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Honored Contributor
Posts: 18,504
Registered: ‎05-23-2010

Re: Which Is More Important?

[ Edited ]

Just a guess here, but the original question/request may have had less to do with providing a correct answer per se than learning to follow directions and learning the method.

 

If the intent was to see if a student could follow directions, the point would be did they read and understand what they were being asked to do and why it was to be done a certain way - to ingrain the method from its core, so the student could apply it to any numbers/problem.

 

Never too early to teach someone to learn to understand what they're reading/are told and not just assuming they know what the instructor wants, or means.

 

We see this every day on these forums. Someone will say "I have a brown dog" and a poster will come along and ask "what color is your dog?" Someone will say "I took my polka-dot cat for a walk" and a poster will say "you just hate dogs" or "what did you do with your yellow cat?"

 

Perhaps 5+5+5 arrives at a correct answer in this instance, but the correct way to reduce the method to its base is 3+3+3+3.  

Life without Mexican food is no life at all
Honored Contributor
Posts: 9,724
Registered: ‎03-09-2010

Re: Which Is More Important?

Well, I've thought about this and even though I think it is a little sad, I hope the teacher explained why.

I can see how it might be beneficial to know the difference when teaching algebra and equations (but it also might be for so many of us-"Did I ever use this in real life down the road?!").

So to me its easier to understand why when you say 5 times 3, which you would then work out 3+3+3+3+3.

But if you work out 3 times five, you would work out 5+5+5.

And for those who don't give a fig about all this, (which I totally understand!) carry on!Woman LOL

"If you walk the footsteps of a stranger, you'll learn things you never knew. Can you sing with all the voices of the mountains? can you paint with all the colors of the wind?"
Honored Contributor
Posts: 14,160
Registered: ‎03-09-2010

Re: Which Is More Important?

Either way of getting the answer is correct, unless the question included prove your answer

 

 

Stop being afraid of what could go wrong and start being positive what could go right.
Honored Contributor
Posts: 17,335
Registered: ‎10-04-2010

Re: Which Is More Important?

How can people waste time on this, the correct answer is all that's needed.  Talk about not wanting our kids to fall behind.  Why should we make these things harder on them.  If you want progress at warp speed in today's world, support the kids, don't throw up obsticles in their way.  JMHO

Esteemed Contributor
Posts: 7,341
Registered: ‎06-10-2010

Re: Which Is More Important?

I can see both sides of this but I am on the side of... know your students.  If a particular student can do better at getting the right answer his own way, I don't think it should go against him.  We have a lot of ADHD kids and kids with other problems that could do well if given the chance to instinctively do what is best for themselves.

 

 I have a grandson that has really struggled with math.   It has been a headache for him for so many years.  Many schools are not equipped to handle these kids or even  a kid who has a hard time with math. I say, if that kid can figure it out for himself....good for him!!

 

My daughter spent thousands of dollars to get my grandson caught up through a well known learning school.   He worked at it and worked at it.  He is a good kid and he tried so hard. They did try several different methods.  The previous teachers had all given him passing grades in math. When the learning center gave him a test to see where he was at......they had a 15 yr. old with a 3rd grade level math in multiplication and division.  I can't remember if fractions were involved.  Adding and subtracting was no problem to my knowledge. My daughter jumped through all kinds of hoops trying to get him help in the schools.  It just didn't happen. Finally, the learning center told her (when he was about 15) that he should be let to use a calculator.   When my daughter and family moved back home to this a few years ago he was about 15.  She decided to home school him his last three years of high school. At least the highschool here told her up front they did not have a program for these kids.

 

 He graduated this year and is doing great.  He realizes he won't be pursuing a career in math.  Of course, it isn't the end of the world, and if he ever has a business or gets into trouble math wise he can always hire someone who understands or use his calculator!

Honored Contributor
Posts: 9,724
Registered: ‎03-09-2010

Re: Which Is More Important?

I really think there are math teachers who are so good at explaining things and then there are some who are really not.

And I've learned that it is how each person's brain is wired which will determine how well they understand the different types of math.

For example, one might be really good at algebra and geometry, but understanding calculus is like trying to break through a brick wall.

I know there are so many things I just don't get and no amount of explaining will get it through, or it might but I'll get a headache, and try to avoid it in the future.

So many like Sudoku. I just don't get it at all.Woman Tongue

My mother is great at bridge and when she tried to teach my son and I some initial steps, we started seeing stars!

Yet I can do other things, that others would think why? or how is this fun?

Some like to read maps and I think forgeddaboudit! Thats like trying to read in a mirror backwardsWoman Frustrated

A great teacher can make it understandable to each student and that is really a gift and an art!

"If you walk the footsteps of a stranger, you'll learn things you never knew. Can you sing with all the voices of the mountains? can you paint with all the colors of the wind?"
Honored Contributor
Posts: 14,443
Registered: ‎10-25-2010

Re: Which Is More Important?

Math is very different than other subjects taught in school.  It is a perfect science.  The answer is always 100% correct or not.

 

Everyone's mind is different.  My father was a great, over the top mathematician.  I heard stories from many people of how he challenged his math teachers because they were wrong.  He didn't study math, it was just second nature to him.  He very seldom used paper and a pencil and never used a calculator or adding machine.  His mind was a math machine.

 

Well, as luck would have it, I did not inherit his math abilities.  I struggled and worked hard and still made just barely passing grades in math.  I learned two forms of math back in the 60's... Traditional and " new math"

 

Today, I still use both forms for different things.  At the school where I volunteer, two years ago, they tried to teach new math after the kids already learned the Traditional math.  The kids were confused.  Parents couldn't help and other teachers in the school couldn't help either.

 

i found myself sitting down with these kids and helping by explaining how to do division the new way at lunch time.  A couple of the teachers who had never seen this type of math were surprised that I knew how to do it and knew it well. They could not understand how someone over the age 60 knew this new math.

 

Well, there is no new math.  Math is math is it doesn't matter what method what you use to get the right answer.  There are many ways or working a problem and all are correct if the correct answer.

 

i remember when I was studying for my Real Estate License.  There was math involved.  The lady next to me was proficient in algebra.  Algebra has always escaped me, even though I took it in HS.

 

She was surprised that I got the correct answer without using algebra.   It took me a bit longer, but I was 100% correct in my answer, the same as her.

 

So, my answer the the OP's question is it doesn't matter how you get the answer as long as you figured it out on your own.  There is no one right or wrong way,  there are many ways of getting the right answer and all are correct.  If the children are learning, and can get the right answer, the teacher is doing a good job.

 

It is best for all involved to use whatever intelligence they have and not be forced into having a one track mind 

Honored Contributor
Posts: 9,139
Registered: ‎04-16-2010

Re: Which Is More Important?

[ Edited ]

My youngest, now 11, began his school life only using Common Core. Pre-school offered the "normal" way (how his dad and I learned math). His older 2 brothers never had Common Core; my 17 year old, now a senior, has had it on occasion but the way states are introducing it, kids his age were simply too old to get the full impact.

 

What we see now is an 11 year old who can add, subtract, multiply, divide and engage in Algebra, Geometry and Intro-Calculus with ease and solve a problem in seconds. It shocks and amazes us (and other parents) how fast he and his peers can work a problem and the ease in which they do so. Do we think parts of it are too much when it comes to HOW they get it being so important? Yes. And we've stated so to his teachers since Day 1. Nothing in life is black or white and often, Common Core is taught as if it is. Our argument with his GT Math teacher was "would you rather he NOT solve the problem if he can't do it YOUR way? How's that going to work in the real world? Also, there are MANY ways to solve a problem....you stress WAY TOO MUCH that your way is the only way. Again, in the real world, that isn't going to fly". 

His math teacher didn't like us too much after that. Oh well. All I can say is that common sense is often not part of Common Core. It needs to be but remember, it's all about the money.

Honored Contributor
Posts: 9,724
Registered: ‎03-09-2010

Re: Which Is More Important?

@Carmie@SahmIam-

Those are both really interesting observations!

I think now and also in the future, there may be less emphasis or concern on the method than it is to getting the correct answer.

Just the time I (and we all) were in school or teaching it, there have been many different methods to arrive at an answer and it was part of the lesson to show the correct work page.

But like you both said, there are many methods to getting the right answer and many new bright minds and theories and methods are emerging so maybe that stickler of teaching the absolute right method will change, (since the "correct" method changes every decade it seems!)

Even the introduction of calculators became acceptable for many times in the classroom to arrive at the correct answer.

I think it would e interesting to see the students come up with their own methods to arrive at the correct answer! How interesting would that be!

"If you walk the footsteps of a stranger, you'll learn things you never knew. Can you sing with all the voices of the mountains? can you paint with all the colors of the wind?"
Honored Contributor
Posts: 13,503
Registered: ‎03-09-2010

Re: Which Is More Important?

If you don't know where you're going, any road will get you there.

 

But -  we all know there can be many roads to the same destination and that's true in math, too.  For me, the answer to a math problem is not enough.  I want to know how I reached that answer so I can repeat the process with different numbers.  Students who can't explain or at least repeat their process may have a correct answer on a lucky guess;  that's not real learning as I understand learning.  However, teachers who insist there's only one method better have a really good explanation why they think that's true.  It shouldn't be just "because I said so."