# Quantile Framework for Mathematics

The Quantile® Framework for Mathematics is a scientific approach to measuring both the difficulty of a mathematical skill, concept or application (called Quantile Skill and Concept [QSC]) and a developing mathematician’s understanding of the QSCs in the following areas: Geometry; Measurement; Number Sense; Numerical Operations; Algebra and Algebraic Thinking; and Data Analysis and Probability. Quantile measures are expressed as numeric measures followed by a “Q” (for example, 850Q), and are placed on the Quantile scale. The Quantile Framework spans the developmental continuum from kindergarten mathematics through the content typically taught in Algebra II, Geometry, Trigonometry and Pre-calculus, from below 0Q (Emerging Mathematician) to above 1600Q. Quantile measures take the guesswork out of determining which mathematical skills a developing mathematician has learned and which ones require additional instruction.

Quantile measures are more than a math score because they help identify the math concepts students know and match them with the concepts they are ready to learn. Quantile measures are linked to specific math concepts. For example, maybe one student needs to review one or two concepts before a current classroom unit on quadrilaterals. Or, they might be able to complete enrichment activities to move ahead even more quickly. Quantile measures help match students to their “optimal” challenge. When they work on materials that they’re ready to learn, they experience more success and less frustration.

Because the Quantile Framework is based on the Rasch measurement model (Rasch, 1960; Wright & Stone, 1979), it provides conjoint measurement for student mathematics ability and the difficulty of mathematics concepts and skills. Sanford-Moore et al. (2014) quantified the mathematical demand of textbook lessons based on the mathematics concepts and skills contained in them. She and her colleagues depicted the lesson continuum by a series of box plots representing the within-grade distributions of lesson difficulties for grades and courses extending from Kindergarten through Algebra 2. Williamson, Sanford-Moore, and Bickel (2016) extended the lesson continuum with the distribution of lesson difficulties associated with Pre-calculus and trigonometry and furthermore provided an interpretive framework for inferring the range of student mathematical ability (1220Q-1440Q; median 1350Q) needed to be ready for college and career.

Additional information on this topic can be found at http://www.Quantiles.com.