The Quantile Framework for Mathematics
Linking Assessment with Mathematics Instruction
Improving Achievement With The Quantile Framework for Mathematics
The Quantile Framework for Mathematics takes the guesswork out of mathematics instruction. The Quantile Framework uses a common, developmental scale to measure mathematics achievement, the difficulty of mathematical skills and concepts, and the materials for teaching mathematics. By placing the curriculum, teaching materials and learner on the same scale, Quantile measures enable teachers to predict which mathematical skills and concepts a child is ready to learn and those that will require additional instruction. Then, children can be matched with the resources that meet their learning needs. With Quantile measures, teachers have a proven metric of mathematics achievement to personalise learning, monitor progress and forecast performance on tests.
More Information, Not More Testing
Rather than requiring an additional assessment, Quantile measures add value to already existing tests. Children who take these assessments receive a Quantile measure—a number followed by a “Q” (i.e., 650Q). A Quantile measure indicates that the child is ready for instruction of a particular mathematical concept and has knowledge of the required skills necessary to learn it.
For example, if the standard for third graders is to master adding and subtracting two- and three-digit numbers without regrouping, teachers use the children’s Quantile measures to forecast which children will have success with this skill and to identify those who may need to learn other skills or concepts before or during the lesson. Mathematics textbooks and other instructional resources are linked with the Quantile Framework, allowing teachers to match learners with targeted materials to help them better understand mathematical concepts or skills.
Learning on a Developmental Scale
Developed to align with the National Council of Teachers of Mathematics “Principles and Standards for School Mathematics,” the Quantile Framework has five content strands—Numbers and Operations, Geometry, Measurement, Algebra/Patterns & Functions, and Data Analysis & Probability. The Quantile scale ranges from Emerging Mathematician (0Q and below) to above 1600Q, and spans the mathematics continuum from concepts taught in kindergarten to those typically taught in Algebra II, Geometry, Trigonometry and Precalculus.
The Quantile scale is a taxonomy—or classification system—of mathematical skills and concepts along the continuum of mathematics development. Each content strand is annotated by “QTaxons,” which describe specific skills, objectives or grade-level expectations. Like a roadmap, QTaxons demonstrate how these skills fall along the continuum of mathematics development. Each QTaxon has a Quantile measure that estimates how difficult it will likely be for a child to learn, as compared with other skills in the taxonomy.
Quantile measures represent children’s mathematics achievement, not their grade level. A class of 30 sixth graders will likely have learners with a range of Quantile measures. Teachers use those varied Quantile measures to personalise learning and remediate as necessary, using tools and resources that match the children’s Quantile measures.
Using Quantile Measures to Support Mathematics Learning
The Quantile Web site offers teachers and parents a wealth of free resources for using Quantile measures to support and simplify personalised mathematics learning.
The QTaxon Search database enables users to search through the entire taxonomy of skills and concepts on the Quantile scale to obtain their difficulty levels. Resources, such as mathematics textbooks, Web links, worksheets, math-literature guides, black line masters and games, can also be found through the search features. The QTaxon Search allows teachers to match children with the instructional materials that best meet their mathematics learning needs.
Teachers can then use the Lesson Plan Builder to bundle these resources and search results to develop personalised lessons based on their mathematics standards. The Lesson Plan Builder enables teachers to link their instructional plans directly to resources that match the varied learning needs of their children and to download them for classroom use.
In addition, the Quantile Web site offers a database of more than 1,000 mathematics terms and concepts connected to the tools on the site. The Quantile map, a graphic representation of the Quantile Framework, is also available. The map is the only tool available that visually illustrates mathematics development and the connections between skills and concepts across the content strands.
The Science Behind The Quantile Framework
Launched in 2004, The Quantile Framework for Mathematics was developed by psychometricians at MetaMetrics, Inc., a privately held educational measurement company based in Durham, North Carolina (United States). The company’s team of psychometricians also developed the widely adopted Lexile Framework for Reading and The Lexile Framework for Writing. Based, in part, on the company’s more than 20 years of psychometric research, the release of the Quantile Framework came after four years of development, including an extensive American field study during the 2003–2004 school year. Today, MetaMetrics continues to pioneer scientifically based measures of achievement that help to link assessment with instruction, foster better educational practices and improve learning by matching children with materials that meet and challenge their abilities.
For more information on how The Quantile Framework for Mathematics can help to link assessment with instruction and improve mathematics achievement, call 1–888–539–4537 or visit www.Quantiles.com.
