Venn diagrams everywhere

I love how often we see venn diagrams in a variety of different contexts. I think they are seen as particularly powerful visualisations and rightly so. Like most mathematics in the media though, I wonder how often people stop to ask questions of them. Sometimes the questions I might ask might be seen as trivial - asking them just because I can, otherwise though I think the lack of questions might reflect the lack of understanding in the visualisation. On the one hand - misuse or or lack of questioning of this is a concern, on the other, as a mathematics teacher, it is a gift for us to bring that kind of relevance to our classrooms. I am just going to show a couple here to deomonstrate my points.

The Wiki Tribune

This is a really exciting project and I am going to support it. If you don't know about it then read here - The WikiTribune. Of course you will have seen the Venn diagram in the article. I hope they dont mind me using it. Clearly it is theirs and I am referencing it...... What are the questions we want to ask about this diagram.....

Are all the possible intersections shown?

What is left out?

Does it matter?

What do the blue areas represent?

What other sets might we include here?

Can the wikitribune reallyy rest entirely in the set of 'facts'

.....

What other questions does this venn diagram provoke? Doubtless we would come up with different answers to the one I have asked.....

The great education debate

I spend quite a bit of time on twitter, or particularly those parts related to education. There is a debate raging about differences between 'Progressive' and 'Traditional teachers'. I am certainly not going to offer my views on that in this blog post - I find it interesting on some levels and frustrating on others. A number of people are suggesting that it could be seen as a false dichotomy. In any case, it prompted one such teacher to produce this Venn diagram....

My instant thought was about the lack of a defined Universal set of 'Things that teachers do'........... Again, I am not complaining, just asking questions. If our students saw it, they would say (hopefully) that both not P and not T should include the area outside the two sets offerred. Again, I find myself asking if this matters, but in any case it prompted me to ask questions!

A thought

And finally, I will share with you a diagram I produced to give a presentation about what we do in our maths department. Even my own diagram made me ask lots of questions and in many ways, I made use of general understanding of Venn diagrams to visualise a point I wanted to make and maybe didn't stick to all the protocols I should have..... 

In conclusion, I ask to what exetnet are we allowed to be flexible with the 'protocolas' of mathematical diagrams in order to help communication. In doing so there is an implication that perhaps mathematical diagrams in their purest form don't communicate as well as they might? All just questions and certainly no criticism of the Venn diagrmas used is intended or implied. We teach Venn diagrams, the mdeia uses them. That is a good combination as far as I am concerned.

Now I am looking for the ToK angle,

cheers!