1. The Quantile Framework® for Mathematics & West Virginia
A Practical Approach:
Linking Assessment to Instruction
Presented by:
Jason Turner, Manager, Professional Services

2. Today’s Session What is the Quantile Framework and
why do I need to know
about it?

3. Today’s Session
Where can Quantile
measures be found?

4. Today’s Session
What can be done with
the Quantile Framework?

5. Today’s Session
How will the Quantile
Framework help students?

6. Today’s Session How can Quantiles be used in the schools
and in the classroom?

7. The Quantile Framework for Mathematics: Question #1
What is the Quantile
Framework for
Mathematics?
Why do I need to
know about it?

8. Common Misconceptions The Quantile Framework is NOT:
An indicator of mastery of specific skills.
A list of mathematical skills.
A curriculum for mathematics.
A mathematics program.
A grade equivalent. 8

9. 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

10. The Quantile Framework
Developmental scale that locates mathematics skills and concepts within a taxonomy.
Mathematical Skill/Topic/Concept Quantile Measure (Q)
Characterizes the problem-solver with a measure on the same developmental scale.
Student Quantile Measure (Q)
The Quantile measure uses a common metric for both 10

11. Let’s define an essential concept
Vocabulary Break:
Let’s define an essential concept

12. 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.

13. 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.

14. The Quantile Measure…
Forecasts the student’s readiness to be successful with the skill after introductory instruction.

15. 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.

16. Let’s define another essential concept
Vocabulary Break:
Let’s define another essential concept

17. 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.

18. 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.

19. The Quantile Framework for Mathematics
Where can Quantile
measures be found?

20. 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

21. 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:

22. West Virginia Educational Standards Test 2 (WESTEST 2)

23. West Virginia Educational Standards Test 2 (WESTEST 2)

24. The Quantile Framework for Mathematics
What can be done
with the Quantile
Framework?

25. Two Issues for Math Educators:
First, how does a teacher
determine student readiness? OR
How does a teacher forecast
student preparedness to learn
mathematical skills or concepts?

26. Two Issues for Math Educators:
Second, how does a teacher establish the measure of difficulty for various skills in mathematics?

27. Quantile Scale Skill Difficulty + Student Readiness
Sally & Jim
1000Q
Skill Difficulty
+ Student Readiness
Raul
900Q
Strengthens Instructional Strategies
+50
800Q
Jacob, Lyn, Victor
- 50
700Q 27 27

28. 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.
Expected
Success
350Q
600Q
850Q
1100Q
1350Q
10%
25%
50%
75%
90%

29. Student Mathematics Ability
Success Rates for Student of Similar Ability with Math Skills of Different Skill Demands
Student Mathematics Ability
Skill Demand
Skill Description
Expected Success
750Q
250Q
Locate points on a number line.
90%
500Q
Use order of operations including parenthesis to simplify numerical expressions
75%
Translate between models or verbal phrases and algebraic expressions.
50%
1000Q
Estimate and calculate areas with scale drawings and maps.
25%
1250Q
Recognize and apply definitions and theorems of angles formed when a transversal intersects parallel lines.
10%

30. Benefits of the Quantile Framework
DETERMINE: student readiness
ESTABLISH: task difficulty
STRENGTHEN: classroom teaching
practices and strategies

31. 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
Let’s take a look at other points in history where UNIFICATION has been important between a theory and application. 31

32. The Quantile Framework for Mathematics
How will the framework help the students and teachers in my district?

33. Picturing Mathematics with the
Quantile Map 33

34. Gaps in learning: Student Ability 350Q Skill Difficulty 850Q
Student: 350Q
Qtaxon: 850Q
What must happen to close this gap?
What must happen to narrow this gap?

35. 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

36. The Quantile Framework: Practical Benefits
Helps 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

37. The Quantile Framework for Mathematics
How can Quantiles be
used in the classroom?

38. Let’s define some more essential concepts
Vocabulary Break:
Let’s define some more essential concepts

39. 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.

40. 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

41. 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.

42. 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 42

43. 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 43

44. The Knowledge Cluster
Accessing the knowledge cluster

45. Knowledge Clusters

46. Knowledge Clusters
Q Taxon ID numbers

47. 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. 47

48. 48

49. . 49

50. Subtract 2- and 3-digit numbers with regrouping.50

51. Quantile Resources

52. Quantile Resources Math Skill Database Math At Home QTaxon Search
Knowledge Clusters
Curriculum Alignment
Textbook lesson alignment
Instructional Resources
“Leading/Reverse” QTaxon Search
Math At Home

53. Quantile Professional Development
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 LEXILES/ or

54. Contact Information
Jason Turner Manager, Professional Development MetaMetrics Inc.