Wednesday, January 03, 2007

thinking about thinking - creativity, problem solving, and learning styles

One of the books I’m in the middle of reading is Archimedes’ Bathtub, by David Perkins, which is a study of breakthrough thinking. I find the subject of problem solving and thinking skills fascinating and wish my kids’ schools spend more time teaching how to think. You may think that that sounds ridiculous – we all seem to naturally mature and figure out how to think, so why should it be taught in school? But in reality, some of us are better thinkers than others, and this is undoubtedly because we employ certain strategies and problem solving techniques (heuristics) better and faster than our peers. Aside from the techniques that go into regular problem solving (e.g. when a teacher says “think about it” – what does that mean? the student sitting in the back of the room staring out the window probably simply does not have a clue!), Perkins focuses on a special type of thinking to address problems that cannot be solved following a sequence of logical steps. These problems demand a creative leap, an insight – are there techniques that can help foster this type of thinking as well?

An example of these type of problems are the lateral thinking puzzles inspired by Edward de Bono’s research, e.g. by adding only a single straight line to this equation, how could you make it true?
5 + 5 + 5 = 550
Obviously, a linear approach does not work – no matter how you rearrange the terms, 5+5+5 still equals 15. Before you can solve this type problem you need to come up with a different way to view the facts – a creative insight (sorry, no hints!)

Edward de Bono thought lateral thinking could be taught and devised a number of techniques that are quite interesting. I am curious if anyone out there knows of a yeshiva classroom that uses de Bono’s “six thinking hats” technique – that teacher deserves a medal!

What I find amazing and which the book does not touch on is the impact differences in learning style have on creative thinking. Without getting into detail, brain research shows that there are 2 basic variables that determine your learning style: 1) whether your preference is for the concrete or abstract; 2) whether your preference is for sequential or random information. There are various tests that predict your learning style within the matrix of these 4 variables, and of course, I once had to try one on myself and my wife (as an aside: it might be a better shidduch predictor than this). My wife is a definite abstract random; I also have an abstract preference, but have only a very slight preference toward randomness over sequence. I was able to predict in advance that a puzzle in Perkins' book like the equation above that I could solve just by looking at it left my wife confounded, but another problem which took the form of a word story left me lost while she solved it as soon as I was done reading the words.

In my home this is known as the “Walt has a split personality” effect. My wife and I were once both simultaneously reading an Ellery Queen mystery (I forgot the title and apologize if by coincidence I am about to ruin a good read for someone) in which one of the main characters was named Walt. I was almost at the end of the book and was stumped. When my wife got to the same point in her reading she immediately saw that the solution to the mystery was that “Walt has a split personality.” True, I might have been biased because I knew that split personality disorder is extraordinarily rare, but I think the more likely explanation is that her abstract-random bias gave her an edge at the insight I was missing with my more linear learning style.

I recall going to parent-teacher orientation at the beginning of this year and hearing my son’s rebbe talk about how the boys this year will mature and really learn to think. Of course, he provided no detail as to how he was going to foster that process along – I doubt he really thought about it before and probably assumed learning to think is something that just happens with the teacher as a passive observer, not an active participant in encouraging. Aren't the basic skills of problems solving, thinking, and reasoning more worthy of a teacher's consideration and curriculum planning than any single set of facts that he/she might impart during the course of a school year?


  1. Arthur Digby Sellers7:45 PM

    How about 5+5+5 does not (= sign with a slash through it) equal 550? Does that count? I solved it with a single straight line (a slash) :)

  2. Yes, that indeed counts. How about finding a second solution (I got the same one as you, but there is another one as well)?

  3. Arthur Digby Sellers12:34 PM

    Ok, I give up...can you tell us the solution?

  4. Change the first + sign into a number 4 by adding a vertical line to the upper left of the symbol. 545+5=550