Monday, September 23, 2013

Principles and Standards

Representation, as articulated in Principles and Standards for School Mathematics, describes how the understanding of mathematics is advanced when concepts are explored in a variety of forms including symbols, graphs, tables, and physical models, as well as spoken and written words. For 8th grade algebra, I use the function-based approach which explores the concept of functions in a variety of forms. Representation may be reflected in a variety of forms such as using manipulatives to model a mathematical idea, expressing an idea verbally, using symbols to rewrite an idea as a mathematical expression, creating tables to show different values an expression may take, and making a graph to give a picture of what is happening in a relationship. Students’ representations shed light on their thought process, and how they organized and approached the problem. Therefore, it is essential that teachers to encourage students to engage with the mathematics and represent their mathematical ideas in ways that make sense to them. Teachers should also encourage the use of multiple representations and technology-assisted representations. Professional development is a major focus of NCTM. Deepening content knowledge enhances student learning by enabling me to anticipate questions, to understand the root of misunderstandings, and to ask deep and open questions.