## 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
• "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...!

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.

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

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.

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.

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

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'.

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