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December 24

The New Mathematics

Greetings, keepers of the eternal flame!

I normally give this desk a miss since I am a mathematical nincompoop. But I learned recently through our article that Time placed New Math on a list of the 100 worst ideas of the 20th century. But did it produce anyone who became a full-time mathematician? I was one of the guinea-pigs subjected to this cruel and inhumane treatment in the UK from around 1968 aged 8. My views are somewhat coloured because I missed the entire first term of lessons, and I was thrown in the deep end with no explanation whatever. My 'mental arithmetic', times tables etc. were previously fairly good. As an aside, did anyone else here suffer this unusual punishment? Did it work for you? At least I got to understand binary, which came in useful when teaching IT in later years.

Obviously, some of the people who underwent this treatment became full-time mathematicians; it is not like there was a ten-year gap in the age distribution of academic staff at the maths departments of US universities at the turn of the century. But can one one say it "produced" them? Did they manage to develop their mathematical prowess even in spite of an ill-advised hyperabstract approach, or did it perhaps come natural to their already (for their age group) advanced abstract insights? It may be impossible to produce other than anecdotal evidence. Possibly the highest honour for one's mathematical achievements is to be a recipient of the prestigious Fields Medal, which was given in 1998 to American mathematician Curtis T. McMullen, the doctoral adviser of the late Maryam Mirzakhani, the first woman to be given the Fields Medal. McMullen was born in 1958 and therefore received his primary maths education during a period in which the abstract approach was in vogue. I have no specific information, though, about how he was schooled and whether there were perhaps stimulating extra-curricular circumstances. --Lambiam 17:39, 24 December 2022 (UTC)[reply]

I'm the right age to have gotten some of the 'new math', though I'm not sure how much filtered through to the rural grade school I attended. It may have been a bad idea, but I can see how it might have seemed like a good one at the time. "The important thing, " in the words of Tom Lehrer, "is to understand what you're doing rather than to get the right answer." Put another way, it seemed like a good idea to put less emphasis on rote memorization and blindly following recipes and more emphasis on learning the concepts involved. It would be like becoming a better baker by learning what yeast and gluten do rather than just memorizing different recipes for bread. If you put it that way it sounds like the new math would even get kids to stop hating math (as much). Perhaps the new math did help at make some people more open to abstract concepts and help them in more advanced studies. On the other hand if your interest in math ends with being able to follow your bank statement then the new math was probably a waste of your time. I think what made the idea truly bad is that it was implemented despite being based on what were only theories on the best ways of learning. So instead of saying "It sounds interesting, let's try some of the ideas on a few of the brightest students first to if it's an improvement," it was "It sounds great, let's completely revamp the curriculum and roll it out to the entire school district." Such a radical adoption of untested methods is rarely a good idea. --RDBury (talk) 20:20, 24 December 2022 (UTC)[reply]

An additional problem was that many teachers did not really understand mathematics, and this new maths even less. They taught it the only way they knew, which was just the same way as before: as a recipe to be followed mindlessly, step by step. --Lambiam 21:09, 24 December 2022 (UTC)[reply]

New Math by Tom Lehrer - worth a listen 😀 I've always liked maths so I never had to learn the stuff in class as I'd worked most of it out long before. Except for geometry where there was stuff new to me. NadVolum (talk) 00:45, 25 December 2022 (UTC)[reply]

Also worth watching is a longer film (36 minutes), What happened to the 'new math'?, that provides a historical perspective. One of the things I learned was the detrimental role played by the profit-driven logic of the US market for elementary-school textbooks. --Lambiam 06:17, 25 December 2022 (UTC)[reply]

Thanks for the link. I didn't know that new math was considered successful in high schools before they tried to expand it to elementary schools. I've read "Why Johnny Can't Add" but I don't remember it as being so much a critique of new math specifically but more of the way it failed to address more systemic problems in education. One example I remember is a teacher who miscopied an example from her math for teachers class, and went on to faithfully pass on the now useless example her students. It's been several decades since I read it though, so my impressions aren't too reliable. Another educational movement which I more experience with is the so-called Moore method, which has some similarities with new math only it's geared toward advanced students. The up-side to my mind was that I got lots of practice proving theorems in point set topology without having to look them up. The down side was that it took an entire semester to cover the material you would have gotten in the first two weeks of a course taught in a more traditional way. Everything's a trade-off I guess. --RDBury (talk) 12:54, 25 December 2022 (UTC)[reply]

Next step, post-fact maths [1] :-) NadVolum (talk) 13:49, 26 December 2022 (UTC)[reply]

Wow, thanks everyone for your interesting and insightful comments, plus the links. I feel a lot happier now about my inability to 'get' maths. Cheers all, MinorProphet (talk) 09:20, 28 December 2022 (UTC)[reply]