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 middlegrades students a oneyear course
that focuses narrowly on algebra or geometry. However, all
middlegrades
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.
Middlegrades 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 middlegrades 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.