## NAEP Mathematics Achievement Levels for Grade 12, 1990–2003

Basic (288) Twelfth-grade students performing at the Basic level should demonstrate procedural and conceptual knowledge in solving problems in the five NAEP content areas. Twelfth-grade students performing at the Basic level should be able to use estimation to verify solutions and determine the reasonableness of results as applied to real-world problems. Twelfth-graders performing at the Basic level should recognize relationships presented in verbal, algebraic, tabular, and graphical forms; and demonstrate knowledge of geometric relationships and corresponding measurement skills. They should be able to apply statistical reasoning in the organization and display of data and in reading tables and graphs. They also should be able to generalize from patterns and examples in the areas of algebra, geometry, and statistics. At this level, they should use correct mathematical language and symbols to communicate mathematical relationships and reasoning processes, and use calculators appropriately to solve problems. Twelfth-grade students performing at the Proficient level should consistently integrate mathematical concepts and procedures to the solution of more complex problems in the five NAEP content areas. Twelfth-graders performing at the Proficient level should demonstrate an understanding of algebraic, statistical, and geometric and spatial reasoning. They should be able to perform algebraic operations involving polynomials, justify geometric relationships, and judge and defend the reasonableness of answers as applied to real-world situations. These students should be able to analyze and interpret data in tabular and graphical form; understand and use elements of the function concept in symbolic, graphical, and tabular form; and make conjectures, defend ideas, and give supporting examples. Twelfth-grade students performing at the Advanced level should consistently demonstrate the integration of procedural and conceptual knowledge and the synthesis of ideas in the five NAEP content areas. Twelfth-grade students performing at the Advanced level should understand the function concept, and be able to compare and apply the numeric, algebraic, and graphical properties of functions. They should apply their knowledge of algebra, geometry, and statistics to solve problems in more advanced areas of continuous and discrete mathematics. They should be able to formulate generalizations and create models through probing examples and counterexamples. They should be able to communicate their mathematical reasoning through the clear, concise, and correct use of mathematical symbolism and logical thinking.

Last updated 15 December 2006 (FW)