Dienes Theory in Mathematics Learning

This is the example of Dienes theory in mathematics learning about the number of diagonal in polygon. The purpose of the learning is to understand the number of diagonal in polygon.

Based on Dienes Theory, the stages are:
1.    Free Play

In this stage, students are given freedom by the teacher to draw triangle, quadrilateral, pentagon, and soon in their book.

2.   Games

In the stage, teacher gives a rule. The rules are:

• Draw diagonal of each polygon. As we know, a diagonal is a line segment connecting two nonadjacent vertices of a polygon.

• Find the number of diagonal in each polygon
  

3.    Searching For communalities

In this stage, students find the similarity about the number of each polygon.

4.   Representation

After students get the similarity about the number of each polygon, in this stage student can represent the figure as below.

5.   Symbolization

In this stage student symbolize the formula of pentagon’s diagonal number from the pattern that they get.

side	3	4	5	6	n	n
number of diagonal	3(3-3) = 0	4(4-3) = 0	5(5-3) = 0	6(6-3) = 0	……….	n(n-3) = 0

6.   Formulation

This is the last of the stage. Student can apply the general formula to another case, such as they can determine the number of polygon with side 23.