implementing response to intervention (rti) response to intervention (rti) ... 100 ones = 10 tens =...
TRANSCRIPT
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
Peg Akin
KP MathematicsPhoenix, AZ
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
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
24
Physical Models
Base Ten Blocks
Digi-Blocks
KP Ten-Frame Tiles
25
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
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
Place Value as an Organizing Principle
28
Big Idea!
Ten-frame formation
100 ones = 10 tens = 1 hundred
Place Value as an Organizing Principle
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
Place Value as an Organizing Principle
31
Addition
Grouping
tens ones
5 + 9
Place Value as an Organizing Principle
32
Addition
Grouping
tens ones
5 + 9
Place Value as an Organizing Principle
33
Addition
Grouping
Addition
Grouping
tens ones
1 4
5 + 9
5 + 9 = 14
Numbernames &symbolsPlace Value
as an Organizing Principle
34 10 + 4
Place Value as an Organizing Principle
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÷3
Curriculum Example: 46÷3tens ones
46
Do I have enough tens to make one or more groups of 3 tens?
?
Curriculum Example: 46÷3tens ones
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?
?
Curriculum Example: 46÷3tens ones
48
? What can I do to keep dividing the remaining ten?
Curriculum Example: 46÷3tens ones
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?
Curriculum Example: 46÷3tens ones
50
? Do I have enough ones to make one or more groups of 3 ones?
Curriculum Example: 46÷3tens ones
51
? Do I have enough ones to make one or more groups of 3 ones?
Curriculum Example: 46÷3tens ones
52
? Do I have enough ones to make moregroups of 3 ones?
Curriculum Example: 46÷3tens ones
53
? Do I have enough ones to make moregroups of 3 ones?
Curriculum Example: 46÷3tens ones
54
? Do I have enough ones to make moregroups of 3 ones?
Curriculum Example: 46÷3tens ones
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?
Curriculum Example: 46÷3
4 63
T Otens ones
56
?
Representational Abstract
Curriculum Example: 46÷3
4 63
T O1
31
_
tens ones
57
?
Representational Abstract
Curriculum Example: 46÷3
4 63
T O1
31
_0
tens ones
6
58
Representational Abstract
?
Curriculum Example: 46÷3
4 63
T O1
31
_0
tens ones
6
5
1 5–1
46 ÷ 3 = 15 R1
59
?
Representational Abstract
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!