In simple term, what was "new math?"

When I got to school in the mid 70s I always heard from the adults, "they are teaching you 'new math.'"

Later in high school I asked a math teacher, who was just a sub that day and blowing off time in PASCAL class, about "new math." Her reply was, "We have had 2 or so "new new maths" ago.

Doesn't answer the question. I've looked it up in wikapedia and seen that it involves "set theory" and do remember some first-grade "set" problems involving circling like sets.

I still don't quite grasp it all. I'm not an idiot but was wondering if some of you math folks could describe what "new math" was. Maybe some of you were older than 10 like I was when exposed to it all.

I'm not a math type, but I was taught New Math; I remember a teacher referring to it that way, probably in 5th grade, which would have been 65/66, the first year we had a separate math teacher.

Keep in mind, that was a REALLY LONG TIME AGO for personal memories. I'm 55 now, I was 11 then. As a personal memory, not from looking around the internet, I remember Miss McCarthy ending lessons with, "What does this teach us?" Or, "What have we learned from this?" Those were probably moments where we all sat there wondering what the heck we were supposed to say, but I don't really remember. I do remember that we got taught sets after we'd already learned basic arithmetic; sets seemed really simple and dumb. They were introduced as a way to understand arithmetic. The relationship to higher mathematics wasn't really introduced, they were just another thing to learn. I do recall one school year ending right as we started getting into some higher concept, I don't remember what it was; 7th grade, Mrs Garcia. I always thought that she'd dragged the lessons out to end there because she didn't understand anything beyond that. 8th grade started with simple algebra, and diagramming equations. I don't know if diagramming equations was part of before new math, but I thought it was really cool that a circle could be shown as an equation.

Math was always math, New Math was a way of teaching it.

The only "new math" I remember is the comedy from Tom Lehrer, which was on some comedy album when I was a kid.

Quote:

Some of you who have small children may have perhaps been put in the embarrassing position of being unable to do your child's arithmetic homework because of the current revolution in mathematics known as the new math. So as a public service here tonight I thought I would offer a brief lesson in the new math. Tonight we're going to cover subtraction. This is the first room I've worked in a while that didn't have a blackboard so we will have to make due with more primitive visual aids, as they say in the "ad biz". Consider the following subtraction problem, which I write up here: 342 - 173.

Now remember how we used to do that. three from two is nine; carry the one, and if you're under 35 or went to a private school you say seven from three is six, but if you're over 35 and went to
Public school you say eight from four is six; carry the one so we have 169, but in the new approach, as you know, the important thing is to understand what you're doing rather than to get the right way. Here's how they do it now.

You can't take three from two, Two is less than three, So you look at the four in the tens place.
Now that's really four tens, So you make it three tens, Regroup, and you change a ten to ten ones, And you add them to the two and get twelve, And you take away three, that's nine.
Is that clear?

Now instead of four in the tens place You've got three, 'cause you added one, That is to say, ten, to the two, But you can't take seven from three, So you look in the hundreds place.

From the three you then use one To make ten ones... (and you know why four plus minus one
Plus ten is fourteen minus one? 'cause addition is commutative, right.)
And so you have thirteen tens, And you take away seven, And that leaves five...

Well, six actually. But the idea is the important thing.

Now go back to the hundreds place, And you're left with two. And you take away one from two,
And that leaves...?
Everybody get one? Not bad for the first day!

Hooray for new math, New-hoo-hoo-math,
It won't do you a bit of good to review math.
It's so simple, So very simple, That only a child can do it!

Now that actually is not the answer that I had in mind, because the book that I got this problem out of wants you to do it in base eight. but don't panic. base eight is just like base ten really
You're missing two fingers. shall we have a go at it? hang on.

You can't take three from two, Two is less than three, So you look at the four in the eights place. Now that's really four eights, So you make it three eights, Regroup, and you change an eight to eight ones, And you add them to the two, And you get one-two base eight,
Which is ten base ten, And you take away three, that's seven.

Now instead of four in the eights place You've got three, 'cause you added one, That is to say, eight, to the two, But you can't take seven from three, So you look at the sixty-fours. "sixty-four? how did sixty-four get into it?" I hear you cry. Well, sixty-four is eight squared, don't you see? (well, you ask a silly question, and you get a silly answer.)

From the three you then use one To make eight ones, And you add those ones to the three,
And you get one-three base eight, Or, in other words, In base ten you have eleven,
And you take away seven, And seven from eleven is four. Now go back to the sixty-fours,
And you're left with two, And you take away one from two, And that leaves...?

Now, let's not always see the same hands. One, that's right! Whoever got one can stay after the show and clean the erasers.

Hooray for new math, New-hoo-hoo-math, It won't do you a bit of good to review math. It's so simple, So very simple, That only a child can do it!

Come back tomorrow night. we're gonna do fractions.
Now I've often thought I'd like to write a mathematics text book because I have a title that I know will sell a million copies. I'll call it tropic of calculus.

New math was largely a term for set theory. Sets have been morphed into crisp sets and fuzzy sets. Fuzzy being a determinant of set membership based upon semantic concepts such as "large number" or "close" or the like. The "set" of people in a room might include people standing in the doorway or people who've just left the room or who are usually in that room but are not now. This embraces concepts of probability as to existence of a member of a set.

I never understood new math. I taught myself algebra and so that school year they thought I knew what I was doing. One complex question stumped most members of the class, I had, as usual, not done the homework but when called upon I correctly guessed "n equals minus two-thirds" which astounded the whole class and most certainly astounded me!

The only problem with mathematics was, as always, the math teachers and the absolute boredom of school.

I recall first learning about sets in pre-school (seriously). It was so simple I never again took sets seriously, until I encountered them again in college. Those were devilish problems involving multiple sets intersecting in various ways.

What I learned about math and school in general is that a good teacher trumps nearly everything else. One math teacher I had tore up the curriculum for that year and re-ordered it so it made logical sense. That was my best year at math

Quote: FleaStiff

New math was largely a term for set theory. Sets have been morphed into crisp sets and fuzzy sets. Fuzzy being a determinant of set membership based upon semantic concepts such as "large number" or "close" or the like. The "set" of people in a room might include people standing in the doorway or people who've just left the room or who are usually in that room but are not now. This embraces concepts of probability as to existence of a member of a set.

I never understood new math. I taught myself algebra and so that school year they thought I knew what I was doing. One complex question stumped most members of the class, I had, as usual, not done the homework but when called upon I correctly guessed "n equals minus two-thirds" which astounded the whole class and most certainly astounded me!

The only problem with mathematics was, as always, the math teachers and the absolute boredom of school.

OK, I've read about "set theory" a few times and I remember in first and second grade or so looking at "sets." We would "circle" the "empty sets" which were groups of nothing. Or circle how many cats, how many kittens, how many cats with kittens. Nonsense like that.


But what is (was?) so good about this idea? I can se its use for marketing purposes-say I want to know how many people in my Las Vregas casino "Arizona Duffman's" who are sports bettors AND poker players but not BJ players to market them to the more profitable BJ tables since they are gamblers. Now, is this a good example of "set theory?"

If it is, why on earth is (was) this so important that they built a "new math" around it?

Yes, I know "new math" didn't work and it is unlikely that any "new math" will ever beat the way we teach arithmitic now. But from the prespective back then, why in simple terms, was this thought a good idea, other than to sell new textbooks?

I'm not a math guy, but my understanding of the idea behind New Math was to introduce children to the abstract underpinnings of math first, before the more concrete applications.

Basically, one approach to mathematics is to say it's just a particular application of logical principles, one of many formal systems. A formal system is a logical system that has precisely defined symbols, axioms, and rules. From the starting definitions, you can build out increasingly complex theorems that will eventually give you all the rules of mathematics. Set theory is integral to defining mathematics formally, hence its emphasis in the curriculum.

New Math was also trying to get across the notion that math as most people know it is just a very small portion of the study of math. So there is nothing special about our representation of a number, hence the inclusion of math in other bases besides 10 -- once again, trying to get children to think very abstractly about mathematical and logical concepts.

I can kind of see why the idea would hold appeal, because most adults (even the educated ones) have a very limited understanding of the nature of math and logical systems. If you can teach them early on higher concepts, then it might be easier to teach them the specific applications. However as we learned it didn't work particularly well.

It was a host of ideas that were introduced into grade school teaching in the 1960's after it was apparent that the Russian schoolchildren were more advanced than American ones.
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Of course some Eastern European countries like Russia, Ukraine and especially Hungary had been excelling in math education for one hundred years.
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A lot of concepts were introduced but some got more attention than others. "Set theory" has always been singled out. It's interesting to note that the Nazi's hated set theory and would murder the professors by tossing them off balconies. It was termed "Jewish mathematics" especially because of it's association with Cantor. The idea of mathematics being controversial goes way back in history to the Greeks who believed that irrational numbers went against God's will. When they discovered that the diagonal of a unit square was irrational (sqrt(2) in modern language), they tried to hush it up. There is a famous story of a man who threatened to reveal the truth on a boat, and was drowned by his friends. Ultimately the unwillingness of Greeks to accept irrational numbers killed their advancement in mathematics.
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Before "new math" people probably didn't routinely say "decimal" since they didn't know any other base systems. You didn't have binary and octal. The only exposure to non-decimal systems was monetary in the British system of pounds and pence or the old Spanish system of pieces of eight (two bits equals a quarter).
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General abstract algebra principles like commutative and transitive were introduced since they were of such importance to modern physics. These concepts were subject to some of the greatest ridicule.
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I find it interesting that most people with a high school education in mathematics are familiar with the terms arc, secant, and tangent and complementary angles from geometry, and at the same time they are familiar with sine, secant, tangent, and cosine, ... but they have no idea why the same words are used for trigonometry as for geometry.