# 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.

The Quantile Framework for Mathematics - By the Numbers

About Quantile Measures, Fact Sheets, Guides, Quantile Maps, and General Questions

Interpreting Test Results

Quantile Parent Guide

Quantile Educator Guide

Knowledge Cluster Brochure

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## What is the Quantile Framework for Mathematics?

The Quantile Framework for Mathematics is a scientific approach that indicates the difficulty of mathematical skills and concepts. Within the Quantile Framework the mathematical skills and concepts are called Quantile Skills and Concepts, or QSCs. In addition, the Quantile Framework locates a student's ability to address new mathematical topics. Each of these measures are on a single scale so that the skill demand and student ability can be matched for targeting instruction.

## What is a "foundational" QSC?

A foundational QSC describes a skill or concept that only requires readiness to learn. Readiness is based upon the learner’s cognitive experiences rather than knowledge of specific mathematical concepts. Most often these QSCs appear in the Pre-K level.

## Why emphasize readiness for instruction and introductory problems such as the first night's homework

A student Quantile measure does not indicate that a student has mastered all of the material with a Quantile measure at or below the student’s Quantile measure.

Introductory problems tend to be straightforward assessments of concept knowledge. More advanced problems that blend with other concepts cloud the picture in terms of predicting the difficulty of the primary concept. Therefore, the Quantile measure of a skill or concept is the mathematical demand at an introductory level.

## How are the Lexile and Quantile Frameworks similar and different from each other?

The Lexile Framework for Reading and the Quantile Framework for Mathematics are both academic measurement systems that make the measurement of student performance and the measurement of material complexity on a single scale possible. Both are based on empirical (observed) relationships between learners and materials. The scales and their units accurately describe measures from beginner to advanced. The scales are independent, meaning that student and material measures can be produced from many assessments and for reading and math materials from many sources. They differ with respect to the academic skill and material measured. On the learner or student side, the Lexile Framework for Reading measures a learner's reading ability, or overall reading comprehension, and the Quantile Framework measures a learner's ready to learn level, the difficulty of level for math skills and concepts. On the materials side, the Lexile Framework measures the complexity of prose text based on quantifiable text features while the Quantile Framework measures the complexity of math skills and concepts based on the mathematical relationships between each skill and concept.

## How do grade levels relate to Quantile measures?

The premise behind The Quantile Framework for Mathematics is simply matching instruction to where a child’s mathematical schema exists. Quantile measures help educators and parents track student growth in mathematics over time, regardless of grade level. Within any classroom, students will have varying mathematical abilities.

Since growth is expected from one school year to the next, Quantile measures do not translate specifically to grade levels. The Quantile Framework provides two sides to the same coin: a measure for students and a measure for skills and concepts. The student Quantile measure describes what the student is capable of understanding. The Quantile Skill and Concept or QSC measure describes the difficulty, or mathematical demand, of that skill.

## What does EM stand for?

Emerging Mathematician (EM): Measures below 0Q are reported as EM---Q (e.g., a Quantile measure of -120 is reported as EM120Q) where “EM” stands for “Emerging Mathematician” and replaces the negative sign in the number. This code is predominantly seen for material and student measures at the early grade levels.

## What does HMC stand for?

Higher Mathematical Content (HMC): Material designated as “HMC” is content for which we have QSCs but the QSCs have not yet been researched to identify their measures. These QSCs are currently in statistics and precalculus.

## What does NMQ stand for?

Not Measurable in Quantiles (NMQ): Material designated as “NMQ” is content that is extensively diverse in QSCs or strands so it cannot be classified within the Quantile framework. Some examples are quizzes, tests, riddles, review sheets/activities, and process skills such as working backwards, justifying, drawing pictures, etc.

## What impact does the Lexile measure of text have on difficulty levels of the mathematics?

There is a considerable amount of discussion and research about the type of text that is used in mathematics. The readability of technical text is very different from such reading experiences as reading trade books, novels, magazines, or newspapers.

In order to minimize the reading demand of some mathematics materials, some parts of a Quantile assessment are built with Lexile measures that are traditionally below expected reading levels of the students addressing the work. The effort is to diminish the reading demand so that the mathematics demand is what is being measured.

## Can I still use the Quantile Framework if my child / student doesn't have a Quantile measure?

It is still possible to use the Quantile Framework to gain insights into the difficulty and the content sequencing of curricula. All of the Quantile tools found in the "Use the Quantile Framework" section of this website are free and can help you identify resources which are appropriate to be used with the curriculum being taught. See the descriptions listed in this FAQ for these tools which include: Math Skills Database, Quantile Teacher Assistant, Find Your Textbook search, or Math@Home. The best way to navigate through the Quantile Framework in order to target resources and meet student needs is with the student Quantile measure.

## How does a student get a Quantile measure?

A student receives a Quantile measure by taking an assessment which reports results as a Quantile measure. Some assessments are developed to report student Quantile measures, while other assessments are linked to the Quantile Framework to report student Quantile measures. Many state education agencies have their year-end accountability assessments reporting student Quantile measures.

## What does a student Quantile measure mean?

The student Quantile measure indicates the student’s ability to successfully work with the math skills and concepts with a similar Quantile measure after an introductory lesson. The student Quantile measure is an indicator of ability when the student’s interaction with the mathematics skill is accompanied with instruction. A student Quantile measure helps to forecast a student’s ability to successfully accomplish the demands of mathematical concepts and skills (Quantile Skills and Concepts or QSCs) at the introductory level with classroom instruction. As the Quantile measure of a student increases, the mathematics material he/she is able to manage becomes more difficult.

## How does a student get a Quantile measure?

A student receives a Quantile measure by taking an assessment which reports results as a Quantile measure. Some assessments are developed to report student Quantile measures, while other assessments are linked to the Quantile Framework to report student Quantile measures. Many state education agencies have their year-end accountability assessments reporting student Quantile measures.

## What does the QSC ID mean? (For example: QSC333)

Each Quantile Skill and Concept, or QSC, has an identification number that consists of two elements: the letters QSC followed by a unique 1, 2, or 3 digit identifying number.

## What is a knowledge cluster?

The entire Quantile Framework is interconnected through the Quantile Skills and Concepts or QSCs (a skill description with its measure). The “knowledge cluster” for a QSC contains that QSC and its links to other QSCs. The links are determined by prerequisite skills and their measures. Each knowledge cluster is assembled to a single focus QSC with supplemental, prerequisite, and impending QSCs. These connections to the focus QSC are built to inform both the content and the measure of the mathematical progression of skills and concepts.

The power of a knowledge cluster allows educators to scaffold instruction by identifying gaps in students’ mathematical background that frustrate student success in a content area. Additionally, the knowledge cluster enriches instruction by informing the interconnectivity and progression of skills and concepts in the field of mathematics.

## What is a prerequisite QSC?

Prerequisite QSCs describe skills and concepts that are important for students to learn before beginning instruction on the focus QSC. For example, the focus QSC described as “Use patterns to continue numerical sequences; identify the rule” has prerequisite QSCs that expect students to be able to identify missing addends among addition facts and use various counting strategies and manipulatives. The various QSCs are combined from different content strands which demonstrates the interconnectivity and the developmental progression in the study of mathematics.

## What is a supplemental QSC?

Supplemental QSCs represent skills that are not necessary but could be useful to enrich a lesson, make connections across topics as well as strands, and help students integrate different mathematical concepts. For the same QSC mentioned above, “Use patterns to continue numerical sequences; identify the rule”, numerous supplemental QSCs in the knowledge cluster are applications in skip counting such as reading thermometers, telling time, or interpreting graphs whose scales are counting in multiple units.

## What is an impending QSC?

An impending QSC to a focus QSC means that the focus QSC is a prerequisite to a new skill or QSC that students will likely learn in their future mathematics studies as they logically progress through their coursework.

This insight provides a more global perspective of the process, connections, and relationships that support a student's understanding of mathematics.

## What is the expected growth in Quantile measures of a student?

Educators, parents, and students often want to understand the expected growth a student should show from year to year in terms of Lexile measures. However, academic growth varies from student to student and is dependent on many variables. From a student's position in their learning journey to the specific instructional methods to time spent in practice many forces can shape growth. Typically, expected growth estimates are made available by companies that develop instructional programs. They are best able to communicate the results anticipated if their program is implemented as intended. While MetaMetrics® is not able to share expected growth, the observed Quantile student measures by U.S. grades is available via the Quantile website here. This Quantile measure by grade information describes the Lexile range that the majority of students are in at each grade. The statistics shared in the table are gathered from a large sample of U.S. students that take tests that report Quantile measures across the U.S. The students were exposed to differing curriculums, practice, etc. To learn more about expected growth read our white paper, What is Expected Growth?.

## Why do we only get one Quantile measure for a student?

All content strands are woven together to form the field called mathematics. The Quantile measure measures overall mathematics ability so it is given as a single value and does not disaggregate a score into various branches of mathematics.

## What resources are available for families to help their child in mathematics?

Math@Home is a search tool for families that provides access to a variety of mathematical resources, such as games, activities, websites, tutorials, and videos that are targeted to a child’s mathematical ability level on the Quantile scale. By entering the student Quantile measure and selecting the appropriate grade level textbook, families can find instructional resources and activities that supplement the textbook lesson and support student learning outside of the classroom.

## How can I use Quantile measures in the classroom?

The real power of the Quantile Framework is in examining the growth of students' mathematical achievement wherever the student may be in the development of his or her mathematical thinking. Students can be matched with resources and engaged in instruction that they will find challenging enough to promote growth with a minimum level of frustration for them. Classroom teachers can confidently forecast students’ ability to be successful with lessons based upon matching the student measures to the Quantile measure of the material in the lessons.