The Quantile^® Framework for Mathematics provides a common, developmental scale for measuring both a student’s mathematics achievement and the difficulty of a mathematical skill or concept. Quantile^® measures help educators to make informed decisions in order to differentiate instruction and forecast a student’s success with new topics by comparing the student’s mathematics development level with the difficulty of a specific mathematical skill. The Quantile Framework comprises of a taxonomy of more than 450 math skills and concepts (called QTaxons), ranging from kindergarten to Precalculus. Each QTaxon has a Quantile measure that describes the skill demand or level of difficulty.

In order to match students with appropriate resources, a textbook or other instructional material must first be calibrated with the Quantile Framework to determine and the association to a QTaxon and its Quantile measure. Textbooks are analyzed at the lesson level by MetaMetrics subject matter experts (SMEs) who are experienced with the Quantile Framework and familiar with the mathematics taught at the appropriate grade level.

While mathematics can be thought of as encompassing two broad categories—mathematical content and mathematical processes—the Quantile Framework focuses on the content that is classified as specific skills and concepts. Therefore, each numbered lesson of an instructional resource, such as a textbook or workbook, is reviewed to determine the mathematical demand of the identified skill as it relates to the QTaxons in the Quantile Framework. Some textbook lessons will include a variety of skills and concepts, but only the QTaxon with the greatest Quantile measure is reported with the lesson.

Textbooks contain a variety of activities and lessons. Mixed review sections of individual lessons are not included in the Quantile calibration. These exercises likely are represented in previous lessons. Many textbooks contain additional material, such as activities involving reading mathematics, writing mathematics, games, and advanced topics at the end of and between chapters. These lessons are not calibrated since they very often represent process skills rather than content skills. Chapter tests also are not calibrated because many different skills and skill demands are represented.

The Calibration Process

• Each textbook lesson is reviewed by SMEs beginning with the lesson and concluding with the student exercises. Consideration is given to the lesson’s intent with emphasis placed on the skills represented in the exercises that would likely be assigned in the first night’s homework.
• The skills represented in the lesson are recorded by a number. Challenge exercises, review
• A second review is completed by a different SME. Any additions or deletions to the selected skills are noted.
• The original SME reviews the material a second time with consideration to the additions and deletions made by the second SME.
• Collaboration between the two SMEs regularly occurs in order to insure appropriate calibration reports.
• Information about the textbook, including its title, ISBN, publisher information, copyright date, chapter names, lesson names and associated skill, is recorded in the Quantile database. As a result, detailed Quantile calibrations are reported on the Quantile website (www.Quantiles.com) in order to inform educators so that their classroom instruction appropriately uses the materials from the textbook.

For more information on getting Quantile calibrations, please contact contact Jessica Whitesell, Director of Publisher Relations, at (919) 547-3426.

Click here to learn how Lexile^® measures support the Common Core Standards’ goal of preparing students for the text demands of college and careers.