Abstract
According to Sfard, there are two different points of view, the "structural" conceptions and the "operational" conceptions, to the mathematical concept. When attempting to adapt this points of view to the algebraic expression, it regards as one object (result) about whether or not it regards a expression as the operation (the process). These points of view are same as "structural" and "the procedure" of Kieran. Also, it is synonymous with the concept, "procepto" of Gray & Tall, too. In this study, it considers about the difficulty of which a student is understood which switches over from the operational conceptions to the operational/structural conceptions and the limit of the operational conceptions and the necessity of the structural conceptions are shown. Next, I investigated the difficulty of the algebraic expression with two sides (the process/the result) of under-standing, for junior high school 3rd grader from the 1st grader. As a result, the following became clear. ・The difficulty of the algebraic expression with duality of understanding exists in any grade. ・The difficulty of the algebraic expression with duality of understanding decreases with the rise of the grade.
