Naive set theory and algebraic laws, such as associativity and commutativity, are pretty much fundamental to understanding advanced mathematics.
Perhaps, they were taught too early in the curriculum. It is possible that children need to learn algorithms and formulas by rote before they understand abstractions. (Nowadays though, I prefer a formal definition first, then examples.)
I don’t think it is bad to teach children abstractions as long as they understand how they are connected with rote techniques.
I probably was taught the new math: Basic math with some weird ideas for long division, esp., plus lots of useless Venn diagrams, and of course the metric system!
But, let’s start by asking what was the “old math”? (The link provided above to Wikipedia was no help. My dad said the new math focused on the aligning of columns (tens, hundreds, etc.), but I can’t imagine doing math without aligning columns as such!
Can you give us more details on what the old math was like?
I started elementary school in 1963. In the 4th and 5th grades I was put in a special math class for the kids considered to be advanced.
These classes used several of the “New Math” concepts, like sets, venn diagrams, different number bases, etc., combined with some more traditional arithmetic but posed in ways which were supposed to make us think about problems in different ways.
I didn’t have much trouble with it, and when I got to algebra in the 7th grade, some of it seemed familiar from the New Math stuff.
So I guess I was a “victim” of New Math, but I kind of liked it.
I will say that the ability of the teacher made a huge difference, however. Much more so than in traditional arithmetic. Any idiot can drill on multiplication tables, or on rules for adding and subtracting, but it took more understanding of the concepts to teach sets and number bases.
I may have been lucky, but my 5th grade teacher not only helped me to understand the difference between the quantity 5, the numeral “5” used to represent that quantity in base 10, and the numerals “101” used to represent the same quantity in base 2, but he made seem obvious.
I heard about this for the first time a couple of days ago when my mother said she was a victim of New Math. Add its alleged comeback to my now-growing-at-an-exponential-rate list of reasons to emigrate to Canada.
FWIW, we (b. 1986) had Venn diagrams (Maryland, elementary school) and communisticdeviatordistributormanifold properties (California, middle school). I loathed them. I’m fairly good at math today; I don’t consider myself particularly interested in math although, as I come from a family of engineers and scientists, you could say I’m probably built for it.
My pre-college math education ('87-'00) seems to have been influenced by this stuff. I remember Venn Diagrams and the enormous amount of emphasis my high school teachers placed on ‘doing the work right’ even if you hadn’t a clue what the answer was. But generally I think I dodged this New Math bullet.
My pre-college math education ('87-'00) seems to have been influenced by this stuff. I remember Venn Diagrams and the enormous amount of emphasis my high school teachers placed on ‘doing the work right’ even if you hadn’t a clue what the answer was. But generally I think I dodged this New Math bullet.
I didn’t get the ‘New Math’, thank OG, but my sister did. My sister was still having problems with math years later.
My Dad is totally anti-‘New Math’. He has a PHD in math. My sisters problem with math and school drove my Dad nuts because he really understands math and couldn’t figure out why they were trying to teach kids in this mannor. I do remember that he could never figure out why they were trying to teach kids higher concepts when they couldn’t do simple problems.
I also seem to remember that Richard Feynman had a rant about ‘New Math’ and how worthless it was in one of his books. I think it was 'Surely You’re Joking, Mr Feynman."
I know I did “New Math” in elementary school. (1975-1980 or so)
I can’t say it warped me. I found it kind of fun. Changing bases was interesting. I remember for my HS final exams - since I couldn’t leave early, I re-did all calculations in binary. After checking my work a few times. (Yes, I was bored.)
I know that my father was boggled when he saw me doing some New Math problems in second or third grade. He was looking down and muttering something about, “Why are you getting set theory, now?” After that he and my mother spent about an hour trying to understand why we were getting stuff they only got in college. I found it a fascinating conversation.
What bothered me is that until I taught myself how to use a slide rule, after leaving college, I never really understood logarithms. It seems to me that most people were most effed up by the New Math were those who were caught between and betwixt changes between doing things the old or new ways.
I never thought about it, but yeah… I, too, was taught the Assoc/Distr/etc properties, Venn Diagrams, etc. as well as basic arithmetic. And I’m glad I was because the concept of a Venn diagram (and I remember being taught that sometime in elementary school (1973-)) has actually been very helpful in my life in understanding other things like people and organizations… but I had no idea until this thread.
I mentioned the Associative properties to my wife and she claims to have never heard of it. I had no idea that it was considered “New Math”… and here I was, entering this thread thinking I had avoided all that “crap”! :wally :smack: :o
I was a “new math” grade schooler. I now teach college courses in computer science, so I guess I see a lot more use to having been taught to work in different number bases and to knowing some discrete mathehmatics (set theory, etc) than many of the prior posters.
What I notice about many of my post-new-math students is that they seem to believe that arithmetic is all there is to mathematics. Their problem-solving skills are stunted because they can’t seem to solve any problem that doesn’t involve actual numbers. If I give them a “word problem” with real numbers, they can get the answer. But if I ask them to do the same thing but keeping some of the quantities as symbols (x, y, etc), they seem completely befuddled by the request. Unfortunately, that’s pretty much what beginning-level programming is all about.
Big “me too” to your entire post. Should one of us start a GQ thread on the subject?
According to that Tom Lehrer link, the old math is one in which 2 - 3 = 9. Very interesting, but very wrong. I guess I prefer the new math, where we got right answers.
You do know that he’s rerally saying (in shorthand way) that 12-3 is 9. That’s what the “carry the one” business is about. Lehrer’s great line about “understanding what yuou’re doing rather than to get the right answer” is in regards to subtracting 7 from 13 and getting (an incorrect) five.
Lehrer’s song is great, and the printed lyrics don’t really convey it. You gotta listen to the original. (Lehrer, by the way, was in math at Harvard.)
I was in elementary school from the mid to late 1960s, so I was also a victim of the New Math. I didn’t understand it, I didn’t get it, my parents couldn’t help me, and I ended up failing math in high school at least once. Might have been twice; I stopped caring about math class by the end of high school, I was so turned off math as a subject.
Thankfully, I did have one old-fashioned teacher in grade six. He drilled us with multiplication and division tables, made sure we could add and subtract perfectly, and had fast mental arithmetic oral quizzes to reinforce everything (“Spoons! What is 25 divided by 5 plus 3? … Too late! Paul, same question! … Too late! Susan?”). To this day, I can do arithmetic both on paper and mentally, no calculator needed.
But the New Math? Never understood it at all, and got quite frustrated trying to.
The so-called “new math” was all I knew, and I didn’t have any problem with it. I remember hearing that parents were confused by it for some reason, but I never understood why. Since I never knew the “old math” there was nothing for me to compare it to.
LOL, I am also a 1961 baby … but I know my crapitude at math is because of moving around. In one school, I learned addition, subtraction, and some fairly basic low level stuff. I moved over the summer, and the new school I was at in the fall expected me to do multiplication, divisaion, fractions and decimals. As review from the previous year. I got stood in a corner for refusing to do the stuff I had learned last year [that I hadn’t learned at all] and a note sent home with me …
Took my parents 3 weeks to drive it into that dimwit byatch’s head that I wasn’t refusing to do the work, I had no freaking clue what the idiot was talking about because I hadn’t learned it YET. In that 3 weeks, my mom used my math book to get me up to speed with the rest of the class, but ever since that time I have been very resistant to learning math. Oddly enough, I can teach myself stuff if I am interested in it. I learned a fair amount of noneuclidian geometry and trig solo - but to this day I can’t prove a geometric theorum to save my life but if you give me a straight edge, compass and other spiffy tools I can draw anything you want me to=)
