Abstract
In this study we clarify the real state of a bidirectional viewpoint of children in
the learning of the ratio, design an instruction for a bidirectional viewpoint in consideration of
the real state and clarify the effect of this lesson. We carried out the examination on
"comparison of height" for fourth and fifth graders who haven't learned ratio. As a result, we
found out that it was difficult to look from a bidirectional viewpoint in the comparison by the
ratio for children and that it was easy to focus on the double and 0.5 times for them. Through
the lesson practice for a bidirectional viewpoint, we also clarified that this lesson was effective
for problem-solvings of ratio because it let children recognize the basic quantity correctly.
