Abstract
This article considers about the important examples of the cognitive load-obstacle arising in a process of mathematical generalization. In Section 2, I explain the summary of basic theory of mathematical generalization while giving four basic styles of mathematical generalization. In Section 3, at first, I list five basic cognitive load-obstacle arising in a process of generalization. Next, I give six important examples of the cognitive load-obstacle arising frequently in the situations of arithmetic/mathematics teaching-learning. Those examples are as follows. Example 1 is an example of the cognitive load-obstacle arising when substitute a number for a letter of a literal expression among many cognitive load-obstacle arising in a process of expansive generalization. Example 2 is an example of the cognitive load-obstacle arising when we force children to think of the meaning of an equivalent system needed when generalize number concept. Example 3 is an example of the cognitive load-obstacle arising in the process that generalize a=a to b=a or F≡F to G≡F. Example 4 is an example of the cognitive load-obstacle arising from cause that the mental image must tranfigure by generalization of figure concept, but it is not able to succeed. Example 5 is an example of the cognitive load-obstacle arising from cause that it is not able to notice that disjunctive generalization occur necessarily from expanding a set of the objects of consideration. Example 6 is an example of the cognitive load-obstacle arising from cause that generalization is impeded by specializing a figure I show some similar examples for each example. In Section 4, I point out about the problems of the actual teaching-leaning as follows. Children who can't overcome the cognitive load-obstacle, as described in Section 3, can't gain the mathematical concepts generalized. However, in no little daily teaching-learning, before children overcome the cognitive load-obstacle, many teacher give the general formula and the solution of problem for children or give many exercises to make children avoid these cognitive load-obstacle. I make these educational problems clear by the flow chart with two different learning route to gain a problem solving.
