[Maths-Education] Ratio and Proportion

[Geoff Roulet]

In response to my (somewhat in jest question) concerning the number of 
vertices, edges and faces on a cone, Rosalie said:

"But this one is a sweet question, provided you don't think about answers 
as 'right' or 'wrong' but just ask students to give convincing arguments 
for an answer. The student could back at us for answering a question with a 
question; they could ask, "When?""

I agree entirely.  My approach to such questions is to take them as 
opportunities to investigate how mathematics has evolved as a human 
enterprise (language) and how it really is not all that precise.  Although 
I see this as a valuable message for teachers and pupils, it is not very 
well received.  I really can not blame them in this time of large-scale 
testing.  They want to know what the "right" answers are since on the test 
there is likely to be little opportunity for the pupils to give convincing 
arguments for their answers.