Last week I wrote a post covering a Washington Post editorial decrying the apparent (and seemingly noticeable) lowering of academic standard in college grads (and by inference almost all schools from K-12, and beyond). We seem to be teaching facts, and a sort of static manner of solving problems (which have concise answers in the back of the book…). Now, mind you, this is not some sort of a diatribe against all forms of education (whether college or not), it is about the idea of teaching students how to think.
We all think we understand this topic (we are all thinking…right?), but there are a wide variety of cognitive modalities and forms of what we could call ‘critical thinking’, ‘problem solving’, ‘deep thinking’, ‘creative thinking’, and so on… In many ways, most of these mental activities are often different to the degree that they are nearly antithetical to each other.
There is a need to have some sort of a foundation for some of these forms of cogitation. And in this regard, something which has always perplexed and bothered me is that math is surely a prime part of this foundation and that this is an idea which I have never seen espoused by a math teacher.
Math is usually presented as…a game, some rote memorization (through endless drills), a means to solve simple problems you might find at home or in some job… the fact is that the study of arithmetic and algebra have longer term results that ‘knowing which of two trains arrived at the station… the underlying logic of transitive, distributive, commutative, and associative laws as well as some of the general methods one uses to solve basic algebra problems slowly sink deeper and deeper into our consciousness. This gives some semblance of order to problem solving (whether apparent or not).
On then other hand, the ability to ideate in a really creative ‘out of the box’ manner is often based upon conflating disparate ideas, concepts, and object in what are ‘new’ ways. The means to develop some of these skills would seem to describe the superficial divide between art and math classes…
In education there are some pretty well known concepts and practices based upon such ideas as Bloom’s Taxonomy, open ended questions, and the Socratic method of questioning. Form my own personal experience; I have had few opportunities to observe these methods…when I was a student, or even when I was a teacher.
My own experience would seem to push me towards the notion that this is yet another of those ‘elephants in the room which nobody notices’. Another way of stating this would be to take notice of the methods used by whatever State teacher of the year uses… Almost every ‘good’ teacher I have met is quite focused upon these methods (whether in secondary school or college).
hmmmm
