We offer several fact sheets and informational materials on the Quantile Framework for Mathematics and how to use it.

## Quantile Map

Our Quantile map helps demonstrate the interconnections of skills and concepts and how you can use the Quantile scale to identify how skills and concepts relate to one another and student learning. There are two versions of the map, our printer-friendly version and poster version.

## General Questions about the Quantile Framework for Mathematics

### What is the Quantile Framework for Mathematics?

The Quantile Framework for Mathematics is a scientific approach that evaluates the difficulty of mathematical skills and concepts as well as a student’s ability to learn new mathematical concepts. Each of these measures are on a single scale so that the skill demand and student ability can be matched for targeting instruction. Learn more about Quantile measures.

### What does a student Quantile measure mean?

A student’s Quantile measure helps to forecast their ability to successfully learn mathematical concepts and master skills (Quantile Skills and Concepts or QSCs) at the introductory level with classroom instruction. As the Quantile measure of a student increases, the mathematics concepts they are able to learn become more complex.

### 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 indicates overall mathematics ability so it is given as a single value and does not disaggregate a score into various branches of mathematics.

### If a student has a significantly higher Quantile measure than his peers should that student be placed in a higher level mathematics course?

Any decisions made about student placement in their course work should not be made based upon a single measure or test result. Many factors can impact a student’s readiness for more complex concepts in mathematics. Those factors include background knowledge, academic motivation and the ability to independently problem-solve at an abstract level.

The Quantile measure indicates a student is probably ready for the difficulty of material presented at a particular level but is not an indicator of mastery. Students need to be ready for the demand of the material, which is what the Quantile measure shows. In the discipline of mathematics, however, students also need to have learned and been successful with previous material in the curriculum. Mathematics concepts are highly dependent on one another. The Quantile measure demonstrates readiness for instruction but does not indicate which topics have been learned.

### How does a student get a Quantile measure?

A student receives a Quantile measure by taking an assessment which reports Quantile measures. Many state departments of education have their year-end accountability assessments reporting student Quantile measures. Learn more about how to get a Quantile Measure.

### How do grade levels relate to Quantile levels?

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.

### Why emphasize “readiness for instruction” and introductory problems?

A student Quantile measure does not indicate that a student has mastered all of the material 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.

### What does a Quantile measure on a particular math skill (QSC) mean?

A unique element of a QSC (Quantile Skill and Concept) is that it has a Quantile measure. The measure of a QSC indicates the difficulty of math skills and concepts at an introductory level (first night’s homework). The taxonomy of math skills, concepts and applications has been through field studies and other research efforts in order to determine these difficulty measures. Read more about QSC measures.

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

Each 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 supporting, 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 parents to scaffold instruction by identifying gaps in students’ mathematical backgrounds 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. Read more about Knowledge Clusters.

### 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 “supporting QSC”?

Supporting 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 supporting 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 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 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.

### How do teachers use Quantile measures in the classroom?

The real power of the The Quantile Framework for Mathematics 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.

### What resources are available to help my 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.

The Summer Math Challenge is a free math skills maintenance program based on grade-level standards that help prepare students for college and careers. The program is targeted to students who have just completed grades 1 through 8 and is designed to help kids retain math skills learned during the previous school year. For six weeks in the summer parents will receive daily emails with fun activities and links to educational resources. When the program ends parents can print an award certificate to celebrate their child’s summer math accomplishment!

### Can I still use Quantile resources if my child doesn’t have a Quantile measure?

Yes, it is still possible to use Quantile resources even if your child doesn’t have a Quantile measure. Both Math@Home and the Summer Math Challenge offer a way to estimate the Quantile measure of a student.