The Sputnik started it; first item to be sent into space, its launch by those no-account Russian commies on 4 October 1957 was an affront to the pride and dignity of U.S. engineers and mathematicians. Described as an “…outer-space raspberry to American pretensions”, it delivered such a severe blow to American technological hegemony, that programs were initiated to train a new generation of engineers. The U.S. had to regain the inside track in the space race and it had to be regained through the school system, where the future is organised.Part of the program was to have a very different approach to the teaching of mathematics at the elementary school level.
Americans called it ‘New Math’. No one is sure what happened to the ‘s’, but Australians replaced it. An understanding of the intricacies of mathematics became a national priority through the western world. Inquiry and discovery, hands-on learning and concept development assumed a dominance over rote learning. It was felt that children of a young age would become more competent if they understood relationships within number and space, and would move easily to more intricate theoretical aspects as they grew older.
The centre-pieces were the teaching of Set Theory and Numbers in other Bases.
Set theory is very complicated. As one of the axiomatic foundations for mathematics, however, at primary school level it provides the language to describe mathematical objects and concepts. Some established truths were represented by using Venn diagrams to describe relationships between sets of things and children were introduced to an unfamiliar mathematics lexicon of some proportion.
The magic of number was also explored through examining numbers in others bases. After all, calculators used Base 2 and an appreciation for such uses should lead to a wiser understanding of the usefulness of Base 10. The use of Cuisenaire rods supported such conceptual development.
It was introduced into the Queensland syllabus in 1966-68 and revised in 1974-76. It was a major change for teachers to adopt a new language as well as adopt teaching strategies that emphasised inquiry and discovery rather than rote recitation of facts. It was a lot to assimilate in a short time and there was an occasional expressed desire to return to the tried and true.
GOOD OLD-FASHIONED MATHS
[Tune: "Sweet Old-fashioned Girl"]
Wouldn’t anybody like to teach some good old-fashioned maths?
[Seven and five are twelve.....]
Wouldn’t anybody care to tread those dear familiar paths?
[Seven from twelve leaves five.....]
Now we’re sweating in a jungle where the null sets lurk,
And hacking through the graticules is just hard work -
Wouldn’t anybody like to teach some good old-fashioned maths?
Wouldn’t anybody like to teach some good old-fashioned maths?
[Tell ‘em just what to do .....]
Wouldn’t anybody like to tread those dear familiar paths?
[Copy this setting out .....]
Now we’re scaling up a mountain cragged with magic squares,
And slipping every yard or so on ordered pairs -
Wouldn’t anybody like to teach some good old-fashioned maths?
Superscript! Closure Law!
How can we take it and come back for more?
Base sixteen! Histogram!
Now that we’ve met them all, who gives a damn?
Wouldn’t anybody like to teach some good old-fashioned maths?
[Ten to one on top .....]
Wouldn’t anybody care to tread those dear familiar paths?
[Ten to the bottom too .....]
Now we’re struggling in a sea where numbers may be odd,
Irrational or negative or even mod. -
Wouldn’t anybody like to teach some good old-fashioned maths?
Many parents and teachers in all parts of the world supported this point of view. Such mathematical language was not used at home and was not easy to comprehend; it demanded a great deal more time at school and at home; it required significant changes to classroom organisation and it involved the use of a variety of structured material.
Besides, the gradual change from the imperial measures to metric meant that both kinds of measurement number sentences were being taught at the same time. It was confusing to hop from one to the other and to teach conversions as a temporary measure. What did one do?
MIX-MATHS POLKA
[Tune: "Hop-Scotch Polka"]
Oh, you hop a little on the New Maths shoe,
You hop a little on the Old Maths too,
You don’t tell the leftie what the right will do
In the MIX-MATHS POLKA.
You hop a little on the powers of ten,
Back to the perches and the roods again,
Then a bit of logic that you cribbed from Venn
In the MIX-MATCH POLKA.
It’s up and down along the number line,
Here comes BOMDAS with a minus sign,
Thought he’d had it, but he still looks fine
In the MIX-MATCH POLKA.
Oh, you hop a little on the New Maths shoe,
You hop a little on the Old Maths too,
You don’t tell the leftie what the right will do
In the MIX-MATHS POLKA.
New Maths fell out of favour by the end of the decade although many teachers continued to use the more dynamic teaching techniques acquired during the period. Classroom mathematics activities became more child-centred, more open and more active, even though the post-Sputnik astronautical intentions faded.
The demise of New Math[s] in the U.S. was encouraged in a lengthy song by Tom Lehrer, a witty mathematician, who delivered it in a rapid lecture style about how to subtract 173 from 342 in base 10 and in base 8. This became a theme song for many and was called “New Math”. Lehrer introduces it, “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 a public school, you say eight from four is six…and 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 answer. “
Ray supported the demise.
NEW MATHS CASUALITY
[Tune: "There's a Bridle Hanging on the Wall"]
There’s a slide-rule hanging on the wall
And a new computer in the hall.
You ask me why the teardrops fall:
There’s a slide-rule hanging on the wall.
There’s a slide-rule hanging on the wall
And some other gadgets, big and small,
Whose names I simply can’t recall…..
There’s a slide-rule hanging on the wall.
With a Brooks book for my guide I used to teach in this school -
I was a chalk-talk “pro”.
But now newfangled Maths had made me feel like a fool -
Don’t know what all young teachers know.
There’s a slide -rule hanging on the wall,
But I just can’t use the thing at all :
The teaching game’s begun to pall
Since that slide-rule’s hanging on the wall.
As with other spectacular innovations, the better aspects of New Maths welded themselves into established teaching practices. The tricky bits dissipated.
