What age do you feel it's appropriate to teach a child multiplication?

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K.Snyder
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What age do you feel it's appropriate to teach a child multiplication?

Post by K.Snyder »

I want a bit of perspective on how old everyone feels a child should be when attempting to teach them multiplication?

3-5 years old

6-8 years old

9-11 years old

12-<

I suppose I hit something before I could post the poll
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What age do you feel it's appropriate to teach a child multiplication?

Post by Bruv »

The trick is to hit them young without them knowing you are teaching them.

It should be fun.
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What age do you feel it's appropriate to teach a child multiplication?

Post by spot »

No child should ever be taught multiplication, either it works the principles out from scratch or it should stay unaware that multiplication even exists. Facts like multiplication should be arcane.
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What age do you feel it's appropriate to teach a child multiplication?

Post by K.Snyder »

Bruv;1384079 wrote: The trick is to hit them young without them knowing you are teaching them.

It should be fun.I can't help but wonder if there's some sort of subconscious virtue lying dormant in the brains of parents that are too unwilling to bestow upon their child the greatest gift imaginable, a head start in ascertaining knowledge.

I say young is absolutely correct but I think it's important to use the correct techniques in doing so...
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What age do you feel it's appropriate to teach a child multiplication?

Post by K.Snyder »

spot;1384080 wrote: No child should ever be taught multiplication, either it works the principles out from scratch or it should stay unaware that multiplication even exists. Facts like multiplication should be arcane.Perhaps I could agree if I were convinced, as it seems you are, that multiplication cannot be approached without pure memorization but it doesn't have to be that way. It's the technique in delivering to them the concept of multiplication that I'm looking for as opposed to simply "knowing" 2x2 is 4.

A table of numbers collected in rows and columns as well as physical quantities representing the single number "1" added together to visually understand why 2x2 apples is adding 1 apple 4 times.

Any attempt to encourage children to memorize multiplication sequences involving the mere multiplication symbol should be immediately disband.
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What age do you feel it's appropriate to teach a child multiplication?

Post by Ahso! »

I think it's best to teach children set concepts and let them apply number of sets in order to devise multiplication. I'm somewhat doubtful memorization of anything in math other than its rules is beneficial instruction. Math is fun for young people who can grasp the concepts.
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What age do you feel it's appropriate to teach a child multiplication?

Post by Oscar Namechange »

Every parent and teacher should have a duty to prepare the child for anything he Is likely to meet In his life.

I'll try and find the link but I remember reading a very good report somewhere that tests had proven that children tend to be more Intelligent when they have been exposed to memory tests even as toddlers. By using education In memory even as babies, they become more able to absorb Information when they start school. A training of the brain sort of thing.

Why would anyone think that a child would never need multiplication In life?
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What age do you feel it's appropriate to teach a child multiplication?

Post by Bruv »

I am numerically dyslexic or so I tell everybody, I have major problems adding and subtracting or anything to do with numbers.

Not long ago I discovered that the number 9 is magic, in that any multiple of 9 adds up to 9, such as 18, 27, 36........if someone had shown me that when I was learning, it may have opened up the number door of my brain.
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What age do you feel it's appropriate to teach a child multiplication?

Post by YZGI »

oscar;1384088 wrote: Every parent and teacher should have a duty to prepare the child for anything he Is likely to meet In his life.

I'll try and find the link but I remember reading a very good report somewhere that tests had proven that children tend to be more Intelligent when they have been exposed to memory tests even as toddlers. By using education In memory even as babies, they become more able to absorb Information when they start school. A training of the brain sort of thing.

Why would anyone think that a child would never need multiplication In life?


Same question I wanted to ask but was afraid it might sum up my intelligence.
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Post by Oscar Namechange »

Bruv;1384091 wrote: I am numerically dyslexic or so I tell everybody, I have major problems adding and subtracting or anything to do with numbers.

Not long ago I discovered that the number 9 is magic, in that any multiple of 9 adds up to 9, such as 18, 27, 36........if someone had shown me that when I was learning, it may have opened up the number door of my brain. I'm the opposite. I can settle a Yankee which Is 11 multiple bets at odds of 4/7... 11/8... 9/4 etc etc within minutes without a calculator...... I just can't spell.
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What age do you feel it's appropriate to teach a child multiplication?

Post by K.Snyder »

oscar;1384088 wrote: Every parent and teacher should have a duty to prepare the child for anything he Is likely to meet In his life.

I'll try and find the link but I remember reading a very good report somewhere that tests had proven that children tend to be more Intelligent when they have been exposed to memory tests even as toddlers. By using education In memory even as babies, they become more able to absorb Information when they start school. A training of the brain sort of thing.Yes but I believe memorization has a ceiling effect at some point and then ultimately fails to convey the real point to learning which is to apply what one has learned to new ideas...

oscar;1384088 wrote: Why would anyone think that a child would never need multiplication In life?And also following from my point above is that at that ceiling effect I think the underlying emphasis is to help children to understand that multiplication is a direct subset of addition. Multiplication is addition and the overall emphasis should be pointed to this effect as opposed to considering multiplication being a different topic altogether when it isn't. It's actually adding groups to other groups. Which means memorization should absolutely never be a consideration among anyone with the serious responsibility in teaching our children
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What age do you feel it's appropriate to teach a child multiplication?

Post by Ahso! »

YZGI;1384092 wrote: Same question I wanted to ask but was afraid it might sum up my intelligence.I don't think anyone made that claim, did they?
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What age do you feel it's appropriate to teach a child multiplication?

Post by K.Snyder »

I'm getting the feeling that many more people than I have realized tends to believe that not all children can be taught the correct techniques in becoming a well educated individual.

The plague of society is to suggest that people are not as smart as others so that they may not contest the impositions of the unethical.

I'm talking about giving every child a better head start in what should be everyone's approach to learning.

Does anyone have a certain age they'd limit to teaching a child the concept of multiplication? I'm sure we can all agree on the language used so far

Ok, I would say around the age of 4, how's that?
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What age do you feel it's appropriate to teach a child multiplication?

Post by Bruv »

I think the chanting of the times tables was what put me off maths.

The whole class would chorus the tables and then when Teacher pointed at you, you had to continue alone.

What excruciating agony for a shy child ?

It's an old joke but true, I knew the tune but I never learned the words.
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What age do you feel it's appropriate to teach a child multiplication?

Post by YZGI »

Ahso!;1384097 wrote: I don't think anyone made that claim, did they?


Not yet but there's still time.
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What age do you feel it's appropriate to teach a child multiplication?

Post by Ahso! »

YZGI;1384101 wrote: Not yet but there's still time.:wah: You know what I meant.
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Post by YZGI »

Ahso!;1384102 wrote: :wah: You know what I meant.


Got it, sorry Kev. Back to child rearing.
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Post by Ahso! »

YZGI;1384104 wrote: Got it, sorry Kev. Back to child rearing.I meant nobody made the claim that children don't necessarily need multiplication. They do, but we have calculators for those who cannot grasp mathematical principles.
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What age do you feel it's appropriate to teach a child multiplication?

Post by Ahso! »

Bruv;1384091 wrote: I am numerically dyslexic or so I tell everybody, I have major problems adding and subtracting or anything to do with numbers.

Not long ago I discovered that the number 9 is magic, in that any multiple of 9 adds up to 9, such as 18, 27, 36........if someone had shown me that when I was learning, it may have opened up the number door of my brain.You're talking about digital root numbers.

Magic 9 - Maths
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What age do you feel it's appropriate to teach a child multiplication?

Post by spot »

K.Snyder;1384085 wrote: Perhaps I could agree if I were convinced, as it seems you are, that multiplication cannot be approached without pure memorization but it doesn't have to be that way. It has never crossed my mind that multiplication involves memorisation. Multiplication is invariably one of several alternative techniques. Those who memorise certain elementary results in order to speed their mental arithmetic are a completely different matter.

As an example of what I mean by technique, and although it's subtraction rather than multiplication, check Tom Lehrer's description at Tom Lehrer - New math Lyrics

If you'd like me to describe the two alternative techniques I use for multiplication I could write them out for the thread. One's what I was taught in school, the quicker one is what was taught to Elizabethan schoolchildren around 1580. Why the second lost favour I've never worked out, it's far more usable.
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What age do you feel it's appropriate to teach a child multiplication?

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K.Snyder;1384076 wrote: I want a bit of perspective on how old everyone feels a child should be when attempting to teach them multiplication?

3-5 years old

6-8 years old

9-11 years old

12-


Depends on the kid, I reckon.

I was reading and studying the encyclopedia and dictionary when I was 4, but math evaded me until I was in college.



My brother, on the other hand, never much cared for reading, but he was doing advanced algebra by the time he was in 6th grade.

So, nurture what the kid wants to learn, when it wants to learn.
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Bruv;1384091 wrote: I am numerically dyslexic or so I tell everybody, I have major problems adding and subtracting or anything to do with numbers.

Not long ago I discovered that the number 9 is magic, in that any multiple of 9 adds up to 9, such as 18, 27, 36........if someone had shown me that when I was learning, it may have opened up the number door of my brain.
Everybody KNOWS that three is the magic number!



Nine is Naughty. :D

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Post by Bruv »

Can't believe I just watched both of them.
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Bruv;1384189 wrote: Can't believe I just watched both of them.
:wah: Kids my age were raised on 'em. There are tons that they showed during commercial time on Saturday mornings as we watched cartoons. Stuff on grammar, history, government, math, ... I still love them.
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Post by Bruv »

Is that why there is so many blues singing, pool playing, cigar smoking illiterates out there ?
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:yh_bye
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What age do you feel it's appropriate to teach a child multiplication?

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Flash cards in their stocking at a very early age. The is no reason that they can't be taught that 2x3=6 or 6x1=6 at the same time they learn that B is for bear or B is for book
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What age do you feel it's appropriate to teach a child multiplication?

Post by spot »

flopstock;1384198 wrote: Flash cards in their stocking at a very early age. The is no reason that they can't be taught that 2x3=6 or 6x1=6 at the same time they learn that B is for bear or B is for book


I'm not sure how that relates to learning how to multiply, though.
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What age do you feel it's appropriate to teach a child multiplication?

Post by Oscar Namechange »

I started school at the age of 4 and a half.

At that age, I knew what 6/4 the field and 10/1 bar 8 meant.... really !!!

The point Is, It's how susceptible each child Is and what they pick up. However, It Is every parents duty to ensure their child Is capable of recieving education.
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Post by Bryn Mawr »

First teach them how to think and how to learn, then teach them the principles and let them take it from there and the younger they start the better they'll be at it.

When they're interested they'll pick up the facts for themselves, all you have to do is help them and make sure they have access.

Teaching them how to interpret information is an essential, teaching them "the interpretation" is just stifling them.
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Post by spot »

I still haven't got over the thread's notion that learning to multiply equates with memorizing a set of times tables. I'm aghast.
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spot;1384928 wrote: I still haven't got over the thread's notion that learning to multiply equates with memorizing a set of times tables. I'm aghast.


Your a Ghast ?

I always knew you was a bit strange.
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Bruv;1384931 wrote: Your a Ghast ?

I always knew you was a bit strange.


Felicity is under the mistaken impression that the large rodent which lives with the Capybara at Bristol Zoo is a Gouti. Maybe strangeness is heritable.
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Post by Ahso! »

I didn't know threads could have notions. Live and learn.
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What age do you feel it's appropriate to teach a child multiplication?

Post by yaaarrrgg »

Kids are able grasp high-level math concepts at a fairly early age. But the important thing is the geometric/conceptual meaning behind the operations. Memorization of tables isn't really math, just memorization.

For preschoolers, for example, you can get wooden blocks and put them in a row. Length shows addition/subtraction (3+4 =7). Arrange them in a rectangle, the area shows multiplication/division (3x4 = 12). So you don't need to give them a table to memorize, but explain a method on how they would construct the table. The important thing is knowing addition deals with manipulating "length," multiplication deals with manipulating "area."
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Post by spot »

I have it in mind that reading Professor Mmaa's Lecture and Edwin Abbott to five year olds works wonders too.
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On the other hand pushing a child at too early an age will only result in the child's survival instinct cutting in and inducing sleep. Laura, pictured below, walked to the Museum, around the Museum (which has at least three floors if not four in parts), around the Waterfront and eventually caved under the pressure. I was a half hour sat on that bench before she stirred. She then wolfed an all-day breakfast and a bottle of milk after which she was back on top form again playing "Bird".

"Bird", for those who've not had the pleasure, involves one person pointing skyward and announcing the passage of something with wings while the other declares "yes, it's a bird" or "no there isn't" depending on l'actualité.

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What age do you feel it's appropriate to teach a child multiplication?

Post by K.Snyder »

Here's an old book that looks to convey the concepts of mathematics well

By page 13 we've already seen a number as high as 9000

http://books.google.com/books?id=pNx6Sj ... &q&f=false
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K.Snyder;1391519 wrote: Here's an old book that looks to convey the concepts of mathematics well

By page 13 we've already seen a number as high as 9000

Robinson's Progressive Practical Arithmetic: Containing the Theory of ... - Horatio Nelson Robinson, Daniel W. Fish - Google Books


That contains a good example of technique, starting on page 37 section 60 and showing an assortment of multiplication methods. All of them rely on using the table lookups as shorthand for finding the result of multiplying two one-digit numbers, so that's it's first technique. It then discusses how to multiply multiple-digit numbers by one digit, then multiple-digit numbers by multiple digits, then special cases with factors or with mutiples of ten.

That's why I asked in the first place what "learning tables" had to do with learning multiplication. It's an optional trivial step. The "learning multiplication" bit is acquiring techniques to handle any number. It may well be that using a calculator is today's default learned technique but if that's so it definitely doesn't require anyone to learn tables.

Why are you so obsessed with learning bloody tables, and what on earth does that have to do with learning how to multiply? I'd really be interested in hearing your answer, I've not seen one yet.
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What age do you feel it's appropriate to teach a child multiplication?

Post by K.Snyder »

spot;1391530 wrote:

Why are you so obsessed with learning bloody tables, and what on earth does that have to do with learning how to multiply? I'd really be interested in hearing your answer, I've not seen one yet.I suppose I hadn't meant tables as most are accustomed to but rather an emphasis to physically verify the concept. The physical interaction going quite far in the child's desire to learn more,regardless if whether he or she understands irrespective of any " birds"
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Post by spot »

A real-world metaphor of the add and subtract concept is the straight line. You can join lines end to end or cut lines into sections and the result is additive or subtractive.

A real-world metaphor of the multiply and divide concept is rectangular area. You can increase or reduce the width or height (using the previous metaphor for add and subtract) and the resulting area represents multiples or fractions of the sides. yaaarrrgg described this a couple of months ago.

You can set up an experimental workspace for both with a bottle of cents, if cents still circulate, and you do it long before they go to school. Whether that's Mathematics or English Vocabulary I'm not sure but I suspect, if you're going to feed it to a child rather than allow the child to discover it, then it's vocabulary. On an undergraduate maths course it would by default be maths. In either case it should be a what-does-it-mean question, not a how-do-I-employ-it question. I still think that these basic operations should emerge in a child's mind as a result of exploration rather than passively watching an adult demonstrate it. The interest, again in both cases, should be where does this take me, what can I now explore that I couldn't without it.

The definition of multiplication is in the book you referenced, page 36 section 54: "Multiplication is the process of taking one of two given numbers as many times as there are units in the other". Any real-world system which demonstrates that in a graphic fashion is ideal for teaching the concept.

The bottle of cents is priceless for exploring far more operations than just the four I've mentioned, it especially gives a physical system to manipulate elementary notions of statistics.
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What age do you feel it's appropriate to teach a child multiplication?

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question: If rote memorization has no place in modern education, why was mathematical ability so much higher in the 1960s when it was used?
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Are you suggesting that children don't learn multiplication tables any longer? My experience is that they do but as a teacher you may know different, by all means tell us.

My position is that learning multiplication tables has nothing to do with understanding how to multiply, other than in the restricted area of single digit numbers multiplied by single digit numbers. Anything bigger than that requires a workable procedure, and I promise that working the procedure doesn't depend on having memorized the tables. Neither has either type of multiplication much to do with understanding what effect multiplication has in the world.

I recall learning in the sixties. I did it because I was interested in learning. Perhaps too few children today have been effectively encouraged to take that interest. It's cool, apparently, to disrespect education. I guarantee it's not a message I've spread, so who's spread it?
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What age do you feel it's appropriate to teach a child multiplication?

Post by Saint_ »

spot;1391628 wrote: Are you suggesting that children don't learn multiplication tables any longer? My experience is that they do but as a teacher you may know different, by all means tell us.


I'm not suggesting it, I'm saying it outright. Approximately 60% of modern high school students do not know their times tables to mastery. If you take the times tables to 12's, which is important for factoring and simplifying rational expressions, that number jumps to 90%. Don't take my word for it, find any teenager on the street or that you know and ask them what 9 X 12 is.

My position is that learning multiplication tables has nothing to do with understanding how to multiply, other than in the restricted area of single digit numbers multiplied by single digit numbers. Anything bigger than that requires a workable procedure, and I promise that working the procedure doesn't depend on having memorized the tables. Neither has either type of multiplication much to do with understanding what effect multiplication has in the world.


You are right...and wrong at the same time. Your approach is needed as a complement to memorization. Times tables are so basic, however, not knowing them by complete memory is the equivalent of trying to read without a vocabulary. It becomes impossible to see patterns. For example: 16/49 ÷ 24/14 = is a nightmare if you do not recognize the common factors of 7 and 8. You may know how to do a complicated problem, say A=πrˆ2, but if the radius is 12, and you do not know what 12 X 12 is, you can't progress. And please don't say "Use a calculator." Calculators make times tables weaker, not stronger.

I recall learning in the sixties. I did it because I was interested in learning. Perhaps too few children today have been effectively encouraged to take that interest. It's cool, apparently, to disrespect education. I guarantee it's not a message I've spread, so who's spread it?


And just who encouraged you to take an interest? That component is missing from our society.
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What age do you feel it's appropriate to teach a child multiplication?

Post by K.Snyder »

spot;1391628 wrote: Perhaps too few children today have been effectively encouraged to take that interest.I would think introducing mathematics to children at a young age would allow them to effectively take an interest in it.

I also think the problem is that children are not encouraged to learn at all until they're sent off to pre-school at the age of 5 years old while the parents feel that the teachers should be the primary educators which is horrendous! It's the other way around!(I speak for America of course)
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What age do you feel it's appropriate to teach a child multiplication?

Post by spot »

Saint_;1391678 wrote: And just who encouraged you to take an interest? That component is missing from our society.I suggest that's a parochial view rather than a worldwide one. It's not true of most teenagers worldwide, it might be of the 5% you interact with.
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What age do you feel it's appropriate to teach a child multiplication?

Post by Saint_ »

K.Snyder;1391681 wrote: I would think introducing mathematics to children at a young age would allow them to effectively take an interest in it.

I also think the problem is that children are not encouraged to learn at all until they're sent off to pre-school at the age of 5 years old while the parents feel that the teachers should be the primary educators which is horrendous! It's the other way around!(I speak for America of course)


Bingo. There once was an expectation of education in America, in most American families. Today, other than predominantly Asian-American families, that has sadly eroded. I'm not judging, just quoting statistics any of you can look up. And yes, it is America's problem, not the world's. Which is why we are slipping in engineering skills worldwide.
yaaarrrgg
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What age do you feel it's appropriate to teach a child multiplication?

Post by yaaarrrgg »

IMO, the big problem with math education is there needs to be more emphasis on the conceptual and geometric meaning of math, less on memorization. The memorization aspect is really not even math, any more than memorizing numbers in a phone book.

When I tutored math, I discovered that college students who struggled at math were not bad at knowing their times tables. What they struggled with was knowing when to add, when to multiply. They struggled with what it all meant at the geometric level. Which is why story problems give kids the most trouble. At that level a table full of numbers won't help a person at all.

The invention of the computer has made rote memorization in math pretty much obsolete. Machines are better at this aspect than humans. My TI92 calculator can solve differential equations. The only natural thing left for the human is understanding the concepts, not really crunching the numbers
Bruv
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What age do you feel it's appropriate to teach a child multiplication?

Post by Bruv »

I have never 'got' numbers.

I have declared my numerical dyslexia earlier, which I lay at the feet of a particularly Scottish Math Teacher, that had no empathy and who's accent at an early age left me cast adrift.

I still have massive problems with any sort of simple numbers, adding, subtracting or multiplying.

As a practical person I know that if I had been given the 'key'....some sort of 'understanding' of how and why it works, I wouldn't still be embarrassed by my inability.

I can solve practical problems by understanding what is needed, but numbers have always been like magic to me, totally incomprehensible......I wish they weren't.
I thought I knew more than this until I opened my mouth
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Accountable
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What age do you feel it's appropriate to teach a child multiplication?

Post by Accountable »

yaaarrrgg;1391992 wrote: IMO, the big problem with math education is there needs to be more emphasis on the conceptual and geometric meaning of math, less on memorization. The memorization aspect is really not even math, any more than memorizing numbers in a phone book.

When I tutored math, I discovered that college students who struggled at math were not bad at knowing their times tables. What they struggled with was knowing when to add, when to multiply. They struggled with what it all meant at the geometric level. Which is why story problems give kids the most trouble. At that level a table full of numbers won't help a person at all.

The invention of the computer has made rote memorization in math pretty much obsolete. Machines are better at this aspect than humans. My TI92 calculator can solve differential equations. The only natural thing left for the human is understanding the concepts, not really crunching the numbers
Funny. I was in a training session just Saturday and two of my fellow teachers (not math teachers) were going on and on about how their own children are being tortured with word problems without first being taught the times tables. :D

It seems that a balance needs to be struck. I know I don't always have a calculator with me when I need to multiply, figure a percentage for a tip, for instance. I've had to figure angles without a calculator, too. But such skills are pretty useless without having some idea about when to use them. Being in a "softer" area of education (social studies) I understand how much easier it is to teach someone how to do something (the mechanics) than to teach them when or why to do it. It's funny to me how many mechanics and carpenters claim to suck at math, when they use it seamlessly every day at work.

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