Quantiles
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THE QUANTILE FRAMEWORK
The Quantile Scores… • Will be reported on WESTEST 2 score reports WESTEST 2 Sample Score Report • What is it?
The QUANTILE FRAMEWORK is… Like a “gauge” or a “yardstick” It’s a way to measure the development of: a student’s mathematical knowledge AND the difficulty of math skills & topics
The Quantile Framework… • A Developmental Scale that locates mathematical skills and concepts within a taxonomy. • Characterizes the problem-solver (student) with a measure on the same developmental scale
Skills are Rated by QTaxons… • What is a Q-Taxon? A Mathematical skill or concept • Where does the list of Q-Taxons come from? National Council of Teachers of Math (NCTM) State Curriculums • How are the strands determined? Based on content strands from NCTM and state standards
The QUANTILE MAP • Offers a snapshot of the skills & concepts (QTaxons) within a curriculum of 5 content strands. • Offers insight into the developmental framework of the Quantile Framework. • Offers information about the level of difficulty of the skills and concepts (Q-Taxons).
The Quantile Framework… • How were Quantile measures for Q-Taxons developed? • Identifying items that met psychometric criteria • Identifying items that are representative of the Q-Taxon and match what is typically taught during a first lesson on that subject • Relationships with both precursory and impending Q-Taxons
Knowledge Clusters QT 655
QT 622
QT 644
QT 210 QT 308
QT 263 QT 275
QT 208: Solve one-step linear equations and inequalities and graph the solutions of the inequalities on a number line. QT 97 QT 180 QT 132
QT 605 QT 623
QT 604
QT 548 QT 218
Quantile Scale Development • Field Study February 2004 • Tests for Grades 2 through Algebra II • Ancillary Materials: rulers, protractors, calculators, and reference sheets • Sample of 9,847 students in 34 schools across 6 states
What does the Measure Mean? • A range for the quantile measure of a student identifies the learning frontier of mathematics skills in which a student can have success after some introductory instruction. • A Quantile measure for the skill offers insight into its difficulty for a student to initially learn that concept.
Instructional Implications… DIFFERENTIATED INSTRUCTION • Understand content progression • Determine student readiness • Differentiate instruction by linking students with appropriate instruction at their level
Instructional Implications… INSTRUCTIONAL NEEDS OF THE STUDENT • How does the range of ability levels in the classroom match with the targeted Q-Taxon Quantile measure? • How will we help to prepare the students who are not ready for the topic? • Are there students who might need enrichment? How can their needs be addressed?
The Quantile Website
www.Quantiles.com
Applications of the Quantile Measure on the website… • Textbooks • Websites & Games • Worksheets & Other Downloadables • Math Literature Connections • Other Instructional Products
QUANTILE WEBSITE
Q-TAXON SEARCH
MATH AT HOME
The Quantile Framework is NOT: • An indicator of mastery of a specific skill • A list of mathematics skills • A curriculum for mathematics • A mathematics program • A grade equivalent • A measure for a worksheet or test
The Quantile Framework does help: • Predict readiness • Monitor student math progress • Adapt instructional methods • Understand pre-requisite skills for advanced concepts • Match students to appropriate materials at their level • Link big math concepts to state curriculum • Forecast student performance on end-of-year tests
The Quantile Scores… • Will be reported on WESTEST 2 score reports WESTEST 2 Sample Score Report • What is it?
The QUANTILE FRAMEWORK is… Like a “gauge” or a “yardstick” It’s a way to measure the development of: a student’s mathematical knowledge AND the difficulty of math skills & topics
The Quantile Framework… • A Developmental Scale that locates mathematical skills and concepts within a taxonomy. • Characterizes the problem-solver (student) with a measure on the same developmental scale
Skills are Rated by QTaxons… • What is a Q-Taxon? A Mathematical skill or concept • Where does the list of Q-Taxons come from? National Council of Teachers of Math (NCTM) State Curriculums • How are the strands determined? Based on content strands from NCTM and state standards
The QUANTILE MAP • Offers a snapshot of the skills & concepts (QTaxons) within a curriculum of 5 content strands. • Offers insight into the developmental framework of the Quantile Framework. • Offers information about the level of difficulty of the skills and concepts (Q-Taxons).
The Quantile Framework… • How were Quantile measures for Q-Taxons developed? • Identifying items that met psychometric criteria • Identifying items that are representative of the Q-Taxon and match what is typically taught during a first lesson on that subject • Relationships with both precursory and impending Q-Taxons
Knowledge Clusters QT 655
QT 622
QT 644
QT 210 QT 308
QT 263 QT 275
QT 208: Solve one-step linear equations and inequalities and graph the solutions of the inequalities on a number line. QT 97 QT 180 QT 132
QT 605 QT 623
QT 604
QT 548 QT 218
Quantile Scale Development • Field Study February 2004 • Tests for Grades 2 through Algebra II • Ancillary Materials: rulers, protractors, calculators, and reference sheets • Sample of 9,847 students in 34 schools across 6 states
What does the Measure Mean? • A range for the quantile measure of a student identifies the learning frontier of mathematics skills in which a student can have success after some introductory instruction. • A Quantile measure for the skill offers insight into its difficulty for a student to initially learn that concept.
Instructional Implications… DIFFERENTIATED INSTRUCTION • Understand content progression • Determine student readiness • Differentiate instruction by linking students with appropriate instruction at their level
Instructional Implications… INSTRUCTIONAL NEEDS OF THE STUDENT • How does the range of ability levels in the classroom match with the targeted Q-Taxon Quantile measure? • How will we help to prepare the students who are not ready for the topic? • Are there students who might need enrichment? How can their needs be addressed?
The Quantile Website
www.Quantiles.com
Applications of the Quantile Measure on the website… • Textbooks • Websites & Games • Worksheets & Other Downloadables • Math Literature Connections • Other Instructional Products
QUANTILE WEBSITE
Q-TAXON SEARCH
MATH AT HOME
The Quantile Framework is NOT: • An indicator of mastery of a specific skill • A list of mathematics skills • A curriculum for mathematics • A mathematics program • A grade equivalent • A measure for a worksheet or test
The Quantile Framework does help: • Predict readiness • Monitor student math progress • Adapt instructional methods • Understand pre-requisite skills for advanced concepts • Match students to appropriate materials at their level • Link big math concepts to state curriculum • Forecast student performance on end-of-year tests
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