group was terrible (He disliked children and I'm pretty sure he signed up only for the long holidays). Some of the older 'amateurs' were good teachers, some were so bad at their jobs that in any other occupation, like road sweeping, they would have been given the sack long ago.

At least nowadays teachers will all have some formal teaching qualifications rather than starting from a non-education degree (or less) and winging it.

While the science of education has matured, and the quality of the teachers has improved, and hopefully continues to improve, over time, not all is necessarily improving. In the areas I'm best placed to judge the 'level' of what is being taught nowadays compared to what was taught in my day - basically science and mathematics - I think I do see some 'dumbing down'. I think it is politically motivated, so that successive governments can claim that there are better national exam results now than were delivered under their predecessors.

What damages education is when, as it has in the UK, it becomes a political football. I don't think any generation since mine has made it from one end of their education to the other without some major upheaval in how education in the UK is organised. Politicians get involved and educators get ignored. I looked through the national curriculum a few years back and it was remarkably clear, from the ways certain 'learning goals' were worded, that political goals had become embedded in the system by the government. Parts almost read like a 'New Labour' manifesto. In my day there was no national curriculum, so tampering with the level or content of curricula was not possible in the same way as it is now, with effectively direct government control of the syllabus.

[IanB]

So I'm just going to drop this here without comment:

https://youtu.be/wgv9BkV-L78?t=24m40s

[VK5RC]

My three daughters, now in late teens /early twenties,  all learnt times tables to 12 by age 10. One did high level maths (IB), as I did in 1979, I could not help her with her maths.
The variability of the education system is huge.
An acquaintance is a headmaster of a secondary school (ages 12 to 17) in a rough area - he is struggling to get most students to the level of being able to read /write to be able to fill in a job application, enough maths to do simple shopping etc and the social skill set - arrive on time etc- to be able to keep the job. 

[bitseeker]

So I'm just going to drop this here without comment:

https://youtu.be/wgv9BkV-L78?t=24m40s

I'd never seen this show or Countdown, before. Great choice in Rachel Riley. Nothing like having a math(s) lover as presenter to whip up the answer on the spot. Oh, those poor guys.

[bd139]

On education, my 14 year old has just started doing calculus, and she’s not the only one. Depends where your kids go to school and how you stimulate them as they are growing up. This is a UK state school for ref, nothing fancy.

Honestly the main problem with education is shitty teachers and they are beyond criticism in the UK as too many protections are afforded. This makes it a race to the bottom. Academies are fixing this turd despite the press stories.

[BradC]

Honestly the main problem with education is shitty teachers and they are beyond criticism in the UK as too many protections are afforded. This makes it a race to the bottom. Academies are fixing this turd despite the press stories.

We have the opposite problem. We have adequate teachers that spend so much time dealing with the undisciplined little shits that get sent to schools by useless parents (who have the idea that the school should be responsible to turn their unwanted/unloved offspring into functioning human beings) that they don't have time to impart knowledge to the kids that are there who really want to learn.

That's what we get when we pay people to breed. The people who should be breeding either can't afford to or leave it too late, while the dregs push out another kid when they want a new flat screen tv to collect the "baby bonus". Yay for society.

[bd139]

Not much you can do about dickheads. Just remember they'll starve first when it comes to it.

[BradC]

Not much you can do about dickheads. Just remember they'll starve first when it comes to it.

You'd think that, but procreation favours the stupid. They'll just outbreed us all.

[@rt]

I never learned all of the times tables.
Certain combinations sunk in, and so did all of the squares,
and the rest I have to start where I know, and add the rest.

Not as fast as from memory (tables meaning recalled from memory),
but I haven’t seen it as any real hinderance.

[bd139]

Not much you can do about dickheads. Just remember they'll starve first when it comes to it.

You'd think that, but procreation favours the stupid. They'll just outbreed us all.

That’s why they’ll starve

[Gribo]

I have never learned the tables, I can still do all multiplications to 1000 instantly (along with all the integer roots). My kid is currently studying multiplication by counting n, I am teaching him all the shortcuts

[SL4P]

When my youngest were very young, I wrote a simple application for Windows - MathMatrix
Which not only developed their table skills, but it also *visually* reinforced the scalar, dimensional aspect of the work.  Timing & scoring helped make it a competition.

Their later maths aren’t perfect, but they easily understand how numbers and values affect each other.
I must test them out when i next see them!  24/21 years old.

[james_s]

Honestly the main problem with education is shitty teachers and they are beyond criticism in the UK as too many protections are afforded. This makes it a race to the bottom. Academies are fixing this turd despite the press stories.

We have the opposite problem. We have adequate teachers that spend so much time dealing with the undisciplined little shits that get sent to schools by useless parents (who have the idea that the school should be responsible to turn their unwanted/unloved offspring into functioning human beings) that they don't have time to impart knowledge to the kids that are there who really want to learn.

That's what we get when we pay people to breed. The people who should be breeding either can't afford to or leave it too late, while the dregs push out another kid when they want a new flat screen tv to collect the "baby bonus". Yay for society.

A problem we have in the US is that with the way the standards are set up, teachers kind of have their hands tied and the more creative types are pushed out in favor of those who can run what are effectively education factories. There is so much focus on standardized tests and standardized metrics of the teacher's success that there is little room for thinking outside the box.

[bd139]

Not much you can do about dickheads. Just remember they'll starve first when it comes to it.

You'd think that, but procreation favours the stupid. They'll just outbreed us all.

You are probably right.

One of my favourite films

[niladherbert]

As one currently suffering through the last 2 months of high school before hopefully going on to learn electrical and electronic engineering, how important is binomial, differential calculus and other hard maths things?

[Rerouter]

niladherbert, electrical you can honestly get through aslong as you know basic algebrea (like grade 6 stuff), electronic engineering you want a solid grasp on statistics, exponentials, and algebra, but i have not really come across anything that i have absolutely needed calculus for,

however you can think of them like tools, they only matter to you if you can think of something to do with it, most of my math skills have applied to bashing out stupid patterns and relations in excel, whereas if i had better access to tools like solidworks simulation for thermal and stress, they may longer apply to me,

[bd139]

Yep. I think most calculations I have done over the years outside of university were "within 10% ballpark" calculations and solving canned equations and using canned engineering calculators provided by vendors. Even stuff like filter design is just "download TI's tool and plug shit into it" or "solve this formula".

Edit: this was a shock coming from university where they hammered us with math that I never used.

[Zero999]

As one currently suffering through the last 2 months of high school before hopefully going on to learn electrical and electronic engineering, how important is binomial, differential calculus and other hard maths things?

Very important to pass any decent EE qualification exam.

When it comes to doing the job, it depends on what you're doing. Quite often simulation tools do all of the advanced maths for you, but it's still important to understand how they work.

[NivagSwerdna]

As one currently suffering through the last 2 months of high school before hopefully going on to learn electrical and electronic engineering, how important is binomial, differential calculus and other hard maths things?

As a non-EE some years ago I did MITx 6.002x (which I think can now be found at https://www.edx.org/course/circuits-electronics-1-basic-circuit-mitx-6-002-1x-0) ...No doubt about it you needed calculus (although Wolfram Alpha etc really help).  But Calculus is fun!   

[bd139]

But Calculus is fun!   

That's the right approach to the problem (I also enjoy it). Don't see it as a chore or a wall. It's a puzzle from which you win understanding.

[madires]

I sometimes regret that I only learned the tables up to 10x10 (there are some times when knowing 13x12 would be useful without having to do long multiplication: measuring with yardsticks for instance). But there is a limited window for acquiring this skill and I am far beyond it.

I don't agree You can learn at any age, it just might take more time.

[BillB]

Hmmm.  I agree that the automation tools/simulators/calculators/etc have certainly reduced the need for a strong working knowledge of higher math for a lot of EE work these days.

Regarding memory, at this point, I'm just happy when I remember to put on pants before I leave the house in the morning.

[IanB]

As one currently suffering through the last 2 months of high school before hopefully going on to learn electrical and electronic engineering, how important is binomial, differential calculus and other hard maths things?

If you find those maths things hard, then you will likely find much of the content of an engineering degree hard. Even if you don't specifically have to use those mathematical tools, your engineering studies will involve many other complex and abstract topics to wrap your head around.

The reason universities ask for good A level grades from students applying for entry is to select for aptitude to get through the course material. So treat your A level studies like training to run a marathon. What you are studying is improving your mental fitness to get through your university course.

[CatalinaWOW]

While all of the tools make the job easier, if you don't understand what went into them you are at their mercy.  I can't count the times that a simulation program has given a garbage answer.  In some cases the garbage would be obvious to anyone.  Not so in others.  In all cases fixing it so that it wasn't garbage required one of a few approaches.  Just trying stuff until the answer looks reasonable.  Or insight into why the garbage might have occurred and what to do about it.  Or passing the job off to someone more talented, maybe by asking a question on a forum.

You can all decide which approach you like better.

[james_s]

But Calculus is fun!   

That's the right approach to the problem (I also enjoy it). Don't see it as a chore or a wall. It's a puzzle from which you win understanding.

For some reason I always thought calculus sounded scary and hard, even just the name. Then I learned a bit of it by accident and realized it's actually not all that difficult and it's actually quite interesting and useful, I think some of the concepts should be taught earlier in regular highschool math.

[james_s]

I sometimes regret that I only learned the tables up to 10x10 (there are some times when knowing 13x12 would be useful without having to do long multiplication: measuring with yardsticks for instance). But there is a limited window for acquiring this skill and I am far beyond it.

I don't agree You can learn at any age, it just might take more time.

At some point that time can approach infinite depending on how much life one has left, however learning the multiplication tables is likely within the grasp of most. There are apps you can get now for your phone to do that. I actually re-learned mine up to 12x12 recently because I realized I'd forgotten a lot of them, I'd also forgotten how to do some fairly basic math so I picked that back up. It's the result of relying far too heavily on calculators for years, I'm now seeing the value of doing some of the math by hand to keep the brain sharp.

[free_electron]

Hey siri , how much is two times two.

[bitseeker]

Siri: The same as two plus two. Let me know if you need help with that.

[james_s]

My mom is a tutor and often complains that kids will get out a calculator to solve something like 14 + 9, or 3 * 8. That's the sort of stuff one ought to be able to do in their head faster than getting out the calculator.

[CatalinaWOW]

Hey siri , how much is two times two.

My experience with Siri is that the first response will be - "I can't find anything called two times two for sale, but here are listings for two by two.", followed by "You must be joking." and sooner or later you will get it to respond with four.  By then you could have gotten the response even on a calculator.

The best answer for why to learn the times table comes from an experience I had many years ago when teaching an engineering technology class.  For a variety of reasons many of the students had a lot of trouble with the class (AC Circuits, with impedance, phase calculations, and so on).  One student came for help during office hours.   His problem - he didn't know which buttons to push on the calculator to do the multiplications required.  He had forgotten that an X was an abbreviation for times, similar problems for +, - and the division symbol.  I mean why memorize that crap when there is a calculator to do all the arithmetic?   

When you think you can't dumb something down anymore, someone will come along and prove you wrong.

[bitseeker]

His problem - he didn't know which buttons to push on the calculator to do the multiplications required.  He had forgotten that an X was an abbreviation for times, similar problems for +, - and the division symbol.

Woah.

[EEVblog]

I'm pretty sure Sagan is learning his times tables, he's in year 2. I've seen the big chart hanging up in the classroom.

[EEVblog]

At some point that time can approach infinite depending on how much life one has left, however learning the multiplication tables is likely within the grasp of most. There are apps you can get now for your phone to do that. I actually re-learned mine up to 12x12 recently because I realized I'd forgotten a lot of them

I have to admit that I've caught myself occasionally not being sure of some times table stuff I used to know completely.

[mtdoc]

For some reason I always thought calculus sounded scary and hard, even just the name.

Just call it Mooculus - it sounds less scary.

Actually that link is an excellent online resiurce for learning calculus. Also good for older farts like me who want to wake up 35 year dormant calculus synapses...

[Cerebus]

Just call it Mooculus - it sounds less scary.

If you want it to sound less scary, just translate it from its original Latin: pebble. (Calculus was named back in the days when the lingua franca of academics was Latin.)

[BradC]

Calculus was named back in the days when the lingua franca of academics was Latin.

I still get weirded out when my Dentist talks about it in the context of nasty stuff on teeth. I'm ok with the mathematical kind, but insinuating lackadaisical dental hygiene is a bridge too far.

[bitseeker]

Calculus, dental, and bridge all in the same post. Impressive.

[Cerebus]

If he'd mentioned renal calculii at the same time we'd have thought he was taking the piss.

[helius]

Of course if you you're really nuts, you could memorize your times tables in brass...

[VK3DRB]

I find many Australian electronics engineers do not know their times table. What I don't understand is how they can even get into their uni course not knowing their times tables. Worse still is their spelling. If it were not for spell checkers, these engineers would be hopelessly lost. The fault is not theirs. It is our education systems that allows students to automatically move into the next grade irrespective of how dim they are.

From my observations (having lived in the USA), American engineers are generally much better at grammar than Australian engineers.

[NiHaoMike]

I find many Australian electronics engineers do not know their times table. What I don't understand is how they can even get into their uni course not knowing their times tables. Worse still is their spelling. If it were not for spell checkers, these engineers would be hopelessly lost. ...
From my observations (having lived in the USA), American engineers are generally much better at grammar than Australian engineers.

I see that a lot online. (To be fair, some of them are not fluent in English and have a legitimate excuse.) On a particular mobile device forum back in the day, there was a member who never seems to use the shift key or spell checker and has not improved at all in 3 years or so, earning him a complaint thread from unhappy members. One girl replied that if he wants a good job or smart girl later in life, his bad writing would make it a lot harder.

[GlennSprigg]

Thank you to ALL who contributed here, and for many reasons. (Too many to mention).
I also thank 'EEVBlog' for bringing up a good point.....  (As well as 'Sagan's level in his year).
That being that 'US' adults think we remember the 'basics', but how quickly we forget without 'Revision' xx
No-one is 'supposed' to instantly know what 36 x 46 is, without WORKING IT OUT, (without aid xx).
Again... the 1st step is obviously '6 x 6', for which there is no 'help' but KNOWLEDGE, unless counting 'beans'.
MOST adults "know", that 6 x 6 = 36. And 8 x 8 = 64. And 7 x 5 =35......, but this is not regimented now.
MANY kids, in what ever year, DO understand this, because SOMEONE drummed it in to them, and that's good.
However, it is by far lacking today, in general basic education. Please push this with kids/grandkids   

[mtdoc]

However, it is by far lacking today, in general basic education.

Absolutely not true!

In fact, in the US, knowing the multiplication tables by the end of third grade (ages 8-9) is part of the Common Core Standard which states: “By the end of Grade 3, know from memory all products of two one-digit numbers.” 

My boys, who are now 9 and 12, both learned their multiplication tables through 12x12 in the 3rd grade.

[IanB]

No-one is 'supposed' to instantly know what 36 x 46 is, without WORKING IT OUT, (without aid xx).
Again... the 1st step is obviously '6 x 6', for which there is no 'help' but KNOWLEDGE, unless

I see your point, but '6 x 6' is not obviously the first step, especially if doing mental arithmetic. In fact, trying to do long form multiplication in your head this way is likely to lead to too many partial sums to keep track of, and it gets very difficult.

A more productive first step is 40 x 36 = 1440, and then 6 x 36 = 216, and then add them to give 1656.

I believe the modern curriculum tries to show children more ways to look at and understand multiplication rather than just learning by rote the primitive way of doing it on paper, and this has the positive effect of building stronger mental tools for thinking about arithmetic. This actually would make the way I showed above more accessible to the modern child than to the child of yesteryear.

[helius]

I see your point, but '6 x 6' is not obviously the first step, especially if doing mental arithmetic. In fact, trying to do long form multiplication in your head this way is likely to lead to too many partial sums to keep track of, and it gets very difficult.

A more productive first step is 40 x 36 = 1440, and then 6 x 36 = 216, and then add them to give 1656.

Code: [Select]

   36
x  46
------
   3
  186
  2
+124
------
  216
+1440
------
 1656
Isn't what you did exactly "long form multiplication"?

[Brumby]

Yeah ... It is.

[IanB]

Yeah ... It is.

No, it isn't 

I couldn't possibly do everything helius wrote down in my head.

"Six sixes are 36, keep the 6, carry the three. Six times 30 is 180, add the carried 30 makes 210, add the original 6 makes 216. Remember that. Now 4 x 6 is 24, keep the 4, carry the 2. Four threes are 12, add the carried 2 for 14, add the 4, ... oh crap, now where was I? Let's start over...  "

You're nuts if you think someone can keep track of all that in their head as they go along.

[helius]

It was harder to make the columns line up in bbcode then to do the mental arithmetic 

When you want to remember a series of digits (like 216) while you work with other digits, it helps to convert them into rhyming words or trenchant images. So you might remember "junior prom" instead of the digits and then convert it back later after you had 1440.

[T3sl4co1l]

You're nuts if you think someone can keep track of all that in their head as they go along.

Seriously, short and long term memorization tricks are just something you practice at.  Maybe you can't ever do it, maybe not. But if you aren't practicing it at all, you definitely aren't going to do it.

Tim

[IanB]

Just so it's clear, I wrote 40 x 36 and 6 x 36 because both of these were possible to do directly from memory without doing them bit by bit.

For example, 40 x 36 is easily recognizable as a variation of 2 x 72 or 12 x 12, both of which are known to be 144. Similarly, 6 x 36 is a variation of 3 x 72, which is then instantly 216.

Therefore I only had to keep track of 1440 and 216 in my head and add them together.

[mtdoc]

You're nuts if you think someone can keep track of all that in their head as they go along.

It is possible with practice. When I was a kid I used to do that with long multiplication as a challenge. My dad (who was an engineer with a degree in math) used to show me off to his friends doing this.  Which is why, perhaps, he really thought I should be an engineer.  Sometime later I began to dislike math and went another direction (biology).

Now my feeble middle aged mind has problems with much simpler math problems.... 

My kids - who did learn their multiplication tables, refuse to try and do anything "in their head" beyond what they've memorized already. When I ask them to try they say  "Why? just use a calculator" -  despite that fact that they do know very well how to do it with paper and pencil. 

[coppice]

Yeah ... It is.

No, it isn't 

I couldn't possibly do everything helius wrote down in my head.

"Six sixes are 36, keep the 6, carry the three. Six times 30 is 180, add the carried 30 makes 210, add the original 6 makes 216. Remember that. Now 4 x 6 is 24, keep the 4, carry the 2. Four threes are 12, add the carried 2 for 14, add the 4, ... oh crap, now where was I? Let's start over...  "

You're nuts if you think someone can keep track of all that in their head as they go along.

Back before pocket calculators lots of people used slide rules or log tables. However, some of us learned to multiply 7 figure numbers in our heads. The deep mystical secret of this capability - practice.

[IanB]

Back before pocket calculators lots of people used slide rules or log tables. However, some of us learned to multiply 7 figure numbers in our heads. The deep mystical secret of this capability - practice.

OK, whatever you say. If you can multiply 2367735 by 8364229 in your head, then I'm the Queen of Sheba.

Sure, I believe some savants can do this trick, but I'm not sure it is the best use of brain cells for mere mortals to learn how to do it 

[rstofer]

I see your point, but '6 x 6' is not obviously the first step, especially if doing mental arithmetic. In fact, trying to do long form multiplication in your head this way is likely to lead to too many partial sums to keep track of, and it gets very difficult.

A more productive first step is 40 x 36 = 1440, and then 6 x 36 = 216, and then add them to give 1656.

Code: [Select]

   36
x  46
------
   3
  186
  2
+124
------
  216
+1440
------
 1656
Isn't what you did exactly "long form multiplication"?

How about this:  36 * 50 = 1800 (half of 36 times 100) and 36 * 4 = 144.  1800 - 144 = 1656.  That PARTICULAR problem is easy to do in your head.

[T3sl4co1l]

Back before pocket calculators lots of people used slide rules or log tables. However, some of us learned to multiply 7 figure numbers in our heads. The deep mystical secret of this capability - practice.

OK, whatever you say. If you can multiply 2367735 by 8364229 in your head, then I'm the Queen of Sheba.

Sure, I believe some savants can do this trick, but I'm not sure it is the best use of brain cells for mere mortals to learn how to do it 

Easy.  Mere mortals have no need of such precision, so let's approximate it as:
2.5 x 10^6 (~7% high)
* 8 x 10^6 (~4% low)
= 20 x 10^12 + 3% or 2.06 x 10^12.

Need more decimals?  Get a better slide rule.

Real result: 19.804... x 10^12, slightly lower, surprisingly.

And yeah, math savants can do real time combinatorics on that many figures, I think?

Tim

[Cerebus]

OK, whatever you say. If you can multiply 2367735 by 8364229 in your head, then I'm the Queen of Sheba.

"So, Ian, how did you get this nickname, Queenie?"
"Well, I was posting on this forum..."

[Brumby]

Yeah ... It is.

No, it isn't 

Yeah, it is.

I couldn't possibly do everything helius wrote down in my head.

"Six sixes are 36, keep the 6, carry the three. Six times 30 is 180, add the carried 30 makes 210, add the original 6 makes 216. Remember that. Now 4 x 6 is 24, keep the 4, carry the 2. Four threes are 12, add the carried 2 for 14, add the 4, ... oh crap, now where was I? Let's start over...  "

You're nuts if you think someone can keep track of all that in their head as they go along.

The way I was taught is exactly how you expressed it...

A more productive first step is 40 x 36 = 1440, and then 6 x 36 = 216, and then add them to give 1656.

  36 x
  46
----
 216
1440
====
1656

[IanB]

  36 x
  46
----
 216
1440
====
1656

Yes, and isn't that rather simpler than this: ?

  36 x
  46
----
  36
 180
 240
1200
====
1656

[james_s]

Simpler as in less writing, but not nearly as easy to do, at least for me.

[Johnboy]

There was a book published in the US that advocated the abacus/soroban method of multiplying from "left to right", establishing the magnitude before the small stuff. This approach makes sense for several reasons to me-- but the main one is that we don't really need precision, just accuracy. Things constructed using slide rules ended up being somewhat overengineered for safety, sure-- but no one cares about the umpteenth significant digit. There's a story I read somewhere about a certain professor calculating the last few digit(s) in his head and pretending to read them off the rule.

Again, I'm only bringing this up because learning "times tables" by rote is useful, sure, particularly the squares and cubes-- but parallel calculators really were a great teaching tool for this. Punching numbers in just doesn't impart the same feel to me.

[bd139]

Here's how I do 36x46 in my head with tables. Use place value system:

Sum := AB * CD

R := B*D
R := R + (A*D*10)
R := R + (B*C*10)
R := R + (A*C*100)

Example:

6*6 -> 36
36 + (3*6*10) -> 216
216 + (4*6*10) -> 456
456 + (3*4*100) -> 1656

Note lack of temporary variables other than the accumulator R.

You can do this with decimals by counting the place values in later. Just move the decimal over by the number of digits to the right of all of the decimals together.

[GlennSprigg]

WOW.... All very interesting reading, for many reasons, as were put forward !!!! (Thank you all).
(I'm the original 'Poster' of this statement/question).
I know there are many other ways of performing 'maths', either in your head or on paper   
However, when I mentioned that the "first step is 6 x 6", that is irrelevant in regard to what I meant 
I simply meant that kids these days should know that "6 x 6 = 36", as that can't be broken down!.......

To our Overseas friends, I'm in Australia, and our primary schools go to year 6, and then start 'High'
school at 11 years old. (Some are 12). As stated, some kids 'know' the times tables, as it is/was
drummed into them by diligent teachers and/or parents, (which is good!), but the fact remains that
it is not (now) enforced (here) as a curriculum requirement... though I CERTAINLY think it should be! 

Out of interest though...  I learnt LOTS of shortcuts in Maths!!!...  like......
To multiply by 11, add the digits and put them in the middle.....
35 x 11....  3+5 =8...   result = 385   (Do in your head in 2 secs!)
63 x 11....  6+3 =9...   result = 693
If the 'addition' adds up to more than '9' then carry the '1'..... like.....
68 x 11....  6+8 =14...  carry the '1' to the '6'...  result = 748  (Do in your head in 2 secs!)
Do you know that ALL multiples of '9', have the digits add up to '9' ??.....
9x9 = 81   (8+1 = 9)
9x7 = 45   (4+5 = 9)
9x123 = 1107   (1+1+0+7 = 9)
9x3764 = 33876   (3+3+8+7+6 = 27.   2+7 = 9) 

There are so many more it is not funny !!!!
Just teach our kids/grandkids the basics !!   

[coppice]

Back before pocket calculators lots of people used slide rules or log tables. However, some of us learned to multiply 7 figure numbers in our heads. The deep mystical secret of this capability - practice.

OK, whatever you say. If you can multiply 2367735 by 8364229 in your head, then I'm the Queen of Sheba.

Sure, I believe some savants can do this trick, but I'm not sure it is the best use of brain cells for mere mortals to learn how to do it 

Its interesting how technology often makes people think that humans are not capable of tasks that used to be accomplished routinely by humans. Those are most often physical things, but increasingly the way machines have removed the pressing need to train various mental tasks is making people think only very special humans could ever do them before the machines. You didn't need to be a savant to multiply two numbers in your head. It just took enough practice doing it on paper, until you could take away the paper.

[BradC]

Its interesting how technology often makes people think that humans are not capable of tasks that used to be accomplished routinely by humans. Those are most often physical things, but increasingly the way machines have removed the pressing need to train various mental tasks is making people think only very special humans could ever do them before the machines. You didn't need to be a savant to multiply two numbers in your head. It just took enough practice doing it on paper, until you could take away the paper.

Admittedly not with paper, but my highschool Chem teacher (who was in his 60's at the time) could, and regularly did multiply or divide 7 digit numbers on the blackboard faster than we could get them into a Casio fx82 and get an answer out.

He was cool. His "continuity" demonstrator to illustrate the conductivity of certain liquids was a bit of wood with a bayonet socket screwed to each side and wired in series with a bit of 24/0.20 figure 8 and a standard 2 pin plug. In the top socket he put a standard 240V light bulb. In the bottom socket he put a standard 240V light bulb sans glass and filament leaving a pair of probes that he would dip in the liquid. We were amused when he lay it on the desk one day and forgot about it, only to lean on the probes later in the lesson. RCD's were invented, but not installed.

[Johnboy]

Back before pocket calculators lots of people used slide rules or log tables. However, some of us learned to multiply 7 figure numbers in our heads. The deep mystical secret of this capability - practice.

OK, whatever you say. If you can multiply 2367735 by 8364229 in your head, then I'm the Queen of Sheba.

Sure, I believe some savants can do this trick, but I'm not sure it is the best use of brain cells for mere mortals to learn how to do it 

Its interesting how technology often makes people think that humans are not capable of tasks that used to be accomplished routinely by humans. Those are most often physical things, but increasingly the way machines have removed the pressing need to train various mental tasks is making people think only very special humans could ever do them before the machines. You didn't need to be a savant to multiply two numbers in your head. It just took enough practice doing it on paper, until you could take away the paper.

And sometimes using paper is unnecessary in the first place. Here are examples of several methods by which those skills can be acquired (although it's admittedly a little cringeworthy in places).

[GlennSprigg]

Wow, what an interesting Saga that all was... (again  )
(I'm the original 'poster' again...)
My hat's off to the gentleman from the U.S. (and others...), that stated that their kids
ARE taught the times-tables, and that it is a 'requirement'...  That's GOOD !! 
But it still sadly doesn't 'here'. (In Australia. No Aussie jokes please  )......
I can/have asked my 1st year high-school grand-kids, and their friends, the likes of....
"What is 6x6", or "what is 8x4".... let alone.... "what is 9x7"... (F%$# that's hard!),
and NONE of them can tell me !!!  They ALL have iPhone/Android 'Tablets' these days
in class, (so no need for ancient 'Calculators' ), [lets show them a slide-rule haha].

What is it about a lot of you responders, that make you think that any/all of your own
'methods', and the 'Effort' it takes to remember it/them, is ANY better than SIMPLY
remembering BASIC times-tables, from/with which anyone can calculate anything ??
I RESPECT all your 'abilities'..... but what are you fighting against Seriously ??
May we all, (teachers, parents, grandparents) simply teach our kids the 'basics' 

'Brumby' seems to prefer 'Yep..', 'Nope..', {quote} then 'yep..' without 'adding' to
anything at all except his unadulterated 'Piousness'.... He seems to now 'seek' out
my many/varied Posts now, (even though I have moved on...), from a time that he
chose to (attempt to) 'Belittle' me repeatedly.... when I 'dared' to ask for a resolution
on this 'Forums' MAIN? forum topic.  This 'Demi-God' (in his Godness & Greatness)
decided at 2am one morning, (with nothing else to do obviously), to RANT at me, and
tell me I am just a "TROLL"... (Haah?! it was MY post he was continuously abusing??).
After swallowing my pride/rights, I apologized to him, and explained all that I could.....
'HE' then ridiculed me about what I offered, and repeated how 'I'm' just a "TROLL" ?
Well I have many scientific interests, that go WAY beyond listening to this "No-Life",
and as such I keep posting/discussing in areas "I Hope" is beyond 'his' REALM.....
I'm a peaceful Pensioner, who likes to invoke dialog with REAL people, not Demi-Gods...

[Cerebus]

Well if you want a peaceful life, why make a post that dredges up some spat you've had elsewhere with Brumby in an unrelated topic? That does seem to be trolling for a response. 

Oh and please, less smilies, less brackets, less ... ellipses, less random punctuation in general and RANDOM changing into ALL CAPS in the middle of run on sentences. It makes it incredibly hard to read what you've written.

[Halcyon]

I'm a bit late to the conversion however my thoughts are as follows...

The traditional "times tables", i.e. multiplication of two numbers between 1 and 12 is largely irrelevant these days. Unless your profession, hobby or interests involve reciting a table of figures which don't change, but that's just data recall.

The function and knowledge of how maths works is far more important than remembering results. Remember BODMAS/BEDMAS? Brackets, Exponents, Divide, Multiply, Add and Subtract... in that order.

I'm the first to admit that I can't do mathematics in my head, even simple equations. Yet, for the most part, I know how maths works and with a calculator I can come to a correct result.

[rstofer]

I'm a bit late to the conversion however my thoughts are as follows...

The traditional "times tables", i.e. multiplication of two numbers between 1 and 12 is largely irrelevant these days. Unless your profession, hobby or interests involve reciting a table of figures which don't change, but that's just data recall.

Or your continuing education.  I don't see how anybody can graduate from EE school without being able to do simple multiplication and division.  There simply isn't time to use a calculator for things like factoring polynomials.  You just look at the coefficients and the factors jump out of the paper.  If they don't, you're in for a long night.

I will agree that the average burger-flipper probably doesn't need arithmetic or times tables.  A lack of basic calculating skills is why they're flipping burgers in the first place.

The function and knowledge of how maths works is far more important than remembering results. Remember BODMAS/BEDMAS? Brackets, Exponents, Divide, Multiply, Add and Subtract... in that order.

And strictly left to right within a precedence level. 6 ÷ 2(1+2) = 9, not 1.

http://www.slate.com/articles/health_and_science/science/2013/03/facebook_math_problem_why_pemdas_doesn_t_always_give_a_clear_answer.html

I'm the first to admit that I can't do mathematics in my head, even simple equations. Yet, for the most part, I know how maths works and with a calculator I can come to a correct result.

I'm of the opinion that more class time should be spent on setting up problems (word problems) and less time grinding through page-long solutions.  Spend the time to learn Matlab or wxMaxima and let the computer do the number crunching.  symbolab.com and desmos.com get a lot of traffic from my house.

[IanB]

The function and knowledge of how maths works is far more important than remembering results. Remember BODMAS/BEDMAS? Brackets, Exponents, Divide, Multiply, Add and Subtract... in that order.

And strictly left to right within a precedence level. 6 ÷ 2(1+2) = 9, not 1.

Really though, this kind of high school level rule following doesn't have much place in the professional world. Once you leave school and get into advanced studies it becomes more important to communicate effectively and unambiguously. For example the above expression has a spacing and grouping that would suggest this:
$$6 \over 2(1+2)$$
Rather than this:
$${6 \over 2} (1+2)$$
In any professional publication one or other of the above forms would be expected and preferred.

If it was really wanted on a single line one would probably write something like this: \$(6 / 2)(1+2)\$

[helius]

I don't think I have ever seen the ÷ sign as part of a pset past Algebra I... certainly not in High School.

[hendorog]

About a week ago we attended a teacher/parent meeting with our son (last year of primary school).
The teacher suggested we work with him to improve his times tables as it will be required in his intermediate next year.

He has done them in the past as part of homework, along with spelling, but the school hasn't been consistent and so things have slipped a bit. Every year there is a different approach. This lack of consistency seems to be one of the issues with early schooling, at least in this country.

The other issue in the teacher meetings, is that the teachers seem to be stuck in transmit mode.

[rstofer]

In any professional publication one or other of the above forms would be expected and preferred.

If it was really wanted on a single line one would probably write something like this: \$(6 / 2)(1+2)\$

I was thinking about Fortran.  Or any other language that has operator precedence.  Yes, there is a missing '*' before the '(' but still, the result will be 9.  I'm using this as an object lesson for my grandson in the use of parenthesis to force the order of evaluation.

[AG6QR]

My kids are in elementary school, and have been learning their multiplication tables.  I told them to do it the way I did:

To multiply by two, just double the number.

To multiply by three, double it and add another copy of it.

To multiply by four, double it and double the result.

To multiply by five, halve it and move the decimal one place to the right.

To multiply by six, double it and triple it.

To multiply by seven...  Sevens are hard.  We'll come back to them.

To multiply by eight, double it, double the result, and double that.

To multiply by nine, subtract one from the number to get the tens digit, then for the ones digit, choose the number that, when added to the tens digit, sums to nine.

To multiply by ten, move the decimal point.

You don't need the 11s and 12s any more than you need the 13s, 14s, 15s, etc.  You can get them via the normal methods for two-digit multiplication.

Now, back to the sevens.  To multiply seven by any other number, use the rule for the other number.  That still leaves seven times seven.  You have to remember that it's 49.

Out of 100 multiplication facts, there's only one you've got to memorize.  7x7=49.  Surely you can memorize that one.


Naturally, with practice, you'll start to memorize some of the other multiplication facts, and get faster at them.   But you can also get pretty fast at doubling with practice.  Does it really matter whether you memorize them or figure them out on the fly?

[Brumby]

Normally I would not engage in this sort of thing [edit] too deeply [/edit], but the accusations are pretty intense and have been made public.  So here it goes...

I do apologise in advance to the rest of the membership and promise to not engage in a lengthy debate.

'Brumby' seems to prefer 'Yep..', 'Nope..', {quote} then 'yep..' without 'adding' to
anything at all except his unadulterated 'Piousness'.... He seems to now 'seek' out
my many/varied Posts now,

Really?  I tried to avoid posting in any of "your" threads because of the risk of this sort of reaction, but I thought I would add my own two cents' worth in the hope that things had settled.  This was done with no sense or intention of malice, yet it seems simply posting in one of "your" threads is malice enough.

(even though I have moved on...),

Clearly you haven't.  The previous fracas was over 2 months ago.

from a time that he
chose to (attempt to) 'Belittle' me repeatedly.... when I 'dared' to ask for a resolution
on this 'Forums' MAIN? forum topic.

See below.

This 'Demi-God' (in his Godness & Greatness)
decided at 2am one morning,

See below.

(with nothing else to do obviously),

See below.

to RANT at me,

See below.

and
tell me I am just a "TROLL"...

See below.  Read what I wrote.

(Haah?! it was MY post he was continuously abusing??).
After swallowing my pride/rights, I apologized to him, and explained all that I could.....
'HE' then ridiculed me about what I offered, and repeated how 'I'm' just a "TROLL" ?
Well I have many scientific interests, that go WAY beyond listening to this "No-Life",
and as such I keep posting/discussing in areas "I Hope" is beyond 'his' REALM.....
I'm a peaceful Pensioner, who likes to invoke dialog with REAL people, not Demi-Gods...

Like you said:

Wow, what an interesting Saga that all was... (again  )

I'm sorry that you feel the need to tear me down, but it is clear you need to.  I don't believe I have said anything is this thread to warrant such a tirade, but it seems rather obvious you were looking for an excuse to resurrect ill feeling from a previous exchange.

To those wondering - yes, there was an apology (totally unsolicited and completely unexpected), but it was a PM to me.  I would have thought a post to the forum would have been more appropriate.  What hasn't been stated is that my reply was sent 62 minutes later.  Since that PM was private communication sent to me, it would be inappropriate for me to disclose it - but I am happy to present my response - the "RANT" - for others to judge.  Here is the complete, unedited message:

I can understand your embarrassment - but when people were telling you to "walk away", they were actually giving you the best advice to minimise that embarrassment.  You chose to ignore that and demand it gets resolved the way you wanted - which only made it worse.  In the end, you were still pig-headedly pressing for your solution.  Sorry - but that is arrogant and typical of trolls.

Now that the thread has been locked, it will fade and most people will not think about it again - but it will be there as a permanent record.

We tried to tell you the best way ... but noooooo!  You had to keep pushing.


Please note that this response is not an invitation to engage in further discussion on the matter.  It has been given as an acknowledgement of your reaching out and to encapsulate key points.  I hope there will never be a need to speak of these again.

I have been an active member on this forum for a number of years now - and I leave it to other members to judge me on my actions.

[John Coloccia]

My kids are in elementary school, and have been learning their multiplication tables.  I told them to do it the way I did:

To multiply by two, just double the number.

To multiply by three, double it and add another copy of it.

To multiply by four, double it and double the result.

To multiply by five, halve it and move the decimal one place to the right.

To multiply by six, double it and triple it.

To multiply by seven...  Sevens are hard.  We'll come back to them.

To multiply by eight, double it, double the result, and double that.

To multiply by nine, subtract one from the number to get the tens digit, then for the ones digit, choose the number that, when added to the tens digit, sums to nine.

To multiply by ten, move the decimal point.

You don't need the 11s and 12s any more than you need the 13s, 14s, 15s, etc.  You can get them via the normal methods for two-digit multiplication.

Now, back to the sevens.  To multiply seven by any other number, use the rule for the other number.  That still leaves seven times seven.  You have to remember that it's 49.

Out of 100 multiplication facts, there's only one you've got to memorize.  7x7=49.  Surely you can memorize that one.


Naturally, with practice, you'll start to memorize some of the other multiplication facts, and get faster at them.   But you can also get pretty fast at doubling with practice.  Does it really matter whether you memorize them or figure them out on the fly?

I think about it a different way, but this is generally how I do math too. Memorization is nice so you can recall basic things instantly, but it's useful to have a "feel" for numbers as well. At least it is if you use them frequently for work. Because what do you do when 5*33 comes up? Something like that came up a week or two ago, and I blurted out "that's 165." They're like, "why do you know that off the top of your head?" or something to that effect.  I explained, "well, that's just 33/2 * 10...30/2 is 15, and another 1.5 gives me my three, so it's 16.5 * 10." And of course, I look like a weirdo, but it's actually pretty easy to do. Most numbers are close to other numbers that are easy to deal with, and then it's just a matter of fixing it up a bit.

Very useful for someone like me that has an absolutely atrocious memory. If I actually had to memorize multiplication tables and things like that, I'd be toast. I think stuff like this is what they're trying to do with our new math curriculum in the US, but the way it's implemented is horrible. We've traded one blind procedure for another without giving any real understanding.

If it were me, I wouldn't even teach long division and multiplication. It's not a useful skill for most people, IMHO. That's what calculators are for. I would only teach techniques that allow you to calculate reasonably sized values in your head, and arithmetic tests would be SHOW NO WORK...points off if you write anything but the answer.

[Distelzombie]

As someone on the first page already said: Learning by tables is inherently flawed. It can easily be seen/understood what we mean by using this analogy I came up just now:
A metalworker learns some basic things about temperatures and metals. He knows at a certain point the metals starts to glow. He uses a device that measures color and brightness and gives him a number. He memorized a table that gives him the temperature in degrees Celsius. that corresponds to the number. (It's hypothetical.)
0 = 0°
0.5 = 150°
1 = 300°
2 = 400°
3 = 500°
...
7 = 900°
...
13 = 1500°

One day he wonders what would happen if he heats the metal further and further. (This doesn't have to be absolutely realistic, I warn ya) So he builds a heater, leaves the room and observes the reading on the device while cranking up the heat. The reading and thus the reading rises up to 13. (That is unfortunately the maximum the device can read... Hehe "unfortunately"! See what I did here? [It's lame.]) He awaits any further changes and keeps heating.
At some point the device starts reading lower numbers again. (It's a VERY robust device) He has no reason to distrust the device and assumes his heater broke (I'd actually hope so, but nvmd) and that it really is starting to cool down. He waits for the reading to reach zero and then moves to disassemble the device - and immediately went up in plasma vapors once he came anywhere near it.
Huh? What was his mistake? 

Well, first: He forgot to turn off the heater, and second: He didn't know how the underlying mechanics of particle excitation change the wavelength of the energy emission of the heated material, and how limited his devices response to certain frequency ranges is. The device was made to aid in quick temperature assessment in the range of 700 to 450nm energy emissions. He didn't knew that the device couldn't register high energy gamma rays and would show zero instead of billions.

You see, being forced to memorize the contents of a table instead of learning how to create said contents from nothing, can kill you.

Even if you just provide a table for error-checking purposes you are making a fool out of people: If they don't learn how to properly troubleshoot the mistakes they made they are not having a good understanding of the whole thing in the first place.
Just look at the state of Logic in everyday life. It's almost gone entirely!

[GlennSprigg]

Well if you want a peaceful life, why make a post that dredges up some spat you've had elsewhere with Brumby in an unrelated topic? That does seem to be trolling for a response. 

Oh and please, less smilies, less brackets, less ... ellipses, less random punctuation in general and RANDOM changing into ALL CAPS in the middle of run on sentences. It makes it incredibly hard to read what you've written.

Dear 'Cerebus'.....  I was not aware that Mathematics was a favorite topic of 'Aardvarks', or why you read this far?
'HE' was mentioned, because he usually makes some Pious remarks when I post something, & here was no exception !
I have ZERO interest in 'your' thoughts beyond that, so please stick to 'licking ants' mate......

OH... and as for your...... "and please, less smilies, less brackets, less ... ellipses, less random punctuation " diatribe,
do you now feel like a 'bigger' 'man' in your personal attack, beyond your apparent need to lick 'someone's' butt ().
Well, every 'punctuation' mark I use is for a reason, as raw text says/highlights/means nothing..........

Ignoring YOU (from now on), will be easy.....   Back to the REAL commenters that the rest of us love here.....

[GlennSprigg]

Oh.. shit... I almost forgot 'Brumby' !!!!!!!
I know you can't help it mate....  "Gods" can't !!!!!!!!!
(Maybe spend less time trying to defend yourself at 2 or 3 Am with nothing else to do......)

Anyway, I sincerely thank the 'general' (mere) population who engaged in this meaningful
dialog, in a meaningful & productive way, and truly enlightened me. Thank you !
Glenn Sprigg.  (No name ever hidden  )

[Cerebus]

Well if you want a peaceful life, why make a post that dredges up some spat you've had elsewhere with Brumby in an unrelated topic? That does seem to be trolling for a response. 

Oh and please, less smilies, less brackets, less ... ellipses, less random punctuation in general and RANDOM changing into ALL CAPS in the middle of run on sentences. It makes it incredibly hard to read what you've written.

Dear 'Cerebus'.....  I was not aware that Mathematics was a favorite topic of 'Aardvarks', or why you read this far?
'HE' was mentioned, because he usually makes some Pious remarks when I post something, & here was no exception !
I have ZERO interest in 'your' thoughts beyond that, so please stick to 'licking ants' mate......

OH... and as for your...... "and please, less smilies, less brackets, less ... ellipses, less random punctuation " diatribe,
do you now feel like a 'bigger' 'man' in your personal attack, beyond your apparent need to lick 'someone's' butt ().
Well, every 'punctuation' mark I use is for a reason, as raw text says/highlights/means nothing..........

Ignoring YOU (from now on), will be easy.....   Back to the REAL commenters that the rest of us love here.....

You've got troll written all over you mate, otherwise why would you turn a polite request to adopt a more readable writing style into a "personal attack" and spend so much time crafting such a personalised reply. Well, perhaps crafting is too  skilled a word for it, but it's clear the intent was to try and get some intemperate response out of me. As to ignoring me, good, but I bet you don't have the self control to let me have the last word.

[Brumby]

Wow, what an interesting Saga that all was... (again  )
(I'm the original 'poster' again...)
My hat's off to the gentleman from the U.S. (and others...), that stated that their kids
ARE taught the times-tables, and that it is a 'requirement'...  That's GOOD !! 
But it still sadly doesn't 'here'. (In Australia. No Aussie jokes please  )......
I can/have asked my 1st year high-school grand-kids, and their friends, the likes of....
"What is 6x6", or "what is 8x4".... let alone.... "what is 9x7"... (F%$# that's hard!),
and NONE of them can tell me !!!  They ALL have iPhone/Android 'Tablets' these days
in class, (so no need for ancient 'Calculators' ), [lets show them a slide-rule haha].

What is it about a lot of you responders, that make you think that any/all of your own
'methods', and the 'Effort' it takes to remember it/them, is ANY better than SIMPLY
remembering BASIC times-tables, from/with which anyone can calculate anything ??
I RESPECT all your 'abilities'..... but what are you fighting against Seriously ??
May we all, (teachers, parents, grandparents) simply teach our kids the 'basics' 

'Brumby' seems to prefer 'Yep..', 'Nope..', {quote} then 'yep..' without 'adding' to
anything at all except his unadulterated 'Piousness'.... He seems to now 'seek' out
my many/varied Posts now, (even though I have moved on...), from a time that he
chose to (attempt to) 'Belittle' me repeatedly.... when I 'dared' to ask for a resolution
on this 'Forums' MAIN? forum topic.  This 'Demi-God' (in his Godness & Greatness)
decided at 2am one morning, (with nothing else to do obviously), to RANT at me, and
tell me I am just a "TROLL"... (Haah?! it was MY post he was continuously abusing??).
After swallowing my pride/rights, I apologized to him, and explained all that I could.....
'HE' then ridiculed me about what I offered, and repeated how 'I'm' just a "TROLL" ?
Well I have many scientific interests, that go WAY beyond listening to this "No-Life",
and as such I keep posting/discussing in areas "I Hope" is beyond 'his' REALM.....
I'm a peaceful Pensioner, who likes to invoke dialog with REAL people, not Demi-Gods...

Well if you want a peaceful life, why make a post that dredges up some spat you've had elsewhere with Brumby in an unrelated topic? That does seem to be trolling for a response. 

Oh and please, less smilies, less brackets, less ... ellipses, less random punctuation in general and RANDOM changing into ALL CAPS in the middle of run on sentences. It makes it incredibly hard to read what you've written.

Dear 'Cerebus'.....  I was not aware that Mathematics was a favorite topic of 'Aardvarks', or why you read this far?
'HE' was mentioned, because he usually makes some Pious remarks when I post something, & here was no exception !
I have ZERO interest in 'your' thoughts beyond that, so please stick to 'licking ants' mate......

OH... and as for your...... "and please, less smilies, less brackets, less ... ellipses, less random punctuation " diatribe,
do you now feel like a 'bigger' 'man' in your personal attack, beyond your apparent need to lick 'someone's' butt ().
Well, every 'punctuation' mark I use is for a reason, as raw text says/highlights/means nothing..........

Ignoring YOU (from now on), will be easy.....   Back to the REAL commenters that the rest of us love here.....

Oh.. shit... I almost forgot 'Brumby' !!!!!!!
I know you can't help it mate....  "Gods" can't !!!!!!!!!
(Maybe spend less time trying to defend yourself at 2 or 3 Am with nothing else to do......)

Anyway, I sincerely thank the 'general' (mere) population who engaged in this meaningful
dialog, in a meaningful & productive way, and truly enlightened me. Thank you !
Glenn Sprigg.  (No name ever hidden  )

[Distelzombie]

Nice archiving, Brumby.

Anyway. GlennSprigg it took me a while to write and imagine my post on the last page. Could at least say something?

[Brumby]

Nice archiving, Brumby.

After the last effort, it seemed judicious.

[IanMacdonald]

Far too much educational time is spent on hifalutin' maths like integral calculus or imaginary numbers, and far too little on the skills which are needed by most people.

Mind you, same is true in other subjects. For example the manic obsession with using OOP coding for even the tiniest program in comp sci courses, whilst the same students have no idea how to avoid typical IT security gotchas. 

Education is like a building; if the foundations are no good, the rest will eventually fall over. The more top-heavy you make it, the sooner that will happen.

Make a good foundation, and people will add more structures to it over time, as required.

[Distelzombie]

Exactly. I always wondered why there are no Philosophy classes in normal elementary and upwards schools. (Germany)

[rstofer]

Far too much educational time is spent on hifalutin' maths like integral calculus or imaginary numbers, and far too little on the skills which are needed by most people.

A lot of us are engineers by education and we hope our offspring take a similar path.  That path WILL require imaginary numbers (particularly for EEs using Euler's identity) and it will require all 4 semesters of calculus (up through differential equations).  Of course, we are not 'most people'.  We can do hard math...

Trade education is available at most community colleges and, just guessing, ALL junior colleges in California.  That's good!  We need trained techs!  There's room for both types, engineers and techs.

[rstofer]

Exactly. I always wondered why there are no Philosophy classes in normal elementary and upwards schools. (Germany)

It is a required course at our local junior college or as a lower division requirement of Cal State colleges and universities.  There may be a way to avoid it by substituting another general education class but I don't think so.

[Distelzombie]

Exactly. I always wondered why there are no Philosophy classes in normal elementary and upwards schools. (Germany)

It is a required course at our local junior college or as a lower division requirement of Cal State colleges and universities.  There may be a way to avoid it by substituting another general education class but I don't think so.

It should start in elementary school, or at least in middle school. Definitely. I mean you learn basic Logic, Ethics ... stuff! Very important.




Edit: I think nobody is taking my post back then seriously: https://www.eevblog.com/forum/chat/the-importance-today-of-_times-tables_/msg1488705/#msg1488705
So here is one more knowledgable person with the same opinion, in paper form. I can produce more if needed: https://bhi61nm2cr3mkdgk1dtaov18-wpengine.netdna-ssl.com/wp-content/uploads/2017/03/FluencyWithoutFear-2015-1.pdf

[GlennSprigg]

Nice archiving, Brumby.
Anyway. GlennSprigg it took me a while to write and imagine my post on the last page. Could at least say something?

Dear Distelzombe you are SO right and deserve a reply !!!
(I apologize for being distracted by that "war of words"  )
I read your reply twice, and it is interesting to say the least. I'm pretty sure I get what you are saying mate,
with your analogy, however I don't think it relates to the point that I was trying to push forward......
I understand limits of 'scale' within known 'norms' and outside of those 'norms. (I was also an electronic
Instrument Technician). I can appreciate under/over off-scale readings in ways that you might not think
I can.  (The technical term is 'burnout'). GIVEN, that if a relative reading went seemingly ridiculously high
etc, (as in your 'norm' from 0-7 now being say '18'... (would not be registered as such though), then we
would need to rethink all the parameters. However my friend, this does not change the basic maths I pose??

We are not talking about running out of 'Basic' numbers..... (digits 0-9), but the NEED to know the BASICS
off by heart, like 6x6, or 5x5, or 8x8.... (Ok... the 'typical' kids poster goes up to 12x12 !).
When a question/problem/step is say.....  7x7 you NEED to know that the answer is '49' (What is simpler?)

I'm left wondering what people have against 'knowing' except that they don't know/remember !!!!
Why do people fight it ??  Just re-learn, and pass it on to kids/grandkids if 'teachers/parents' won't/can't ??
Simple example....      23 x 54... Not initially KNOWN, but easily calculated...
    23
 x 54
-----
'ASSUMING' the 1st step is 4 x 3, (= 12), HOW ARE YOU GOING TO KNOW THAT !!  if not by logic/heart.
Do you see what I mean ?? There are no SUB steps to 'calculate' that, unless counting 'beans' etc ??
People have quoted other ways to say "Simplify Fractions" etc etc but that's not relevant... xx

FORGET all the dialog in this post, from the original question/statement through to HERE......
I'm now re-asking/stating a simple maths question, (no 2 digit numbers in the question)......
What is    6x9    !!!!!!!   What is WRONG with simply KNOWING that it is  '54' ?? in the middle of a
complex multi-stage calculation you are working on?   Someone else here might say......
"Oh.... well that's the same as 6x10 = 60, -6 = 54..."  (at every step in your 'sumation'?)....
Maybe I would be 'knit-picking' if I then said/asked... "how do you know automatically  that 6x10 = 60"...
(well, that's obvious ??).....   no it is not to the uneducated.  So is '8x8' or '6x6'..........

What 'confuses' me, is why people 'fight' it ??   Just 'RE'-Learn it !!!   

[Distelzombie]

Your point was, or is, that you explain "students being unable to calculate equations" with "they are not learning tables anymore", right?
May point with that post was to show you (and others) how problematic it can be when you never learn why 6x6 equals 6. ("It's devils work!" ... No it's logic.)
I wonder why didn't saw the real problem with your "niece"s abilities, when you finally asked her what 30*40 is. (Why quotation marks, btw?) It' is obviously the she lacks the "number-sense". Since someone explained they ARE learning tables in early school, you should see the answer already.
You also lack the number-sense, don't you? (Judging by your questions.) You probably never learned to aquire a sort of number-sense.
As I've shared in the post before, learning by tables doesn't give you a very good number-sense. (The bottom link)


I don't know if I have a good number-sense or not, but I would go at the problem like this:
23*54 // 20*50 + 20*4 + 3*50 + 3*4 // 10*50*2=1000 + 2*4*10=80 + 3*50=150 + 3*4=12 // 1000+150+12=1162 + 80= 1242 (I am a slow calculator)
That's the simplest way I could find while I was writing it down here. I would probably use a slightly different route if I had less time to think about the route. (Especially at the end where I was switching the interim results around) And I haven't learned that. That's just done a priori.


"HOW ARE YOU GOING TO KNOW THAT" 3*4 equals 12? I go the easy route on such small number if I can not remember the result right of the bat: 4+4+4. May sometimes be faster as trying to remember the result.


"We are not talking about running out of 'Basic' numbers..... (digits 0-9), but the NEED to know the BASICS
off by heart, like 6x6, or 5x5, or 8x8.... (Ok... the 'typical' kids poster goes up to 12x12 !).
When a question/problem/step is say.....  7x7 you NEED to know that the answer is '49' (What is simpler?)"
Running out, huh? You say poster, does that mean it is readily available at a moments notice? That is very bad if you actually want to learn something real. You're just learning how to look up a result in a table if you're not careful. Anyway:
That is simple, yes. But it also MAKES YOU simple.


"What is    6x9    !!!!!!!   What is WRONG with simply KNOWING that it is  '54' ?? in the middle of a
complex multi-stage calculation you are working on?   Someone else here might say......
"Oh.... well that's the same as 6x10 = 60, -6 = 54..."  (at every step in your 'sumation'?)....
Maybe I would be 'knit-picking' if I then said/asked... "how do you know automatically  that 6x10 = 60"...
(well, that's obvious ??).....   no it is not to the uneducated.  So is '8x8' or '6x6'.........."
Nothing is wrong with knowing the result, if you got to it yourself beforehand. And isn't "60-4" just as fast as remembering the result anyway?
How do you know automatically that 6x10 = 60? That's not nitpicking, that is: Not understanding the basics of Mathematics. OFCOURSE it is not obvious to the uneducated. What is your point?


People fight it because it is frustrating, excruciatingly boring and it goes against current educational-psychology and make students cry. (proof available, see link) I just got a good feeling from finding the right solution to this mathematical problem. Like the feeling you get when you finish something you were building. You don't get that when you learn tables!


Kind regards

[Bud]

Bullshit. I did not cry when i learned it and it helped me all my life.

[DimitriP]

People fight it because it is frustrating, excruciatingly boring and it goes against current educational-psychology and make students cry.

Yeah..so is writing, saying please and thank you, dotting "I"s and crossing "t"s, washing  hands after using the restroom, tying your shoelaces, filling up the car with gas, replacing the empty roll of toilet paper,  calling mom and dad on their birthdays and anniversary, putting on clean socks and underwear after taking a shower.
And lest add "doing laundry" to the list of frustrating and excruciatingly boring tasks that we routinely perfom daily.

As for the "current" educational psychology...well...since it's "current"..we should give it a few years until it changes.
We are not talking about learning to fly a plane by memorizing which buttons and levers to push pull of flip.
And we are not even talking about "learning by tables".

We are talking about "The Times Tables"
We are talking about hearing "8x8" and the next thing that pops into your head is "64".

Like being in a swimming pool playing Marco..........Jonathan - Ha! just kidding ...Polo!     ( I don't know the geographic distribution of this game - so this might not mean much to many)

I don't know how one cannot "know " WHY eight times eight is sixty four.
If you take eight bags of marbles with eight marbles in each and you count them all, ( that can be boring the second time you do it ) .....and provided you can count up to 64 !!! , you'll "know" why 6x6 is 64.  ( of course counting ...is yet just another table, just like knowing the days of the week, and the names of each month...tables...funny how that works)

I'll stop here before a let everyone know how I really feel .

I guess Bud put it best

Bullshit. I did not cry when i learned it and it helped me all my life.

[Distelzombie]

Did does nobody get it?
I was criticizing tables because you can't as easily calculate what's beyond those tables as someone who learned math differently.
Am I so unprecise?

[Cerebus]

Did does nobody get it?
I was criticizing tables because you can't as easily calculate what's beyond those tables as someone who learned math differently.
Am I so unprecise?

No, I get your point, I just don't see much mileage in any continued debate. I doubt there's much chance of you changing the minds of the "It was good enough for me" school of thought. When you have participants who bewail that children nowadays do not learn times tables in the way they were taught in maths classes, but eschew all that they were taught in English classes I suspect you're on a hiding to nothing.

[IanB]

Did does nobody get it?
I was criticizing tables because you can't as easily calculate what's beyond those tables as someone who learned math differently.
Am I so unprecise?

If we know the tables we can more easily calculate what is beyond the tables. That is the whole point of the tables, they are building blocks.

For example, if I want to know what is 16 x 14, I can quickly see it is the same as 4 x 8 x 7, and I know right away that 8 x 7 = 56. So now 4 x 56 is easy, it is 224 (again, because I know right away that 4 x 50 = 200 and 4 x 6 = 24).

So, we don't agree with you. It is not a case of learning one thing or another, it is a case of learning all the things, and learning many different ways. The more you learn, the more you can do.

[Brumby]

Did does nobody get it?
I was criticizing tables because you can't as easily calculate what's beyond those tables as someone who learned math differently.
Am I so unprecise?

You presume that by learning their tables people don't bother to learn anything past that ... which is absurd.

I learned my tables by wrote in primary school and use that stored information often.  It is efficient in day-to-day use.  You don't need to know why 6 x 9 = 54 - you just need to know that it does.  6 x 9 = 54 is one operation.  It is quick.   Aside from 9 + 9 + 9 + 9 + 9 + 9 being painful and slow, by having to go through 5 operations to get an answer the opportunity to make an error increases by a factor of 5.

But knowing that doesn't stop you from exploring numbers further.  Once you know your tables, seeing patterns becomes easier; understanding why 6 x  9 = 54 becomes trivial and finding alternative expressions to go from 6 x 9 to an answer of 54 is not that hard.  Do your 10 times table and tell me you don't see any patterns!

I think anyone who has not learned up to at least the 10x table is at a disadvantage - but with calculators so freely available these days, it doesn't have the same impact as it did many years ago.

Perhaps this is the argument - that because calculators are so ubiquitous, learning the tables isn't as necessary as it once was - but explaining how things work is still valid.

Can't say I agree completely.  If I had my way I'd say, by all means do the "how and why" - but let's get the tables down pat along the way.

[CatalinaWOW]

I recently had a graphic demonstration.  While teaching a younger relation to play Cribbage.  A game which requires finding combinations of cards which add to fifteen.  This person understood the idea of addition perfectly and could use a calculator, but had not successfully memorized addition tables.  In gameplay the individual was reduced to counting pips on various card combinations to test the sum.  This is just a game, and is just addition, but it illustrates the penalty exacted by not having the tools internalized.  A number sense is just another name for a slightly different version of the same thing.

[rstofer]

Did does nobody get it?
I was criticizing tables because you can't as easily calculate what's beyond those tables as someone who learned math differently.
Am I so unprecise?

I guess it really comes down to the fact that not many agree with you.  It doesn't matter how a person learns to multiply, the times tables being one method of learning, what's important is that they learn to multiply.  I don't see how you can posit that numbers beyond the times tables present any kind of challenge.  For a decimal system, worst case, all we need is up through the 9's.  Everything else is carry and add.  The largest conceivable product is 9x9 which is 1 and carry the 8.

Over time, people will discover for themselves methods for doing the work faster.  Or they won't.  Some people just hate math.

[Brumby]

I recently had a graphic demonstration.  While teaching a younger relation to play Cribbage.  A game which requires finding combinations of cards which add to fifteen.  This person understood the idea of addition perfectly and could use a calculator, but had not successfully memorized addition tables.  In gameplay the individual was reduced to counting pips on various card combinations to test the sum.  This is just a game, and is just addition, but it illustrates the penalty exacted by not having the tools internalized.  A number sense is just another name for a slightly different version of the same thing.

Fifteen two and the rest won't do!

IMO, this is an example of someone who has never given much effort to doing arithmetic by hand - always using a calculator, even for simple addition.  As a result, they just don't become familiar with the association of 6's and 9's or 7's and 8's with the magic number 15.

You've summarised this eloquently:

...but it illustrates the penalty exacted by not having the tools internalized.

[bd139]

They actually teach them this in the format "number bonds" now at school at the age of 5 here because hammering that intuition in early while the brain is mushy is pretty important.

Quite impressed if I'm honest. My 14 year old is learning calculus already.

Reminds me of this bit of Star Trek:

[rstofer]

The real discussion should be on a) the inability to read a technical statement and b) the hatred of word problems.  The two are deeply related.

Maybe it's really an appreciation for word problems that works to filter STEM students.

You don't have to love them but you do have to solve them.  Life is a word problem!

[Distelzombie]

The question was "Why are time tables no longer important" or "not tought in school anymore" and brought up a point for that.
I could go asking you to cite studies to prove your point, while providing studies that prove my point. But I don't really care.

No, I get your point, I just don't see much mileage in any continued debate. I doubt there's much chance of you changing the minds of the "It was good enough for me" school of thought. When you have participants who bewail that children nowadays do not learn times tables in the way they were taught in maths classes, but eschew all that they were taught in English classes I suspect you're on a hiding to nothing.

He is right. I'm on a hiding to nothing. (I had to search that saying, but meh)
I am not responsible for your children. If you want to follow the tradition than that's it. I thought I could teach you about educational psychology, but I am not equipped for that.

Word problems are good, imo. (Do you see any "imo"s in my other statements, btw?)

[james_s]

The real discussion should be on a) the inability to read a technical statement and b) the hatred of word problems.  The two are deeply related.

Maybe it's really an appreciation for word problems that works to filter STEM students.

You don't have to love them but you do have to solve them.  Life is a word problem!

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.

[NiHaoMike]

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.

[DimitriP]

"If you have one bucket that holds 5 gallons and another bucket that holds 2 gallons, how many buckets do you have ?"   

Common core , socially caring infused version:
If you have 2 buckets that hold 4 gallons each, and your neighbour has 2 buckets that hold 3 gallons each how many buckets should you give to him so you both have the same number of buckets?

[rstofer]

I am not responsible for your children. If you want to follow the tradition than that's it. I thought I could teach you about educational psychology, but I am not equipped for that.

I'm of the totally unqualified opinion that all the psycho babble around education has lead to lower and lower results.  Everybody feels good about themselves even when they can't add.  A real unspoken problem around 'new math' and it's successors is the fact that parents can't help their kids with the homework.  This makes both the kids and the parents feel depressed and the kids think their parents are stupid.  It wasn't the way we were taught!  It's almost an elitist kind of thing; the teachers are smarter than everyone else.  That's why they make so much more money than a EE.  Oh, wait...

I remember having to do arithmetic on the blackboard in front of the other students.  It was get the right answer or be laughed at.  Nobody was worrying about MY feelings.

What I remember about junior highschool on Oct 5th 1957 (the day after Sputnik was launched) was a complete turnaround in teaching math and science.  It was learn by doing, get up here and show us!  I was in the 7th grade...

[Distelzombie]

Don't blame the teachers for your inability to keep up with the children. Praise them

Also the teachers are only - kind of - following orders. If they differ too much from the schools or states educational plan, they can look for a different job. At least here in germany

[GlennSprigg]

PHEW!!... I couldn't have believed it would get this far ??  (My original post...).
I 'THINK' that most people understand/understood what I was initially proposing?...

However....  "Distelzombie", I am left with no other recourse than to assume that...
"never the twain shall meet" (it's beyond this scope here x), so I bow out to 'you' :-)

That being said, I 'tried' to show respect to your comments/thoughts, but to no avail.
I think everyone else knows that when I mentioned "maths with single digits", I meant
just that my friend.... NOT 'knowing' off by heart what is  "13x17" or "23x49"...
The BASIC single-digit memorized 'results' are but the first, of REPEATED steps for the
next level???  But everyone else KNOWS that, and what I mean???

In the latter part of this post/comments, 'BRUMBY'  did say it all, with simple clarity and I thank him !!!!
However... 'someone else' said, in answer to 'Distelzombie'....
  "No, I get your point, I just don't see much mileage in any continued debate. I doubt there's much chance of you changing the minds of the
  "It was good enough for me" school of thought. When you have participants who bewail that children nowadays do not learn times tables in
  the way they were taught in maths classes, but eschew all that they were taught in English classes I suspect you're on a hiding to nothing."
simply 'smacks' of ill-informed aggression with the goal of 'belittling' me.... (He knows ) :-)

[GerryBags]

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.

[Distelzombie]

PHEW!!... I couldn't have believed it would get this far ??  (My original post...).
I 'THINK' that most people understand/understood what I was initially proposing?...

However....  "Distelzombie", I am left with no other recourse than to assume that...
"never the twain shall meet" (it's beyond this scope here x), so I bow out to 'you' :-)

That being said, I 'tried' to show respect to your comments/thoughts, but to no avail.
I think everyone else knows that when I mentioned "maths with single digits", I meant
just that my friend.... NOT 'knowing' off by heart what is  "13x17" or "23x49"...
The BASIC single-digit memorized 'results' are but the first, of REPEATED steps for the
next level???  But everyone else KNOWS that, and what I mean???

In the latter part of this post/comments, 'BRUMBY'  did say it all, with simple clarity and thank him !!!!
However... 'someone else' said, in answer to 'Distelzombie'....
  "No, I get your point, I just don't see much mileage in any continued debate. I doubt there's much chance of you changing the minds of the
  "It was good enough for me" school of thought. When you have participants who bewail that children nowadays do not learn times tables in
  the way they were taught in maths classes, but eschew all that they were taught in English classes I suspect you're on a hiding to nothing."
simply 'smacks' of ill-informed aggression with the goal of 'belittling' me.... (He knows ) :-)

I have no idea if you want to say that I misread what you wrote or something else. Clearly, I am incapable of understanding your written accent or slang. I also don't want to involve more than read-through into this anymore.
That "someone else" (Cerebus) is right with what he said. If you want to be heard, make sure you're speaking the same language. (That is quite hypocritical, but meh.)

[Cerebus]

  "No, I get your point, I just don't see much mileage in any continued debate. I doubt there's much chance of you changing the minds of the
  "It was good enough for me" school of thought. When you have participants who bewail that children nowadays do not learn times tables in
  the way they were taught in maths classes, but eschew all that they were taught in English classes I suspect you're on a hiding to nothing."
simply 'smacks' of ill-informed aggression with the goal of 'belittling' me.... (He knows ) :-)

You're supposed to be ignoring me, remember - looks like that 'last word' was just too tempting for you, even if you had to get it in sideways. As it is, I didn't have you specifically in mind, but if the caps fits, feel free to wear it. I must have become unnaturally important in your world to have already become a "he who must not be named", I'm honoured.

[GlennSprigg]

Me..   Moi   (To the ant eater)... I didn't mention your name??? YOU did !! :-)
You 'TOLD' me previously , NOT to 'speak' after your last Diatribe.....
However, YOU chose to ADD your verbal diarrhea SINCE then, which I simply quoted !!!
So I reacted to that..... (fuck you are pathetic mate...)  ..........
Back to normality with everyone else.....  Just move on (or shut up, or eat ants whatever...)

[Cerebus]

Me..   Moi   (To the ant eater)... I didn't mention your name??? YOU did !! :-)
You 'TOLD' me previously , NOT to 'speak' after your last Diatribe.....
However, YOU chose to ADD your verbal diarrhea SINCE then, which I simply quoted !!!
So I reacted to that..... (fuck you are pathetic mate...)  ..........
Back to normality with everyone else.....  Just move on (or shut up, or eat ants whatever...)

As to the claimed 'diatribe' (by the way, that is the proper usage of single quote marks) can you point to this 'diatribe', quote it? No, because it's all in your imagination. I have not commanded you not to speak, I have been nothing but reasonably civil to you, even in the face of provocation. I am still being reasonably so.

You are the one who has used phrases like "(fuck you are pathetic mate...)  " — and what kind of twisted mind thinks that piling smileys after cursing in someone's face is even sane?

May I advise you not to pick a battle of words, with anybody. It's not exactly your natural medium, is it?

I doubt many people know of Dave Sim's "Cerebus the Aardvark" comic (its circulation back in the day was so small that 'cult' is making it sound more popular than it was), especially a retiree from Aus. Heck, you can't even tell from Dave's and Gerhardt's drawings or my avatar that it is an aardvark unless someone tells you. So you must have gone out of your way to research the nickname, merely to give yourself what you hoped would be some ammunition to pelt me with, or make me quake in my boots at your awesome internet research skillz, after one short comment to one of your messages. That's mighty odd behaviour, obsessional even. Flattered though I am by the attention, I've got a girlfriend thanks and, bluntly, you're not impressive enough to be of interest. You are more like a mosquito, mildly distracting, but of no real consequence. Now, buzz off...


===*===


If anybody's going to the bar I'll have a pint of apricot brandy and a bag of chocolate coated ants. Thanks. 

For the avoidance of any doubt, lest anyone think I'm being too heavy handed with Ms. Spring, here is the 'diatribe' and the "You 'TOLD' me previously , NOT to 'speak' after your last Diatribe....." with which I earned his effervescent but ineffective opprobrium:

Well if you want a peaceful life, why make a post that dredges up some spat you've had elsewhere with Brumby in an unrelated topic? That does seem to be trolling for a response. 

Oh and please, less smilies, less brackets, less ... ellipses, less random punctuation in general and RANDOM changing into ALL CAPS in the middle of run on sentences. It makes it incredibly hard to read what you've written.

Dear 'Cerebus'.....  I was not aware that Mathematics was a favorite topic of 'Aardvarks', or why you read this far?
'HE' was mentioned, because he usually makes some Pious remarks when I post something, & here was no exception !
I have ZERO interest in 'your' thoughts beyond that, so please stick to 'licking ants' mate......

OH... and as for your...... "and please, less smilies, less brackets, less ... ellipses, less random punctuation " diatribe,
do you now feel like a 'bigger' 'man' in your personal attack, beyond your apparent need to lick 'someone's' butt ().
Well, every 'punctuation' mark I use is for a reason, as raw text says/highlights/means nothing..........

Ignoring YOU (from now on), will be easy.....   Back to the REAL commenters that the rest of us love here.....

You've got troll written all over you mate, otherwise why would you turn a polite request to adopt a more readable writing style into a "personal attack" and spend so much time crafting such a personalised reply. Well, perhaps crafting is too  skilled a word for it, but it's clear the intent was to try and get some intemperate response out of me. As to ignoring me, good, but I bet you don't have the self control to let me have the last word.

[Bassman59]

"If you have one bucket that holds 5 gallons and another bucket that holds 2 gallons, how many buckets do you have ?"   

Common core , socially caring infused version:
If you have 2 buckets that hold 4 gallons each, and your neighbour has 2 buckets that hold 3 gallons each how many buckets should you give to him so you both have the same number of buckets?

That’s not the Common Core at all.

The whole point of the Common Core for math is to teach kids numeracy. That is, put simply, understanding numbers, the numerical analogue to literacy.

Part of numeracy is doing word problems, which require the learner to approach problems in various different ways. Sure, word problems are manufactured, but oftentimes you are faced with a math problem expressed as a word problem.

The other approaches to numeracy (the number bonds already mentioned, and the various strategies) are all intended to get the students to understand what they are doing. It’s more than just the rote memorization of times tables, and more than the algorithmic approach to multiplication. Approaching the problem from many angles is a good thing. I know a lot of parents are baffled when asked to help with math homework. “I don’t understand all of this new stuff!” is one common refrain. Another is, “the old style of math teaching was good enough for us!” to which I reply, “you hated math and barely passed, so clearly it was not good enough.”

My kid is in third grade, doing math at a 6th-grade level. A lot of it is because he enjoys math, and better, he enjoys helping his classmates with their math problems. And help he does, because he truly understands it.

[DimitriP]

The whole point of the Common Core for math is to teach kids numeracy

Thank %DEITY%   for the 21st century geniouses that figured out math was being taught wrong for a few thousands of years.
Those of us still around 20-30 years from now can discuss how it worked out then



 

[mtdoc]

  for the 21st century geniouses that figured out math was being taught wrong for a few thousands of years.

What makes you think math has been taught the same way for thousands of years?  Or for that matter, what makes you think it has ever been taught the same way across different cultures.?

[DimitriP]

  for the 21st century geniouses that figured out math was being taught wrong for a few thousands of years.

What makes you think math has been taught the same way for thousands of years?  Or for that matter, what makes you think it has ever been taught the same way across different cultures.?

Nothing!  That's the point. Throughout  history, somehow it was being done incorrectly. And now it's "fixed".

[mtdoc]

  for the 21st century geniouses that figured out math was being taught wrong for a few thousands of years.

What makes you think math has been taught the same way for thousands of years?  Or for that matter, what makes you think it has ever been taught the same way across different cultures.?

Nothing!  That's the point. Throughout  history, somehow it was being done incorrectly. And now it's "fixed".

What makes you think that the current method does not draw from methods used successfully in the past or currently by other cultures.?

[DimitriP]

What makes you think that the current method does not draw from methods used successfully in the past or currently by other cultures.?

Incompetence.

[Cerebus]

What makes you think that the current method does not draw from methods used successfully in the past or currently by other cultures.?

Incompetence.

Oh, I think you're being a little harsh on yourself. 

[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.