Idea Seeds #04 - Problems, Convergent or Divergent
A Guide for the Perplexed
Ask any person involved with curriculum development to list the main topics to be covered in the curriculum they are developing and with a high probability ‘Problem solving’ will be one of them. They have been buzz words for some time now. However when you ask these curriculum developers what ‘Problem solving’ entails; the ‘process’ of solving problems or the actual ‘practical solving of real open ended problems’, or both, or something else all together, you will find that many are not very sure at all.
Ernst, (Fritz), Schumacher, in his excellent book titled: ‘A guide for the perplexed’ helped me a great deal in getting to grips with the nature of problems. Some short excerpts from his book will hopefully provide those of you who have not already been exposed to them, with some ’idea-seeds’ to ponder on.
“We know there are solved problems and unsolved problems….. First let us look at solved problems. Take a design problem, say, how to make a two-wheeled, manpowered means of transportation. Various solutions are offered, which gradually and increasingly ‘converge’ until finally a design emerges which is simply ‘the answer’: a bicycle, an answer that turns out to be amazingly stable in time.” The more you study the problem intelligently the more the design ‘converges’ to a single stable solution. He classifies these problems as ‘convergent problems’.
There are other problems, he says, that highly intelligent people set out to study and solve and come up with answers that appear to be exact opposites. He classifies these as ‘divergent problems’. The more they are clarified and developed the more they diverge to the point that the answers contradict each other, and appear to be exact opposites. ‘The education of our children’ he describes as a classic ‘divergent problem’ where some education advisors will say: “Education is the process by which existing culture is passed on to the next generation. Those who have (or are supposed to have) knowledge and experience ‘teach’ and those who as yet lack knowledge and experience ‘learn’ This is quite clear and implies that there must be a situation of authority and discipline. Nothing could be simpler, more logical and straightforward. When it is a matter of passing on existing knowledge from knowers to learners, there must be discipline among the learners to receive what is being offered. In other words, education calls for the establishment of authority for teachers and for discipline and obedience on the part of pupils.”
Education: Freedom vs Obedience
Another group of education advisors will say: “Education is nothing more or less than the provision of a ‘facility’. The educator is like a good gardener who is concerned to make available good, healthy, fertile soil in which a young plant can grow strong roots to extract the nutrients it requires. The young plant will develop in accordance with its own laws of being, which is far more subtle than any human being can fathom, and will develop best when it has the greatest possible freedom to choose exactly the nutrients it needs. Education for these advisors calls for the establishment, not of ‘discipline and obedience’, but ‘freedom’. Here then are the perfect opposites, Freedom (Do as you like.) versus Obedience (Do as I tell you.) that result from ‘divergent problems’.”
The Problem of Opposites can be Transcended
We all know that both of these methods are successfully used to educate children and that some educators are much better than others no matter which method they purport to be using. So how can these opposites yield successful results? ‘Logic’ because of its insistence that if one thing is true its opposite cannot be true does not help here. Fritz Schumacher suggests if you ask good educators to explain to you what you should do to become successful, like them, they will say: “All you need to do is ‘love’ the little horrors.” This means that if you ignore the ‘logic’ and introduce spontaneously the ‘higher human levels’ of love, empathy, compassion, and understanding, then the problem of opposites can be transcended. This means that ’Divergent problems’ cannot be solved in the sense of establishing a ‘correct formula’ or some sort of solution recipe.
Education can Change.
This then is another must-be-understood concept that must be added to your ‘problem solving checklist’, the ability to recognize when problems are ’convergent’ and when they are ‘divergent’. Problems that include a people factor will always be ‘divergent’ and result in many solutions, from complete opposites to anything in between making assessment very difficult in a teaching situation. Because of this most teaching is focused on ‘convergent problems’, and not the real ‘divergent problems’ we are faced with in our everyday lives. Can this focus be changed? It can.
Remember ‘idea-seeds’ are those shown in ‘italics’. Make sure you fully understand what they mean to you and then start thinking about and listing examples of where ‘divergent problems’ have been solved using solutions that appear to be exact opposites. A few examples to start you off:
In Politics think:
- Freedom versus Order;
- Republicans versus Democrats;
- Democracy versus Communism;
- Justice versus Mercy.
- Capitalism versus Communism.
- Entertainment versus Propaganda.
- Nelson Mandela versus all the others.
Most people now have access to the internet which is why not more detail on the people quoted in the text is given. You will find a great deal of information on all the people mentioned in this, and future, articles as they are all famous, or at the very least, well known in their fields of expertise.
More by this Author
Forget about passion and work on finding the balance between being content in yourself and being involved in the big problems in world.
Edna Millay wrote in one of her sonnets about Euclid, that through ‘geometry’ you “can look on beauty bare” and make the links between it and ‘nature’s wonders’.
Heed , Nobel Laurette in Physics, Richard Feynman's wise words: “Learn by trying to understand the innumerable little and simple things you see around you in terms of other ideas.”
No comments yet.