Classroom Compass
Volume 3 Number 3
Spring 1997

Mathematics in the Middle Grades: Excerpts from NCTM Standards

Number and Number Relationships Geometry Algebra

Curriculum and Evaluation Standards for School Mathematics from the National Council for Teachers of Mathematics (NCTM) provides recommended levels of mathematics understanding for students in grades K-12. In most instances, the NCTM Standards recommends levels for eighth graders that correspond to the TIMSS questions.

Number and Number Relationships

In grades 5-8, the mathematics curriculum should include the continued development of number and number relationships so that students can ­ Understand, represent, and use numbers in a variety of forms (integer, fraction, decimal, percent, exponential, and scientific notation). In the middle school years, students come to recognize that numbers have multiple representations, so the development of concepts for fractions, ratios, decimals, and percents and the idea of multiple representations of these numbers need special attention and emphasis. To provide students with a lasting sense of number and number relationships, learning should be grounded in experience related to aspects of everyday life or to the use of concrete materials designed to reflect underlying mathematical ideas.

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Geometry

In grades 5-8, the mathematics curriculum should include the study of the geometry of one, two, and three dimensions in a variety of situations so that students can ­ Identify, describe, compare and classify geometric figures. Students discover relationships and develop spatial sense by constructing, drawing, measuring, visualizing, comparing, transforming, and classifying geometric figures. Discussing ideas, conjecturing, and testing hypotheses precede the development of more formal summary statements. In the process, definitions become meaningful, relationships among figures are understood, and students are prepared to use these ideas to develop informal arguments. The informal exploration of geometry can be exciting and mathematically productive for middle school students.

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Algebra

In grades 5-8, the mathematics curriculum should include explorations of algebraic concepts and processes so that students can ­ Understand the concepts of variable, expression, and equation. Understanding the concept of variable is crucial to the study of algebra; a major problem in students' efforts to understand and do algebra results from their narrow interpretation of the term. Many students assign a numerical value to a letter from the start; others ignore the letter, and still others treat the letter as shorthand for an object (b means boy rather than number of boys). Students need to be able to use variables in many ways. Two particularly important ways in grades 5-8 are using a variable as a placeholder for a specific unknown, as in n + 5 = 12, and as a representative of a range of values, as in 3t + 6.

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These excerpts are from Curriculum and Evaluation Standards for School Mathematics. Order from NCTM, 1900 Association Drive, Reston, VA 22091. Telephone: 1-800-235-7566.