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The middle grades represent a significant turning point in students' lives. During the middle grades, students solidify conceptions about themselves as learners of mathematics. They arrive at conclusions about their competence in mathematics, their attitudes, their interest, and their motivation. These conceptions will influence how they approach the study of mathematics in later years, which in turn will affect their later career and personal opportunities.

If middle school students find both challenge and support in their mathematics classes, they will be drawn to the subject. They will be able to use their emerging capabilities of finding and imposing structure, conjecturing and verifying, thinking hypothetically, comprehending cause and effect, and engaging in abstraction and generalization.

As in all the grade bands, students in the middle grades need a balanced mathematics program that encompasses all ten Standards, including significant amounts of algebra and geometry. Algebra and geometry are crucial to success in the later study of mathematics and also in many situations that arise outside the mathematics classroom. Students should see that these subjects are interconnected with each other and with other content areas in the curriculum. For example, students might be asked to explain the number of tiles that will be needed to make borders around pools of various lengths and widths, as in figure 2. Students might develop various formulas to express this relationship on the basis of a table or their reasoning about the situation; for example, "You need L + 2 tiles across the top and the same number across the bottom. And you need W tiles on the left and the right. So all together, the number of tiles needed is T = 2(L + 2) + 2W."

 Fig. 2. The "swimming pool" problem

Students' understanding of these crucial ideas should be developed over all three years in the middle grades and across a broad range of mathematics content. This approach is a challenging alternative to the practice of offering a select group of middle-grades students a one-year course that focuses narrowly on algebra or geometry. However, all
middle-grades students will benefit from a rich and integrated treatment of mathematics content. By the end of the eighth grade, students should have a solid background in algebra and other areas that will prepare them to enter substantive high school courses.

Middle-grades mathematics also needs to prepare students to deal with quantitative situations in their lives outside school. For example, consumer magazines regularly publish comparisons of characteristics of various consumer products, such as the quality of peanut butter, the duration of rechargeable batteries, or the cost, size, and gas mileage of automobiles. When using data from such sources, students need to determine which data are appropriate for their needs, to understand how the data were gathered at the source, and to consider limitations that could affect interpretation.

Special attention must be given to the preparation and ongoing professional support of middle-grades teachers. They need a deep understanding of mathematical ideas, pedagogical practices, interdisciplinary teaching approaches, how students learn mathematics, and adolescent development. States and provinces need to give much more attention to the development of special preparation programs for teachers of mathematics in the middle grades.

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