Different approach to solve math problem

[Anonymous]

In some testing and assessment they want to see each stage of the answer worked out. Or points are taken off. It's just how it is - so your kid may figure it out quickly in their head but they still need to show the logical steps to the answer.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:The way I explained it to my kid was that
(1) the teacher didn't actually need to know the answer to the problem. They need to know whether the kid understands the math. If you do it in your head and make a mistake, the teacher doesn't know whether you understand or whether you just made a careless mistake. They can't see where you went wrong.
(2) At some point, you won't be able to do the math in your head. The numbers will be too big or there will be too many steps. Best to get in the habit of showing your work.
(3) You can get partial credit if you show your work.

1) and 3) don't explain why correct answers lose points for not having shown work.

Because the work is considered part of a correct answer. Do you understand what a proof is? Many times a correct answer is not one number, it is all of the steps written in the correct way leading logically to a single number. Do you also think English teachers should only assess spelling and ignore grammar and syntax?

This is fine if the student is actually asked to solve a challenging problem, but being asked to write "proofs" for, say, 2 digit multiplication which are just two numbers which happen to add up to the answer doesn't teach any more than any other form of busy work. The "proof" is contingent upon the reader already understanding the algorithm, which negates the need for a proof in the first place. If you know the algorithm well enough to interpret the shown work, you know it well enough to verify and answer without any shown work.

Proofs only make sense for problems that require some shred or semblance of critical thinking (which is what the proof is meant to communicate), which most kids sadly won't see until highschool or even college

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:The way I explained it to my kid was that
(1) the teacher didn't actually need to know the answer to the problem. They need to know whether the kid understands the math. If you do it in your head and make a mistake, the teacher doesn't know whether you understand or whether you just made a careless mistake. They can't see where you went wrong.
(2) At some point, you won't be able to do the math in your head. The numbers will be too big or there will be too many steps. Best to get in the habit of showing your work.
(3) You can get partial credit if you show your work.

1) and 3) don't explain why correct answers lose points for not having shown work.

Because the work is considered part of a correct answer. Do you understand what a proof is? Many times a correct answer is not one number, it is all of the steps written in the correct way leading logically to a single number. Do you also think English teachers should only assess spelling and ignore grammar and syntax?

This is fine if the student is actually asked to solve a challenging problem, but being asked to write "proofs" for, say, 2 digit multiplication which are just two numbers which happen to add up to the answer doesn't teach any more than any other form of busy work. The "proof" is contingent upon the reader already understanding the algorithm, which negates the need for a proof in the first place. If you know the algorithm well enough to interpret the shown work, you know it well enough to verify and answer without any shown work.

Proofs only make sense for problems that require some shred or semblance of critical thinking (which is what the proof is meant to communicate), which most kids sadly won't see until highschool or even college

If this is how you feel, just let the teacher mark your kid down. Elementary school grades are hardly the most important thing in the world.

[Anonymous]

Anonymous wrote:

Anonymous wrote:The way I explained it to my kid was that
(1) the teacher didn't actually need to know the answer to the problem. They need to know whether the kid understands the math. If you do it in your head and make a mistake, the teacher doesn't know whether you understand or whether you just made a careless mistake. They can't see where you went wrong.
(2) At some point, you won't be able to do the math in your head. The numbers will be too big or there will be too many steps. Best to get in the habit of showing your work.
(3) You can get partial credit if you show your work.

1) and 3) don't explain why correct answers lose points for not having shown work.

2) does.

4) Also the proof shows you didn't just use a calculator. And if you cheat by copying a proof, at least you are spending time writing the proof which exposes your brain to it, so the exercise is doing its job.

[Anonymous]

If the kid really understands the math they should be able to do it both ways no problem.

[Anonymous]

Anonymous wrote:If the kid really understands the math they should be able to do it both ways no problem.

The problem is when kid is good at math but slow terrible at writing, should they get bad math grades / lose all that time to writing?

They don't get extra points in English class for their math prowess.

[Anonymous]

Anonymous wrote:Fluency has nothing to do with speed, and things like minute drills have been shown to not be helpful. It’s much more important for a child to be flexible and have a deep understanding of the relationship between numbers.

Lol

Such a “deep understanding” that they take 10 minutes drawing pictures and doing 10 steps to solve an easy addition problem and then mess up one step and get the wrong answer to boot. Yet can’t double check it quick either.

[Anonymous]

Anonymous wrote:The way I explained it to my kid was that
(1) the teacher didn't actually need to know the answer to the problem. They need to know whether the kid understands the math. If you do it in your head and make a mistake, the teacher doesn't know whether you understand or whether you just made a careless mistake. They can't see where you went wrong.
(2) At some point, you won't be able to do the math in your head. The numbers will be too big or there will be too many steps. Best to get in the habit of showing your work.
(3) You can get partial credit if you show your work.

+1

[Anonymous]

Anonymous wrote:

Anonymous wrote:If the kid really understands the math they should be able to do it both ways no problem.

The problem is when kid is good at math but slow terrible at writing, should they get bad math grades / lose all that time to writing?

They don't get extra points in English class for their math prowess.

Being able to demonstrate a proof is part of being good at math.

I work in a highly quantitative and technical field, and a really important skill is to be able to explain to others clearly and succinctly why your methods gets the correct answer. If you are an engineer computing the amount of weight that a bridge can support, it's of no use to come back to the design committee and just say "10,000 tons" -- you have to be able to walk people through your process so that they can ask questions and be confident that you used an appropriate method to get the right answer.

So yes, demonstrating how you arrived at the answer should be a graded activity for math.

[Anonymous]

the answer is all that matters.

Anybody who tells you differently is selling you something.

[Anonymous]

Anonymous wrote:the answer is all that matters.

Anybody who tells you differently is selling you something.

Does it? I can teach a parrot to say multiplication tables correctly, does that mean the parrot understands multiplication?

[Anonymous]

Anonymous wrote:

Anonymous wrote:If the kid really understands the math they should be able to do it both ways no problem.

The problem is when kid is good at math but slow terrible at writing, should they get bad math grades / lose all that time to writing?

They don't get extra points in English class for their math prowess.

My kid was terrible (and hated) writing a paragraph showing how they solved it. It made him hate math. He'd get the math correct but then get marked down due to his writing.

[Anonymous]

Anonymous wrote:the answer is all that matters.

Anybody who tells you differently is selling you something.

Not true in STEM, but maybe that's not where you're aiming?

[Anonymous]

Anonymous wrote:

Anonymous wrote:the answer is all that matters.

Anybody who tells you differently is selling you something.

Does it? I can teach a parrot to say multiplication tables correctly, does that mean the parrot understands multiplication?

If you tell the parrot that Larleaux has 17 boxes that each contain 12 pens, and Larlisle has 24 boxes that each contain 11 pens, and then ask the parrot how many pens they have altogether, and the parrot says "468 pens, polly wanna cracker," its fairly certain the parrot can do arithmetic even if he didn't tell you exactly how he got the answer. There are humans that can do that level of arithmetic in their heads quickly, and it's not unusual or rare. (I can do it in my head, but not very fast.)

[Anonymous]

Anonymous wrote:

Anonymous wrote:the answer is all that matters.

Anybody who tells you differently is selling you something.

Not true in STEM, but maybe that's not where you're aiming?

In stem why does it matter how I get my roots? Or how I multiply? I know that 9 x 5 is 45 and where the curve crosses the axis and that's what matters.

People and teachers get caught up on memorizing things and concepts not what matters. It's like these new math things that were supposed to revolutionize math but just left us all confused.