General questions about the Quantile Framework

About skills and their measures (*Quantile Skills and Concepts* or *QSCs*)

### General questions about the Quantile Framework

#### 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 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.

### About student 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.

#### 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.

#### If a student has a significantly higher Quantile measure than other students’ normative measures 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 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.

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

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.

For more information about Quantile ranges and grade levels, please read Quantile Measures: Typical Grade Ranges (PDF)

#### 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.

### About skills and their measures (*Quantile Skills and Concepts* or *QSCs*)

#### 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.

#### 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 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 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 "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 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 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.

### About use in schools and classrooms

#### 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.

#### 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 do I use the *Math Skills Database*?

The Math Skills Database is a search engine that allows you to search the Quantile Framework using your state curriculum, including the Common Core Mathematics Standards. The results list displays the state goals aligned to the Quantile Framework “QSCs”.

The description of the skill with its measure is called a *Quantile Skill and Concept* or *QSC*. There are over 500 QSCs in the Quantile Framework. The Quantile measure can be used to show how difficult one skill is in relation to the others. By clicking through the results list from a search to a QSC's individual description page, you will find resources aligned to that skill as well as the skill’s related skills, called a *Knowledge Cluster.*

Related skills are all hyperlinked to their respective detail pages. Continue clicking through related skills to find other QSCs related to the one of initial interest, but at a measure most appropriate to the student measure.

#### How do I use the *Find Your Textbook* search?

The Find Your Textbook search informs teachers and parents about the difficulty of each lesson in a textbook measured on the Quantile scale. Using this value, teachers are able to match the measures with student Quantile measures in order to differentiate and motivate student learning. Additionally, this insight about the difficulty of the material helps to gage the amount of time that might be necessary to insure student confidence in their work.

#### How do I use the *Quantile Teacher Assistant*?

Time is short and math instruction needs to be focused. The Quantile Teacher Assistant helps educators to utilize the Quantile Framework for Mathematics in order to differentiate math instruction and to locate resources that can help identify those skills that are most relevant to the topic of the day. This tool has been aligned with state mathematics curriculum standards and to the Common Core State Mathematics standards. Some of the prerequisite and supplemental QSCs from the knowledge clusters are offered along with resources that can supplement instruction in the classroom.

#### 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, and Math@Home.

The best way to navigate through the Framework in order to target resources and meet student needs is with the student Quantile measure. Contact us using this form and your inquiry will be directed to the appropriate person. Please also feel free to call and speak with our Business Development team (919-547-3427) about how to link your assessment product with our Framework. Remember, our goal is not to assess students more, but to get more value out of the assessments that are given.

### About Quantile measures and instructional resources

#### What are the benefits of calibrating resources to the Quantile Framework?

The Quantile Framework for Mathematics brings value to instructional and assessment products. It does this by bridging the gap between student ability and skill demand, and gives meaning to measurement data in mathematics instruction.

Classroom teachers need the data in order for their instruction to be data-driven. By having your resources calibrated to the Quantile taxonomy, teachers will have the information at their fingertips. The resources are also linked to all state standards, including the Common Core. These calibrations and alignments will empower teachers to target their instruction to the needs of their students in a timely manner.

Easy access to a product line that informs classroom teachers’ formative processes offer the appeal of easy access that saves planning time and promotes targeted instruction within the framework of their grade level or course curriculum.

#### What are the benefits of calibrating textbooks to the Quantile Framework?

The Quantile Framework for Mathematics bridges the gap between student ability and skill demand, and gives meaning to measurement data in mathematics instruction. When mathematics textbooks are calibrated to the Quantile scale, each lesson is identified with one or more *Quantile Skills and Concepts* or *QSCs*.

Classroom teachers need data so that their instruction can be data-driven. By having your textbooks calibrated to the Quantile taxonomy, teachers will have the information at their fingertips. These calibrations will empower teachers to target their instruction to the needs of their students in a timely manner.

Easy access to textbook lesson details inform classroom teachers' formative processes, saves planning time, and promotes targeted instruction within the framework of their grade level or course curriculum.

#### How do assessments and/or instructional products report a student Quantile measure?

We have a team of experts here to help. Please contact us to discuss process and options which will be appropriate for your assessment or product.