Link between arithmetic and higher math ability?

Jul 2014
96
2
Seattle
I have noticed that some very talented mathematicians, physicists, engineers or just "math people" who understand many advanced concepts in mathematics have no basic arithmetical ability. I have also noticed kids who have excellent arithmetical ability get stuck when they move on to algebra. Of course there are plenty of exceptions, people who are good at arithmetic and higher math and people who are bad at both.

I was just wondering, what are your opinions on the link between these two things? Has anyone else noticed this kind of link? Is there no link whatsoever and thus there are people in every category?
 
Jul 2014
96
2
Seattle
Sorry moderators. This was supposed to be posted in the general math forum. I have no idea what happened. Please feel free to delete it and I'll repost if you can't move the thread.
 
Last edited:

Benit13

Math Team
Apr 2014
2,166
739
Glasgow
Being able to do hard things correctly and being able to do easier things quickly are generally different skills. That being said, many schools now teach arithmetic and have arithmetic tests, so I would expect most degree students to have reasonable arithmetic skills.
 

CRGreathouse

Forum Staff
Nov 2006
16,046
936
UTC -5
I think that there is almost no link between the two. Sometimes studying math gives you a bit more practice with arithmetic, and doing arithmetic gives a bit of insight into the basics of algebra, but on the whole there's not much in common between the two.
 
Jul 2014
96
2
Seattle
I think that there is almost no link between the two. Sometimes studying math gives you a bit more practice with arithmetic, and doing arithmetic gives a bit of insight into the basics of algebra, but on the whole there's not much in common between the two.
That was what I thought but then I thought of the likes of Euler, Gauss, Von Neumann, Alexander Aitken who were amazing mathematicians who made excellent discoveries and were amazing at arithmetic. There is of course also many "lightning calculators" who had no special talent for higher mathematics (although it is interesting that many of them were not educated so you could see their arithmetical ability as an expression of mathematical ability). I think perhaps the reason many great mathematicians may have been good at arithmetic is that they had extensive knowledge of the properties of numbers at a time when it was easier to apply those properties to find solutions (rather than just reaching for a pocket calculator as we do now). Thanks for your input. :)
 
Aug 2014
44
5
Somewhere between order and chaos
I don't think there is any link. Arithmetic is simply a matter of being able to mindlessly plug numbers into an algorithm to get a result. Mathematics is a matter of being able to think logically and understand abstract concepts. The two are completely unrelated. Skill in arithmetic does not equate to actual mathematical ability, nor does it hinder it.

I remember in elementary school I hated math and had a lot of difficulty with long division. Once I got to high school and learned what real mathematics is about, I fell in love with math, and that love has lasted to this day.
 
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Jul 2014
96
2
Seattle
I don't think there is any link. Arithmetic is simply a matter of being able to mindlessly plug numbers into an algorithm to get a result. Mathematics is a matter of being able to think logically and understand abstract concepts. The two are completely unrelated. Skill in arithmetic does not equate to actual mathematical ability, nor does it hinder it.

I remember in elementary school I hated math and had a lot of difficulty with long division. Once I got to high school and learned what real mathematics is about, I fell in love with math, and that love has lasted to this day.
Traditional or school arithmetic is all about plugging numbers, that doesn't mean arithmetic has to be. As I said in my other post, a true understanding of the properties of numbers means you can solve problems creatively in your own way when you know what each of the arithmetical operations actually are. The simplest example of this would be the way most people multiply by ten (just add a zero, although unfortunately most don't care why it works or how this would be if we didn't have a base 10 system) and the same for multiplying by 5 that lots of people use. I agree about long division, I hated it so much; there are far more efficient ways of doing division. I used to constantly get into trouble because I did division the way I wanted to and just gave in the answer. My teacher would say no, you have to set it out properly and show your working etc.

I think so many more people would fall in love with math if only they got past high school math which is all procedure, it's so monotonous I'm not surprised people don't like it. I just wish people knew that isn't what math is really all about.

Thanks for your input.