So, what is multiplication?

coolul007

What I find interesting, many of you have tried to turn this into a personal issue instead of a mathematical one. It is not about people it is whether the 'definition" fits the problem. If it does use it, if it doesn't, find a better one.

Stephen Tashi

I agree that having a variety of pictures is a good thing. I disagree that there are any serious consequences from the way people answer questions like this. For one thing, the way that people imagine things probably isn't as consistent as the way they answer questions about their imagination. I can't imagine this type of thread damaging the career of any budding mathematicians. If they have the talent to do math, they will enjoy these discussions in the way that people enjoy discussions about "What's your favorite beer?" or "Who's your favorite author?".

hillzagold

Won't someone think of the children?

Ahem. The author in the column from the initial post had to make 5 separate entries explaining to emailers who disagreed with him. I myself initially disagreed with him and believed that multiplication was repeated addition and exponentiation was repeated multiplication. When I had to do 2x3.3, I broke it up into 2 + 2 + 2 + .3x2, and went my whole life. But reading Devlin's column made my realize that I was defining multiplication as repeated addition, and was defining this instance of repeated addition using multiplication! I was pretty confused until Devlin explained a key difference being multiplied values can have different units, such as kilowatts and hours, and I could finally accept multiplication as it's own distinct operation.

As one poster previously mentioned, seeing multiplication and exponentiation as repeated addition made understanding i²=-1 completely impossible for me. It's presumably still impossible for at least 95% of America. But some posters argue that it's necessary to that children can master multiplication at all. May I propose we try and make a pros and cons list?


Pros:
This is the status quo, at it is what almost the entire country, including many of the teachers, honestly believes.
It's apparently easier to learn and understand, to those simple 1st grader minds. (?)
It can be retaught properly later, maybe in middle school or high school or even college. (?)

Cons:
It is mathematically flawed, according to any mathematician you can find who speaks your language.
It makes more advanced concepts, from fractions up to complex numbers and beyond, more confusing.(?)
It actually can't be retaught properly later, with a dependable success rate. (?)







Would anyone like to contribute to this list in any way?

coolul007

I think of the children, being taught one thing and then having to "unlearn" it later in favor of a better concept later, is the confusing part. And what if the better concept never comes. The state of lower education is not in favor of the rigor of mathematics, but some "touchy feely" form to make the children have a false sense of confidence. Mathematics is a system that does not have a lot of "stand alone" concepts. (I will get a large reaction for that last statement) I tutor high school students, the part most of them are missing is the foundation for understanding the concepts being taught to them. The modern trend is also to rename a lot of concepts, some good some bad, fractions, rational numbers, etc. Vocabulary and English should be taught in that class not mathematics.

Studiot

Motivation is all.

Of course this applies to all ages, not only children.

It is easy to demotivate.
Just teach a list of arbitrary definitions and statements, really designed to keep pupils quiet and sitting up straight.

No go down the pub and ask a darts player who has just scored 347 and who flunked school, what he need to finish and I guarantee he will know more quickly than any 5 maths professors put together.

coolul007

The dole is always a counterexample to staying in school...

Studiot

That's pretty disrespectful of the young.

The average youth unemployment rate (through no fault of their own) currently stands at 25% and reaches over 50% in some areas.

Those who do get jobs do so, not on their academic record but by knowing the rich and powerful, if recent news articles are to be believed.

go well

dalcde

I think that multiplication is the unique operation which satisfies the distributive property, and, when applied to integers, is equivalent to repeated addition.

agentredlum

I think it is...add e to itself 3 times, then add some more 'stuff'