National Council of Teachers of Mathematics

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 langu

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ar graphs showing the number of problems solved correctly. Specialized terminology (for example: some some more, some some went away, and equal groups) used by Saxon to show relationships between word problems does seem to help students recognize patterns in real-life problems. Applying the mathematical label gives students an ideal of how to figure out a solution. Successfully finding solutions to their own problems gives students confidence in their own abilities in mathematics and increases their self-esteem. The third goal is that students will become mathematical problem solvers is building on the same tools used to increase students' confidence in their own abilities. As students experience being competent in mathematical skills and concepts, they apply these to the problems that they encounter in their own lives. This is an area where the Saxon text is weaker. It does not supply real-life situations where mathematics can be used, except for the word problems given in the practice sets. Enterprising teachers may use cross-curriculum studies to supply these problems. In the science unit on the geology of the earth, students can brainstorm ideas on how to build a model of the earth. Different solutions can all be co

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