The National Council of Teachers of Mathematics has produced a list of five goals which students in a well-taught classroom should achieve. This paper will outline how these five goals can be attained by students in a fourth-grade classroom using the Saxon text, Math 54: An Incremental Development (Hake & Saxon, 1996). Examples of how to incorporate each goal individually into the class's lessons will follow.
A good mathematics curriculum will help a teacher instill these goals in students. The best method of disseminating these goals to students is within the context of mathematics study and through opportunities for cross-disciplinary teaching; the five goals cannot be effectively taught in isolation from one another or from other subjects.
The five goals can be summarized as follows:
1. Students will learn to value mathematics.
2. Students will become confident in their own ability to use mathematical concepts in their daily life.
3. Students will be able to solve problems using mathematical concepts and solutions.
4. Students will learn to communicate mathematically.
5. Students will learn to reason mathematically (National, 1991).
The five goals build on one another in a non-linear fashion. A student will not be able to reason mathematically if that student is unable to think or communicate using mathematical terms and ideas. Likewise, students will not be able to use mathematical concepts and ideas to solve problems if they have not learned the language and vocabulary associated with the mathematical model and the arithmetic skills necessary.
The language of mathematics must be employed in the classroom whenever it is applicable. This implies cross-curricular teaching in order for students to be exposed to the flexibility of mathematical terminology and to understand how problems in other subjects can be made simpler by the way that they are framed or presented. Cross-curricular...