Representations

Representations - Marissa McCarty

The representation standard addresses the ways in which mathematical ideas are represented. The standard emphasizes that the process is just as valuable as the product. The standard states that when students gain understanding of using mathematical representations to solve problems, they gain a set of tools that will help to expand their skills for problem solving in many areas including mathematics.

Instruction for all grade levels (kindergarten through grade 12) should help students to be able to: As students progress through the grade levels, their understanding and use of representations should progress as well.
 * use problem solving to build mathematical knowledge;
 * solve problems in mathematics and other areas as well;
 * use various strategies to solve problems; and
 * reflect on the process of how to solve a problem mathematically.

Students Pre-K-2 should be able to create and use representations to organize mathematical ideas. They should be able to apply and translate mathematical representations in order to solve problems. Young students should be able to represent their thoughts into drawings, oral and written language, and invented and conventional symbols. While the emphasis is on students learning the standard mathematical symbols they should be able to explore other representations as well. Outside of just mathematics, students in this age group should be able to use representations to model physical and social phenomena as well. As a teacher, you should look to students' analysis of representations in order to gain understanding of their insights and development in mathematical thinking.

Students grades 3-5 should be able to use various types of representations of mathematical ideas. They should use these representations to investigate mathematical relationships. In this age group it is important to show understanding of multiplication and place value through the use of mathematical representations. Students should work with standard kinds of representations including charts, graphs and equations to model and solve problems. The use of representations will help students to explain to others how they were able to get the answer. Representations serve as a tool for building problem solving abilities. Students should start to work with mental images as well as external ones.

Students in grades 6-8 should be able to deepen their understandings by creating and comparing different forms of representations. In the middle grades, representations should be used in every aspect of mathematical problem solving. Students should be using representations to show the understanding of linear relationships as well as proportionality. These students should be able to show flexibility in their representations by using tables, graphs and different equations to show their understanding of the problem. Students should start to use representations for exponential and scientific notation when appropriate.

Students in grades 9-12 should be able to chose the correct representation to achieve the desired goal. Students in these grade levels should have a quite extensive base of representations that they understand. At this level students should understand that graphs are good for showing information visually where symbolic representations are easier to work with and use the correct one for what you are trying to solve. The most important part at this grade level is that students are able to chose the right representation in order to achieve the desired goal.

Examples of Representations include: 1. Students in grades 3-5 could see a lesson worked out as such: Hopping on the Number Line 2. Students in grades 9-12 could see a lesson worked out as such: [|Domain Representations]