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The Quantile® Framework for Mathematics is a tool that a growing number of educators are using to take the guesswork out of mathematics instruction. States across the nation are reporting Quantile measures for their students because the Quantile measure empowers educators to utilize the best practices in mathematics and meet the needs of ALL learners.
If you are a Principal or an Educator interested in understanding the Quantile Framework for Mathematics and how it can increase student achievement, improve mathematics instruction, and help teachers differentiate instruction seamlessly, then you have come to the right place!
Overview
The Quantile Framework is a developmental scale that empowers educators to:
- target instruction
- forecast student understanding
- improve mathematics instruction and achievement
- forecast performance on high-stakes, end-of-year tests
- identify appropriate resources to differentiate instruction
It demonstrates which mathematics skills a learner is ready for and which ones require further instruction. Teachers can determine a student’s readiness to learn more advanced skills. They can also determine how likely a student is to successfully solve more complex problems if provided with targeted instruction.
The Quantile Framework uses a common, developmental scale to describe a student’s mathematical achievement and the difficulty of specific mathematical skills and concepts from prekindergarten through precalculus.
Now the mathematics curriculum, the materials to teach mathematics, and the students themselves are all described with the same metric.
How Does It Work?
The process is simple. Once linked to a state end-of-grade assessment or norm-referenced test, the measures are made available to teachers in the form of a class roster from the student report. Then teachers can make educated decisions about mathematics instruction. We offer a suite of free on-line tools for teachers to differentiate their instruction to meet the needs of the diverse learners in their classroom.
How Can Instruction Be Targeted to Meet a Learner's Needs?
We know that learning is developmental. This means that every student will learn at their own pace in their own time along a developmental path, marked with achievable milestones. Just like with reading, if a book is too hard or too easy, little progress is made. However, when we target the right book for the right student we can increase reading success. The same applies for mathematics. When students are presented with tasks that are too hard or too easy, growth is limited. However, using a tool like the Quantile Framework, teachers can evaluate if the skills a student is learning in the classroom are right for him/her.
Take Jenny for example: Jenny is a good student in every sense of the word. She has regular attendance, is engaged in class discussions, and asks questions when she thinks she's stuck. She turns in her homework every day. She is conscientious and appears to put forth a good effort. Although she seems to struggle at times, she gets help during the tutorial sessions offered by her math teacher. However, her teachers and parents have noticed that she has difficulty making sense of new skills and concepts and they truly don't see a real difference in her end-of-grade test scores between this year and last year.
- Why is Jenny having such a hard time?
- What can be done to help Jenny learn?
- Is Jenny learning the right skills and concepts appropriate for her?
By locating Jenny's Quantile measure on her end-of-year test report and then referencing the skills and concepts on the Quantile scale (via the QTaxon database), teachers can match the state's curriculum to the skills and concepts Jenny is ready to learn.
During progress report time or at a parent-teacher conference, Jenny's parents can see what she is ready to learn. These skills can be compared to the skills which she is currently developing or has a strong command. This information can then be used to better provide support at home throughout the school year and during the summer to ensure academic progress.
Click here to find out exactly how teachers and parents can use Jenny's Quantile measure to understand what skills she is ready to learn. (You need Macromedia Flash to view this page. Get Flash)
The Quantile Framework provides a tool to identify and match resources within the school to meet the needs of every learner. Depending upon their needs, some teachers might use Quantile measures to differentiate instruction through flexible groups, pace the curriculum, guide curriculum mapping, recognize the need to share or sort resources and even distribute some plans across grade levels.
Understanding a Student's Quantile Measure
The Quantile measure on a student's report is a number followed by the letter Q. Measures range from EM, which stands for 'Emerging Mathematician,' to above 1400Q.
The Quantile measure for a student provides the following types of information for the educator:
- where along the mathematics continuum (the journey in math from early skills to more advanced ones) the student lies
- what specific skills a student is ready to learn next
- what skills a student has relative command of upon which to build new skills
- how difficult an upcoming skill in the curriculum is compared to the student's mathematical understanding
- what level of success a student is expected to have on an upcoming topic or skill
- when multiple measures are taken all year, a prediction of how that student will perform on high-stakes tests
Educators can use Quantile measures to match students, by readiness level, to level-appropriate instructional materials and to forecast understanding. For example, a student with a Quantile measure of 500Q would be ready for instruction of mathematics problems at a demand level of 500Q.
The Quantile measure for an individual or student is the level at which he or she is ready for instruction (50% competency with the material) and has knowledge of the prerequisite mathematical concepts and skills necessary to succeed. The Quantile scale ranges from Emerging Mathematician (0Q and below) to above 1400Q.
The Quantile measure does not relate to a specific grade, per se, so the score is developmental as it spans the mathematics continuum from prekindergarten mathematics through the content typically taught in Algebra II, Geometry, Trigonometry and Precalculus. The measure tells a teacher what mathematics the student is ready for next. It provides insight into how a learner will handle homework the very night a new concept is taught.
A range for the Quantile measure of a student is 50Q above and 50Q below the Quantile measure of a student (44% - 56% competency). This range identifies the learning frontier of mathematics skills in which a student can have success after some introductory instruction.
Teachers can search the QTaxon database for a list of specific skills and concepts which align to their own state's curriculum standards.
States which report Quantile measures also have specific state custom maps which demonstrate the alignment of QTaxons to state standards for each grade level.
Once teachers have targeted their instruction, anchored by their state standards, they can match their students' Quantile measures to the difficulty of the skills and concepts they have to teach.
With this information, they are empowered to plan more targeted lessons, differentiate instruction, and understand their student's strengths and weaknesses in mathematics. A child's readiness to learn is the missing link to providing differentiated instruction. The Quantile Framework for Mathematics enables educators to plan lessons with ease.
Coupled with our professional development, teachers can use our three-step process to make the Quantile measure actionable in the classroom, use our free suite of on-line tools to match skills/concepts to students, search the database for knowledge clusters, find resources, and more!
What Does the Database Provide?
The database is accessed through the QTaxon Search. Within the results page, one can click on each of the skills/concepts to see the knowledge cluster for that QTaxon (skill/concept). The knowledge cluster is a group of skills related to a particular QTaxon. It provides information about what skills come before that skill and what skills would provide support or enrichment. This information is provided for the entire taxonomy of skills/concepts along the mathematics continuum from skills taught from prekindergarten through precalculus.
Further, after searching for skills that the student is ready to learn, educators can click on the links provided that lead to resources such as worksheets, games, websites, mathematics textbook lessons, and more.
Teachers can refer parents to these resources, or select our Request Info Form, which allows a parent/teacher to send the measure and child’s grade/state to our research associate who can provide a more detailed explanation of what the measure means.
Resources
Resources such as fact sheets, the Quantile map, typical grade ranges and more can be found on the Resources page.