I may be way behind in this conversation, but I have questions about Dolciani.....

[hmsch4me]

I picked up the book from the library and I like it a lot, however, I've been reading a lot of old posts about this book and the importance of choosing one from the 1960s or 1970s. This was during the time I went to school and it was my understanding that it was when "new math" came out that we starting having serious trouble with math in this country. I'm not trying to be confrontational here, just curious. Am I getting this all wrong? I was under the impression that we had much stronger math students coming out of the 50s and earlier than we did in the 70s and today.

 

I'd love feedback and discussion on this!

[hmsch4me]

nt

[Storm Bay]

I remember this as I went to school in the 1960s and 1970s. However, I don't think that the way the Algebra is taught is the problem, it was the lack of drill and solidity of the arithmetic facts that New Math brought. I did Arithmetic for grades 1-4, then started New Math. We did a lot of arithmetic. Lots and lots of it, including lots of drilling, so naturally there was proficiency in this.

 

However, it seems to me that whichever math style is used, it never works well enough and a new style of math teaching is introduced. I highly doubt there is a perfect one-size-fits-all math style. Also, some people are going to have difficulty with math regardless of the method or math style used at the time.

 

This is my relatively uneducated opinion, as I was turned off math by an inept school system. I'll leave this for the math experts to discuss.

[Myrtle]

I picked up the book from the library and I like it a lot, however, I've been reading a lot of old posts about this book and the importance of choosing one from the 1960s or 1970s. This was during the time I went to school and it was my understanding that it was when "new math" came out that we starting having serious trouble with math in this country. I'm not trying to be confrontational here, just curious. Am I getting this all wrong? I was under the impression that we had much stronger math students coming out of the 50s and earlier than we did in the 70s and today.

 

I'd love feedback and discussion on this!

 

If you want references, they do exist, but it would take some effort on my part to go dig them back up. Basically what you would find was that there was a steady number of math majors in the US up until about 1974/76 and that since then the absolute number of math majors in the United States has not increased in the past 30 years. There is some speculation that number of foreign students studying math has increased from the 50's and 60s but the statistics don't distinguish between domestic and foreign degree earning students, from what I can find.

 

The fact that math majors have not increased at all while the student population has doubled is chilling.

 

New Math was started by a group of Ed Begel, who was a Yale mathematician. The group that he founded was receiving National Science Foundation funding in an effort for American math education to catch up to the Russians as a result of Sputnik. Despite the common assertions that there is some nostalgic golden age of math education, Ralph Raimi, a mathematician who is older than Methusula, lived through it all wrote a fair description of pre-1960s school math here. So, it seems that there was justification in wanting to make some improvements.

 

Begel's group was known as the SMSG and produced math texts that they put in the public domain. These were not made public until they had been thorougly tested with real classrooms by real teachers, were revised multiple times to reflect what was needed by the teachers, and everyone was super pleased with the result. Any textbook publishers could come in and "plagerize" as much SMSG material as they wished and it was hoped that this mannah from directly from mathematicians and making it easier on the publishers by donig their work for them would somehow straighten everyone out.

 

Instead, what happened was, textbook publishers wanted the appearance of New Math without being very careful to make sure the content was there. The textbooks were cheap knock offs. The people buying the textbooks for the schools didn't have the math background to know the difference, and while there were enough mathematicians to personally retrain high school teachers in special summer seminars, there weren't enough for the elementary school teachers. Later it was decided that the rigor (By that I mean mathematical rigor which is not the same thing as academic rigor) that was making the high school math wonderful was appropriate for children learning arithmetic as well. This is widely recognized as a mistake by everyone and we have Tom Lehrer to entertain us with his song commemorating this silliness. I will say that it's not completely clear if it's considered a mistake in theory or if in practice the teachers and publishers weren't emphasizing the right thing.

 

I recently acquired a book authored by Ed Begle, the man himself, called "The Mathematics of Elementary School" which was intended for the training of elementary school teachers. I wasn't impressed and found nothing I could use. It has a chapter on sets, and a very odd chapter on how to make flow charts of all things, and the rest of the book simply looks like the kind of solid math discussion you'd see in Saxon Math. Perhaps in the preface when Begle said he had carefully selected topics because he predicted these would be the future of math education he was spot on (minus the flow charts)!

 

Here is a post from a math teacher from a recent thread on another forum who was taught New Math and is discussing how set theory doesn't get developed but existed in every book:

 

Just to be clear - this is what I am complaining about, not about set theory in general, which would be silly, or even about it being taught in school. The "set theory" I was taught went nowhere, yet was Chapter 1 of every textbook from something like 7th grade to 11th grade, with identical content (and not much more than learning some notation, really). OK, got that, let's either expand on it, make connections, or drop it, anything but repeat it ad nauseum. This isn't about the concepts of set theory, which I assume permeates much of mathematics, but rather the notation and vocabulary learned in Chapter 1 that was not necessary for understanding the later content, as evidenced by the fact that the notation and vocabulary was never, or at least almost never, used again in the book.

 

And so that was the problem with many of those New Math books, they box checked topics without really developing them. And we have that going on today in many math books as well, hence the phrase that the American math curriculum is a mile wide and an inch deep.

 

So, the question is, does Doliciani do this? I have reason to believe that those textbooks don't. A recent commenter to my blog said that he had corresponded with Ralph Raimi (who was no friend of the math book that we are actually using :D) and said that Raimi recommended the older Dolicianis to him.

 

Of course, here is another issue.

 

How do you teach it?

 

 

If the teachers in the 60s had to be given crash math classes in order to teach, would a parent without a math background or teacher's manual be able to do it? I don't know. It's not that you wouldn't technically understand the algebra, maybe it's that you would likely not appreciate some of the more subtle ways that it's presented, the steps in solutions are slightly different, the vocabulary might seem unnecessarily technical and so you wouldn't incorporate that into your speech, you might not know which theorems are important and which are trivial. The book that I'm using (which is not a Doliciani but is from that era) just doesn't put out flashing lights and dancing girls whenever it does something important. Sometimes it's in the problem set and it turns out it's a very important problem in math and I very nearly skipped over it because we only do the odds...that kind of thing. So one would need to be careful.

[Charon]

I picked up the book from the library and I like it a lot, however, I've been reading a lot of old posts about this book and the importance of choosing one from the 1960s or 1970s. This was during the time I went to school and it was my understanding that it was when "new math" came out that we starting having serious trouble with math in this country. I'm not trying to be confrontational here, just curious. Am I getting this all wrong? I was under the impression that we had much stronger math students coming out of the 50s and earlier than we did in the 70s and today.

 

I'd love feedback and discussion on this!

 

 

Actually, I think we had more math majors in the early 70s than ever before. Begel, the guy that headed the largest move to institute New Math (the SMSG), as Princeton trained mathematician who studied under Lefschetz. I think he even has a theorem named after him. The reason "everybody knows" that New Math was an abject failure is more the result of a systematic campaign waged against it, primarily by Morris Kline. It wasn't just New Math but really rigor in mathematics, in general, I think. I really kind of think it even gets into a professional contest between pure math and applied math (like they are competing with each other for public interest and funding).

 

At any rate, if you get a quality text, then it is likely as close as you will ever get to getting math handed down by society's mathematicians. And, the halmarks of New Math -- the set theory and logic and proofs and such -- are a lot closer to what mathematics as practiced by mathematicians is like.

[hmsch4me]

I can get to feeling so lost in this world of mathematics, yet want my children to have a good solid math. Thanks again.