L is for Learning the Art of Abstraction

| April 30, 2014

I have spent most of this rainy morning reading through my “primer partner’s” posts in the attempt to come up with a good introduction to her work. As I sit here trying to isolate a common theme which spans her posts, to identify the general approach which characterizes her notes, I realise that there is one major challenge which is intrinsic to this task. One skill, rather, that is necessary in order to write a good introduction; the ability to extract the abstract structure of things.

The extraction of abstract concepts from information is an issue which has been explored by a variety of domains, in particular that of Cognitive Psychology. In the field of psychology, this concept has been investigated in the context of mental models and problem solving. Let me give you an example of a typical experiment which could be used to assess this ability;

Participants would be given a set of problems. For example;

Problem 1: A patient has cancer. In order to destroy the mass of tumour cells, a large amount of radiation is required. However, high amounts of radiation will also damage the healthy tissue surrounding the tumour. How will doctors manage to cure the patient?

Solution 1: Pointing lots of small amounts of radiation towards the tumour from different directions.

Problem 2: An army is trying to invade a fortress which is surrounded by mines. The mines are set so that the heavy weight of a tank will cause them to explode. However, a smaller weight will fail to activate the mines. How will the army succeed in conquering the fortress?

Solution 2: The soldiers can get off their tanks and approach the fortress by foot.

When participants are presented with a similar set of problems, they often fail to spot similarities in abstract structure (i.e. Smaller efforts from many directions solve the problem) and tend to concentrate more on similarities in content. I believe that teaching students to extract abstract concepts from concrete situations is one of the fundamental goals of education, as it gives them tools to take information from one problem and apply it to multiple ones, fostering independence.