Function of Diagrams
Given that nearly 38% of the primary school pupils interviewed were successful in solving the problems after simply drawing a diagram, can we identify what function the diagram is playing in these cases? Two elements are involved in comprehending (or undentnding) a problem.
The first arises from the Newmam instruction " Tell me what the question is asking you to do".
This is effectively asking whether the child understands the structure of the problem.
It does not probe understanding of the second element which any involves understanding of the concepts.
lt was clear that some children understood the"sticks" problem in terms of knowing that they had to find the length of the shorter stick but did not have an understanding of the"difference" concept.
From our observations, it appers that the very act of drawing a diagram focuses the child's attention on what the numbers represent rather than the numbers as abstract entities.
In this sense. the function of a diagram may be to act as an altermative form of"expressing the problem in one's own words".
Having focused on the meaning of the numbers and their relationships within the problem, it then appears that the diagram can act as a key aid in the transformation stage.