Quantile Framework for Mathematics
The Quantile Framework for Mathematics is a unique measurement system that uses a common scale to describe a student’s mathematical achievement level as well as the difficulty of specific skills and concepts. The Quantile Framework describes a student’s ability to solve mathematical problems and the demand of the skills and concepts typically taught in kindergarten mathematics through Algebra II, Geometry, Trigonometry and Pre-calculus. The Quantile measure describes the difficulty levels of the math skills and concepts the student is most likely ready to learn.
Quantile measures are reported with the scores of students taking Mathematics SOL tests in grades 3 through 8, Algebra I, Geometry, Algebra II.
Virginia’s Focus on Math Achievement and The Quantile Framework for Mathematics
The Quantile Framework measures mathematics skills and concepts. Since the demand of the skills and concepts is placed on the same scale as student achievement, Quantile measures help educators to predict which mathematical skills and concepts a student is ready to learn and those who will likely require instruction. These measured skills and concepts in the Quantile Framework are all aligned to the Virginia Standards of Learning. The skills and concepts are also aligned to thousands of teaching resources such as textbook lessons, web tools, and downloadable resources, all available through the Quantiles.com website.
The Quantile scale ranges from Emerging Mathematics Skills (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 Pre-calculus. The Quantile Framework is a taxonomy – or classification system – of mathematical skills and concepts along the continuum of mathematics development. Each skill or concept is called a “QTaxon” and has an associated difficulty measure. The Quantile Framework has five content domains – Numbers and Operations, Geometry, Measurement, Algebra/Patterns & Functions, and Data Analysis & Probability. Like a roadmap, QTaxons guide students and educators along a path of mathematics development. The measure of each QTaxon estimates how difficult the skill will be for a student to learn when compared to the student measure. The measure of the QTaxon also compares how difficult one skill is to another in the taxonomy.
Quantile measures determine students’ mathematics achievement, not their grade level. A class of 30 sixth graders will likely have students with a wide range of Quantile measures. Educators can use those varied Quantile measures to target instruction and remediate as necessary, using tools and resources that match the students’ Quantile measures.
The Virginia Quantile Map (PDF) provides a graphic representation of the Quantile Framework, showing several example QTaxons identified at a variety of Quantile measures along the five mathematics content strands. It provides a context for understanding how test results relate math ability to problem solvability.
These resources and more may be accessed by using the menu to the right. The menu includes links to detailed information for parents and educators, frequently asked questions, and related assessment and school improvement resources.