What's It Mean to "Get" Math?
Justin Katz
With my children not yet to the age at which I might have to consider battles with their teachers for their young mathematical souls, my opinion of the "new math" isn't sufficiently strong to inspire rants. Still, such statements as the following raise fundamental questions:
One problem, [Pat Cooney, math coordinator for six public schools in Ridgefield, CT,] says, is that parents remember math as offering only one way to solve a problem. "We're saying that there's more than one way," Cooney says. "The outcome will be the same, but how we get there will be different." Thus, when a parent is asked to multiply 88 by 5, we'll do it with pen and paper, multiplying 8 by 5 and carrying over the 4, etc. But a child today might reason that 5 is half of 10, and 88 times 10 is 880, so 88 times 5 is half of that, 440 -- poof, no pen, no paper.
"The traditional way is really a shortcut," Cooney says. "We want kids to be so confident with numbers that it becomes intuitive."
Or, the parent might understand that numbers can be broken into their components, with the functions performed on each and then added together at the end. In that case, they would break 88 into 80 and 8, multiply each by five — referencing a chart that they memorized decades ago and never forgot — and then add the results together: 400 plus 40 is 440. That's ultimately what the traditional method teaches. Poof. No pen, no paper, and yet a fundamental understanding of what each digit represents and its relationship to the others.
Although, as I said, I don't have thorough experience with it, the New Math appears to treat numbers as whole things that may be broken up and combined. The traditional approach is to treat numbers as representative symbols of multiple things that can join together or break apart. In the former case, everything is ultimately a fraction of a greater whole; in the latter, everything greater than one is a collection of independent items that have relationships. (Even fractions, in that view, are smaller individuals that make up the larger grouping, sort of like discussing atoms in molecules.)
Would it be too much to inject a quip about the fundamental difference between the liberal and the conservative mind, here?
"New Math"?? Was there a problem with the "Old Math"?
If I am not mistaken, people schooled in "old math" sent us the moon, developed computers, etc. So what problem are we trying to solve by introducing "New Math"?
You can build a house many ways ...sticks, straw, bricks, etc. But the one common element amongst all of them, assuming you want a lasting & sustainable house, is a solid foundation.
And the building of the foundation can be the hardest part (digging in all that rocky soil, hauling granite, mortor, etc.). The building of the rest of the house can be fun and can be where you get to "express yourself" and be "creative".
It seems the "New Math" crowd wants to avoid the hard, mundane work of building the foundation, and skip to the fun part.
Also, if the "Old Method" is a "short-cut", even better. People today already suffer from information over-load, so a short cut is most helpful.
By the way, I wonder if Pat "I struggle with basic math" Crowley used "New Math" when he told us last December that Inflation had out-paced Education spending?
In fact, Education Spending had out-paced Inflation by over 40% for the period Pat "I struggle with basic math" Crowley addressed.
Using his "New Math" skills, he stupidly (or slyly) compared 5 years of Spending growth to 7 years of Inflation.
Still waiting for his boss and financial whizz Bob Walsh (who "has always been upfront"), not to mention the folks over at that stink-tank RIFutureless that carried Pat's classic mis-information piece, to issue a correction.
"New Math" is one of those parts of the plan to systematically develop an entire generation of kids to friggin stupid to sustain themselves in the real world and will therefore vote themselves into a full socialist state with cradle to grave protections.
Like graduating kids that can't read, the hallmark of the NEA and AFT. They'll blame the parents but ultimately it's the teachers that are signing off and moving these kids up through the grades and onto graduation.
Yes, it would be too much. Frankly, it's already too much that you divide the world into conservative and liberal minds. Must be easy living in a world without shades of gray.
As a math major and math teacher, I agree with Pat Cooney to some extent. There are multiple ways to solve the same problem. But in my view, the ‘new math’ or alternative reasoning needs to be based on thorough understanding and implementation of the traditional way of multiplication. The reality is a vast majority of children have no interest in ‘reasoning’ 88 times 5 by 5 is ½ of 10 and 88 times 10 is 880 so …. They want the shortcut. Once they understand the ‘shortcut’ and become proficient in it that is the time to show the reason method. The reason method becomes valuable in other areas of match such as the dreaded word problems. It is tougher to justify learning how to do even basic math with the use of computers/calculators.
I recently tutored an 8th grade student who used a calculator to add single digit numbers.
I don’t see how any of this is applicable to some difference between a conservative and liberal mind.
But I will say that in my view, it is very sad that the field of education has become a productivity based field not unlike manufacturing plants where success is based on numbers and %’s. This is one of those areas where the ‘traditional’ way is superior to the ‘new’ way. Unfortunately, we live in a culture where ‘everything’ has to be quantifiable.
How about starting out with teaching arithmetic? My stepson not only can't multitply 88 by 8, he can't multiply 3 times 4!
Thank you Thompson Middle School.
Sorry Andrew. They're too busy teaching 'social justice' to teach your kid how to think for himself.
http://www.rifuture.org/showDiary.do?diaryId=3484
M Steven,
Amen to "the ‘new math’ or alternative reasoning needs to be based on thorough understanding and implementation of the traditional way of multiplication."
Well said and I couldn't agree with you more.
However, I stongly disagree with you when you lament that education "success is based on numbers and %’s" and that "this is one of those areas where the ‘traditional’ way is superior to the ‘new’ way."
Measuring success in education based on numbers and %s is NOT new.
Teachers have been issuing report cards with Letters, Numbers & %s since the beginning of time.
What is new is the Social Promotion, along with the evolution and expansion of the nanny-state into our Public schools, causing performance to cratered, thus requiring public oversight via NCB, Testing, etc.
Get rid of the social promotion and change the mindset from one in which Public Education is viewed as a "Right" to one in which it is viewed as a "Privelage" (and thus the garbarge that isn't interested in learning is kicked to the curb like yesterday's trash) and performance will improve naturally and you will see the NCB and other oversight go away overnight.
Of course, these actions should also be coupled with eradication of the Teachers' Union, which has nothing to do with "teaching".
George,
I think we really do agree. What I meant about judging success based on %/numbers was referring to teachers and school systems, not students. I am not against the grading system for students. I am against the ‘grading’ system for teachers and school systems where their performance is judged by the standardized student test scores along with graduation rates. I see where my post was not clear about that.
Public education is a ‘right’ – a right like all rights that also comes with responsibilities – as in responsibilities for the student and for the parents of the student. I’m sure you and I would agree that the ‘other R’ is often left out of the equation.
I also agree with you on the social promotion, evolution of the nanny-state into public education and the teachers’ unions. The purpose for most unions has little to do with the quality of the product; it is all about less work, more money and guaranteed employment. And who wouldn’t want that?
msteven
MSteven,
We need more teachers like you, period.
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"New Math"?? Was there a problem with the "Old Math"?
If I am not mistaken, people schooled in "old math" sent us the moon, developed computers, etc. So what problem are we trying to solve by introducing "New Math"?
You can build a house many ways ...sticks, straw, bricks, etc. But the one common element amongst all of them, assuming you want a lasting & sustainable house, is a solid foundation.
And the building of the foundation can be the hardest part (digging in all that rocky soil, hauling granite, mortor, etc.). The building of the rest of the house can be fun and can be where you get to "express yourself" and be "creative".
It seems the "New Math" crowd wants to avoid the hard, mundane work of building the foundation, and skip to the fun part.
Also, if the "Old Method" is a "short-cut", even better. People today already suffer from information over-load, so a short cut is most helpful.
By the way, I wonder if Pat "I struggle with basic math" Crowley used "New Math" when he told us last December that Inflation had out-paced Education spending?
In fact, Education Spending had out-paced Inflation by over 40% for the period Pat "I struggle with basic math" Crowley addressed.
Using his "New Math" skills, he stupidly (or slyly) compared 5 years of Spending growth to 7 years of Inflation.
Still waiting for his boss and financial whizz Bob Walsh (who "has always been upfront"), not to mention the folks over at that stink-tank RIFutureless that carried Pat's classic mis-information piece, to issue a correction.
Posted by: George Elbow at July 31, 2008 7:49 AM"New Math" is one of those parts of the plan to systematically develop an entire generation of kids to friggin stupid to sustain themselves in the real world and will therefore vote themselves into a full socialist state with cradle to grave protections.
Like graduating kids that can't read, the hallmark of the NEA and AFT. They'll blame the parents but ultimately it's the teachers that are signing off and moving these kids up through the grades and onto graduation.
Posted by: Greg at July 31, 2008 9:08 AMYes, it would be too much. Frankly, it's already too much that you divide the world into conservative and liberal minds. Must be easy living in a world without shades of gray.
Posted by: Pragmatist at July 31, 2008 10:16 AMAs a math major and math teacher, I agree with Pat Cooney to some extent. There are multiple ways to solve the same problem. But in my view, the ‘new math’ or alternative reasoning needs to be based on thorough understanding and implementation of the traditional way of multiplication. The reality is a vast majority of children have no interest in ‘reasoning’ 88 times 5 by 5 is ½ of 10 and 88 times 10 is 880 so …. They want the shortcut. Once they understand the ‘shortcut’ and become proficient in it that is the time to show the reason method. The reason method becomes valuable in other areas of match such as the dreaded word problems. It is tougher to justify learning how to do even basic math with the use of computers/calculators.
I recently tutored an 8th grade student who used a calculator to add single digit numbers.
I don’t see how any of this is applicable to some difference between a conservative and liberal mind.
But I will say that in my view, it is very sad that the field of education has become a productivity based field not unlike manufacturing plants where success is based on numbers and %’s. This is one of those areas where the ‘traditional’ way is superior to the ‘new’ way. Unfortunately, we live in a culture where ‘everything’ has to be quantifiable.
Posted by: msteven at July 31, 2008 10:59 AMHow about starting out with teaching arithmetic? My stepson not only can't multitply 88 by 8, he can't multiply 3 times 4!
Posted by: andrew burton at July 31, 2008 12:47 PMThank you Thompson Middle School.
Sorry Andrew. They're too busy teaching 'social justice' to teach your kid how to think for himself.
http://www.rifuture.org/showDiary.do?diaryId=3484
Posted by: Greg at July 31, 2008 12:52 PMM Steven,
Amen to "the ‘new math’ or alternative reasoning needs to be based on thorough understanding and implementation of the traditional way of multiplication."
Well said and I couldn't agree with you more.
However, I stongly disagree with you when you lament that education "success is based on numbers and %’s" and that "this is one of those areas where the ‘traditional’ way is superior to the ‘new’ way."
Measuring success in education based on numbers and %s is NOT new.
Teachers have been issuing report cards with Letters, Numbers & %s since the beginning of time.
What is new is the Social Promotion, along with the evolution and expansion of the nanny-state into our Public schools, causing performance to cratered, thus requiring public oversight via NCB, Testing, etc.
Get rid of the social promotion and change the mindset from one in which Public Education is viewed as a "Right" to one in which it is viewed as a "Privelage" (and thus the garbarge that isn't interested in learning is kicked to the curb like yesterday's trash) and performance will improve naturally and you will see the NCB and other oversight go away overnight.
Of course, these actions should also be coupled with eradication of the Teachers' Union, which has nothing to do with "teaching".
Posted by: George Elbow at July 31, 2008 10:12 PMGeorge,
I think we really do agree. What I meant about judging success based on %/numbers was referring to teachers and school systems, not students. I am not against the grading system for students. I am against the ‘grading’ system for teachers and school systems where their performance is judged by the standardized student test scores along with graduation rates. I see where my post was not clear about that.
Public education is a ‘right’ – a right like all rights that also comes with responsibilities – as in responsibilities for the student and for the parents of the student. I’m sure you and I would agree that the ‘other R’ is often left out of the equation.
I also agree with you on the social promotion, evolution of the nanny-state into public education and the teachers’ unions. The purpose for most unions has little to do with the quality of the product; it is all about less work, more money and guaranteed employment. And who wouldn’t want that?
msteven
Posted by: msteven at August 1, 2008 10:22 AMMSteven,
Posted by: George Elbow at August 1, 2008 11:20 PMWe need more teachers like you, period.