The Quantile Framework® for

Mathematics & West Virginia

A Practical Approach:Linking Assessment to

InstructionPresented by:

Jason Turner, Manager, Professional Services

jturner@lexile.com

Today’s Session

What is the Quantile

Framework and

why do I need to know

about it?

Today’s Session

Where can Quantile

measures be found?

Today’s Session

What can be done with

the Quantile Framework?

Today’s Session

How will the Quantile

Framework help students?

Today’s Session

How can Quantiles be

used in the schools

and in the classroom?

The Quantile Framework for Mathematics: Question #1What is the

QuantileFramework for Mathematics?

Why do I need toknow about it?

An indicator of mastery of specific skills.

A list of mathematical skills. A curriculum for mathematics. A mathematics program. A grade equivalent.

Common MisconceptionsThe Quantile Framework is NOT:

The Quantile Framework… …is like a “yardstick”

---it’s the way to measure the development of:

Students’ mathematical knowledge and Difficulty of math skills and topics

Developmental scale that locates mathematics skills and concepts within a taxonomy.

Characterizes the problem-solver with a measure on the same developmental scale.

The Quantile measure uses a common metric for both

The Quantile Framework

Student Quantile Measure (Q)

Mathematical Skill/Topic/Concept Quantile Measure (Q)

Vocabulary Break:

Let’s define an essential concept

What is a Quantile Measure (QMeasure)?

QMeasures are applied to both students and math skills and concepts.

Students: The Quantile measure for an individual or student is the level at which he or she is ready for instruction and has knowledge of the prerequisite mathematical concepts and skills necessary to succeed. When applied to students, the QMeasure indicates the student’s readiness for instruction.

What is a Quantile Measure (QMeasure)?

QMeasures are applied to both students and math skills and concepts.

Skills & Concepts: When applied to mathematical skills and concepts, QMeasures indicate the task difficulty associated with a skill or concept relative to other mathematical skills and concepts. For example, the skill of rounding whole numbers to a given place value has a QMeasure of 410Q.

The Quantile Measure…

Forecasts the student’s readiness to be successful with the skill after introductory instruction.

The Quantile Measure…

Also refers to the difficulty of a mathematical skill or concept, or how difficult the skill or concept (QTaxon) is compared to others.

Vocabulary Break:

Let’s define another essential concept

What is a QTaxon? Derived from taxonomy (a

category or group) A specific

mathematical skill or concept, e.g., to perform long division with remainders is a specific mathematical skill or concept, or QTaxon.

Within the Quantile Framework, QTaxon is the formal term for skill or concept.

Why Do I Need To Know About It? Developmental Scale: Allows districts

and schools to track growth. Common Scale: Places task difficulty

and student readiness on the same scale. Differentiation & Targeting: Provides math teachers the means to

differentiate and target math instruction based on the

student’s status.

The Quantile Framework for Mathematics

Where can Quantile

measures be found?

Where can I find the Quantile measure?

State End-of-Grade Tests (Texas, West Virginia, North Carolina, & Wyoming)

Scholastic Math Inventory (SMI) Voyager V-Math Pearson PASeries

Where can I find the Lexile measure?• A student’s Lexile measure can be

found on the student report for the WESTEST 2 for grades 3 -8 and 10.

• More information on a student’s Lexile measure based on the WESTEST 2 score is available on the West Virginia Department of Education’s Web site at:• http://wvde.state.wv.us.oaa

West Virginia Educational Standards Test 2 (WESTEST 2)

West Virginia Educational Standards Test 2 (WESTEST 2)

The Quantile Framework for Mathematics

What can be donewith the Quantile

Framework?

Two Issues for Math Educators:First, how does a teacherdetermine student

readiness?OR How does a teacher

forecaststudent preparedness to

learnmathematical skills or

concepts?

Two Issues for Math Educators:

Second, how does a teacher establish the measure of difficulty for various skills in mathematics?

+ Student Readiness

Skill Difficulty

Strengthens Instructional Strategies

Quantile Scale

700Q

800Q

900Q

1000Q

+50

- 50

Sally & Jim

Raul

Jacob, Lyn, Victor

Success Rates for Students of Different Mathematics Ability with a Skill at a Defined Quantile Measure

Student Mathematics

Ability

Skill - Locate points in all quadrants of the coordinate plane using

ordered pairs.

ExpectedSuccess

350Q

600Q

850Q

1100Q

1350Q

850Q

850Q

850Q

850Q

850Q

10%

25%

50%

75%

90%

Success Rates for Student of Similar Ability with Math Skills of Different Skill Demands

Student Mathematics

AbilitySkill

Demand Skill DescriptionExpected Success

750Q 250Q Locate points on a number line. 90%

750Q 500Q Use order of operations including parenthesis to simplify numerical expressions 75%

750Q 750Q Translate between models or verbal phrases and algebraic expressions. 50%

750Q 1000Q Estimate and calculate areas with scale drawings and maps. 25%

750Q 1250Q Recognize and apply definitions and theorems of angles formed when a transversal intersects parallel lines. 10%

Benefits of the Quantile Framework

DETERMINE: student readiness

ESTABLISH: task difficulty

STRENGTHEN: classroom teaching

practices and strategies

Benefits of the Quantile Framework

LINK: student ability to skill difficulty (using a common measure)

FORECAST: student success rate

(after introductory lessons) TRACK: growth over time

The Quantile Framework for Mathematics

How will the framework

help the students andteachers in my

district?

Picturing Mathematics with the Quantile Map

Gaps in learning:

Student Ability 350Q

Skill Difficulty 850Q

What must happen to close this gap?

Student: 350Q Qtaxon: 850Q

What must happen to narrow this gap?

The Quantile Framework: Practical Benefits

Helps teachers…

Differentiate instruction • by linking students with

instruction at their level • by knowing the Quantile

level of the skill or concept and matching it with the Quantile measure of the student

Determine student readiness • by knowing each student’s

Quantile measure

Forecast student success with specific skills and concepts

The Quantile Framework: Practical BenefitsHelps teachers…

Monitor student math progress• by tracking student growth

using the Quantile developmental scale

Describe pre-requisite skills needed to learn more advanced mathematical concepts

Tailor teaching methods in the classroom to ensure a greater level of understanding and application

Determine supplementary and upcoming skills for students in need of enrichment

The Quantile Framework for Mathematics

How can Quantiles be

used in the classroom?

Vocabulary Break:

Let’s define some more essential concepts

What is a Prerequisite QTaxon?

For any mathematical skill or concept there are prerequisite skills and concepts necessary to succeed.

When we refer to Prerequisite QTaxons, we mean those skills that are necessary to be successful with the skill in question.

For example, to successfully perform division with remainders, one must be able to successfully perform simple division without remainders.

What’s an Impending QTaxon?

Every mathematical skill or concept is building toward another skill or concept.

For example, the multiplication of single digit numbers comes after the addition of double digit numbers, and is, therefore, an impending skill…

Impending QTaxons are the skills that ‘come next’ or are the next steps in the Quantile taxonomy

What’s a Supplemental QTaxon? A Supplemental QTaxon is a

mathematical skill or concept which broadens, enhances or deepens knowledge of a skill or concept, but is not necessary for success with that skill or concept.

For example, a Supplemental QTaxon of “Calculate the areas of triangles, parallelograms, trapezoids, circles and composite figures”, is “Use models to develop formulas for finding areas of triangles, parallelograms, trapezoids, and circles” This skill enhances understanding of the QTaxon in question, but is not necessary for success.

An Essential Feature of the Quantile Framework:The Knowledge Cluster!

Precursory skills to ensure prior knowledge

Supporting skills to connect and add depth across content strands

Quantile measures to address the degree of difficulty for each skill

The Power of the Knowledge Cluster To inform instruction and address the

needs and abilities of each student

To add depth and breadth to concepts in mathematics

To adjust Individual Education Plans according to Quantile measures

The Knowledge Cluster

Accessing the knowledge cluster

Knowledge Clusters

Knowledge Clusters

Q Taxon ID numbers

A QTaxon and It’s Knowledge Cluster

QT-M-254 Investigate and determine

the relationship between the diameter and the

circumference of a circle and the value of pi; calculate the

circumference of a circle.

Subtract 2- and 3-digit numbers with regrouping.

Quantile Resources

Quantile Resources

Math Skill Database QTaxon Search

• Knowledge Clusters• Curriculum Alignment• Textbook lesson alignment• Instructional Resources• “Leading/Reverse” QTaxon Search

Math At Home

Quantile Professional Development helps put the Quantile Framework to work for you

and your students. Our Master Facilitators empower you with the knowledge and skills

to implement the Quantile Framework in your classroom.

QUANTILES IN YOUR DISTRICT:Understand how the Quantile Framework for Mathematics was developed and learn to use Quantiles to understand task difficulty.

STEP 1: UNDERSTANDING AND USING THE QUANTILE FRAMEWORK FOR

MATHEMATICS:Hands on practice using the tools for differentiating mathematics to meet standards. Learn to use Quantiles to understand task difficulty and student readiness.

STEP 2: PUTTING QUANTILES TO WORK IN YOUR CLASSROOM: This workshop offers strand specific, in-depth study of the connections along the mathematics curriculum.

For more information, call 1-888-LEXILES/919-547-3400 or email profdev@Lexile.com.

Quantile Professional Development

Contact Information

Jason TurnerManager, Professional DevelopmentMetaMetrics Inc.jturner@lexile.com