R.M.Alger

“New Math” Entertainingly Skewered

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When I lived in Nevada, I suffered through this “revolutionary” math systems with my sister’s homework.

The process was cumbersome, complicated, and unintuitive. Often, “new math” didn’t produce the correct answer; a ton of special rules needed to be created to solve the flaws in the process.

Well, I’m glad people are starting to catch on, and are realizing that a new system is not necessary a better one.

Here is an entertaining video that lays down the convoluted process of “new math” subtraction. I love it when he says, “In the new approach, as you know, it is more important to understand what you are doing then to get the right answer.”

It is connected to the dryer but more informative:

-Ryan

P.S.---I also like this guys rendition of the elements Here.

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I must protest the negative characterization of "the new math." It seems there are many flavors of "new math" that are all painted with the same black brush. In high school in the '70s, I used the original "new math" textbook series, UICSM (University of Illinois Committe on School Mathematics) by Beberman and Vaughan. It was a rigorous course, and in our high school, the kids who intended to go into engineering or the sciences took the UICSM math courses. I think back on these courses so fondly that I have actually started collecting the old textbooks! Still need Book 1. Here is a *LINK* that discusses UICSM math a bit; you can google for more information. A quote from the article:

"...Herbert Vaughan, a professor of mathematics who felt that if mathematics were made rigorous by the precise use of language and notation, then children would better be able to learn it; and the person who put it all together, Max Beberman, who believed fervently that one learned better if one was led to discover the mathematics rather than being told it."

The use of these textbooks in high school demystified mathematical notation and made further study so much easier. Another wonderful thing about the course was the "guess and prove" concept. We would be given a set of exercises to do, and would discover a theorem through working the problems, and then be required to prove it, formally, deriving it from previous theorems. We were never told that it was OK to get the wrong answer, but it WAS important to understand HOW the answers were derived and why they were right.

I showed one of the textbooks to my husband, and he found it interesting how they taught logarithms. After presenting exponents, they presented the idea of an inverse exponent. Many pages later, you find out that you've mastered logarithms!

I can still remember trying to teach my mother about number bases other than 10. She had the "old math" (1930's!!) and she absolutely could not grasp the concept. UICSM alums don't have that problem.

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I must protest the negative characterization of "the new math." It seems there are many flavors of "new math" that are all painted with the same black brush.

The “new math” is criticized for good reason. Keep in mind that it was not just a theory; It was widely practiced from kindergarten to high school, and failed miserably.

Grades declined overall, those taught under the “new math” had, on average, lower mathematical reasoning skills; there was even a lack of the most basic arithmetic skills. The growth of the “new math” saw a near universal decline in the quality of math education.

In fact, math education still hasn’t recovered from its rapid decline in the 60’s and 70’s.

This is because, contrary to many claims, the “new math” didn’t help young people understand math better and more abstractedly, it merely replaced older algorithms with newer, more complicated ones, which were harder to teach and learn, especially without proper context.

Saying that, I do hate ‘process mathematics’, that detaches itself from any reasoning or real understanding. Taught properly, “new math” can be a great teaching tool for helping students better understand the abstractions of math.

Why create an algorithm on a base 8 system within the framework of the existing base 10 system? It is not more practical, and if it is not used to illustrate a deeper point, it does nothing but complicate and confuse.

Many of the proponents of the ‘new math’ were not mathematicians, but politicians, eager to prove (after sputnik) that we were not lagging behind the Russians in the sciences.

Now, almost half a century later, we live in the most prosperous country in the world, which also has the worst math scores in the all of the western world, and even lags behind some 2nd world countries.

Since we spend more money- per student- on education then most countries, you can conclude that it is how the material is being taught that is the problem.

The educational trends started in the 1960’s haven’t stopped, but gotten worse; in no small part due to the educational policies and ideas started in the sixties.

-Ryan

P.S. --- What you mention is not what I usually associate with the "new math”. The derogatory reference usually refers to what I described above, just a more complicated way of achieving the same result; and not the creative problem solving or teaching you describe.

As I said, the “new math” can be helpful as a teaching tool, and a way to better understand complicated concepts.

I remember having to learn dozens of convoluted algorithms to help my sister with her homework (some would take up half a page for a simple four digit multiplication problem); she was never taught ‘why’ these worked, or what they meant, it was ‘process mathematics’, through and through, just pointlessly made more complicated.

That is what I think about when somebody mentions the “new math”

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I can see a purpose to the cluster problems. The only was I was able to do large number multiplication in my head was through a similar method (something along the lines of (263*30=(200+60+3)30=200*30+60*30+3*30 blah blah blah.) When I tried the old fashion method, numbers got jumbled in my head, and I lost track of what I was doing. But the problem with this method is I am using things I did not learn until jr. high algebra (maybe even high school algebra 2.)

So although it is extremely useful, it might be too advanced for young kids to comprehend.

Saying that, I do hate ‘process mathematics’, that detaches itself from any reasoning or real understanding. Taught properly, “new math” can be a great teaching tool for helping students better understand the abstractions of math.

Teaching math in depth needs to be reserved for older students. Fifth graders can not understand the distributive property, or things of that nature. (Hell, most high school students do not understand it.) What needs to happen with the young kids is that teachers need to make sure they know how to solve a problem first. Understanding it should come at a later age when they first understand the methods of solving it.

Why create an algorithm on a base 8 system within the framework of the existing base 10 system? It is not more practical, and if it is not used to illustrate a deeper point, it does nothing but complicate and confuse.

I agree, the Arabic number system has always been in base ten, and no man or woman (or snooty "educator") can change that fact!

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When I lived in Nevada, I suffered through this “revolutionary” math systems with my sister’s homework.

The process was cumbersome, complicated, and unintuitive. Often, “new math” didn’t produce the correct answer; a ton of special rules needed to be created to solve the flaws in the process.

Well, I’m glad people are starting to catch on, and are realizing that a new system is not necessary a better one.

Here is an entertaining video that lays down the convoluted process of “new math” subtraction. I love it when he says, “In the new approach, as you know, it is more important to understand what you are doing then to get the right answer.”

It is connected to the dryer but more informative:

-Ryan

P.S.---I also like this guys rendition of the elements Here.

Hilarious! Although . . . I must say it would be stronger if the correct answer in the "old math" approach segment at the start of the video was provided for the actual problem shown at the reveal. The original problem is 342-173, for which the answer is 169. However, the problem shown at the reveal has suddenly become 342-176 for which the answer is 166 and NOT the mistaken 169 indicated.

I'm surprised nobody pointed this out to the filmmaker.

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Great stuff! I'm sharing with my mother, who works in a primary school. She's told me before about the problems the kids have learning basic arithmetic. She helps tutor in addition to her other duties. One startling example of the failure of her school's math program is that when she asked the students what numbers add to 10, the only combination they could come up with was 5 and 5. She's told me the teachers instruct their students in multiple ways to do problems and encourage them to try them all out and pick whatever method they prefer. Then they move onto the next math function. The result is the kids don't get enough practice using any method and fail to develop the skills to move beyond addition and subtraction.

I don't think in principle there is anything wrong with learning different ways to solve problems. The problem is that these teaching methods neglect the role of automatization in learning. First, you learn how to solve the problem, and you learn how and why the algorithm you use works. Then you commit that algorithm to memory by repetition so that using it becomes automatic. That way later on you don't have to waste time re-deriving ways to add and subtract when you're solving integrals. If you have to think about how to add two numbers together, or need to rely on a calculator to get the answer, you have not mastered addition. I think it's pathetic that schools are actually discouraging kids from absorbing the material, and they do it in the name of making them better critical thinkers!

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I think it's pathetic that schools are actually discouraging kids from absorbing the material, and they do it in the name of making them better critical thinkers!

is a fairly poignant critique of math education and textbooks.

I think the worst part is when she reads the preference by the editor in one of these books, which basically says that good math skills are not worth it, because we now have calculators.

This is a math textbook, mind you, which first and only purpose should be to teach mathematics.

Imagine if you opened the Rise and Fall of the Roman Empire and on the first page it said, ‘there is little purpose in looking back in history, or reading history at all for that matter, sense we now have CNN’.

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I think the worst part is when she reads the preference by the editor in one of these books, which basically says that good math skills are not worth it, because we now have calculators.

I do not understand this logic, because everyone needs basic arithmetic skills for any higher level math. I cannot imagine doing a long arduous algebra problem with a calculator. To me, that would almost be impossible. Kids need to know head/paper math to do any kind of upper level math.

And, even if they somehow could use a calculator for higher level math, can you imagine a world where grown men and women cannot do any sort of arithmetic without using a calculator. Sadly, I have seen examples of it (where a COLLEGE economics professor had to write .8=8/10 on the chalk board) and I can assure, it would be a very sad, sad world.

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When I lived in Nevada, I suffered through this “revolutionary” math systems with my sister’s homework.

The process was cumbersome, complicated, and unintuitive. Often, “new math” didn’t produce the correct answer; a ton of special rules needed to be created to solve the flaws in the process.

Well, I’m glad people are starting to catch on, and are realizing that a new system is not necessary a better one.

Here is an entertaining video that lays down the convoluted process of “new math” subtraction. I love it when he says, “In the new approach, as you know, it is more important to understand what you are doing then to get the right answer.”

It is connected to the dryer but more informative:

-Ryan

P.S.---I also like this guys rendition of the elements Here.

Hilarious! Although . . . I must say it would be stronger if the correct answer in the "old math" approach segment at the start of the video was provided for the actual problem shown at the reveal. The original problem is 342-173, for which the answer is 169. However, the problem shown at the reveal has suddenly become 342-176 for which the answer is 166 and NOT the mistaken 169 indicated.

I'm surprised nobody pointed this out to the filmmaker.

I have a headache. How did you figure out that 173 changed to 176? I've watched the video 3 times - and I don't get any of it...except it seems if I used Base 8 to figure my taxes, I wouldn't owe as much.

IRS: How did you determine that you owed $147?

Me: I used Base 8. You got a problem with that?

IRS: Yes, you owe $22 plus interest and penality.

10/15/2007 6 mos .50% .11 penality

4/15-6/30 76 days @ 8%

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Hilarious! Although . . . I must say it would be stronger if the correct answer in the "old math" approach segment at the start of the video was provided for the actual problem shown at the reveal. The original problem is 342-173, for which the answer is 169. However, the problem shown at the reveal has suddenly become 342-176 for which the answer is 166 and NOT the mistaken 169 indicated.

I'm surprised nobody pointed this out to the filmmaker.

The filmmaker realised the mistake 10 months ago and posted this updated video - http://www.youtube.com/watch?v=GAm3KWiDPKU

The link that was given on the forums, was to the uncorrected one. :huh:

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I do not understand this logic, because everyone needs basic arithmetic skills for any higher level math. I cannot imagine doing a long arduous algebra problem with a calculator. To me, that would almost be impossible. Kids need to know head/paper math to do any kind of upper level math.

I believe the answer to your comment is right there. The educators pushing these programs do not expect students to take higher level math! In fact, I don't think they expect the students to ever use math at all outside of class. I wonder if a lot of these people weren't students years back who complained, "but when am I going to ever need to know this stuff?" This whole approach stinks of pragmatism. The point is you don't know when you'll need it. A balanced education means preparing a child's mind to make judgments in any situation they might face, and there's no predicting when those judgments might be required of them. It also gives them the skills needed to pursue their values. What if they want to become a mathematician or scientist? Educators are deciding for an entire generation of children that helping them to deal with reality and reach their dreams is a waste of class time.

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I do not understand this logic, because everyone needs basic arithmetic skills for any higher level math. I cannot imagine doing a long arduous algebra problem with a calculator. To me, that would almost be impossible. Kids need to know head/paper math to do any kind of upper level math.

I believe the answer to your comment is right there. The educators pushing these programs do not expect students to take higher level math! In fact, I don't think they expect the students to ever use math at all outside of class. I wonder if a lot of these people weren't students years back who complained, "but when am I going to ever need to know this stuff?" This whole approach stinks of pragmatism. The point is you don't know when you'll need it. A balanced education means preparing a child's mind to make judgments in any situation they might face, and there's no predicting when those judgments might be required of them. It also gives them the skills needed to pursue their values. What if they want to become a mathematician or scientist? Educators are deciding for an entire generation of children that helping them to deal with reality and reach their dreams is a waste of class time.

So how do they expect people to accomplish things like engineering, physics, or anything pertaining to higher level math. Do they believe technology is at a peak and we can no longer achieve or something?

This is why you should leave teaching math to mathematicians!

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I'm never sure exactly what "new math" refers to. I'm sure that math is taught differently today than it was 50 years ago, but it isn't necessarily the case that all of the changes have been bad. Looking back on my math education, I'm never exactly sure of what was "old math" and what was "new math."

That said, I strongly disagree with the negative comments expressed here about teaching non-base-10 number systems.

I learned about other number bases in the 5th grade, in the late 1960's. Somebody must have told me at the time that this was "new math", and I remember that many adults then were questioning its usefulness. But as a student, I found it to be quite interesting, and it helped to deepen my understanding of base-10, in much the same way that studying a foreign language can help one understand better the grammar of one's own language. Furthermore, the knowledge turned out to be directly useful to me as an adult in my chosen line of work - computer programming.

That's because computers use binary (base-2) numbers: it's much easier to build a base-2 computer than one that uses base-10. The result is that somebody who programs computers at a low level is going to need to understand what base-2 is all about: what do those strings of 1's and 0's mean? Furthermore, it's very easy to translate base-2 numbers into either base-8 ("octal") or base-16 ("hexadecimal"), so one sees number expressed in these bases a lot in computer programs. Somebody who didn't understand what these were all about would be lost trying to understand some programs.

So, far from being useless, knowledge of other number bases is a good thing to have in today's world. (Of course, in 5th grade, we were expected to translate numbers into other bases like 5, 7 and 12, but my point is that it's not so much the choice of base that matters; it's the idea that using these different bases gives one a better grasp of how our position-sensitive number system works, as opposed to something archaic like Roman numerals.)

Also, in 5th grade, we learned about sets, which is another thing I heard questioned by some adults back then. We learned what sets were, and what operations like intersection and union meant. Again, these are powerful tools to help one's thinking and again, they happen to be very useful - even essential - concepts if one ends up programming computers.

I thought that math in the 5th grade was so much fun that I couldn't have cared less that there was some big controversy over what we were being taught. I was too busy learning the new material.

....

I am not defending the whole idea of "new math", because I don't even know what all it includes, and I do have evidence that in some ways, math is not taught as well as it once was. For instance, I was required to know multiplication tables (3rd grade) and how to to long division (4th grade), so that I could multiply and divide any numbers in my head or on paper. This was probably before "new math", so maybe I got the best of both worlds - rigorously learning arithmetic skills (which might be "old math") and then learning some very useful abstractions that earlier students might not have learned at such an early age as I was taught them - if ever. I do think it's important to learn to be comfortable manipulating numbers, because numbers describe so much of the world. If kids are not being taught to multiply and divide today, that's a big mistake.

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Hilarious! Although . . . I must say it would be stronger if the correct answer in the "old math" approach segment at the start of the video was provided for the actual problem shown at the reveal. The original problem is 342-173, for which the answer is 169. However, the problem shown at the reveal has suddenly become 342-176 for which the answer is 166 and NOT the mistaken 169 indicated.

I'm surprised nobody pointed this out to the filmmaker.

The filmmaker realised the mistake 10 months ago and posted this updated video - http://www.youtube.com/watch?v=GAm3KWiDPKU

The link that was given on the forums, was to the uncorrected one. :huh:

Thanks, Michael!

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I am not defending the whole idea of "new math", because I don't even know what all it includes

Have you watched the "inconvenient truth" vid linked above? The presenter gives a pretty good idea of the methodology taught, with concrete examples. The important element here is not that educators are teaching new algorithms. There are three main points to consider:

1) Some books discourage using any algorithms at all, forcing the students to "reason out" problems individually. This ignores the fact that an algorithm is a method of solving problems that has been "reasoned out". The universal algorithms are easy and work every time. Why would you want to deny a child the knowledge that exists and can help them be more efficient thinkers?

2) The books that use algorithms do not teach the simple, time-tested techniques that all the parents know. Instead, every example is more complicated and less efficient. The students have more trouble learning how to use these algorithms and the parents are clueless about how to help them.

3) In at least one of the new teaching methods, practice using algorithms is considered a waste of class time. The presenter highlighted a quote in the publication to that effect, and showed the subsequent volume which foregoes manual arithmetic in favor of using calculators. The students are essentially taught that they don't need to know the material!

The "New Math" has little to do with teaching new algorithms. The algorithms are only meant to stop arithmetic from being automatized. Whether it's using unfamiliar methods of getting the answer, letting the students flounder on their own, or not allowing enough practice time to retain the knowledge, the "New Math" shrinks the scope of a student's knowledge by forcing them to be concrete-bound. The educators want the kids to face each problem as if it was their first, retaining nothing of their experiences that would help them to learn the basic principles of mathematics.

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....

The "New Math" has little to do with teaching new algorithms. The algorithms are only meant to stop arithmetic from being automatized. Whether it's using unfamiliar methods of getting the answer, letting the students flounder on their own, or not allowing enough practice time to retain the knowledge, the "New Math" shrinks the scope of a student's knowledge by forcing them to be concrete-bound. The educators want the kids to face each problem as if it was their first, retaining nothing of their experiences that would help them to learn the basic principles of mathematics.

I was only pointing out that my exposure to what was called "new math" was beneficial, and in fact taught me some very useful concepts, such as sets and set operations, and the use of other number bases. I wanted to point out the latter especially, because some people here had disparaged this knowledge, as if perhaps it was a waste of time to learn. (People had also claimed that this was a waste of time or "too hard" 40 years ago when I was in elementary school.) It sure wasn't a waste of time for me.

As far as not teaching algorithms (I assume you're talking about algorithms to do things like multi-digit multiplication and long division); that is not good; one would indeed be mentally crippled if he had to figure out afresh how to multiply each time he was presented with a new problem. My exposure to "new math" came only after I'd already been taught to perform these operations in earlier grades. But once I understood the algorithms, and could easily multiply and divide, I was ready for something more abstract back then.

I didn't watch the video; my network connection is way too slow for that, so I was instead responding to specific issues people here had raised in their writings.

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I was only pointing out that my exposure to what was called "new math" was beneficial, and in fact taught me some very useful concepts, such as sets and set operations, and the use of other number bases. I wanted to point out the latter especially, because some people here had disparaged this knowledge, as if perhaps it was a waste of time to learn. (People had also claimed that this was a waste of time or "too hard" 40 years ago when I was in elementary school.) It sure wasn't a waste of time for me.

That's great, and I agree if that's the context of learning other skills it can be very beneficial. However my understanding is that the "new math" is not just a list of alternate techniques, but a new way of teaching math. In fact it begins before multi-digit multiplication, with addition and subtraction.

In the humor video, the presenter gets the wrong answer while using one of the new algorthims and jokes - as the "new math" slogan goes - that the idea is to know what you're doing, rather than to get the right answer. The irony is students have no idea what they're doing, and the system keeps them from knowing it.

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Note that the presenter in the video with the song is lip-syncing to the Tom Lehrer song from the 1960s, so there's nothing "new" about his making fun of "new math."

Apparently I was raised on what was at the time the "new math," attending grades K - 7 from 1966-67 to 1974-75, and I've always been rather excellent at math. So it doesn't seem to have affected me negatively. To me it was just "math."

What I don't understand is what the song apparently says the "old math" did for subtraction. "2 take away 3 is 9, carry the 1?" What the...? I can almost see 2 - 3 = 9 (implicitly doing 12 - 3), but where does the bloody 1 come from?

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Note that the presenter in the video with the song is lip-syncing to the Tom Lehrer song from the 1960s, so there's nothing "new" about his making fun of "new math."

Ah, I didn't realize. I knew that "new math" wasn't new, but I just thought the sound was off-sinc. :huh:

What I don't understand is what the song apparently says the "old math" did for subtraction. "2 take away 3 is 9, carry the 1?" What the...? I can almost see 2 - 3 = 9 (implicitly doing 12 - 3), but where does the bloody 1 come from?

From the 10s place.

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What I don't understand is what the song apparently says the "old math" did for subtraction. "2 take away 3 is 9, carry the 1?" What the...? I can almost see 2 - 3 = 9 (implicitly doing 12 - 3), but where does the bloody 1 come from?

From the 10s place.

No, because he carried it - put it over the 10s place. I can't figure out what's going on.

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