Mathematics Framework Changes

2009 Framework Changes

For grades 4 and 8, the mathematics framework for the 2009 assessment is similar to earlier frameworks that guided previous mathematics assessments. The grade 12 framework was updated, adding objectives addressing mathematics content beyond that typically taught in a standard 3-year course of study in high school mathematics. These changes are expected to assist in reporting on how well-prepared grade 12 students are for postsecondary education and training and to enable NAEP to report on how well prepared twelfth-grade students are for postsecondary education and training. The challenge for the 2009 assessment was to find the essential mathematics that can form the foundation for these postsecondary paths. These should include use of quantitative tools, broad competence in mathematical reasoning, mathematics required for postsecondary courses, and the ability to integrate and apply mathematics in diverse problem-solving contexts. Analysis of the 2005 framework revealed that some revisions would be necessary to meet this challenge.

Below is a summary of the changes to the framework.

Mathematics Content

  • Objectives for grades 4 and 8 remain the same
  • New topic of "mathematical" reasoning added at grades, 4, 8, and 12
  • New objectives for grade 12 introduced

Mathematical Complexity

  • New clarifications and new examples to describe the levels of mathematical complexity added to framework

2005 Framework Changes

The changes to the mathematics framework introduced in 2005 for grades 4 and 8 were minimal, which allowed for the continued reporting of results from previous assessments beginning with 1990. The achievement levels at grade 4 and 8 did not change, and the content areas remained the same. The overall item types (multiple choice, short-constructed response, and extended-constructed response) continued to be used, the use of manipulatives, and the calculator policy did not change for grades 4 and 8 in 2005. The cognitive dimension used to classify mathematics items did change in 2005 for grades 4 and 8. The 2005 framework replaces the dimensions of mathematical ability and power (which require inferences about the student responding to the item) with the dimension of mathematical complexity (which describes the mathematical expectations of an item).

The 2005 mathematics framework for grade 12 introduced changes from the previous framework in order to reflect adjustments in curricular emphases and to ensure an appropriate balance of content. Consequently, the twelfth-grade results in 2005 and subsequent years cannot be compared to previous assessments in mathematics. There were, however, some questions from the 2000 assessment that fit the requirements in the new framework and were used again in 2005. A special analysis was performed by the Human Resources Research Organization to see how students' performance on this set of items differed between the two years. To download a copy of this analysis, visit the Human Resources Research Organization website.

Changes to the grade 12 NAEP mathematics assessment in 2005

  2005 Mathematics assessment Previous Mathematics assessment
Content areas Four content areas, with measurement and geometry combined into one because the majority of twelfth-grade measurement topics are geometric in nature Five content areas
Distribution of questions across content areas    
     Number properties and operations 10% 20%
     Measurement and geometry 30% 15% and 20%
     Data analysis and probability 25% 20%
     Algebra 35% 25%
Reporting scale 0-300 single-grade scale 0-500 cross-grade scale
Calculators Students given the option to bring their own graphing or scientific calculator Students provided with standard model scientific calculator

Last updated 23 October 2013 (FW)