Entry Slip (Sep 25th)---Mathematical understanding and multiple representations

After reading the article " The Role of Representation(s) in Developing Mathematical Understanding", I understand that mathematical representation is a very important tool for understanding and communication, and it can help students to better understand mathematical concepts. I am convinced by authors' argument about the mutual influence between the two forms of representations. The external representation such as number, graphs, equations and charts could help students to gradually build of mental images, and then understand mathematics concepts. On the other hand, internal representation such as mental image and idea could help students  to solve problems through externalizing of mental images. As stated in the article " The development of students' mathematical understanding and representational thinking requires the combination of multiple representations as well as the interaction of both internal and external representations".(p.126)

In this article, authors introduce several external and internal mathematical representations. For example, numbers and sets, blocks and symbols. I think one of the mathematical representations not included in this article is number line. Using number line could be helpful in fostering children's number sense especially when we teach children addition and subtraction. By moving around on the line, students can have the mental image of how many increased or decreased. And number line is convenient to be used in the daily life. When students use ruler, they can use the knowledge of number line to make measurements. When they walk on the street, they can use the idea of number line to estimate the journey. 

In the Math classroom, teachers need to try to use multiple representations to try to facilitate students' understanding of mathematical concepts, and "emerge out of [students]' interaction with the social and material settings of activity. (p.124)