Weakness in mental arithmetic = weakness in math?

[Tobias Funke]

Alright. Let us suppose I really do need to improve on my arithmetic, but how should I go about? Should I first memorize the basic facts (like 7+4=11) before I move on and deal with bigger numbers, or should I just practice doing many different arithmetic problems in my head and wait for an improvement? I want to ask the posters here: When you think 7+4, does the answer come in an instant or after some counting?

Certain things, using involving 7 for some reason, aren't instantaneous for me. 7+8 for example, I'd either do (7+3)+5 or (8+2)+5, but either way I have the answer in 2 seconds tops. Or 7 x 6, for example, I would do as (7 x 3) x 2 since I have 7 x 3 memorized better than 7 x 6. Again, that takes less than 2 seconds.

How much you need to memorize is up to you though. I'm sure there are some people that would be mortified if I, someone with a math degree and a math teacher, told them I don't have 7 x 6 memorized, but I do just fine.

 

[Troponin]

I was never very good at mental arithmetic either, so I've set a mission to practice until I am good.
After receiving Feynman's lectures on physics from my wife for my birthday, I read through his "tips on physics." He starts right off on tips on differentiation (he does a type of logarithmic differentiation) and then talks about carrying around a little notebook to practice basic math whenever you get the chance.

Since reading that...I've been carrying around a notebook like a little Feynman wannabe and practicing. I was surprised how quickly I was able to learn things like squares and roots. Whenever I'm bored, I run through squares in my head and I can do anything up into the 60's within a second or two...either I have the number memorized by now, or a number is near a number that has been stuck in my brain, or I know it follows a pattern that allows me to skip multiplication steps, etc., etc.

It's become a tremendous help in my studies. Being able to accurately estimate an answer helps to tell if I'm on the right track for an answer. And when learning new material, it is a HUGE help. You can run through problem sets to make sure you understand how to set up the problem MUCH quicker.
Instead of setting up the problem, slowly working through the calculation with a calculator and going to the back of the book to check your answer...you set up the problem, get a quick estimation of your answer and see how it checks in the back of the book.
If you've obviously set it up correctly, you can move to the next one.
It has helped tremendously in my mathematical modeling, if nothing more than allowing me the time to work through many more problems in a given study period.

 

[chiro]

Halfway through an undergraduate course in engineering, I'm now planning to review math fundamentals from pre-algebra, algebra, geometry to trigonometry and finally calculus because, as you may know, having a solid foundation in math is vital for any engineering course, and I've always been weak in math. I also happen to be very weak in mental arithmetic (adding, multiplying, etc. in head). Even a calculation as simple as 4+7 makes me think for many seconds, and when I can't figure the answer out I use my fingers to count! If this is for addition what can we say about subtraction? For addition involving two negative integers I always use the calculator so as not to make a mistake, even for such numbers as -7-3.

Does having these problems impair one's ability to learn new math concepts? Should I improve on mental math before I start reviewing?

To me math is simply the science of representation. I think your ability to abstract, recognize patterns, generalize and synthesize information is more important than having say a quick ability to make some algebraic calculations.

I wouldn't worry too much about it.

 

[Saladsamurai]

I would definitely work on it a little. Don't spend days at a time on it, just work on a few problems here and there while doing the other stuff. You are an engineer for Pete's sake, multitask!

Believe it or not people, you can punch numbers into a calculator wrong when you are in a hurry. You should be able to detect whether the answer that it returns is reasonable or not.

As engineers we also do a lot of "back-of-envelope" calculations. You shouldn't need a calculator for those.

Trust me, if you have to grab a calculator for every simple arithmetic problem, you are going to look like a jerk.

Just be aware of your weaknesses and make effort in your down time to strengthen them. You'll be fine.

 

[flamrim]

I'm a big fan of the Trachtenberg system

 

[kirab]

Here's what you do:

If you know programming, write a program that randomly generates a list of 100 subtraction problems where the largest integer is 10. So stuff like 10 - 2, 7 - 8 etc. Give yourself 10 minutes to complete it. After you have finished it and have gotten a PERFECT score, create another set of problems and increase the difficulty if you want (by allowing a higher integer to be the max).

After you finish 10 of these sheets, move on to multiplication and division if you want. This is basically what my grade 4 teacher did for us every day before class began, and it helped a lot in doing mental math.

 

[rajdeepghai]

53^2 + 62 - 3^3 = 2898

I took 1 minute 51 seconds to do this one, ending up with a wrong answer: 2571.

Do you have any hope for me?

Even 2898 is wrong...
53^2 + 62 + 3^3 = 2898
53^2 + 62 - 3^3 = 2844

And of course there is hope. While there are several books of shortcuts and quick arithmetic, not too many teach a more fundamental and basic understanding of numbers and patterns.

I have recently found a program on numerical understanding and appreciation that sounded very interesting and good. Sent them a message yesterday and am waiting more details.

Its expensive but if it is worth it, I might take it up. Will keep informed incase anyone is interested

 

[GregA]

I think mental arithmetic a skill well worth training

Don't take this as condescending, but the same advice as I gave to my cousin last year as I was helping her with maths I give to you...spent some quality time reciting you're multiplication tables because though its a pain in the arse to learn them; with multiplication I'd say you'll perform pretty much all your mental calculations resorting to this look-up table in some way.

As for addition & subtraction I'd say that something like 4+7 comes immediately but to try and imagine myself naively calculating it I suppose I'll notice that 3 is less than ten, and for want of another way of putting it 'borrow' 3 from the 4 leaving just a 1 left to add on to the 10 I've made

 

[Hurkyl]

One of my favorite quotes is:

"I'm a mathematician, darn it, not an arithmetician!"

 

[symbolipoint]

One of my favorite quotes is:

"I'm a mathematician, darn it, not an arithmetician!"

That one is great.

What most people need to understand is that mathematically instensively educated people are not human calculation machines. We may know and are able to use number properties, may understand shape relationships, but we do not need to handle even slightly complicated numeric calculations in our head.

We may examine a set of values and features in a situation, assign numbers to parts of these features, transform or transcribe expressions and equations to relate these features, and perform "Arithmetic-algebraic" operations to find a formula for an unknown value which we are interested in having. We can then make meaningful use of this value. Even with this wonderful composition of skills and understanding, some of us can not handle money-sale transactions with counting back change - cashiering work - at least, not efficiently.

 

[Count Iblis]

You could also http://www.centreforthemind.com/publications/SavantNumerosity.pdf"

 

[GregA]

One of my favorite quotes is:

"I'm a mathematician, darn it, not an arithmetician!"

Heh!...yeah I hear you Hurkyl!
If I tell anyone new back home that I'm studying maths they never fail to hit me with some pointless sum they can't add up for themselves (ok sometimes they fail at doing this but not very often)

Though getting back to the op for all practical purposes you don't need to be ****-hot with mental arithmetic; just good enough that if you type say 123 + 456 into your calculator and get an even number you at least know you've screwed up with your button pressing as opposed to blindly continuing

 

[ImAnEngineer]

I try to do as much arithmetic as possible in my head, even on tests. For me it's easier to focus without a calculator and it makes me feel more satisfied and confident if it turned out i was able to do it without the machine. If I'm not sure if the answer is correct, or I have spare time I use the calculator to check my answers.

 

[LSDwhat?]

what ??

On my University a calculator isn't allowed for calculus classes there few where its allowed.

 

[symbolipoint]

what ??

On my University a calculator isn't allowed for calculus classes there few where its allowed.

That which you find is not universal. Many or even most Calculus classes will allow use of at least a scientific calculator on tests; even if a graphing calculator were allowed, you would at least expect that your full solution and steps must be shown in order to receive any credit.