Special thanks to Deb Armitage, Exemplars consultant and task contributor/editor, for her contribution.
Title I teachers are often challenged with assessing students' mathematical understanding. Traditional worksheets, chapter/unit tests, and norm-referenced tests typically do not provide enough support in discovering what a student truly understands about mathematical concepts. Teachers have found much needed support from the research of the National Council of Teachers of Mathematics (NCTM) and Exemplars.
Like the NCTM standards, Exemplars material places a greater emphasis on the "process standards." By focusing on mathematical problem solving and communication, Title I teachers are able to look more closely at what students' work shows about their mathematical understanding. A stronger emphasis on process encourages teachers to demonstrate and support students in learning a variety of strategies for solving a problem. Exemplars encourages students to show different methods for solving problems. A variety of approaches allows teachers and students to discuss the merits of each strategy. The individual student can then embrace an approach that s/he is comfortable using to determine a correct outcome. By encouraging communication in mathematics, Title I teachers are better able to pinpoint where problems in students' thinking arise and can provide more meaningful feedback as a result. This feedback then encourages students to focus on areas that need improvement.
The process of problem solving and communication helps students gain confidence in their ability to solve problems. Shifting the major emphasis from finding the correct answer (only) and placing it instead on the process and communication of "thinking" improves the mathematical disposition of many students. Increasingly, Title I students become more comfortable with mathematical problems when they have a "tool kit" of possible strategies to consider, an understanding of mathematical language, and a belief that their way of solving a problem is just as valid as a neighbor's strategy.