RTI Teams: Best Practices in Elementary Mathematics Interventions Jim Wright www.interventioncentral.org

1
RTI Teams Best Practicesin Elementary
MathematicsInterventionsJim Wrightwww.intervent
ioncentral.org
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PowerPoints from this workshop available
athttp//www.interventioncentral.org/math_work
shop.php
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Workshop Agenda
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RTI is a Model in Development

• Several proposals for operationalizing response
  to intervention have been madeThe field can
  expect more efforts like these and, for a time at
  least, different models to be testedTherefore,
  it is premature to advocate any single model.
  (Barnett, Daly, Jones, Lentz, 2004 )

Source Barnett, D. W., Daly, E. J., Jones, K.
M., Lentz, F.E. (2004). Response to
intervention Empirically based special service
decisions from single-case designs of increasing
and decreasing intensity. Journal of Special
Education, 38, 66-79.
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Georgia Pyramid of Intervention
Source Georgia Dept of Education
http//www.doe.k12.ga.us/ Retrieved 13 July 2007
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How can a school restructure to support RTI?

• The school can organize its intervention efforts
  into 4 levels, or Tiers, that represent a
  continuum of increasing intensity of support.
  (Kovaleski, 2003 Vaughn, 2003). In Georgia, Tier
  1 is the lowest level of intervention, Tier 4 is
  the most intensive intervention level.

Standards-Based Classroom Learning All students
participate in general education learning that
includes implementation of the Georgia
Performance Standards through research-based
practices, use of flexible groups for
differentiation of instruction, frequent
progress-monitoring.
Tier 1
Needs Based Learning Targeted students
participate in learning that is in addition to
Tier 1 and different by including formalized
processes of intervention greater frequency of
progress-monitoring.
Tier 2
SST Driven Learning Targeted students
participate in learning that is in addition to
Tier I II and different by including
individualized assessments, interventions
tailored to individual needs, referral for
specially designed instruction if needed.
Tier 3
Specially Designed Learning Targeted students
participate in learning that includes specialized
programs, adapted content, methodology, or
instructional delivery Georgia Performance
standards access/extension.
Tier 4
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The Purpose of RTI in Secondary Schools What
Students Should It Serve?
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Math Intervention Planning Some Challenges for
Elementary RTI Teams

• There is no national consensus about what math
  instruction should look like in elementary
  schools
• Schools may not have consistent expectations for
  the best practice math instruction strategies
  that teachers should routinely use in the
  classroom
• Schools may not have a full range of assessment
  methods to collect baseline and progress
  monitoring data on math difficulties

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Focus of This Math Interventions Workshop

• Intervention and assessment strategies that
  supplement the core curriculum
• NOTE If greater than 20 percent of students in a
  classroom or grade level experience significant
  math difficulties, the focus should be on giving
  the teacher skills for effective whole-group
  instruction or on improving the core curriculum

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Big Ideas About Student Learning
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Big Ideas Student Social Academic Behaviors
Are Strongly Influenced by the Instructional
Setting (Lentz Shapiro, 1986)

• Students with learning problems do not exist in
  isolation. Rather, their instructional
  environment plays an enormously important role in
  these students eventual success or failure

Source Lentz, F. E. Shapiro, E. S. (1986).
Functional assessment of the academic
environment. School Psychology Review, 15, 346-57.
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Big Ideas Learn Unit (Heward, 1996)

• The three essential elements of effective student
  learning include
• Academic Opportunity to Respond. The student is
  presented with a meaningful opportunity to
  respond to an academic task. A question posed by
  the teacher, a math word problem, and a spelling
  item on an educational computer Word Gobbler
  game could all be considered academic
  opportunities to respond.
• Active Student Response. The student answers the
  item, solves the problem presented, or completes
  the academic task. Answering the teachers
  question, computing the answer to a math word
  problem (and showing all work), and typing in the
  correct spelling of an item when playing an
  educational computer game are all examples of
  active student responding.
• Performance Feedback. The student receives timely
  feedback about whether his or her response is
  correctoften with praise and encouragement. A
  teacher exclaiming Right! Good job! when a
  student gives an response in class, a student
  using an answer key to check her answer to a math
  word problem, and a computer message that says
  Congratulations! You get 2 points for correctly
  spelling this word! are all examples of
  performance feedback.

Source Heward, W.L. (1996). Three low-tech
strategies for increasing the frequency of active
student response during group instruction. In R.
Gardner, D. M.S ainato, J. O. Cooper, T. E.
Heron, W. L. Heward, J. W. Eshleman, T. A.
Grossi (Eds.), Behavior analysis in education
Focus on measurably superior instruction
(pp.283-320). Pacific Grove, CABrooks/Cole.
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Big Ideas The Four Stages of Learning Can Be
Summed Up in the Instructional Hierarchy
(Haring et al., 1978)

• Student learning can be thought of as a
  multi-stage process. The universal stages of
  learning include
• Acquisition The student is just acquiring the
  skill.
• Fluency The student can perform the skill but
  must make that skill automatic.
• Generalization The student must perform the
  skill across situations or settings.
• Adaptation The student confronts novel task
  demands that require that the student adapt a
  current skill to meet new requirements.

Source Haring, N.G., Lovitt, T.C., Eaton, M.D.,
Hansen, C.L. (1978). The fourth R Research in
the classroom. Columbus, OH Charles E. Merrill
Publishing Co.
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National Mathematics Advisory Panel Report13
March 2008
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Math Advisory Panel Report athttp//www.ed.gov/
mathpanel
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2008 National Math Advisory Panel Report
Recommendations

• The areas to be studied in mathematics from
  pre-kindergarten through eighth grade should be
  streamlined and a well-defined set of the most
  important topics should be emphasized in the
  early grades. Any approach that revisits topics
  year after year without bringing them to closure
  should be avoided.
• Proficiency with whole numbers, fractions, and
  certain aspects of geometry and measurement are
  the foundations for algebra. Of these, knowledge
  of fractions is the most important foundational
  skill not developed among American students.
• Conceptual understanding, computational and
  procedural fluency, and problem solving skills
  are equally important and mutually reinforce each
  other. Debates regarding the relative importance
  of each of these components of mathematics are
  misguided.
• Students should develop immediate recall of
  arithmetic facts to free the working memory for
  solving more complex problems.

Source National Math Panel Fact Sheet. (March
2008). Retrieved on March 14, 2008, from
http//www.ed.gov/about/bdscomm/list/mathpanel/rep
ort/final-factsheet.html
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Elbow Group Activity What are common student
mathematics concerns in your school?

• In your elbow groups
• Discuss the most common student mathematics
  problems that you encounter in your school(s). At
  what grade level do you typically encounter these
  problems?
• Be prepared to share your discussion points with
  the larger group.

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Mathematics is made of 50 percent formulas, 50
percent proofs, and 50 percent imagination.
Anonymous
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Who is At Risk for Poor Math Performance? A
Proactive Stance

• we use the term mathematics difficulties
  rather than mathematics disabilities. Children
  who exhibit mathematics difficulties include
  those performing in the low average range (e.g.,
  at or below the 35th percentile) as well as those
  performing well below averageUsing higher
  percentile cutoffs increases the likelihood that
  young children who go on to have serious math
  problems will be picked up in the screening. p.
  295

Source Gersten, R., Jordan, N. C., Flojo, J.
R. (2005). Early identification and interventions
for students with mathematics difficulties.
Journal of Learning Disabilities, 38, 293-304.
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Profile of Students with Math Difficulties
(Kroesbergen Van Luit, 2003)

• Although the group of students with
  difficulties in learning math is very
  heterogeneous, in general, these students have
  memory deficits leading to difficulties in the
  acquisition and remembering of math knowledge.
  Moreover, they often show inadequate use of
  strategies for solving math tasks, caused by
  problems with the acquisition and the application
  of both cognitive and metacognitive strategies.
  Because of these problems, they also show
  deficits in generalization and transfer of
  learned knowledge to new and unknown tasks.

Source Kroesbergen, E., Van Luit, J. E. H.
(2003). Mathematics interventions for children
with special educational needs. Remedial and
Special Education, 24, 97-114..
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The Elements of Mathematical Proficiency What
the Experts Say
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(No Transcript)
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Five Strands of Mathematical Proficiency

1. Understanding Comprehending mathematical
   concepts, operations, and relations--knowing what
   mathematical symbols, diagrams, and procedures
   mean.
2. Computing Carrying out mathematical procedures,
   such as adding, subtracting, multiplying, and
   dividing numbers flexibly, accurately,
   efficiently, and appropriately.
3. Applying Being able to formulate problems
   mathematically and to devise strategies for
   solving them using concepts and procedures
   appropriately.

Source National Research Council. (2002).
Helping children learn mathematics. Mathematics
Learning Study Committee, J. Kilpatrick J.
Swafford, Editors, Center for Education, Division
of Behavioral and Social Sciences and Education.
Washington, DC National Academy Press.
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Five Strands of Mathematical Proficiency (Cont.)

1. Reasoning Using logic to explain and justify a
   solution to a problem or to extend from something
   known to something less known.
2. Engaging Seeing mathematics as sensible, useful,
   and doableif you work at itand being willing to
   do the work.

Source National Research Council. (2002).
Helping children learn mathematics. Mathematics
Learning Study Committee, J. Kilpatrick J.
Swafford, Editors, Center for Education, Division
of Behavioral and Social Sciences and Education.
Washington, DC National Academy Press.
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Three General Levels of Math Skill Development
(Kroesbergen Van Luit, 2003)

• As students move from lower to higher grades,
  they move through levels of acquisition of math
  skills, to include
• Number sense
• Basic math operations (i.e., addition,
  subtraction, multiplication, division)
• Problem-solving skills The solution of both
  verbal and nonverbal problems through the
  application of previously acquired information
  (Kroesbergen Van Luit, 2003, p. 98)

Source Kroesbergen, E., Van Luit, J. E. H.
(2003). Mathematics interventions for children
with special educational needs. Remedial and
Special Education, 24, 97-114..
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What is Number Sense? (Clarke Shinn, 2004)

• the ability to understand the meaning of
  numbers and define different relationships among
  numbers. Children with number sense can
  recognize the relative size of numbers, use
  referents for measuring objects and events, and
  think and work with numbers in a flexible manner
  that treats numbers as a sensible system. p. 236

Source Clarke, B., Shinn, M. (2004). A
preliminary investigation into the identification
and development of early mathematics
curriculum-based measurement. School Psychology
Review, 33, 234248.
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What Are Stages of Number Sense? (Berch, 2005,
p. 336)

1. Innate Number Sense. Children appear to possess
   hard-wired ability (neurological foundation
   structures) to acquire number sense. Childrens
   innate capabilities appear also to be to
   represent general amounts, not specific
   quantities. This innate number sense seems to be
   characterized by skills at estimation
   (approximate numerical judgments) and a
   counting system that can be described loosely as
   1, 2, 3, 4, a lot.
2. Acquired Number Sense. Young students learn
   through indirect and direct instruction to count
   specific objects beyond four and to internalize a
   number line as a mental representation of those
   precise number values.

Source Berch, D. B. (2005). Making sense of
number sense Implications for children with
mathematical disabilities. Journal of Learning
Disabilities, 38, 333-339...
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The Basic Number Line is as Familiar as a
Well-Known Place to People Who Have Mastered
Arithmetic Combinations
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Internal Numberline

• As students internalize the numberline, they are
  better able to perform mental arithmetic (the
  manipulation of numbers and math operations in
  their head).

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 1920 21 22 23 24 25 26 27 28 29
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Mental Arithmetic A Demonstration

• 332 x 420 ?

Directions As you watch this video of a person
using mental arithmetic to solve a computation
problem, note the strategies and shortcuts that
he employs to make the task more manageable.
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\Mental Arithmetic Demonstration What Tools Were
Used?
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Math Computation Building FluencyJim
Wrightwww.interventioncentral.org
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"Arithmetic is being able to count up to twenty
without taking off your shoes." Anonymous
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Benefits of Automaticity of Arithmetic
Combinations (Gersten, Jordan, Flojo, 2005)

• There is a strong correlation between poor
  retrieval of arithmetic combinations (math
  facts) and global math delays
• Automatic recall of arithmetic combinations frees
  up student cognitive capacity to allow for
  understanding of higher-level problem-solving
• By internalizing numbers as mental constructs,
  students can manipulate those numbers in their
  head, allowing for the intuitive understanding of
  arithmetic properties, such as associative
  property and commutative property

Source Gersten, R., Jordan, N. C., Flojo, J.
R. (2005). Early identification and interventions
for students with mathematics difficulties.
Journal of Learning Disabilities, 38, 293-304.
35
Associative Property

• within an expression containing two or more of
  the same associative operators in a row, the
  order of operations does not matter as long as
  the sequence of the operands is not changed
• Example
• (23)510
• 2(35)10

Source Associativity. Wikipedia. Retrieved
September 5, 2007, from http//en.wikipedia.org/wi
ki/Associative
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Commutative Property

• the ability to change the order of something
  without changing the end result.
• Example
• 23510
• 25310

Source Associativity. Wikipedia. Retrieved
September 5, 2007, from http//en.wikipedia.org/wi
ki/Commutative
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How much is 3 8? Strategies to Solve
Source Gersten, R., Jordan, N. C., Flojo, J.
R. (2005). Early identification and interventions
for students with mathematics difficulties.
Journal of Learning Disabilities, 38, 293-304.
38
Math Skills Importance of Fluency in Basic Math
Operations

• A key step in math education is to learn the
  four basic mathematical operations (i.e.,
  addition, subtraction, multiplication, and
  division). Knowledge of these operations and a
  capacity to perform mental arithmetic play an
  important role in the development of childrens
  later math skills. Most children with math
  learning difficulties are unable to master the
  four basic operations before leaving elementary
  school and, thus, need special attention to
  acquire the skills. A category of interventions
  is therefore aimed at the acquisition and
  automatization of basic math skills.

Source Kroesbergen, E., Van Luit, J. E. H.
(2003). Mathematics interventions for children
with special educational needs. Remedial and
Special Education, 24, 97-114.
39
Big Ideas Learn Unit (Heward, 1996)

• The three essential elements of effective student
  learning include
• Academic Opportunity to Respond. The student is
  presented with a meaningful opportunity to
  respond to an academic task. A question posed by
  the teacher, a math word problem, and a spelling
  item on an educational computer Word Gobbler
  game could all be considered academic
  opportunities to respond.
• Active Student Response. The student answers the
  item, solves the problem presented, or completes
  the academic task. Answering the teachers
  question, computing the answer to a math word
  problem (and showing all work), and typing in the
  correct spelling of an item when playing an
  educational computer game are all examples of
  active student responding.
• Performance Feedback. The student receives timely
  feedback about whether his or her response is
  correctoften with praise and encouragement. A
  teacher exclaiming Right! Good job! when a
  student gives an response in class, a student
  using an answer key to check her answer to a math
  word problem, and a computer message that says
  Congratulations! You get 2 points for correctly
  spelling this word! are all examples of
  performance feedback.

Source Heward, W.L. (1996). Three low-tech
strategies for increasing the frequency of active
student response during group instruction. In R.
Gardner, D. M.S ainato, J. O. Cooper, T. E.
Heron, W. L. Heward, J. W. Eshleman, T. A.
Grossi (Eds.), Behavior analysis in education
Focus on measurably superior instruction
(pp.283-320). Pacific Grove, CABrooks/Cole.
40
Math Intervention Tier I or II Elementary
Secondary Self-Administered Arithmetic
Combination Drills With Performance
Self-Monitoring Incentives

1. The student is given a math computation worksheet
   of a specific problem type, along with an answer
   key Academic Opportunity to Respond.
2. The student consults his or her performance chart
   and notes previous performance. The student is
   encouraged to try to beat his or her most
   recent score.
3. The student is given a pre-selected amount of
   time (e.g., 5 minutes) to complete as many
   problems as possible. The student sets a timer
   and works on the computation sheet until the
   timer rings. Active Student Responding
4. The student checks his or her work, giving credit
   for each correct digit (digit of correct value
   appearing in the correct place-position in the
   answer). Performance Feedback
5. The student records the days score of TOTAL
   number of correct digits on his or her personal
   performance chart.
6. The student receives praise or a reward if he or
   she exceeds the most recently posted number of
   correct digits.

Application of Learn Unit framework from
Heward, W.L. (1996). Three low-tech strategies
for increasing the frequency of active student
response during group instruction. In R. Gardner,
D. M.S ainato, J. O. Cooper, T. E. Heron, W. L.
Heward, J. W. Eshleman, T. A. Grossi (Eds.),
Behavior analysis in education Focus on
measurably superior instruction (pp.283-320).
Pacific Grove, CABrooks/Cole.
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Self-Administered Arithmetic Combination
DrillsExamples of Student Worksheet and Answer
Key
Worksheets created using Math Worksheet
Generator. Available online athttp//www.interve
ntioncentral.org/htmdocs/tools/mathprobe/addsing.p
hp
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Self-Administered Arithmetic Combination Drills
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How to Use PPT Group Timers in the Classroom
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Cover-Copy-Compare Math Computational
Fluency-Building Intervention

• The student is given sheet with correctly
  completed math problems in left column and index
  card. For each problem, the student
• studies the model
• covers the model with index card
• copies the problem from memory
• solves the problem
• uncovers the correctly completed model to check
  answer

Source Skinner, C.H., Turco, T.L., Beatty, K.L.,
Rasavage, C. (1989). Cover, copy, and compare
A method for increasing multiplication
performance. School Psychology Review, 18,
412-420.
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Math Shortcuts Cognitive Energy- and Time-Savers

• Recently, some researchershave argued that
  children can derive answers quickly and with
  minimal cognitive effort by employing calculation
  principles or shortcuts, such as using a known
  number combination to derive an answer (2 2
  4, so 2 3 5), relations among operations (6
  4 10, so 10 -4 6) and so forth. This
  approach to instruction is consonant with
  recommendations by the National Research Council
  (2001). Instruction along these lines may be much
  more productive than rote drill without linkage
  to counting strategy use. p. 301

Source Gersten, R., Jordan, N. C., Flojo, J.
R. (2005). Early identification and interventions
for students with mathematics difficulties.
Journal of Learning Disabilities, 38, 293-304.
46
Math Multiplication Shortcut The 9 Times
Quickie

• The student uses fingers as markers to find the
  product of single-digit multiplication arithmetic
  combinations with 9.
• Fingers to the left of the lowered finger stands
  for the 10s place value.
• Fingers to the right stand for the 1s place
  value.

Source Russell, D. (n.d.). Math facts to learn
the facts. Retrieved November 9, 2007, from
http//math.about.com/bltricks.htm
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Students Who Understand Mathematical Concepts
Can Discover Their Own Shortcuts

• Students who learn with understanding have less
  to learn because they see common patterns in
  superficially different situations. If they
  understand the general principle that the order
  in which two numbers are multiplied doesnt
  matter3 x 5 is the same as 5 x 3, for
  examplethey have about half as many number
  facts to learn. p. 10

Source National Research Council. (2002).
Helping children learn mathematics. Mathematics
Learning Study Committee, J. Kilpatrick J.
Swafford, Editors, Center for Education, Division
of Behavioral and Social Sciences and Education.
Washington, DC National Academy Press.
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Application of Math Shortcuts to Intervention
Plans

• Students who struggle with math may find
  computational shortcuts to be motivating.
• Teaching and modeling of shortcuts provides
  students with strategies to make computation less
  cognitively demanding.

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Math Computation Motivate With Errorless
Learning Worksheets

• In this version of an errorless learning
  approach, the student is directed to complete
  math facts as quickly as possible. If the
  student comes to a number problem that he or she
  cannot solve, the student is encouraged to locate
  the problem and its correct answer in the key at
  the top of the page and write it in.
• Such speed drills build computational fluency
  while promoting students ability to visualize
  and to use a mental number line.
• TIP Consider turning this activity into a
  speed drill. The student is given a kitchen
  timer and instructed to set the timer for a
  predetermined span of time (e.g., 2 minutes) for
  each drill. The student completes as many
  problems as possible before the timer rings. The
  student then graphs the number of problems
  correctly computed each day on a time-series
  graph, attempting to better his or her previous
  score.

Source Caron, T. A. (2007). Learning
multiplication the easy way. The Clearing House,
80, 278-282
50
Errorless Learning Worksheet Sample
Source Caron, T. A. (2007). Learning
multiplication the easy way. The Clearing House,
80, 278-282
51
Math Computation Two Ideas to Jump-Start Active
Academic Responding

• Here are two ideas to accomplish increased
  academic responding on math tasks.
• Break longer assignments into shorter assignments
  with performance feedback given after each
  shorter chunk (e.g., break a 20-minute math
  computation worksheet task into 3 seven-minute
  assignments). Breaking longer assignments into
  briefer segments also allows the teacher to
  praise struggling students more frequently for
  work completion and effort, providing an
  additional natural reinforcer.
• Allow students to respond to easier practice
  items orally rather than in written form to speed
  up the rate of correct responses.

Source Skinner, C. H., Pappas, D. N., Davis,
K. A. (2005). Enhancing academic engagement
Providing opportunities for responding and
influencing students to choose to respond.
Psychology in the Schools, 42, 389-403.
52
Math Computation Problem Interspersal Technique

• The teacher first identifies the range of
  challenging problem-types (number problems
  appropriately matched to the students current
  instructional level) that are to appear on the
  worksheet.
• Then the teacher creates a series of easy
  problems that the students can complete very
  quickly (e.g., adding or subtracting two 1-digit
  numbers). The teacher next prepares a series of
  student math computation worksheets with easy
  computation problems interspersed at a fixed rate
  among the challenging problems.
• If the student is expected to complete the
  worksheet independently, challenging and easy
  problems should be interspersed at a 11 ratio
  (that is, every challenging problem in the
  worksheet is preceded and/or followed by an
  easy problem).
• If the student is to have the problems read aloud
  and then asked to solve the problems mentally and
  write down only the answer, the items should
  appear on the worksheet at a ratio of 3
  challenging problems for every easy one (that
  is, every 3 challenging problems are preceded
  and/or followed by an easy one).

Source Hawkins, J., Skinner, C. H., Oliver, R.
(2005). The effects of task demands and additive
interspersal ratios on fifth-grade students
mathematics accuracy. School Psychology Review,
34, 543-555..
53
How to Create an Interspersal-Problems Worksheet
54
Additional Math InterventionsJim
Wrightwww.interventioncentral.org
55
Math Review Incremental Rehearsal of Math Facts
Step 1 The tutor writes down on a series of
index cards the math facts that the student needs
to learn. The problems are written without the
answers.
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Math Review Incremental Rehearsal of Math Facts
KNOWN Facts
UNKNOWN Facts
Step 2 The tutor reviews the math fact cards
with the student. Any card that the student can
answer within 2 seconds is sorted into the
KNOWN pile. Any card that the student cannot
answer within two secondsor answers
incorrectlyis sorted into the UNKNOWN pile.
57
Math Review Incremental Rehearsal of Math Facts
58
Math Review Incremental Rehearsal of Math Facts
59
(No Transcript)
60
Measuring the Intervention Footprint Issues of
Planning, Documentation, Follow-ThroughJim
Wrightwww.interventioncentral.org
61
Essential Elements of Any Academic or Behavioral
Intervention (Treatment) Strategy

• Method of delivery (Who or what delivers the
  treatment?)Examples include teachers,
  paraprofessionals, parents, volunteers,
  computers.
• Treatment component (What makes the intervention
  effective?)Examples include activation of prior
  knowledge to help the student to make meaningful
  connections between known and new material
  guide practice (e.g., Paired Reading) to increase
  reading fluency periodic review of material to
  aid student retention. As an example of a
  research-based commercial program, Read Naturally
  combines teacher modeling, repeated reading and
  progress monitoring to remediate fluency
  problems.

62
Interventions, Accommodations Modifications
Sorting Them Out

• Interventions. An academic intervention is a
  strategy used to teach a new skill, build fluency
  in a skill, or encourage a child to apply an
  existing skill to new situations or settings.
  An intervention is said to be research-based
  when it has been demonstrated to be effective in
  one or more articles published in peerreviewed
  scientific journals. Interventions might be based
  on commercial programs such as Read Naturally.
  The school may also develop and implement an
  intervention that is based on guidelines provided
  in research articlessuch as Paired Reading
  (Topping, 1987).

63
Interventions, Accommodations Modifications
Sorting Them Out

• Accommodations. An accommodation is intended to
  help the student to fully access the
  general-education curriculum without changing the
  instructional content. An accommodation for
  students who are slow readers, for example, may
  include having them supplement their silent
  reading of a novel by listening to the book on
  tape. An accommodation is intended to remove
  barriers to learning while still expecting that
  students will master the same instructional
  content as their typical peers. Informal
  accommodations may be used at the classroom level
  or be incorporated into a more intensive,
  individualized intervention plan.

64
Interventions, Accommodations Modifications
Sorting Them Out

• Modifications. A modification changes the
  expectations of what a student is expected to
  know or dotypically by lowering the academic
  expectations against which the student is to be
  evaluated. Examples of modifications are
  reducing the number of multiple-choice items in a
  test from five to four or shortening a spelling
  list. Under RTI, modifications are generally not
  included in a students intervention plan,
  because the working assumption is that the
  student can be successful in the curriculum with
  appropriate interventions and accommodations
  alone.

65
Writing Quality Problem Identification
Statements
66
Writing Quality Problem Identification
Statements

• A frequent problem at RTI Team meetings is that
  teacher referral concerns are written in vague
  terms. If the referral concern is not written in
  explicit, observable, measurable terms, it will
  be very difficult to write clear goals for
  improvement or select appropriate interventions.
• Use this test for evaluating the quality of a
  problem-identification (teacher-concern)
  statement Can a third party enter a classroom
  with the problem definition in hand and know when
  they see the behavior and when they dont?

67
Writing Quality Teacher Referral Concern
Statements Examples

• Needs Work The student is disruptive.
• Better During independent seatwork , the student
  is out of her seat frequently and talking with
  other students.
• Needs Work The student doesnt do his math.
• Better When math homework is assigned, the
  student turns in math homework only about 20
  percent of the time. Assignments turned in are
  often not fully completed.

68
Math Computation Fluency RTI Case Study
69
RTI Individual Case Study Math Computation

• Jared is a fourth-grade student. His teacher,
  Mrs. Rogers, became concerned because Jared is
  much slower in completing math computation
  problems than are his classmates.

70
Tier 1 Math Interventions for Jared

• Jareds school uses the Everyday Math curriculum
  (McGraw Hill/University of Chicago). In addition
  to the basic curriculum the series contains
  intervention exercises for students who need
  additional practice or remediation. The
  instructor, Mrs. Rogers, works with a small group
  of children in her roomincluding Jaredhaving
  them complete these practice exercises to boost
  their math computation fluency.

71
Tier 2 Standard Protocol (Group) Math
Interventions for Jared

• Jared did not make sufficient progress in his
  Tier 1 intervention. So his teacher referred the
  student to the RTI Intervention Team. The team
  and teacher decided that Jared would be placed on
  the schools educational math software, AMATH
  Building Blocks, a self-paced, individualized
  mathematics tutorial covering the math
  traditionally taught in grades K-4.Jared
  worked on the software in 20-minute daily
  sessions to increase computation fluency in basic
  multiplication problems.

72
Tier 2 Math Interventions for Jared (Cont.)

• During this group-based Tier 2 intervention,
  Jared was assessed using Curriculum-Based
  Measurement (CBM) Math probes. The goal was to
  bring Jared up to at least 40 correct digits per
  2 minutes.

73
Tier 2 Math Interventions for Jared (Cont.)

• Progress-monitoring worksheets were created using
  the Math Computation Probe Generator on
  Intervention Central (www.interventioncentral.org)
  .

Example of Math Computation Probe Answer Key
74
Tier 2 Math Interventions for Jared
Progress-Monitoring
75
Tier 3 Individualized Plan Math Interventions
for Jared

• Progress-monitoring data showed that Jared did
  not make expected progress in the first phase of
  his Tier 2 intervention. So the RTI Intervention
  Team met again on the student. The team and
  teacher noted that Jared counted on his fingers
  when completing multiplication problems. This
  greatly slowed down his computation fluency. The
  team decided to use a research-based strategy,
  Explicit Time Drills, to increase Jareds
  computation speed and eliminate his dependence on
  finger-counting.During this individualized
  intervention, Jared continued to be assessed
  using Curriculum-Based Measurement (CBM) Math
  probes. The goal was to bring Jared up to at
  least 40 correct digits per 2 minutes.

76
Explicit Time Drills Math Computational
Fluency-Building Intervention

• Explicit time-drills are a method to boost
  students rate of responding on math-fact
  worksheets.
• The teacher hands out the worksheet. Students
  are told that they will have 3 minutes to work on
  problems on the sheet. The teacher starts the
  stop watch and tells the students to start work.
  At the end of the first minute in the 3-minute
  span, the teacher calls time, stops the
  stopwatch, and tells the students to underline
  the last number written and to put their pencils
  in the air. Then students are told to resume work
  and the teacher restarts the stopwatch. This
  process is repeated at the end of minutes 2 and
  3. At the conclusion of the 3 minutes, the
  teacher collects the student worksheets.

Source Rhymer, K. N., Skinner, C. H., Jackson,
S., McNeill, S., Smith, T., Jackson, B. (2002).
The 1-minute explicit timing intervention The
influence of mathematics problem difficulty.
Journal of Instructional Psychology, 29(4),
305-311.
77
Tier 3 Math Interventions for Jared
Progress-Monitoring
78
Tier 3 Math Interventions for Jared

• Explicit Timed Drill Intervention Outcome
• The progress-monitoring data showed that Jared
  was well on track to meet his computation goal.
  At the RTI Team follow-up meeting, the team and
  teacher agreed to continue the fluency-building
  intervention for at least 3 more weeks. It was
  also noted that Jared no longer relied on
  finger-counting when completing number problems,
  a good sign that he had overcome an obstacle to
  math computation.