3 January 2018

Lost Vocabulary

While reading the Victorian maths textbook 'Elementary Algebra for Schools' I spotted quite a few words and phrases which are rarely used in modern secondary schools. I'm not saying that this vocabulary has disappeared from the field of mathematics, but I doubt you will hear these terms in GCSE lessons.

Let's take a quick look at some interesting words and how they were used in the 1800s.

Unity
Meaning (in this context): the number one.
  • "When the coefficient is unity it is usually omitted. Thus we do not write 1a, but simply a".
  • "If the product of two quantities be equal to unity, each is said to be the reciprocal of each other".
  • "Subtract 3x2 - 5x + 1 from unity, and add 5x2 - 6x to the result".
  • "We proceed now to the resolution into factors of trinomial expressions when the coefficient of the highest power is not unity".

Resolve into Factors
Meaning: factorise (UK) or factor (US) - see Colin Beveridge's post 'Factorise or Factor'.
  • "Resolve into factors x2 - ax + 5x - 5a".
  • "The beginner should be careful not to begin cancelling until he has expressed both numerator and denominator in the most convenient form, by resolution into factors where necessary". 
  • "Resolve 4a2(x3+18ab2) - (32a5+9b2a3 into four factors". 

Diminished
Meaning: made smaller or less.
  • "The sum of -3x, -5x, -7x, -x is -16x. For a sum of money diminished successively by £3, £5, £7 and £1 is diminished altogether by £16".
  • "Divide 105 into two parts, one of which diminished by 20 shall be equal to the other diminished by 15".

Whence
Meaning: as a consequence of which.
  • "Whence the result follows".
  • "Whence x = 1 is the only solution"

Involution
Meaning: multiplying an expression by itself.
Evolution
Meaning: the operation of finding the root of an expression.

Antecedent and Consequent
Meaning: the first and second term of a ratio respectively.

  • "The ratio a:b is equal to the ratio ma:mb; that is, the value of a ratio remains unaltered if the antecedent and the consequent are multiplied or divided by the same quantity".
  • "A ratio is said to be a ratio of greater inequality, of less inequality, or of equality, according as the antecedent is greater than, less than, or equal to the consequent. 
[There are loads of interesting terms in the ratio chapter - including commensurable and subduplicate.]

Transposition
Meaning: The act of transferring something to a different place.
[This hasn't disappeared, but the use of the phrase 'by transposition' or 'transposing' in worked examples is something we don't see in schools anymore].

There are many more words and phrases in this book which seem to have disappeared from the daily mathematical vocabulary of secondary schools - far too many to list here. Whence I will save the rest for another post. I hope you find all this as interesting as I do. No doubt someone will now contact me to say that they use all these words in their classroom on a regular basis...!







7 comments:

  1. Yes, this is an interesting list and thanks for it. I haven't any use for it in teaching just now, but I've been reading some histories or biographies of people from that era and this should help parsing the original quotes.

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  2. Top stuff. I now feel the need to use whence in my classroom.

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  3. Very interesting, Jo - thanks. Yes, 'whence' has gone, but 'hence' very much still here! And, as one who is constantly trying to improve her own maths, what an annoying word that can be at times... On a related note, it's good to see the move back to the use of terms such as 'alternate angle' and 'improper', rather than 'Z-angles', 'top-heavy' etc. Whilst these can help, temporarily, in the teaching of the concepts, too many students in the past have clung to them, and therefore not learned the proper terms. And 'reciprocal' - why have so many assumed that this will make eg primary students cry? They like the impressive-sounding words! Wondering whether 'subtended' for circle theorem could make a comeback? Omitted in some modern textbooks.

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    1. I think that primaries have started moving back towards formal vocabulary recently. It makes sense - young children are very capable of coping with words that adults perceive as complex, as shown by my five year old happily using words like digraph and phoneme.

      I also noticed that subtended is starting to disappear at GCSE, not sure why. What a shame. Formal vocabulary makes our explanations clearer.

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  4. The concept of 'unity' doesn't really appear anymore until you look at 'roots of unity' when studying complex numbers...

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  5. 'Whence' is a great word. I enjoyed your use of it at the end of the post. If Russell Brand were a Maths teacher he would be using 'whence' and perhaps 'forthwith' and maybe 'forsooth'.

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  6. Interesting list and fun way to learn new vocabularies.
    Thanks for sharing :)

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