Table 1 Expected educational effects and methods of transforming

1

Making knowledge stable (target: general phenomenon knowledge)

Let learners use concrete phenomenon knowledge belonging to general knowledge repeatedly.

(iii)

2

Making knowledge stable (knowledge of numerical relationships)

Let learners use the knowledge of numerical relationships repeatedly.

(ii-1)

(v)

3

Learning how to use knowledge of numerical relationships

Let learners apply the numerical relationship knowledge to various situations.

(ii-1)

(ii-2)

(v)

4

Making knowledge stable (knowledge of material concept)

Let learners use the knowledge of material concept repeatedly.

(ii-2)

5

Learning to apply conditions

Let learners become aware of the boundaries of applying conditions by using situations that can apply knowledge (positive example) and/or cannot apply it (negative example)

(iii)

(iv)

6

Learning the hierarchy of material classes

Let learners become aware of material classes by finding the difference among problem solving processes in which a material belonging to the target class appears (positive example) and/or not belonging to the class (negative example).

(iii)

(iv)

7

Increasing learners’ motivation to solve the problem

Making the problem easier with simplification.

(i) Deletion

8

Increasing learners’ ability for complications

Transitioning to advanced problems by making the problems more complicated.

(i) Addition