You, a professional in the technical field, can’t keep up with tutoring work for your nine-year old kid’s math homework. What exactly was this new math that stymied parents and elder sibblings?
New Math - of course, it is not new at all now. It was a 1960s thing. (And even then, I who finished high school in 1970, was never subjected to it. I can remember my mother, who was a primary school teacher, talking about having to teach it, though.)
Why do New Math teachers have a problem telling holidays apart?
Because OCT 31 is DEC 25.
And here’s what Cecil’s minions* had to say about it: What exactly was the “new math”? - The Straight Dope
- Assuming I can call the SDSAB “minions” without stepping on any toes.
I see. Simply introducing some advanced fields at an earlier age. Thanks for the wiki link (as always, I forget to surf before asking.)
That joke also works for computer programmers.
It seems to me that the only “new math” topic to have survived into the 21st century is algebraic inequalities. (Previously they only taught equations in high school algebra, as far as I know.)
New Math is just like Old Math, if you’re missing two fingers.
(With apologies to Tom Lehrer)
I have a t-shirt that says that. I would wear it when I taught bases to my students.
I remember new math well. It was an early sixties thing, and at my school it was set theory and bases. I was in seventh grade and my parents were stunned. They had no clue how to help me. I came to school one morning and on my desk was a paperback math book with a bright yellow cover. I understand it now, but I was lost the rest of seventh grade.
My sister was two years behind me in school. She got Set Theory in 6th grade (right around 1960, maybe 61); I didn’t get it until starting college in 1966.
My take: “New Math” was designed by mathematicians who were familiar with their field but had forgotten the art of teaching. So they tried to teach everything in the abstract right from the start, because it was perfectly clear to them – forgetting that what’s clear to them is clear as mud to beginners.
Old Math: Negative numbers are numbers less than zero. Deal with it.
New Math: For each real number a we assume that there exists another corresponding real number, denoted by -a and called the additive inverse of a having the property that a + (-a) = 0.
Yes, that’s exactly how negative numbers were introduced in my Algebra I textbook (Dolciani et al) in 1965. It sounded like something a lawyer would have written. I’ll write another separate post with another (similar) view I had about it.
That is a perfectly appropriate definition of negative numbers for an algebra textbook. But you should have received an introduction to them along the lines of your old math definition far before taking Algebra I, when learning basic arithmetic skills.
Okay, another thought about New Math.
Imagine you’re building a house, but you don’t have much experience at it. So you design it very very poorly, and you have to keep making fixes as you build, and as you discover problems.
You pour the foundation and put up the frame. Then it occurs to you that you didn’t think to put the pipes and conduits under the foundation and sticking up through it in were the walls would be. So you dig under the cement and drill holes in the foundation and stick the pipes and conduit up through it.
Then you realize that you didn’t really get them in the right places, and besides the bathroom opens into the kitchen, but the kitchen sink and bathroom plumbing are on far opposite walls of their respective rooms – so you need that much more pipe to get the water to them all, than if you had put the kitchen sink back-to-back with bathroom sink, tub, and toiler. Oh well.
Now you’re ready to build your second house. This time, you plan ahead. You carefully plan where the walls, fixtures, lights, and sockets will be. You lay the pipes and conduit before pouring the foundation, and have them sticking up in all the right places.
Now a bystander happens by, and sees the foundation with the pipes and wires sticking up in various places, but it’s not obvious to him why they are placed as they are, because you haven’t put up the frame for the walls yet.
Okay, let’s talk about math instead. Algebra, and modern math in general, was largely developed in its modern form (more-or-less) over the past 400 years. But it grew as a hodge-podge, without much planning or foresight. So you had a lot of excess baggage, things like notations that were hard to work with, definitions that weren’t helpful in forming proofs (see the .999… thread), and so forth.
Early in the 20th century, there was a symposium of mathematicians and teachers about it. They took all the hodge-podge and organized it – settling on definitions and notations, and an order in which things should be taught so that each new topic, theorem, or definition builds logically and orderly upon what came before. This was like organizing your house so you knew where you would need the conduits before pouring the foundation. Rigorous thinking was developed and precise language was developed (see definition of Negative Number, above).
Eventually, mathematicians got to know this so well, they forgot that it had been any other way. They started teaching the abstractions without any concrete motivations, because it was all so clear to them – how could anyone not understand a definition of negative numbers like that?
So to beginning students, it was like seeing a foundation with the conduits sticking up, but not being able to fathom why they were placed where they were. The architects put the conduits just so because they had it all planned out, and they knew where everything was going. But the naive students couldn’t know that; they could only see a jumble of wires and pipes sticking up.
That’s New Math.
When I was in 9th grade Algebra I, along with that lawyerly definition of negative numbers, we also learned a bunch of other abstract tid-bits. Like the properties of equality: It is reflexive, symmetric, and transitive. All pretty obvious, but why make rules about it? These rules were never explicitly mentioned again, even though we made implicit use of them all the time. I don’t think those rules are consciously discussed again until upper-division college algebra, when you get into equivalence classes. For the 9th grader, it was all just mental masturbation (and not even much fun for most of the class).
Right, but that introduction needed to be there in the Algebra class too (whether lectured by the teacher or in the textbook), because some students had somehow missed it. More to the point, even for students who knew about negative numbers, that definition went right over their heads because it was all so abstract and not even obvious (to a beginner) what the definition was talking about. The teacher should have reviewed negative numbers (in the simpler “number less than zero” terms that students might already know) and show how that arcane definition, in fact, defines just that. That connection was missing. It was a lot like that for every other new topic we learned, including stuffs that students might really not have previously seen. Abstract rules, definitions, and notations, all in legalistic language, without much of the “plain English” interpretations of what it all meant. Instead, just lots of abstract symbolic manipulations. That’s what New Math was. ETA: It was like, you should just eventually learn what it all “really means” by osmosis or something.
Heck, I was in a college class on Introductory Oceanography once, which had a lot of middle-aged “re-entry” students in it. When the subject at hand was the extremely cold temperatures at various very-deep depths (negative numbers!), one of the older students raised her hand to ask what a negative number was.
I got set theory starting in second grade. (Set, universal set, subset, union, and intersection.) That’s also the year I started learning base 8.
This may have something to do with the fact that I didn’t learn my multiplication tables until fourth grade.
Me too. Set theory was big. My 9th grade math class was basically set theory and vector algebra. I still have my text book and it is as dense and incomprehensible as any math book I ever seen and I have degrees in math and physics.
In the same years, late 60’s when I was in middle school, we also go new English. There were new ways of diagraming sentences, new words for the parts of words, phonics were bad, bad, bad and reading speed was critical. I actually never heard of phonics until I reached college. It seemed to me to be a great new invention. By the time I reached high school all evidence of this new English was gone and my teachers spent the next 4 years lamenting our poor grammar, spelling and writing skills. Unfortunately, they didn’t have time to go back to those subjects, we had to learn Milton and Camus.
My son is just finishing his third week of first grade.
Since I haven’t had elementary level math in over 30 years I’ve found it ineresting how they teach the first steps of basic match.
Right now they are “deconstructing” numbers. Taking for instance a 7 and showing it as 1+6, 2+5, 3+4, 4+3, 5+2, 6+1.
Is this something new or do I just not remember back 36 years ago?
I was wondering how far down the thread I’d have to go to find this. Lehrer was brilliant.
My kids went through elementary school in the 80’s and 90’s. I was generally pleased at the math teaching methods except that the kids weren’t forced to memorize arithmetic facts which I think is great to have for day to day life.
But from 1st grade on they got concepts of algebra that I didn’t see (in class) until 8th grade.
They all scored well on achievement tests and got through calculus and statistics, which was all they needed.
In the introduction to his song, Lehrer also remarked that the purpose of New Math was “to understand what you’re doing rather than get the right answer.”
You studied Camus in English class?