Response to Intervention and Early Mathematics Intervention: Recommendations for Implementation Kathleen Hughes
Jacob Williams
The University of Texas at Austin
Department of Special Education
Meadows Center for Preventing Educational Risk: Mathematics Institute for Learning Disabilities and Difficulties
Funded by the Texas Education Agency:
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
1
Advance Organizer
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Overview of RtI Early Math Project
Mathematics Difficulties & National Math Panel Assessment & Progress Monitoring
Tier 2 Intervention Booster Lessons
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
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RtI Early Math Project
Management
•  Diane P. Bryant, Ph.D.
–  Project Director
–  Curriculum development and PD in mathematics
–  Member of state task force on mathematics & RtI for upper
elementary & middle school
–  Co-author of mathematics tests and publications
•  Brian R. Bryant, Ph.D.
–  Project Coordinator for Assessment
–  Over 20 years of test development experience
–  Co-author of various tests and publications
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
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Overview of RtI Early Math
Project Activities
•  Stakeholder Contacts & Communication
–  Focus groups [teachers-beginning and June 2008, curriculum and mathematics
specialists, Director of Mathematics Curriculum for TEA ([Paula Moeller)]
–  Mathematics coordinators (districts in which we conducted the studies:
meetings and observation)
–  Superintendents, Assistant Superintendents, Executive Directors (school
districts)
–  Core Group
–  TEA curriculum
–  TETNs (for education service centers)
–  Web casts
–  Invited Workshops (Region 11 workshop, Region 11 leadership conference;
Region 12; TEPSA; national conferences)
–  Consultants’ input (national - intervention and assessment)
–  RtI Specialists input (school district)
–  Lesson and Assessment Feedback (verbal and rating scales)
–  Principals’ input (schools in which we conducted the studies)
–  Education Service Centers - Math Specialists - requested input about school
selection for Intervention Scale-up (2008-2009)
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
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State Involvement Tier 2 Intervention
Sites
TEMIs
2006-2007
Assessment
Pilot Conroe (2),
2006-2007
Initial Research
Region 13 PISD,
BISD (1), PISD (3),
DVISD, L-C ISD (1)
2007-2008
Pilot/Research:
Region 4 LaPorte
Region 12 CCI (MW)
Region 13 PISD (3),
DVISD
2007-2008
Assessment
Sites
2008-2009: Bilingual
(Spanish) Assessments
Scale-up & Interventions
Pilot
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
DVISD (Popham)
Region 17
L-C
(North)
2008-2009
16 ESCs (ISUP)
Tier 3
5
Mathematics Difficulties
•  Research shows developmental delays
–  Number Sense
–  Arithmetic Combinations
–  Counting strategies
–  Procedural and conceptual knowledge to solve
problems
–  Possible memory or cognitive deficits
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
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Mathematics Education: National Math Panel, Final Report 2008
Report Highlights:
•  Core Principles of Math Instruction
–  Pre-K to 8th grade mathematics areas should
be streamlined and include well-defined topics
–  Proficiency with whole numbers, fractions,
and certain aspects of geometry and
measurement are the foundations for algebra
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
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National Math Panel, cont.
•  Conceptual understanding, computational
and procedural fluency, and problem solving
skills are equally important and mutually
reinforce each other
•  Students should develop immediate recall of
arithmetic facts to free the “working
memory” for solving more complex problems
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
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RtI Assessment & Progress Monitoring
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
9
Tier I: Identification of At-Risk
Math Students
•  Assessment
–  Texas Early Mathematics Inventory-Progress Monitoring, TEMI-PM (universal screener) •  Fluency based
•  Completed three times per year (Fall, Winter,
Spring)
–  Texas Early Mathematics Inventory-Outcome, TEMI-O •  Mathematics problem solving
•  Computation
•  Measures broader based TEKS
•  Completed three times per year (Fall, Winter,
Spring)
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
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TEMI-PM •  Designed to identify Tier II students
•  Kindergarten, 1st and 2nd grade
•  Four Subtests
–  Kindergarten:
•  Magnitude comparisons
•  Number sequence
•  Subitizing
•  Number identifications
–  1st and 2nd grade:
•  Magnitude Comparison
•  Number sequence
•  Place value
•  Addition/subtraction combinations
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
11
Using Grade 1 Number Sequences as an example…
Page markers.
“STOP” signs.
© 2008 Meadows Center
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TEMI-O
•  TEMI-O Subtests:
–  Mathematics Problem Solving and Computation
–  Designed to assess broad based mathematics
TEKS
•  Number, Operation, and Quantitative Reasoning
•  Patterns, Relationships, and Algebraic Thinking
•  Geometry and Spatial Reasoning
•  Measurement
•  Probability and Statistics
•  Underlying Processes and Mathematical Tools
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
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Place
Marker
Stimulus Picture
Response Choices
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
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Page marker.
“CONTINUE”
© 2008 Meadows Center arrows.
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RtI & Tier 2 Intervention
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
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Intervention Description
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Eleven Units
Instruction occurs daily for 25-30 minutes
Small groups
Eight days of lessons per unit
Progress Monitoring weekly
Lessons:
–  Warm-Up (3 minutes)
–  Lessons: Modeling, Guided Practice, Independent
Practice (20-24 minutes)
–  Cool-down (3 minutes)
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
17
Procedures & Features of Tier II
Intervention*
•  Groupings: homogeneous grouping with 3 - 5 students per
group
•  Duration: 4 times per week for 25 minutes; PM 5th day
•  Lesson Design: mixed (instructional content-IC), scaffolded,
scripted interventions; explicit, strategic, “think aloud;” error
correction; factual, procedural, and strategic learning
•  Instructional Content: IC ranges focusing on difficult numbers;
vocabulary; (e.g., greater than/less than); number, operation,
quantitative reasoning; patterns/relationships/algebraic
thinking; problem solving; other TEKS (implicit)
*Based on Research for Students with Difficulties/
Disabilities
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
18
Procedures & Features of Tier II
Intervention
•  Representations:
–  physical (concrete)
–  visual (pictorial)
–  abstract (numbers/symbols)
•  Materials: number charts (100s), 5- and 10-frames, counters,
cubes, number lines, base-ten materials, dot cards, fact cards,
place value cards
•  Progress monitoring: daily checks (independent practice); aim
checks
•  Stretch Your Skills
•  Bubble answers
•  Fidelity Checks
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
19
Lesson Format
•  Preview
–  Gives context to the lesson
•  “Today we are going to make numbers using
rods and units.”
•  Modeling
–  Teacher models skill to be introduced
–  Review of material, students complete modeling
with teacher
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
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Lesson Format •  Guided Practice
–  Application of skills taught in modeling
–  Practice skill in various representations
–  Error correction
–  Multiple opportunities to respond
•  Independent Practice
–  Students complete independently for 1-2 minutes
–  Students check and correct with teacher
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
21
Data Collection •  Daily
–  Independent Practice
–  Use to guide intervention instruction
–  Not to be used for grades
•  Weekly
–  Aim checks; “Mini” versions of the TEMI-PM
–  Allow for aim lines, trends, progress over time
–  Track progress of intervention
•  Annually
–  Beginning, middle and end of year
–  Flexible, change groupings based on progress from BOY to
MOY or MOY to EOY
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
22
Daily Progress Monitoring Example •  Used to guide instruction, monitor struggling students, provide
error correction, or assist in readjusting groups
1st
Grade
Unit 6
Tutor: Diane
School: Little
Kids Elementary
WEEK 1
Students
Hughes,
Kathleen
Lessons
1-3
2/18
Attendance
WPS
Lessons
4-6
2/19
OCN (/5)
Behavior
Attendance
ASF (/10)
ROT (/
6)
(1st)
ROT (/
10)
(2nd)
/5
/10
/6
/10
Porterfield,
Jennifer
/5
/10
/6
/10
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
Behavior
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Graphing Progress Monitoring Data
ASC
PV
NS
MC
TEMI-PM&TEMI-AC
•  Data collected on the Aim
Checks is graphed using
Microsoft Excel
140
130
120
110
Total Number Correct
100
90
80
70
60
30
50
FALL
30
40
20
10
0
13
21
13
32
33
18
30
33
34
12
14
15
10
18
22
8
12 16
11
12
9
19
6 10
4 8 10 7 10
4
0
BOY 1A 2B 3C 4D 5E(MOY)6A 7B 8C 9D 10E
(EOY)
PM
PM
PM
Units
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Sample Fidelity of Implementation Rating Scale
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Resources
•  The Meadows Center
–  http://meadowscenter.org/
•  The Math Institute of the Meadows Center
–  http://meadowscenter.org/institutes/math/
default.asp
•  TEMI Tests; administration manual, tests, norms,
excel program to graph data
•  Assessment Central
–  earlymathintervention.org/assessment
–  user name: austin\assessment
–  password: s3rp!2008!
Meadows Center for Preventing Educational Risk—Mathematics Institute for Learning Disabilities and Difficulties
The University of Texas at Austin ©2009 University of Texas System/Texas Education Agency
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