[Maths-Education] Ratio and Proportion

[Dick Tahta]

Seventy years ago,  Henri Lebesgue wrote scathingly about  the doctrine
that distinguishes ratio from the number that measures it .... " a
distinction to which certain people hold strongly and which appears comical
to me".   For him ratio and proportion were historical relics, the
preservation  of which led him to describe mathematics as "no longer a
monument but a heap".

The OEC lists at least nine usages for the word "proportion".   The first -
a relation of part to whole - goes back to Chaucer.  There are some
historical mathematical usages,  some of which earned the scorn of another
Frenchman, Lagrange.  The only currently relevant mathematical meaning is
that of the original Greek word alogon  (= sameness of ratio, and so for
Lebesgue equality of decimal number).  It is  scandalous that the compilers
of NNS Key Stage 3 should be invoking a literary rather than a mathematical
sense.  Is it known who the author(s) of this particular betise might be?
Can he/she/they be named - and shamed?

Dick Tahta