The role of representations

In the article, two kinds of mathematical representations are included such as external and internal representations. Both representations are influenced by each other. The representations facilitate the students' ability to make a comparison. Students can formulate internal representations to solve problems and to understand math ideas. Besides, representations help us understand external manifestations of math concepts such as graphs, algebraic equations, charts, and tables. Only teacher-oriented presentations are excluded from this article.

The representations include many activities. Social activities enhance students’ ability to interpret, communicate effectively through external and internal representations so that students can understand the process and its products. The activity Pictures theory, the use of visual and concrete modes of representation, and culture activities help students to understand math concept through their own experience. Moreover, students have the opportunity to interact with one another and the teacher due to these representations. Representations play an essential role in understanding math. 

I can use arrays multiplication concepts of a mathematical representation (from grade 3) that might be helpful for students in developing understanding. Arrays are useful representations of multiplication concepts.

For example, the array has 4 rows and 5 columns. Students notice that the groups in each array are equal and think of the rows as equal groups. My students will use equal groups to multiply 4 by 5. Students have 4 groups of counters and each group has 5 counters, students will add them together they have a total 20 counters.