Standard 5: Number and Number Relations
from the NCTM Standards

In grades 5-8 the mathematics curriculum should include the continued development of number and number relationships so that students can understand and apply ratios, proportions, and percents in a wide variety of situations.

In the middle school years, students come to recognize that numbers have multiple representations, so the development of concepts for fractions, ratios, decimals, and percentages and the idea of multiple representation of these numbers needs special attention and emphasis. The ability to generate, read, use, and appreciate multiple representations of the same quantity is a critical step in learning to understand and do mathematics. 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. Students should encounter number lines, area models, and graphs as well as representations of number that appear on calculators and computers (e.g., forms of scientific notation). Students should learn to identify equivalent forms of a number and understand why a particular representation is useful in a given setting (page 87).

Standard 13: Measurement in the Middle School
from the NCTM Standards

In grades 5-8 the mathematics curriculum should include extensive concrete experiences using measurements so that students can

• extend their understanding of the concept of perimeter, area, volume, angle measure, capacity, and weight and mass
  
  
• develop formulas and procedures for determining measures to solve problems.
  

The development of the concepts of perimeter, area, volume, angle measure, capacity, and weight is initiated in grades K-4 and extended and applied in grades 5-8. From their exploration, students should develop multiplicative procedures and formulas for determining measures. The curriculum should focus on the development of understanding, not on the rote memorization of formulas (page 116).

As students progress through grades 5-8, they should develop more efficient procedures and, ultimately, formulas for finding measures. Length, area, and volume of one-, two- and three-dimensional figures are especially important over these grade levels (page 118).

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

Science Education Program Standards
Excerpts from the National Science Education Standards

The program standards are criteria for the quality and conditions for school science programs. They focus on issues at the school and district levels that relate to opportunities for students to learn and opportunities for teachers to teach science.

In an effective science program, a set of clear goals and expectations for students must be used to guide the design, implementation, and assessment of all elements of the science program. A science program begins with the goals and expectations for student achievement; it also includes the selection and organization of science content into curriculum frameworks, ways of teaching, and assessment strategies. The goals for a science program provide the statements of philosophy and the vision that drives the program and the statements of purpose that the program is designed to achieve.

Curriculum frameworks should be used to guide the selection and development of units and courses of study. The curriculum framework provides a guide for moving the vision presented in the goals closer to reality. Teachers use the guide as they select and design specific school and classroom work. By specifying the sequence of topics in the curriculum, the guide ensures articulation and coherence across the curriculum. Using the framework, teachers design instruction that is based on the prior experiences of students but avoids unnecessary repetition. The framework guides the students as they move through their schooling.

Teaching practices need to be consistent with the goals and curriculum frameworks. The program standards do not prescribe specific teaching behaviors, nor should district or school policies. There are many ways to teach science effectively while adhering to the basic tenets of the National Science Education Standards, but they must be consistent with the goals and framework of the district.

Support systems and formal and informal expectations of teachers must be aligned with the goals, student expectations, and curriculum frameworks. An effective science program requires an adequate support system, including resources of people, time, materials and finance, opportunities for staff development, and leadership that works toward the goals of the program. It is encoded formally in policy documents such as a teacher's handbook and informally in the unwritten norms that determine routines. The support system must support classroom teachers in teaching science as described in the Standards (page 210-211).

The above excerpts are reprinted, by permission of the National Academy Press, from the National Science Education Standards. Copyright 1996 by the National Academy of Sciences, courtesy of the National Academy Press, Washington, D.C.