An assessment framework is like a blueprint, laying out the basic design of the assessment by describing the mathematics content that should be tested and the types of assessment questions that should be included. It also describes how the various design factors should be balanced across the assessment. This is an assessment framework, not a curriculum framework, nor does it address what (or how) mathematics should be taught. This report attempts to determine the mathematical skills that should be assessed in 2009 on NAEP at grades 4, 8, and 12. Following an overview, defining an assessment framework and describing the need for a new framework at grade 12, this report divides into five chapters. Chapter Two, "Mathematics Content," contains descriptions of the five major content areas of mathematics (Number Properties and Operations; Measurement; Geometry; Data Analysis, Statistics and Probability; and Algebra) and specific objectives for grades 4, 8 and 12. Chapter Three, "Mathematical Complexity," examines the three levels of mathematical complexity in NAEP assessment--low, moderate, and high--and offers examples of each. Chapter Four, "Item Formats," describes the NAEP mathematical test items which are written in one of three formats--multiple choice, short constructed response, or extended constructed response--and gives examples of each. Finally, each form of the NAEP mathematics assessment must be balanced according to a number of different factors, including content, level of complexity, and format. Chapter Five, "Design of Test and Items," describes the guidelines for balancing each factor. This chapter also addresses other issues of design such as sampling, use of calculators, tools and manipulatives, and accessibility for all students. The report also includes NAEP Mathematical Achievement Level Descriptions for grades 4, 8, and 12. (Contains 12 exhibits and a bibliography.).