[Maths-Education] Ratio and Proportion

[Hugh.Burkhardt@nottingham.ac.uk]

Nice one, Dave

"God made the natural numbers.
All the rest is Man's work."
	Kronecker

(Women might have been more sensible.)


Formal technical definitions can be helpful, but only when they are 
widely agreed.
Fine distinctions tend not to be -- as here.

Does anyone doubt that this distinction is sterile?*

"Proportionality" involves not just two but a fairly complex network 
of interlinked concepts, representations and contexts.

As always, growing understanding (always incomplete) is about 
building lots of the connections.

As always, students need to learn to be streetwise -- and only to 
humour pedants when they have power.

Bottom line.  Has anyone seen a recent question in a 'serious' exam 
which asks for a formal distinction between Ratio and Proportion?  I 
hope not

Hugh

*   It may  nonetheless worry some students.

I remember, as an undergraduate, often wondering why no-one explained 
the difference between "Wave Mechanics" (Year 2) and Quantum 
Mechanics" (Year 3).  I only learned in graduate school that, if you 
try to make one, it is not useful.

Similarly, eg "oblong" v "rectangle".
This kind of example can lead into a useful, indeed essential, 
discussion of the difference between technical and informal language 
( which many students still never meet; they think that maths has to 
be exdactly the way it is) including the cost-benefit analysis of 
whether to define a "square" as one or not.