Abstract
The purpose of this study is to examine whether a mapping-style lesson process model would enhance children’s ability to think progressively from the viewpoint of integration, and to create a deeper learning of mathematics, in contrast to earlier practices where integration and progression are captured in parallel.
A lesson for this purpose was planned and carried out in a 5th grade unit of " formula and calculation ". Initially, the number to multiply and the number to be multiplied are inductively considered by changing the condition of a side of an equilateral triangle that is made of, for example, 4 or 3 marbles, where the word expression of equation is generalized as “ (number of marbles in a side-1) x 3.” To further expand the range of the formula’s application, pupils then find the formula for squares in an integrated and progressive way by utilizing their experience in creating formulae for equilateral triangles. Furthermore, based on the formulas for the equilateral triangles and squares, pupils also consider the case of a pentagon from an integrated point of view, and generalize the fact that the number to multiply is the number of sides of the shape in a word expression of the formula.
Through this practice, we found that a lesson development, in which the subject level gradually becomes harder without any unreasonable jump using the mapping-style lesson process model, is able to further their learning; pupils are able to progressively connect the triangle formula to different polygons from an integration viewpoint.
