implementing response to intervention (rti) response to intervention (rti) ... 100 ones = 10 tens =...

Implementing Response to Intervention (RtI)

For Teaching Whole Number Concepts and Skills to Students with Learning Disabilities (LD)

1NUMERACY CONFERENCE FOR ADMINISTRATORS

WICHITA, KANSASMARCH 2, 2011

Presenters

Alida Anderson

American University Washington, DC

[email protected]

Peg Akin

KP MathematicsPhoenix, AZ

[email protected]

RTI – A Pictorial

3

Note Page

4

Overview

5

• Math issues facing students with LD

• New numeracy standards for all

• RtI background, principles, and implementation

• Intervention principles for numeracy

• Numeracy intervention / Students with LD

Overview

6Students with LD

Response toIntervention

Numeracy Standards

RtI Background, Principles,

and Implementation

RtI Background, Principles,

and Implementation

7

The Promise of RtI

Early identification

Universal design for learning (UDL)

Intervention

Prevention

Improved instruction for ALL 8

The Reality of RtI

Implementation variability

Guidance to establish/sustain

Stakeholder involvement

Lack of information on math instruction

No definitive benchmark skill sets9

RtI Principles for Mathematics (See Chart 1)

Tiers

Identification

Intervention

Growth/response

Evaluation

Special education10

Implementing RtI in Mathematics (See Chart 2)

Definition Focus Program Instruction Instructor Setting Grouping Time Assessment

11

RtI Implementation Issues

Diverse paths

Different models and standards

Needs analysis

Resource mapping (see Chart 3)

12

Tier Student needs / School services in place

Instructional Setting

Behavior Assessment Curriculum Instructional Strategies

Tier 3

Tier 2

Tier 1

Customizing RtI (See Chart 3)

13

Math Issues Facing Students with Learning Disabilities (LD)

14

Math Difficulties for Students with LD (see Chart 4, adapted from Mercer, 1994)

Perception Memory Language Behavior Auditory Reasoning Motor

15

Math Difficulties for Students with LD

Conceptual vs. procedural difficulties

Procedural: Incorrect or misordered procedures

Conceptual: incorrect response from absent or incorrect principles or concepts

16

LD/Math-Related Problems (see Chart 4)

Conceptual vs. procedural difficulties?– Perception – Executive function

Dysfluency (efficiency, accuracy, flexibility)

Lacking a sense of ‘ten-ness’ (Fiefer & De Fina, 2005)

17

18

Conceptual or Procedural Error?

New Numeracy Standards for All

New Numeracy Standards for All

19

National Council of Teachers of Mathematics (2000)

National Research Council (2006)

National Math Advisory Panel (2008)

Common Core State Standards initiative (2010)20

Recommending Organizations

Conceptual understanding of key ideas

Procedural fluency

Problem solving

Outcomes for All

21

Content for All

Place value

Basic operations

Problem solving skills

22

Explicit instruction

Organizing principles serve as anchors

Physical models to represent place value

Opportunities to articulate understanding

Practice based on prior understanding

Instruction for All

23






Instruction for All

24

Physical Models

Base Ten Blocks

Digi-Blocks

KP Ten-Frame Tiles

25






Instruction for All

26

Place ValuePlace ValuePlace Value

Comparing

Ordering

DivisionMoney

Equivalence

SubtractionCounting

Addition

Grouping

Written algorithms

Multiplication

Numbernames &symbols

Place Value as an Organizing Principle

27

10 ones = 1 ten

Equivalence

CountingGrouping


28

Big Idea!

Ten-frame formation

100 ones = 10 tens = 1 hundred


29

Equivalence

CountingGrouping

10 20 30 40 50

60 70 80 90 100

5 + 9

Addition

GroupingPlace Value as an Organizing Principle

30

tens ones

5 + 9


31

Addition

Grouping

tens ones

5 + 9


32

Addition

Grouping

tens ones

5 + 9


33

Addition

Grouping

Addition

Grouping

tens ones

1 4

5 + 9

5 + 9 = 14

Numbernames &symbolsPlace Value

as an Organizing Principle

34 10 + 4


35

Grouping

Numbernames &symbols

Equivalence

6 hundreds60 tens600 ones

2 tens20 ones

9 ones

Common Core Readiness??

ACT, Inc. determined how students who score in the ACT’s “college ready” range performed on the items deemed reflective of common-core content.

Reported in Education Week, January 12, 2011

36

Inference: Early intervention is needed to build numeracy skills.

“The weakest math area was number and quantity, where only 34 percent showed proficiency in skills considered foundational to later math study.”

Intervention Principlesfor Numeracy

37

Student-teacher ratio

Repetition

Scripted procedures/lessons

Pace

Sequence

Concrete representations

Intervention Principles (See Chart 5)

Student-teacher ratio

Repetition

Scripted procedures/lessons

Pace

Sequence

Concrete representation

38

39

1. Screen all students.2. Focus on whole numbers.3. Use explicit, systematic instruction.4. Base word problem instruction on common structures.5. Represent mathematical ideas visually.6. Develop fluent retrieval of basic arithmetic facts.7. Monitor progress.8. Use motivational strategies.

Assisting Students Struggling with Mathematics: RtI for Elementary and Middle Schools

39

Institute of Education Sciences Recommendations (See Chart 6)

Teach for

Understanding

Teach for

Understanding40

“Ideal” Intervention Curriculum(from NCTM, NRC, NMAP, CCSS, IES)

“Ideal” Intervention Curriculum(from NCTM, NRC, NMAP, CCSS)

•Diagnostic assessment to identify gaps in knowledge and skill

•Coherent, sequenced instruction

•Explicit focus on the base-ten system

•Every topic anchored to place value

•Concrete-Representational-Abstract approach throughout

•Common physical model

•Development of reasoning skills through questioning and discussion

•Ample opportunity for students to communicate mathematical understanding

•Targeted progress monitoring

•Application of mathematical concepts to contextual problems

•Transitional strategies•Frequent practice41

Numeracy Intervention / Students with LD

Numeracy Intervention / Students with LD

42

RtI-Math-LD Intersection (See Chart 7)

43

Curriculum Feature(math)

Intervention Principle(RtI)

Learning Difficulty(LD)

•Coherent, sequenced instruction

•Explicit focus on the base-ten system

•Every topic anchored to place value

•Concrete-Representational-Abstract approach throughout

•Common physical model

•Transitional strategies

•Development of reasoning skills through questioning and discussion

44

Look for these features!

Curriculum Example: 46÷3

45


Curriculum Example: 46÷3tens ones

46

Do I have enough tens to make one or more groups of 3 tens?

?


47

? Do I have enough tens to make another group of 3 tens?

Do I have enough tens to make one or more groups of 3 tens?

?


48

? What can I do to keep dividing the remaining ten?


49

? Do I have enough ones to make one or more groups of 3 ones?

? What can I do to keep dividing the remaining ten?


50



51



52

? Do I have enough ones to make moregroups of 3 ones?


53



54



46 ÷ 3 = 15 R1or

46 ÷ 3 = 15 1/3

1 5

1

55

? How many ones do I have left?

? How many groups of 3 tens do I have?

? How many groups of 3 ones do I have?


4 63

T Otens ones

56

?

Representational Abstract


4 63

T O1

31

_

tens ones

57

?



4 63

T O1

31

_0

tens ones

6

58


?


4 63

T O1

31

_0

tens ones

6

5

1 5–1

46 ÷ 3 = 15 R1

59

?


Instructional Support for CCSS Begins Now

Professional Development should . . .

• Communicate expectations• Be motivational• Strengthen teachers’ knowledge of mathematics• Guide teachers’ instructional practice• Support teachers’ growth• Be ongoing and continuous• Build and sustain momentum

Great Things Are Possible!

implementing response to intervention (rti) response to intervention (rti) ... 100 ones = 10 tens =...

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