Appendix C: National Assessment for Educational Progress---Definitions
and Further Information\*

Mathematics Achievement Levels---Grade 4

Basic: Fourth-grade students performing at the Basic level should show
some evidence of understanding the mathematical concepts and procedures
in the five NAEP content strands. Fourth-graders performing at the Basic
level should be able to estimate and use basic facts to perform simple
computations with whole numbers; show some understanding of fractions
and decimals; and solve some simple real-world problems in all NAEP
content areas. Students at this level should be able to use---though not
always accurately---four-function calculators, rulers, and geometric
shapes. Their written responses are often minimal and presented without
supporting information.

Proficient: Fourth-grade students performing at the Proficient level
should consistently apply integrated procedural knowledge and conceptual
understanding to problem solving in the five NAEP content strands.
Fourth-graders performing at the Proficient level should be able to use
whole numbers to estimate, compute, and determine whether results are
reasonable. They should have a conceptual understanding of fractions and
decimals; be able to solve real-world problems in all NAEP content
areas; and use four-function calculators, rulers, and geometric shapes
appropriately. Students performing at the Proficient level should employ
problem-solving strategies such as identifying and using appropriate
information. Their written solutions should be organized and presented
both with supporting information and explanations of how they were
achieved.

Mathematics Achievement Levels---Grade 8

Basic: Eighth-grade students performing at the Basic level should
exhibit evidence of conceptual and procedural understanding in the five
NAEP content strands. This level of performance signifies an
understanding of arithmetic operations---including estimation---on whole
numbers, decimals, fractions, and percents. Eighth-graders performing at
the Basic level should complete problems correctly with the help of
structural prompts such as diagrams, charts, and graphs. They should be
able to solve problems in all NAEP content strands through the
appropriate selection and use of strategies and technological
tools---including calculators, computers, and geometric shapes. Students
at this level also should be able to use fundamental algebraic and
informal geometric concepts in problem solving. As they approach the
Proficient level, students at the basic level should be able to
determine which of the available data are necessary and sufficient for
correct solutions and use them in problem solving. However, these
eighth-graders show limited skill in communicating mathematically.

Proficient: Eighth-grade students performing at the Proficient level
should apply mathematical concepts and procedures consistently to
complex problems in the five NAEP content strands. Eighth-graders
performing at the Proficient level should be able to conjecture, defend
their ideas, and give supporting examples. They should understand the
connections between fractions, percents, decimals, and other
mathematical topics such as algebra and functions. Students at this
level are expected to have a thorough understanding of Basic level
arithmetic operations---an understanding sufficient for problem solving
in practical situations. Quantity and spatial relations in problem
solving and reasoning should be familiar to them, and they should be
able to convey underlying reasoning skills beyond the level of
arithmetic. They should be able to compare and contrast mathematical
ideas and generate their own examples. These students should make
inferences from data and graphs; apply properties of informal geometry;
and accurately use the tools of technology. Students at this level
should understand the process of gathering and organizing data and be
able to calculate, evaluate, and communicate results within the domain
of statistics and probability.

Reading Achievement Levels---Grade 4

Basic: Fourth-grade students performing at the Basic level should
demonstrate an understanding of the overall meaning of what they read.
When reading text appropriate for fourth-graders, they should be able to
make relatively obvious connections between the text and their own
experiences, and extend the ideas in the text by making simple
inferences.

Proficient: Fourth-grade students performing at the Proficient level
should be able to demonstrate an overall understanding of the text,
providing inferential as well as literal information. When reading text
appropriate to fourth grade, they should be able to extend the ideas in
the text by making inferences, drawing conclusions, and making
connections to their own experiences. The connection between the text
and what the student infers should be clear.

Reading Achievement Levels---Grade 8

Basic: Eighth-grade students performing at the Basic level should
demonstrate a literal understanding of what they read and be able to
make some interpretations. When reading text appropriate to eighth
grade, they should be able to identify specific aspects of the text that
reflect overall meaning, extend the ideas in the text by making simple
inferences, recognize and relate interpretations and connections among
ideas in the text to personal experience, and draw conclusions based on
the text.

Proficient: Eighth-grade students performing at the Proficient level
should be able to show an overall understanding of the text, including
inferential as well as literal information. When reading text
appropriate to eighth grade, they should be able to extend the ideas in
the text by making clear inferences from it, by drawing conclusions, and
by making connections to their own experiences---including other reading
experiences. Proficient eighth-graders should be able to identify some
of the devices authors use in composing text.