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What is the Quantile Framework for Mathematics?
The Quantile Framework for Mathematics is a scientific approach to measurement that locates a student’s ability to think “mathematically” in a taxonomy of math skills, concepts, and applications. The Quantile Framework measures a student's mathematical achievement and concept/application solvability on the same scale, enabling educators to use Quantile measures to monitor a student’s development in math and forecast performance on end-of-year tests. Click here to understand exactly how teachers and parents can use Quantile measures. (You need Macromedia Flash to view this page. Get Flash.)
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What does a student's Quantile measure mean?
A Quantile measure indicates how well a student understands mathematical concepts and skills at his or her grade level. To interpret what a Quantile measure means for a specific student, two pieces of information are needed: the Quantile score, and the grade level during which the student received the Quantile score. For example, a higher Quantile measure within a specific grade range indicates that a student probably has very few problems with grade-level material (textbooks and assignments) in school. A lower Quantile measure indicates that a student most likely struggles to understand and succeed with grade-level material.
The purpose of the Quantile Framework is to help identify materials and resources that are targeted to the student's learning frontier, and thus will be challenging, but not frustrating. The learning frontier is the range to which instruction is focused, fifty Quantiles above and fifty Quantiles below the student's measure.
In other words, once a student's Quantile measure and grade are known, mathematical concepts, topics, materials, and resources can be identified within that same Quantile range. Click here for more typical grade level ranges.
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 are forecasted to understand with 50% likelihood. As a student grows, he or she can be matched with more demanding concepts and skills. Likewise, the concepts and skills become more demanding, and then the student grows.
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How can I use Quantile measures at home?
Parents can identify which skills to strengthen in their child through everyday activities that integrate mathematics skills. These skills can be identified by searching for QTaxons using the QTaxon Search. A search with a broader range, such as 200 Quantiles below their child's measure to 75 Quantiles below their child's measure, will yield a list of skills to enhance and further develop. In doing so, the child will be strengthening skills upon which new skills can be built. Learn more about the QTaxon Search on the Resources page.
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What is a Quantile measure on a particular math skill?
This number with a Q is a Quantile measure. When given for a math skill, it refers to the difficulty of this skill or concept, or how difficult it is compared to others.
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How can I align my product/service to the Quantile Framework?
If you are interested in learning more about how Quantiles can add value to your product, please send an inquiry to Trilby Berger, Director, Strategic Partnerships, or visit our partner pages, Assessment & Instruction Companies or Textbook Publishers.
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What is problem solvability?
Problem solvability is the Quantile difficulty of introductory mathematical concepts or problems, similar to what you might find on a first night’s homework assignment. The Quantile measure of a skill/concept is the difficulty of the task.
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Why the emphasis on readiness and introductory problems (first night's homework)?
The Quantile theory predicts the solvability of individual concepts (how well an individual will demonstrate mastery of a concept or skill). 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.
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What do the Quantile codes mean? (EM, NMQ, etc.)
Quantile codes are used in conjunction with the Quantile measure to indicate special characteristics of the material. To learn more about them, see the Resources page.
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What is a QTaxon?
A taxon is the root of the word taxonomy, meaning a taxonomic category or group. In terms of the Quantile Framework, a QTaxon defines a specific mathematical topic, concept or skill and is used to annotate the framework.
Each QTaxon has a Quantile measure (expressed as a number followed by the letter “Q”) which estimates its solvability in the taxonomy of the framework. QTaxons are linked to supplemental and prerequisite QTaxons which illustrate the interconnectivity of The Quantile Framework and the natural progression of mathematical skills needed to solve increasingly complex problems. The framework comprises more than 500 QTaxons which educators can use to monitor progress and target instruction by comparing a student’s Quantile measure with the measure of a particular QTaxon. Each QTaxon aligns with one of five Quantile content strands—Numbers and Operations, Geometry, Measurement, Algebra/Patterns & Functions, and Data Analysis & Probability—and the process strands described by the National Council of Teachers of Mathematics (NCTM).
Learn more about the science behind QTaxon Quantile measures.
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What is a supplemental QTaxon?
Supplemental QTaxons 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.
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What is a prerequisite QTaxon?
Prerequisite QTaxons describe skills and concepts that should be mastered before beginning instruction on the main QTaxon. For example, before adding two-digit numbers, students should be able to add single-digit numbers. Thus, the Prerequisite QTaxons display the interconnectivity and progression of mathematical topics in the Quantile Framework.
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What is a foundational QTaxon?
A Foundational QTaxon 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.
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What is a knowledge cluster?
A knowledge cluster illustrates a main QTaxon and its supplemental and prerequisite QTaxons. Knowledge clusters depict the interconnectivity of skills, concepts and applications within the Quantile Framework.
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What are the five mathematics content strands?
The National Council of Teachers of Mathematics (NCTM), the world’s largest mathematics education organization founded to ensure the highest quality of mathematics instruction for all students, determined that mathematical skills, concepts and applications fall into five broad categories/strands: Numbers and Operations, Geometry, Measurement, Algebra and Data Analysis and Probability.
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What is the Quantile Map?
The Quantile Map is a graphic representation of the Quantile Framework, depicting sample QTaxons arranged by strand and Quantile measure. The map is the only tool available that illustrates mathematics development and the connections between QTaxons across the content strands. Educators can use the map to target instruction and forecast student progress based on which mathematical skills the student should have mastered on a strand-by-strand basis and at each Quantile measure.
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What is a Quantile?
A Quantile is the unit of measure on the Quantile scale. Quantiles measure student mathematical achievement and concept/application solvability similar to the way Lexiles measure reading ability and text difficulty. This measure is depicted with a simple number followed by the letter “Q” (as Lexiles are followed by an “L”). The Quantile Framework spans the developmental continuum from kindergarten mathematics through the content typically taught in Algebra II, Geometry, Trigonometry and Pre-calculus—from Emerging Mathematician (OQ and below) to above 1400 Quantiles.
For example, a student with a Quantile measure of 500Q is likely to be ready for instruction of mathematics problems at a demand level of 500Q.
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How do I get a Quantile measure?
Students who take a mathematics achievement test that is linked with the Quantile Framework will receive a Quantile measure. Educators can use these Quantile measures to match students to level-appropriate instructional materials and forecast understanding.
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How do grade levels relate to Quantile levels?
Because of the many problems associated with grade-level equivalents, there is not a direct translation from a specific Quantile measure to a specific grade level. Within any classroom, there will be a range of student mathematical abilities and a range of instructional materials.
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How can I use Quantile measures in the classroom?
By connecting students’ Quantile measures to Quantile-leveled resources, the Quantile Framework provides educators with actionable information from mathematics assessments and diagnostic tools that they can use to target instruction, forecast understanding, and improve mathematics achievement. Click on Principals & Educators to learn how!
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How to do I use QTaxon Search and/or the Textbook Search engine?
See our Resources page for directions on how to use our free suite of on-line tools.
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How can I receive copies of my state's grade level Quantile Maps?
Custom, grade-specific state maps are made available to all states who report Quantile measures. These custom maps are given directly to the state agencies. Please visit the individual Web sites of the respective state to obtain a copy of these maps.
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How can I request more information about my child's Quantile measure?
If you still have questions regarding a student's Quantile measure, please use our contact form and our research associate will be happy to help you.
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What if I don't have student Quantile measures?
A Quantile measure on a QTaxon identifies the difficulty of the skill or concept at the introductory level. For example, a classroom teacher might observe that a student is consistently successful with mathematics materials at a 400Q skill demand, but struggles with material at the 600Q and 700Q levels. It would be reasonable to infer that the student likely performs at approximately 500Q. Understandably, this Quantile measure is an estimate, but with repeated formative assessments, a teacher who is familiar with the skill demand in terms of a Quantile measure can become confident that the estimate is not unreasonable. With this Quantile measure teachers can effectively differentiate instruction.
Additionally, textbooks that have been calibrated means that each lesson in the book has a Quantile measure that identifies the highest skill demand in that lesson. When the textbook is published on the Quantile website (www.Quantiles.com), each lesson in the table of contents identifies one or more QTaxons (along with the Quantile measure). When the classroom teacher recognizes the difficulty of the skill based on its Quantile measure, he is more informed on a daily basis about pacing the instruction and his expectations from certain populations of students in the classroom. Furthermore, textbooks’ lessons do not follow in a linear progression of difficulty. The skill demand in terms of a Quantile measure fluctuates from one lesson to the next. A teacher who is informed on a daily basis upon the difficulty of the material he is teaching will be able to effectively target and pace the mathematics instruction according to the needs of the students in the classroom.
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