venn style thinking
TRANSCRIPT
Venn-style thinkingAn example of mathematical thinking beyond the narrow world of numbers.
Dave C, 2013.
Beneath the numbers that make up mathematics lies a philosophy that goes far beyond simple counting, and teaches us (if we let it) how to measure a social situation.
Let me give you a few examples, starting with this one: the Venn Diagram.
The Venn diagram protects us (if we let it) from falling into the trap of seeing a debate as simply having two sides. Take any controversial issue that you hear discussed on TV; there are champions for one side and champions for the other, neither party allowing for the possibility that there could be any solution other than we-win you-lose.
The issue could be Charter Schools versus Public Schools. One or the other, we would think.
Maybe the solution is Charter Schools, end of story.
The issue could be Charter Schools versus Public Schools. One or the other, we would think.
Maybe the solution is Charter Schools, end of story.
Maybe the solution is Public Schools, end of story.
Maybe the solution is BOTH Public schools and Charter schools.
Maybe these two systems serve different groups within a given society and allow more kids to succeed despite their differences. The BOTH solution allows for diversity.
Maybe the solution is EITHER Public Schools or Charter Schools.
Maybe it doesn’t matter who pays the teachers and sets the rules; any kind of schooling is beneficial.
Or maybe the solution is NEITHER Public Schools or Charter Schools.
Maybe both options fail to address the basic issues. Arguably, this could be that institutionalising education is wrong, and so debating which kind of wrong is therefore pointless.
That’s five different ways of answering what looks like a YES-NO question. But there is another solution suggested by mathematics: the NULL solution.
The NULL solution is not the same as the NEITHER solution. The NEITHER solution lies outside the two circles, whereas the NULL solution lies nowhere and everywhere, existing as a region so small it covers no territory.
The NULL solution says “The question makes no sense”. Like looking for the Inverse Sine of 2 or the number of times zero divides into 2, the NULL solution says, “The question was poorly stated; it has no answer.”
In the case of the Charter School/Public School debate, the NULL solution could mean that “It’s not whether these schools exist but rather how you choose to manage them”. Maybe Charter Schools and Public Schools are only as good or bad as people choose to make them. Maybe both systems of education lend themselves easily to mismanagement, deliberate or accidental.
Perhaps the question should not be “Do we have Charter Schools at all?”, but rather “How do we ensure that Charter Schools are run well?”
And what do we mean by saying “run well”? Does it mean exam scores are high or that the kids are happy, or that the school is making a profit?
And if we can ask these questions of one side, should we not ask these questions of the other side too? That is, shouldn’t we ask the question, “How do we ensure that PUBLIC schools are also run well?”
And what does it mean to run a public school ‘well’? Is it sufficient to cover all your expenses and make a profit? Or are there subtle agendae that lobbyists on each side of the school systems debate want to promote at the expense of clear rational thinking?
I’ve latched onto the debate of Charter Schools versus Public Schools because it is topical in my community at the moment. But the tool that I am illustrating with this example could be – and should be – applied to all situations where two sides of a debate emerge, and seem to be sinking into a swamp of vitriol.
What about the debate over nationwide standardised assessment in education? Maybe it’s not the existence of standardised exams, but rather how these exams can be implemented in a way that does no damage. That’s the NULL solution.
On the other hand, maybe it’s BOTH, EITHER or NEITHER. Maybe schools should decide for themselves whether they want to adopt ‘national standards examinations’, in which case families that like exams are supported as much as families that don’t. That’s respecting diversity. That’s the BOTH solution.
The EITHER solution implies that it doesn’t really matter whether kids are examined or not: an education is an education and will work for a kid, or fail him, regardless of the exam process.
The NEITHER solution implies once again that schooling of any kind is bad, and while I don’t believe this no matter how long I consider the idea, at least considering the idea at all makes me a bit wiser.
People dislike exams because of the damage it does to some kids. Okay, but is it the exam that damages the kids or the forced education that is damaging the kids? Maybe it’s the entire school system that is damaging kids, in which case the forced end-of-year exam is just another brick in the Pink Floyd wall?
Wherever you stand on these issues, and other issues too, I want to suggest to you that Venn-style thinking will widen the scope of your focus to include more possibilities and perhaps arrive at better solutions. But more importantly, I want to show through this example that there is value to learning the philosophy that accompanies mathematical thinking, and that it can be applied in situations that have no smell of mathematics to them.
