The Quantile Framework for Mathematics
LINKING ASSESSMENT WITH MATHEMATICS INSTRUCTION

The Quantile Framework for Mathematics Overview (PDF)

Improving Student Achievement With The Quantile Framework for Mathematics
The Quantile Framework for Mathematics takes the guesswork out of mathematics instruction. The Quantile Framework uses a common, developmental scale to measure student mathematics achievement, the difficulty of mathematical skills and concepts, and the materials for teaching mathematics. By placing the curriculum, teaching materials and students on the same scale, Quantiles enable educators to predict which mathematical skills and concepts a student is ready to learn and those that will require instruction. Then, students can be matched with the resources that meet their learning needs. With Quantiles, educators have a proven measure of student mathematics achievement to target instruction, monitor student progress and forecast performance on high-stakes tests.

More Information, Not More Testing
Rather than requiring an additional assessment, Quantiles add value to already existing tests and instructional programs. A growing number of classroom, norm-referenced and state-level assessments are linked with the Quantile Framework. Students who take these assessments receive a Quantile measure—a number followed by a “Q.” A Quantile measure indicates that the student is ready for instruction of a particular mathematical concept and has knowledge of the required skills necessary to learn it.

For example, if a state standard for third graders is to master adding and subtracting two- and three-digit numbers without regrouping, educators use their students’ Quantile measures to forecast which students will have success with this skill and to identify those who may need to learn other skills or concepts before or during the lesson. Mathematics textbooks and other instructional resources are linked with the Quantile Framework, allowing educators to match students with targeted materials to help them better understand mathematical concepts or skills.

Learning on a Developmental Scale
Developed to align with the National Council of Teachers of Mathematics “Principles and Standards for School Mathematics,” the Quantile Framework has five content strands—Numbers and Operations, Geometry, Measurement, Algebra/Patterns & Functions, and Data Analysis & Probability. The Quantile scale ranges from Emerging Mathematician (0Q and below) to above 1600Q, and spans the mathematics continuum from concepts taught in kindergarten to those typically taught in Algebra II, Geometry, Trigonometry and Precalculus.

The Quantile scale is a taxonomy—or classification system—of mathematical skills and concepts along the continuum of mathematics development. Each content strand is annotated by “QTaxons,” which describe specific skills, objectives or grade-level expectations as defined by each state’s curriculum. Like a roadmap, QTaxons demonstrate how these skills fall along the continuum of mathematics development. Each QTaxon has a Quantile measure that estimates how difficult it will likely be for a student to learn, as compared with other skills in the taxonomy.

Quantiles measure students’ mathematics achievement, not their grade level. A class of 30 sixth graders will likely have students with a range of Quantile measures. Educators use those varied Quantile measures to target instruction and remediate as necessary, using tools and resources that match the students’ Quantile measures.

Using Quantiles to Support Mathematics Instruction
The Quantile Framework Web site—www.Quantiles.com—offers educators and parents a wealth of free resources for using Quantiles to support and simplify differentiated mathematics instruction.

The QTaxon Search database enables users to search through the entire taxonomy of skills and concepts on the Quantile scale to obtain their difficulty levels, resources and specific state curriculum alignments. For example, if Texas teachers search for “decimals,” they are provided with the associated skills and concepts aligned with the state’s standards, the Texas Essential Knowledge and Skills (TEKS), and the difficulty level for each skill or concept. Resources, such as mathematics textbooks, Web links, worksheets, math-literature guides, black line masters and games, can also be found through the search features directly linked to state mathematics standards by grade level. The QTaxon Search allows educators to match students with the instructional materials that best meet their mathematics learning needs, which simplifies the instructional planning process.

Educators can then use the Lesson Plan Builder to bundle these resources and search results to develop differentiated lessons tied directly to their state’s mathematics standards. The Lesson Plan Builder enables teachers to link their instructional plans directly to resources that match the varied learning needs of their students and to download them for classroom use. The Quantile Framework can be used to build teacher professional growth plans as well as to help special education teachers create and meet student Individualized Education Programs (IEP).

In addition, the Quantile Web site offers a database of more than 1,000 mathematics terms and concepts connected to the tools on the site. The Quantile map, a graphic representation of the Quantile Framework, is also available. The map is the only tool available that visually illustrates mathematics development and the connections between skills and concepts across the content strands. In addition, there are customized Quantile maps that align to individual state curricula.

The Science Behind The Quantile Framework
Launched in 2004, The Quantile Framework for Mathematics was developed by psychometricians at MetaMetrics, Inc., a privately held educational measurement company based in Durham, N.C. The company’s team of experienced psychometricians also developed the widely adopted Lexile Framework for Reading. Based in part on the company’s more than 20 years of psychometric research, the release of Quantiles came after four years of development, including an extensive national field study during the 2003-2004 school year. Today, MetaMetrics continues to pioneer scientifically based measures of student achievement that help to link assessment with instruction, foster better educational practices and improve learning by matching students with instructional materials that meet and challenge their abilities.

For more information on how The Quantile Framework for Mathematics can help to link assessment with instruction and improve student mathematics achievement, call 1-888-539-4537 or visit www.Quantiles.com.