Abstract
The purpose of this research is the unit of the junior high school mathematics “square root” and is to make the aspect of the learning process of the student who interprets the meaning of the square root clear using the point of view of representation and a way of thinking. Because a way of a study considers a square root by the operation activity that I have synthesis of representation in a mathematical background, expresses the act by a word and becomes a target, the mathematical activity that the meaning of the square root is understood is performed. And because the student’s characteristic activity that this learning process can see and a description thing are analyzed qualitatively, the aspect of the learning process is made clear.
As a result, the following 3 points became clear.
(1) The operation activity that I have synthesis of representation in a mathematical background and the activity that I express the act in a word and become a target respectively deepen their understanding about the meaning of the square root.
(2) You can replace double meaning understanding with something abundant using the point of view of multiplication as synthesis of representation.
(3) Foundation formation to the learning which understands the meaning of the multiplication of an insight to learning of“ the Pythagorean theorem” and learning of radical root and a complex number at least is born by the operation activity that I have synthesis of representation in a mathematical background and target-ization of the act.
