# Mathematical reasoning

The GED^{®} Mathematical Reasoning Test focuses on two major content areas: quantitative problem solving and algebraic problem solving.

Evidence that was used to inform the development of the Career and College Ready Standards shows that instructors of entry-level college mathematics value master of fundamentals over a broad, shallow coverage of topics. National remediation data are consistent with this perspective, suggesting that students with a shallow grasp of a wide range of topics are not as well prepared to succeed in postsecondary education and are more likely to need remediation in mathematics compared to those students who have a deeper understanding of more fundamental mathematical topics. Therefore, the GED^{®} Mathematical Reasoning Test focuses on the fundamentals of mathematics in these two areas, striking a balance of deeper conceptual understanding, procedural skill and fluency, and the ability to apply these fundamentals in realistic situations. A variety of item types are used in the test, including multiple-choice, drag-and-drop, hot spot, and fill-in-the-blank.

The Career and College Ready Standards include Standards for Mathematical Practice, which describe the types of practices, or behaviors, in mathematics that are essential to the mastery of mathematical content. These standards form the basis of the GED^{®} mathematical practice standards, which assess important mathematical proficiencies, including modeling, constructing and critiquing reasoning, and procedural fluency.

Given these priorities, the GED^{®} Mathematical Reasoning Test adheres to the following parameters:

- Approximately 45 percent of the content in the test focuses on quantitative problem solving, and approximately 55 percent focuses on algebraic problem solving.
- The test includes items that test procedural skill and fluency as well as problem solving.
- The contexts within which problem solving skills are measured were taken from both academic and workforce contexts.
- Approximately 50 percent of the items are written to a Depth of Knowledge cognitive complexity level of 2.
- Approximately 30 percent of the items are aligned to a Mathematical Practice standard in addition to a content indicator.
- The statistics and data interpretation standards are also measured in the GED
^{®}Social Studies and Science Tests. - Candidates are provided with an on-screen calculator, the Texas Instruments TI-30XS Multiview scientific calculator, for use on most of the items on the 2014 GED
^{®}Mathematics Test.

**As of Friday, February 21, 2014, the standard time allowance on the GED ^{®} test - Mathematical Reasoning was increased by 25 minutes.**

- The time allowance for GED Ready™ - Mathematical Reasoning was also increased by 13 minutes.
- Students who took either of these tests before February 21 received an email from GED Testing Service with instructions for receiving a free retake.

## MATHEMATICAL PRACTICES

In addition to the content-based indicators, the GED^{®} mathematics test also focuses on reasoning skills, as embodied by the GED^{®} Mathematical Practices. The mathematical practices framework is based upon two sets of standards: the Standards for Mathematical Practice found in the Career and College Ready Standards for Mathematics; and the Process Standards found in the Principles and Standards for School Mathematics, published by the National Council of Teachers of Mathematics.

The content indicators and mathematical practices found in the GED^{®} Mathematical Reasoning Assessment Targets, though related, cover different aspects of item content considerations. The content indicators focus on mathematical content, as typically seen in state standards frameworks and, to some extent, the Career and College Ready Standards for Mathematics. The indicators describe very specific skills and abilities of which test-takers are expected to demonstrate mastery. In contrast, the mathematical practices focus more on mathematical reasoning skills and modes of thinking mathematically. Most of these skills are non-content-specific, meaning that a mathematical practice indicator could be applied to items that cover a range of content domains (e.g. algebra, data analysis, number sense). The measurement of these skills is very much in keeping with the CCR Standards for Mathematical Practice, which were created in order to “describe varieties of expertise that mathematics educators at all levels should seek to develop in their students” (Career and College Ready State Standards for Mathematics [2010], p.6). The mathematical practices provide specifications for assessing real-world problem-solving skills in a mathematical context rather than requiring students only to memorize, recognize and apply a long list of mathematical algorithms.

While we consider it crucial to assess both content and reasoning, it would be unrealistic to assert that each individual item could address both types of skills. To be sure, there are inter-related concepts to be found in the content indicators and the mathematical practices, especially in the areas of modeling and fluency, but not every item assessing a content indicator interacts seamlessly with a mathematical practice. Rather than force alignments, we seek to create items in which content and practice mesh well together. These items would primarily assess practice, with content serving as the context in which the practice is applied. Items of this type reflect the reasoning and problem-solving skills that are so critical to college and career readiness. Where this type of natural overlap between practice and content is not possible, other items assess the content indicators directly, thereby ensuring coverage of the full range of mathematical content on each test form.