Math calculation v. math reasoning

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What is the difference between these two things?

Is one more important than the other? If so, why?

Thanks!

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[+3] - ehBeth - 11/05/2011[quote="boomerang"] So wouldn't it follow that if someone was good at math reasoning they'd be good at math calculation? [/quote] No. I've got a client right now who has the same...

@boomerang,

Hmm... I'd guess that calculation is more surface (knowing how to get a correct answer but not knowing WHY, just following the rules given). Then reasoning is deeper, being able to take concepts and apply them to other situations that are not exact parallels.

But it might be one of those semantic things.

What is the context in which you've encountered it?

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@sozobe,

Mo just had to do some testing and I'm puzzling over some oddities.

He scored above average on one and well below average on the other. I don't want to say which was which because I don't want to influence the answers here.

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@boomerang,

Maybe Google that specific test and see what they have to say about it.

We just did that when we were trying to figure out what "Quantitative Reasoning" was.

For many of these things there is test-specific language, so our layman's conjecture may not have much bearing on what it actually means.

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@sozobe,

I've done that. They'll tell you what they mean but they don't really address big discrepancies in the scores. I thought the math lovers on here might have some clues for me to follow.

When ever Mo takes these kinds of tests there are always these weird discrepancies that nobody seems to know how to explain. It's always "we had to throw out that score......", etc.

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@boomerang,

Just a guess:

Calculation would be performing the operations: addition, subtraction, etc. to get the right answer.

Math reasoning would be strategizing to solve the problem. (Like how to break down a word problem.) Amy has 5 grapes, Bob has 4 grapes, Carrie has 3 grapes. How do they share the grapes evenly?

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@boomerang,

Huh.

Here's one thing I found, you may have already:

Quote:

Math Calculation Skills [5] Calculation is a test of math achievement measuring the ability to perform mathematical computations. Items include addition, subtraction, multiplication, division, and combinations of these basic operations, as well as some geometric, trigonometric, logarithmic, and calculus operations.

Math Reasoning [6] Math Fluency measures the ability to solve simple addition, subtraction, and multiplication facts quickly. [10] Applied Problems requires the person to analyze and solve math problems. To solve the problems, the person must listen to the problem, recognize the procedure to be followed, and than perform relatively simple calculations. Because many of the problems include extraneous information, the individual must decide not only the appropriate mathematical operations to use but also which numbers to include in the calculation. [18] Quantitative Concepts measures knowledge of mathematical concepts, symbols, and vocabulary. This test consists of two subtests: Concepts and Number Series. In the first subtest, the initial items require counting and identifying numbers, shapes, and sequences. The remaining items require knowledge of mathematical terms and formulas. The subject does not perform any paper-and-pencil calculations. In the second subtest, the task requires the person to look at a series of numbers, figure out the pattern, and then provide the missing number in the series.

(Italics emphasis mine.)

http://www.washougal.k12.wa.us/teach_learn/sped-gbp/EVALUATION/WJ%20III%20Eval%20Subtest%20Descriptions.pdf

It sounds like Math Reasoning could have more of a verbal component -- understanding and processing the language, not just the pure mathematical concepts.

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@DrewDad,

It seems to me that you'd have to be good at one to be good at the other and that's where I get stuck.

If someone could reason through the problem they'd still have to be able to do the calculation to get the answer, right?

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@sozobe,

Here are some puzzles that claim to be mathematical reasoning puzzles:

http://www.rinkworks.com/brainfood/p/math1.shtml

Quote:

You must cut a birthday cake into exactly eight pieces, but you're only allowed to make three straight cuts, and you can't move pieces of the cake as you cut. How can you do it?

Can you place six X's on a Tic Tac Toe board without making three-in-a-row in any direction?

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@DrewDad,

Interesting!

The most I could get was 7 pieces. So much for my math reasoning ability!

1 Reply

@boomerang,

Cut it into quarters, then make a horizontal slice.....

(And I had to peek at the answer.)

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@DrewDad,

Brilliant!

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This is in line with the other answers given, but I would say "math computation" is the ability to do straight up math problems: addition, subtraction, multiplication, division, etc. Math reasoning is the ability to build a math equation given a problem. "If Mary is twice Sue's age and Sue is twelve...".

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@sozobe,

sozobe wrote:

Hmm... I'd guess that calculation is more surface (knowing how to get a correct answer but not knowing WHY, just following the rules given). Then reasoning is deeper, being able to take concepts and apply them to other situations that are not exact parallels.

WELL SAID !
Its a matter of getting the accurate result,
as distinct from UNDERSTANDing the reason that the result is accurate.

Please give Mo my best wishes.

David

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@engineer,

So wouldn't it follow that if someone was good at math reasoning they'd be good at math calculation?

Maybe I just don't know enough about math to get it -- how someone could determine what calculation needs to be used but still be unable to do the calculation.

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@OmSigDAVID,

Mo always welcomes best wishes so consider them sent!

But what about the person who can get the right equation but get the wrong result?

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@boomerang,

I don't know that that is necessarily true, boomer.

My math reasoning and problem solving skills dramatically outpace my actual calculating on paper skills.

there is another discipline involved there...

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@boomerang,

boomerang wrote:

Mo always welcomes best wishes so consider them sent!

But what about the person who can get the right equation but get the wrong result?

The person who can get the right equation but get the wrong result
needs to sharpen his calculation skills, or get a good calculator.

David

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@boomerang,

Math calculating is basic straight forward math calculations - like addition, subtraction, multiplication, division, various equations. The problem would be presented as 2 + 3 = ?

Reasoning is more the word problems - so you have to reason out what you are trying to calculate. Jane had two cats, bob has three cats, how many cats do they have in total?

Same answer, basically same problem, but you need to figure out in the second what you are trying to calculate.

My daughter has participated in the math olympics before - they divide into math calculation or math reasoning. She stinks at math reasoning, but does very well in calcuation.

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@boomerang,

I would think, generally, that if you are good at math reasoning, you would need to be good at math calculation as well - seeing you still need to do the calculations. But perhaps he can gain the understanding - like you if you were show him with jelly beans - you say you have 2 red jelly beans and 3 blue jelly beans - how many jelly beans do you have in total - that to me is almost a visual type of thing.

So maybe not being straight out numbers helps him think it out.

And I love math - especially reasoning.

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Math calculation v. math reasoning

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