Instruction%20and%20Interventions%20within%20Response%20to%20Intervention%20Jim%20Wright%20www.interventioncentral.org

1
Instruction and Interventions within Response to
InterventionJim Wrightwww.interventioncentral.o
rg
2
Resources from This Workshop Available at
http//www.interventioncentral.org/ES_BOCES.php
3
Workshop Agenda
4
Intervention Research Development A Work in
Progress
5
Tier 1 What Are the Recommended Elements of
Core Curriculum? More Research Needed

• In essence, we now have a good beginning on the
  evaluation of Tier 2 and 3 interventions, but no
  idea about what it will take to get the core
  curriculum to work at Tier 1. A complicating
  issue with this potential line of research is
  that many schools use multiple materials as their
  core program. p. 640

Source Kovaleski, J. F. (2007). Response to
intervention Considerations for research and
systems change. School Psychology Review, 36,
638-646.
6
Limitations of Intervention Research

• the list of evidence-based interventions is
  quite small relative to the need of RTI. Thus,
  limited dissemination of interventions is likely
  to be a practical problem as individuals move
  forward in the application of RTI models in
  applied settings. p. 33

Source Kratochwill, T. R., Clements, M. A.,
Kalymon, K. M. (2007). Response to intervention
Conceptual and methodological issues in
implementation. In Jimerson, S. R., Burns, M. K.,
VanDerHeyden, A. M. (Eds.), Handbook of
response to intervention The science and
practice of assessment and intervention. New
York Springer.
7
Schools Need to Review Tier 1 (Classroom)
Interventions to Ensure That They Are Supported
By Research

• There is a lack of agreement about what is meant
  by scientifically validated classroom (Tier I)
  interventions. Districts should establish a
  vetting processcriteria for judging whether a
  particular instructional or intervention approach
  should be considered empirically based.

Source Fuchs, D., Deshler, D. D. (2007). What
we need to know about responsiveness to
intervention (and shouldnt be afraid to ask)..
Learning Disabilities Research Practice,
22(2),129136.
8
What Are Appropriate Content-Area Tier 1
Universal Interventions for Secondary Schools?

• High schools need to determine what constitutes
  high-quality universal instruction across content
  areas. In addition, high school teachers need
  professional development in, for example,
  differentiated instructional techniques that will
  help ensure student access to instruction
  interventions that are effectively implemented.

Source Duffy, H. (August 2007). Meeting the
needs of significantly struggling learners in
high school. Washington, DC National High School
Center. Retrieved from http//www.betterhighschool
s.org/pubs/ p. 9
9
RTI Intervention Key Concepts
10
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.

11
Core Instruction, Interventions, Accommodations
Modifications Sorting Them Out

• Core Instruction. Those instructional strategies
  that are used routinely with all students in a
  general-education setting are considered core
  instruction. High-quality instruction is
  essential and forms the foundation of RTI
  academic support. NOTE While it is important to
  verify that good core instructional practices are
  in place for a struggling student, those routine
  practices do not count as individual student
  interventions.

12
Core Instruction, Interventions, Accommodations
Modifications Sorting Them Out

• Intervention. 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 can be thought of as a set of
  actions that, when taken, have demonstrated
  ability to change a fixed educational trajectory
  (Methe Riley-Tillman, 2008 p. 37).

13
Core Instruction, Interventions, Accommodations
Modifications Sorting Them Out

• Accommodation. An accommodation is intended to
  help the student to fully access and participate
  in the general-education curriculum without
  changing the instructional content and without
  reducing the students rate of learning (Skinner,
  Pappas Davis, 2005). An accommodation is
  intended to remove barriers to learning while
  still expecting that students will master the
  same instructional content as their typical
  peers.
• Accommodation example 1 Students are allowed to
  supplement silent reading of a novel by listening
  to the book on tape.
• Accommodation example 2 For unmotivated
  students, the instructor breaks larger
  assignments into smaller chunks and providing
  students with performance feedback and praise for
  each completed chunk of assigned work (Skinner,
  Pappas Davis, 2005).

14
Core Instruction, Interventions, Accommodations
Modifications Sorting Them Out

• Modification. A modification changes the
  expectations of what a student is expected to
  know or dotypically by lowering the academic
  standards against which the student is to be
  evaluated. Examples of modifications
• Giving a student five math computation problems
  for practice instead of the 20 problems assigned
  to the rest of the class
• Letting the student consult course notes during a
  test when peers are not permitted to do so

15
Big Ideas The Four Stages of Learning Can Be
Summed Up in the Instructional Hierarchy pp.
2-3(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.
16
Increasing the Intensity of an Intervention Key
Dimensions

• Interventions can move up the RTI Tiers through
  being intensified across several dimensions,
  including
• Type of intervention strategy or materials used
• Student-teacher ratio
• Length of intervention sessions
• Frequency of intervention sessions
• Duration of the intervention period (e.g.,
  extending an intervention from 5 weeks to 10
  weeks)
• Motivation strategies

Source Burns, M. K., Gibbons, K. A. (2008).
Implementing response-to-intervention in
elementary and secondary schools. Routledge New
York. Kratochwill, T. R., Clements, M. A.,
Kalymon, K. M. (2007). Response to intervention
Conceptual and methodological issues in
implementation. In Jimerson, S. R., Burns, M. K.,
VanDerHeyden, A. M. (Eds.), Handbook of
response to intervention The science and
practice of assessment and intervention. New
York Springer.
17
RTI Interventions What If There is No Commercial
Intervention Package or Program Available?

• Although commercially prepared programs and the
  subsequent manuals and materials are inviting,
  they are not necessary. A recent review of
  research suggests that interventions are research
  based and likely to be successful, if they are
  correctly targeted and provide explicit
  instruction in the skill, an appropriate level of
  challenge, sufficient opportunities to respond to
  and practice the skill, and immediate feedback on
  performanceThus, these elements could be used
  as criteria with which to judge potential tier 2
  interventions. p. 88

Source Burns, M. K., Gibbons, K. A. (2008).
Implementing response-to-intervention in
elementary and secondary schools. Routledge New
York.
18
Research-Based Elements of Effective Academic
Interventions

• Correctly targeted The intervention is
  appropriately matched to the students academic
  or behavioral needs.
• Explicit instruction Student skills have been
  broken down into manageable and deliberately
  sequenced steps and providing overt strategies
  for students to learn and practice new skills
  p.1153
• Appropriate level of challenge The student
  experiences adequate success with the
  instructional task.
• High opportunity to respond The student
  actively responds at a rate frequent enough to
  promote effective learning.
• Feedback The student receives prompt
  performance feedback about the work completed.

Source Burns, M. K., VanDerHeyden, A. M.,
Boice, C. H. (2008). Best practices in intensive
academic interventions. In A. Thomas J. Grimes
(Eds.), Best practices in school psychology V
(pp.1151-1162). Bethesda, MD National
Association of School Psychologists.
19
Interventions Potential Fatal Flaws

• Any intervention must include 4 essential
  elements. The absence of any one of the elements
  would be considered a fatal flaw (Witt,
  VanDerHeyden Gilbertson, 2004) that blocks the
  school from drawing meaningful conclusions from
  the students response to the intervention
• Clearly defined problem. The students target
  concern is stated in specific, observable,
  measureable terms. This problem identification
  statement is the most important step of the
  problem-solving model (Bergan, 1995), as a
  clearly defined problem allows the teacher or RTI
  Team to select a well-matched intervention to
  address it.
• Baseline data. The teacher or RTI Team measures
  the students academic skills in the target
  concern (e.g., reading fluency, math computation)
  prior to beginning the intervention. Baseline
  data becomes the point of comparison throughout
  the intervention to help the school to determine
  whether that intervention is effective.
• Performance goal. The teacher or RTI Team sets a
  specific, data-based goal for student improvement
  during the intervention and a checkpoint date by
  which the goal should be attained.
• Progress-monitoring plan. The teacher or RTI Team
  collects student data regularly to determine
  whether the student is on-track to reach the
  performance goal.

Source Witt, J. C., VanDerHeyden, A. M.,
Gilbertson, D. (2004). Troubleshooting behavioral
interventions. A systematic process for finding
and eliminating problems. School Psychology
Review, 33, 363-383.
20
Team Activity What Are Challenging Issues in
Your School Around the Topic of Academic
Interventions?

• At your tables
• Discuss the task of promoting the use of
  evidence-based academic interventions in your
  school.
• What are enabling factors that should help you to
  promote the routine use of such interventions.
• What are challenges or areas needing improvement
  to allow you to promote use of those
  interventions?

21
RTI Best Practicesin MathematicsInterventionsJ
im Wrightwww.interventioncentral.org
22
National Mathematics Advisory Panel Report13
March 2008
23
Math Advisory Panel Report athttp//www.ed.gov/
mathpanel
24
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
25
An RTI Challenge Limited Research to Support
Evidence-Based Math Interventions

• in contrast to reading, core math programs
  that are supported by research, or that have been
  constructed according to clear research-based
  principles, are not easy to identify. Not only
  have exemplary core programs not been identified,
  but also there are no tools available that we
  know of that will help schools analyze core math
  programs to determine their alignment with clear
  research-based principles. p. 459

Source Clarke, B., Baker, S., Chard, D.
(2008). Best practices in mathematics assessment
and intervention with elementary students. In A.
Thomas J. Grimes (Eds.), Best practices in
school psychology V (pp. 453-463).
26
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

27
Profile of Students With Significant Math
Difficulties

• Spatial organization. The student commits errors
  such as misaligning numbers in columns in a
  multiplication problem or confusing
  directionality in a subtraction problem (and
  subtracting the original numberminuendfrom the
  figure to be subtracted (subtrahend).
• Visual detail. The student misreads a
  mathematical sign or leaves out a decimal or
  dollar sign in the answer.
• Procedural errors. The student skips or adds a
  step in a computation sequence. Or the student
  misapplies a learned rule from one arithmetic
  procedure when completing another, different
  arithmetic procedure.
• Inability to shift psychological set. The
  student does not shift from one operation type
  (e.g., addition) to another (e.g.,
  multiplication) when warranted.
• Graphomotor. The students poor handwriting can
  cause him or her to misread handwritten numbers,
  leading to errors in computation.
• Memory. The student fails to remember a specific
  math fact needed to solve a problem. (The student
  may KNOW the math fact but not be able to recall
  it at point of performance.)
• Judgment and reasoning. The student comes up with
  solutions to problems that are clearly
  unreasonable. However, the student is not able
  adequately to evaluate those responses to gauge
  whether they actually make sense in context.

Source Rourke, B. P. (1993). Arithmetic
disabilities, specific otherwise A
neuropsychological perspective. Journal of
Learning Disabilities, 26, 214-226.
28
Mathematics is made of 50 percent formulas, 50
percent proofs, and 50 percent imagination.
Anonymous
29
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.
30
The Elements of Mathematical Proficiency What
the Experts Say
31
(No Transcript)
32
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.
33
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.
34
Five Strands of Mathematical Proficiency (NRC,
2002)

• Table Activity Evaluate Your Schools Math
  Proficiency
• As a group, review the National Research Council
  Strands of Math Proficiency.
• Which strand do you feel that your school /
  curriculum does the best job of helping students
  to attain proficiency?
• Which strand do you feel that your school /
  curriculum should put the greatest effort to
  figure out how to help students to attain
  proficiency?
• Be prepared to share your results.

• Understanding Comprehending mathematical
  concepts, operations, and relations--knowing what
  mathematical symbols, diagrams, and procedures
  mean.
• Computing Carrying out mathematical procedures,
  such as adding, subtracting, multiplying, and
  dividing numbers flexibly, accurately,
  efficiently, and appropriately.
• Applying Being able to formulate problems
  mathematically and to devise strategies for
  solving them using concepts and procedures
  appropriately.
• Reasoning Using logic to explain and justify a
  solution to a problem or to extend from something
  known to something less known.
• Engaging Seeing mathematics as sensible, useful,
  and doableif you work at itand being willing to
  do the work.

35
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..
36
Development of Number Sense
37
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.
38
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 include the
   ability 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...
39
Task Analysis of Number Sense Operations (Methe
Riley-Tillman, 2008)

1. Counting
2. Comparing and Ordering Ability to compare
   relative amounts e.g., more or less than ordinal
   numbers e.g., first, second, third)
3. Equal partitioning Dividing larger set of
   objects into equal parts
4. Composing and decomposing Able to create
   different subgroupings of larger sets (for
   example, stating that a group of 10 objects can
   be broken down into 6 objects and 4 objects or 3
   objects and 7 objects)
5. Grouping and place value abstractly grouping
   objects into sets of 10 (p. 32) in base-10
   counting system.
6. Adding to/taking away Ability to add and
   subtract amounts from sets by using accurate
   strategies that do not rely on laborious
   enumeration, counting, or equal partitioning. P.
   32

Source Methe, S. A., Riley-Tillman, T. C.
(2008). An informed approach to selecting and
designing early mathematics interventions. School
Psychology Forum Research into Practice, 2,
29-41.
40
Childrens Understanding of Counting Rules

• The development of childrens counting ability
  depends upon the development of
• One-to-one correspondence one and only one word
  tag, e.g., one, two, is assigned to each
  counted object.
• Stable order the order of the word tags must be
  invariant across counted sets.
• Cardinality the value of the final word tag
  represents the quantity of items in the counted
  set.
• Abstraction objects of any kind can be
  collected together and counted.
• Order irrelevance items within a given set can
  be tagged in any sequence.

Source Geary, D. C. (2004). Mathematics and
learning disabilities. Journal of Learning
Disabilities, 37, 4-15.
41
Math Computation Building FluencyJim
Wrightwww.interventioncentral.org
42
"Arithmetic is being able to count up to twenty
without taking off your shoes." Anonymous
43
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.
44
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
45
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
46
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
47
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.
48
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.
49
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.
50
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..
51
Teaching Math Vocabulary
52
Comprehending Math Vocabulary The Barrier of
Abstraction

• when it comes to abstract
  mathematical concepts, words describe activities
  or relationships that often lack a visual
  counterpart. Yet studies show that children grasp
  the idea of quantity, as well as other relational
  concepts, from a very early age. As children
  develop their capacity for understanding,
  language, and its vocabulary, becomes a vital
  cognitive link between a childs natural sense of
  number and order and conceptual learning.
• -Chard, D. (n.d.)

Source Chard, D. (n.d.. Vocabulary strategies
for the mathematics classroom. Retrieved November
23, 2007, from http//www.eduplace.com/state/pdf/a
uthor/chard_hmm05.pdf.
53
Math Vocabulary Classroom (Tier I)
Recommendations

• Preteach math vocabulary. Math vocabulary
  provides students with the language tools to
  grasp abstract mathematical concepts and to
  explain their own reasoning. Therefore, do not
  wait to teach that vocabulary only at point of
  use. Instead, preview relevant math vocabulary
  as a regular a part of the background
  information that students receive in preparation
  to learn new math concepts or operations.
• Model the relevant vocabulary when new concepts
  are taught. Strengthen students grasp of new
  vocabulary by reviewing a number of math problems
  with the class, each time consistently and
  explicitly modeling the use of appropriate
  vocabulary to describe the concepts being taught.
  Then have students engage in cooperative learning
  or individual practice activities in which they
  too must successfully use the new
  vocabularywhile the teacher provides targeted
  support to students as needed.
• Ensure that students learn standard, widely
  accepted labels for common math terms and
  operations and that they use them consistently to
  describe their math problem-solving efforts.

Source Chard, D. (n.d.. Vocabulary strategies
for the mathematics classroom. Retrieved November
23, 2007, from http//www.eduplace.com/state/pdf/a
uthor/chard_hmm05.pdf.
54
Vocabulary Why This Instructional Goal is
Important

• As vocabulary terms become more specialized in
  content area courses, students are less able to
  derive the meaning of unfamiliar words from
  context alone.
• Students must instead learn vocabulary through
  more direct means, including having opportunities
  to explicitly memorize words and their
  definitions.
• Students may require 12 to 17 meaningful
  exposures to a word to learn it.

55
Promoting Math Vocabulary Other Guidelines

• Create a standard list of math vocabulary for
  each grade level (elementary) or course/subject
  area (for example, geometry).
• Periodically check students mastery of math
  vocabulary (e.g., through quizzes, math journals,
  guided discussion, etc.).
• Assist students in learning new math vocabulary
  by first assessing their previous knowledge of
  vocabulary terms (e.g., protractor product) and
  then using that past knowledge to build an
  understanding of the term.
• For particular assignments, have students
  identify math vocabulary that they dont
  understand. In a cooperative learning activity,
  have students discuss the terms. Then review any
  remaining vocabulary questions with the entire
  class.
• Encourage students to use a math dictionary in
  their vocabulary work.
• Make vocabulary a central part of instruction,
  curriculum, and assessmentrather than treating
  as an afterthought.

Source Adams, T. L. (2003). Reading mathematics
More than words can say. The Reading Teacher,
56(8), 786-795.
56
Math Instruction Unlock the Thoughts of
Reluctant Students Through Class Journaling

• Students can effectively clarify their knowledge
  of math concepts and problem-solving strategies
  through regular use of class math journals.
• At the start of the year, the teacher introduces
  the journaling weekly assignment in which
  students respond to teacher questions.
• At first, the teacher presents safe questions
  that tap into the students opinions and
  attitudes about mathematics (e.g., How important
  do you think it is nowadays for cashiers in
  fast-food restaurants to be able to calculate in
  their head the amount of change to give a
  customer?). As students become comfortable with
  the journaling activity, the teacher starts to
  pose questions about the students own
  mathematical thinking relating to specific
  assignments. Students are encouraged to use
  numerals, mathematical symbols, and diagrams in
  their journal entries to enhance their
  explanations.
• The teacher provides brief written comments on
  individual student entries, as well as periodic
  oral feedback and encouragement to the entire
  class.
• Teachers will find that journal entries are a
  concrete method for monitoring student
  understanding of more abstract math concepts. To
  promote the quality of journal entries, the
  teacher might also assign them an effort grade
  that will be calculated into quarterly math
  report card grades.

Source Baxter, J. A., Woodward, J., Olson, D.
(2005). Writing in mathematics An alternative
form of communication for academically
low-achieving students. Learning Disabilities
Research Practice, 20(2), 119135.
57
Teaching Math Symbols
58
Learning Math Symbols 3 Card Games

1. The interventionist writes math symbols that the
   student is to learn on index cards. The names of
   those math symbols are written on separate cards.
   The cards can then be used for students to play
   matching games or to attempt to draw cards to get
   a pair.
2. Create a card deck containing math symbols or
   their word equivalents. Students take turns
   drawing cards from the deck. If they can use the
   symbol/word on the selected card to generate a
   correct mathematical sentence, the student wins
   the card. For example, if the student draws a
   card with the term negative number and says
   that A negative number is a real number that is
   less than 0, the student wins the card.
3. Create a deck containing math symbols and a
   series of numbers appropriate to the grade level.
   Students take turns drawing cards. The goral is
   for the student to lay down a series of cards to
   form a math expression. If the student correctly
   solves the expression, he or she earns a point
   for every card laid down.

Source Adams, T. L. (2003). Reading mathematics
More than words can say. The Reading Teacher,
56(8), 786-795.
59
Developing Student Metacognitive Abilities
60
Importance of Metacognitive Strategy Use

• Metacognitive processes focus on self-awareness
  of cognitive knowledge that is presumed to be
  necessary for effective problem solving, and they
  direct and regulate cognitive processes and
  strategies during problem solvingThat is,
  successful problem solvers, consciously or
  unconsciously (depending on task demands), use
  self-instruction, self-questioning, and
  self-monitoring to gain access to strategic
  knowledge, guide execution of strategies, and
  regulate use of strategies and problem-solving
  performance. p. 231

Source Montague, M. (1992). The effects of
cognitive and metacognitive strategy instruction
on the mathematical problem solving of middle
school students with learning disabilities.
Journal of Learning Disabilities, 25, 230-248.
61
Elements of Metacognitive Processes

• Self-instruction helps students to identify and
  direct the problem-solving strategies prior to
  execution. Self-questioning promotes internal
  dialogue for systematically analyzing problem
  information and regulating execution of cognitive
  strategies. Self-monitoring promotes appropriate
  use of specific strategies and encourages
  students to monitor general performance.
  Emphasis added. p. 231

Source Montague, M. (1992). The effects of
cognitive and metacognitive strategy instruction
on the mathematical problem solving of middle
school students with learning disabilities.
Journal of Learning Disabilities, 25, 230-248.
62
Combining Cognitive Metacognitive Strategies to
Assist Students With Mathematical Problem Solving

• Solving an advanced math problem independently
  requires the coordination of a number of complex
  skills. The following strategies combine both
  cognitive and metacognitive elements (Montague,
  1992 Montague Dietz, 2009). First, the student
  is taught a 7-step process for attacking a math
  word problem (cognitive strategy). Second, the
  instructor trains the student to use a three-part
  self-coaching routine for each of the seven
  problem-solving steps (metacognitive strategy).

63
Cognitive Portion of Combined Problem Solving
Approach

• In the cognitive part of this multi-strategy
  intervention, the student learns an explicit
  series of steps to analyze and solve a math
  problem. Those steps include
• Reading the problem. The student reads the
  problem carefully, noting and attempting to clear
  up any areas of uncertainly or confusion (e.g.,
  unknown vocabulary terms).
• Paraphrasing the problem. The student restates
  the problem in his or her own words.
• Drawing the problem. The student creates a
  drawing of the problem, creating a visual
  representation of the word problem.
• Creating a plan to solve the problem. The student
  decides on the best way to solve the problem and
  develops a plan to do so.
• Predicting/Estimating the answer. The student
  estimates or predicts what the answer to the
  problem will be. The student may compute a quick
  approximation of the answer, using rounding or
  other shortcuts.
• Computing the answer. The student follows the
  plan developed earlier to compute the answer to
  the problem.
• Checking the answer. The student methodically
  checks the calculations for each step of the
  problem. The student also compares the actual
  answer to the estimated answer calculated in a
  previous step to ensure that there is general
  agreement between the two values.

64
Metacognitive Portion of Combined Problem Solving
Approach

• The metacognitive component of the intervention
  is a three-part routine that follows a sequence
  of Say, Ask, Check. For each of the 7
  problem-solving steps reviewed above
• The student first self-instructs by stating, or
  saying, the purpose of the step (Say).
• The student next self-questions by asking what
  he or she intends to do to complete the step
  (Ask).
• The student concludes the step by
  self-monitoring, or checking, the successful
  completion of the step (Check).

65
Combined Cognitive Metacognitive Elements of
Strategy
66
Combined Cognitive Metacognitive Elements of
Strategy
67
Combined Cognitive Metacognitive Elements of
Strategy
68
Combined Cognitive Metacognitive Elements of
Strategy
69
Combined Cognitive Metacognitive Elements of
Strategy
70
Combined Cognitive Metacognitive Elements of
Strategy
71
Combined Cognitive Metacognitive Elements of
Strategy
72
Applied Problems Pop Quiz

• Q To move their armies, the Romans built over
  50,000 miles of roads. Imagine driving all those
  miles! Now imagine driving those miles in the
  first gasoline-driven car that has only three
  wheels and could reach a top speed of about 10
  miles per hour.
• For safety's sake, let's bring along a spare
  tire. As you drive the 50,000 miles, you rotate
  the spare with the other tires so that all four
  tires get the same amount of wear. Can you figure
  out how many miles of wear each tire accumulates?

Directions As a team, read the following
problem. At your tables, apply the 7-step
problem-solving (cognitive) strategy to complete
the problem. As you complete each step of the
problem, apply the Say-Ask-Check metacognitive
sequence. Try to complete the entire 7 steps
within the time allocated for this exercise.

• 7-Step Problem-SolvingProcess
• Reading the problem.
• Paraphrasing the problem.
• Drawing the problem.
• Creating a plan to solve the problem.
• Predicting/Estimat-ing the answer.
• Computing the answer.
• Checking the answer.

A Since the four wheels of the three-wheeled
car share the journey equally, simply take
three-fourths of the total distance (50,000
miles) and you'll get 37,500 miles for each
tire.
Source The Math Forum _at_ Drexel Critical
Thinking Puzzles/Spare My Brain. Retrieved from
http//mathforum.org/k12/k12puzzles/critical.think
ing/puzz2.html
73
Finding a Way Out of the Research-Based Maze
A Guide for SchoolsJim Wrightwww.intervention
central.org
74
Innovations in Education Efficacy vs.
Effectiveness

• A useful distinction has recently emerged
  between efficacy and effectiveness (Schoenwald
  Hoagwood, 2001). Efficacy refers to intervention
  outcomes that are produced by researchers and
  program developers under ideal conditions of
  implementation (i.e., adequate resources, close
  supervision ). In contrast, effectiveness refers
  to demonstration(s) of socially valid outcomes
  under normal conditions of usage in the target
  setting(s) for which the intervention was
  developed. Demonstrations of effectiveness are
  far more difficult than demonstrations of
  efficacy. In fact, numerous promising
  interventions and approaches fail to bridge the
  gap between efficacy and effectiveness.
  Emphasis added

Source Walker, H. M. (2004). Use of
evidence-based interventions in schools Where
we've been, where we are, and where we need to
go. School Psychology Review, 33, 398-407. p. 400
75
Finding a Way Out of the Research-Based Maze A
Guide for Schools

• Define the Academic or Behavioral Needs Requiring
  Intervention in Detail and Using Standard
  Terminology. Effective interventions cannot be
  reliably identified and matched to student needs
  if those needs are loosely or vaguely defined.
• Overly broad academic goal statement a student
  will know her letters.
• More focused goal statement When shown any
  letter in uppercase or lowercase form, the
  student will accurately identify the letter name
  and its corresponding sound without assistance.
  
• When possible, describe academic behaviors
  selected as intervention target using standard
  terminology to make it easier to locate
  appropriate evidence-based intervention ideas.

76
Finding a Way Out of the Research-Based Maze A
Guide for Schools

• Develop Consensus in Your School About What is
  Meant by Evidence-Based.
• Compile a list of trusted professional
  organizations and journals. Continue to add to
  this list of trusted organizations and journals
  over time.

77
Finding a Way Out of the Research-Based Maze A
Guide for Schools

• Develop Consensus in Your School About What is
  Meant by Evidence-Based.
• Draft a definition of evidence-based. Example
  The International Reading Association (2002)
  provides these guidelines Produce
  objective dataso that different evaluators
  should be able to draw similar conclusions when
  reviewing the data from the studies. Have
  valid research results that can reasonably be
  applied to the kinds of real-world reading tasks
  that children must master in actual classrooms.
  Yield reliable and replicable findings that would
  not be expected to change significantly based on
  such arbitrary factors as the day or time that
  data on the interventions were collected or who
  collected them.
• Employ current best-practice methods in
  observation or experimentation to reduce the
  probability that other sources of potential bias
  crept into the studies and compromised the
  results.
• Checked before publication by independent
  experts, who review the methods, data, and
  conclusions of the studies.

78
Finding a Way Out of the Research-Based Maze A
Guide for Schools

• Develop Consensus in Your School About What is
  Meant by Evidence-Based.
• Adopting a research continuum. It can be useful
  for schools to use a research continuum that
  establishes categories for interventions in
  descending levels of research quality. The
  continuum would be used as an aid to judge
  whether specific instructional practices or
  interventions are supported by research of
  sufficient quantity and quality for use in
  schools.

79
Finding a Way Out of the Research-Based Maze A
Guide for Schools

• Use Impartial On-Line Rating Sites to Evaluate
  Commercial Intervention Products. Cautions to
  keep in mind when using these sites
• They typically rely on existing research only.
• There can potential delays / lag time between the
  publication of new research and these sites
  evaluation of that research.

80
(No Transcript)
81
(No Transcript)
82
Finding a Way Out of the Research-Based Maze A
Guide for Schools

• Know the Research-Based Components That Are
  Building Blocks of Effective Interventions.
  Research indicates (Burns, VanDerHeyden, Boice,
  2008) that, to be maximally effective,
  interventions should
• be matched to the students academic needs
• be delivered using explicit instruction
• provide the student with adequate success in the
  instructional task
• give the student a high opportunity to respond
• provide timely performance feedback.

83
Finding a Way Out of the Research-Based Maze A
Guide for Schools

• Keep Up With Emerging Intervention Research
  Through Knowledge Brokers.
• Districts first define manageable and sensible
  intervention topic areas, such as alphabetics
  and reading fluency.
• Then district or school staff members are
  selected to serve as knowledge brokers based on
  their training, experience, and/or interest.
• Knowledge brokers regularly read educational
  research journals and other publications from
  reputable organizations or government agencies to
  keep up with emerging research in their
  intervention topic area.
• They periodically share their expertise with
  other district RTI planners to ensure that the
  schools are using the best available intervention
  strategies.

84
Defining Academic Problems Get It Right and
Interventions Are More Likely to Be
EffectiveJim Wrightwww.interventioncentral.org
85
Defining Academic Problems Recommended Steps

1. Be knowledgeable of the school academic
   curriculum and key student academic skills that
   are taught. The teacher should have a good
   survey-level knowledge of the key academic skills
   outlined in the schools curriculumfor the grade
   level of their classroom as well as earlier grade
   levels. If the curriculum alone is not adequate
   for describing a students academic deficit, the
   instructor can make use of research-based
   definitions or complete a task analysis to
   further define the academic problem area. Here
   are guidelines for consulting curriculum and
   research-based definitions and for conducting a
   task analysis for more global skills.

86
Defining Academic Problems Recommended Steps

• Curriculum. The teacher can review the schools
  curriculum and related documents (e.g.,
  score-and-sequence charts curriculum maps) to
  select specific academic skill or performance
  goals. First, determine the approximate grade or
  level in the curriculum that matches the
  students skills. Then, review the curriculum at
  that alternate grade level to find appropriate
  descriptions of the students relevant academic
  deficit. For example, a second-grade student
  had limited phonemic awareness. The student was
  not able accurately to deconstruct a spoken word
  into its component sound-units, or phonemes. In
  the schools curriculum, children were expected
  to attain proficiency in phonemic awareness by
  the close of grade 1. The teacher went off
  level to review the grade 1 curriculum and found
  a specific description of phonemic awareness that
  she could use as a starting point in defining the
  students skill deficit.

87
Defining Academic Problems Recommended Steps

• Research-Based Skill Definitions. Even when a
  schools curriculum identifies key skills,
  schools may find it useful to corroborate or
  elaborate those skill definitions by reviewing
  alternative definitions published in research
  journals or other trusted sources. For example,
  a student had delays in solving quadratic
  equations. The math instructor found that the
  schools math curriculum did not provide a
  detailed description of the skills required to
  successfully complete quadratic equations. So the
  teacher reviewed the National Mathematics
  Advisory Panel report (Fennell et al., 2008) and
  found a detailed description of component skills
  for solving quadratic equations. By combining the
  skill definitions from the school curriculum with
  the more detailed descriptions taken from the
  research-based document, the teacher could better
  pinpoint the students academic deficit in
  specific terms.

88
Defining Academic Problems Recommended Steps

• Task Analysis. Students may possess deficits in
  more global academic enabling skills that are
  essential for academic success. Teachers can
  complete an task analysis of the relevant skill
  by breaking it down into a checklist of
  constituent subskills. An instructor can use the
  resulting checklist to verify that the student
  can or cannot perform each of the subskills that
  make up the global academic enabling
  skill.For example, teachers at a middle school
  noted that many of their students seemed to have
  poor organization skills. Those instructors
  conducted a task analysis and determined that--in
  their classrooms--the essential subskills of
  student organization included (a) arriving to
  class on time (b) bringing work materials to
  class (c) following teacher directions in a
  timely manner (d) knowing how to request teacher
  assistance when needed and (e) having an
  uncluttered desk with only essential work
  materials.

89
Defining Academic Problems Recommended Steps

• Describe the academic problem in specific,
  skill-based terms (Batsche et al., 2008 Upah,
  2008). Write a clear, brief description of the
  academic skill or performance deficit that
  focuses on a specific skill or performance area.
  Here are sample problem-identification
  statements
• John reads aloud from grade-appropriate text much
  more slowly than his classmates.
• Ann lacks proficiency with multiplication math
  problems (double-digit times double-digit with no
  regrouping).
• Tye does not turn in homework assignments.
• Angela produces limited text on in-class writing
  assignments.

90
Defining Academic Problems Recommended Steps

• Develop a fuller description of the academic
  problem to provide a meaningful instructional
  context. When the teacher has described the
  students academic problem, the next step is to
  expand the problem definition to put it into a
  meaningful context. This expanded definition
  includes information about the conditions under
  which the academic problem is observed and
  typical or expected level of performance.
• Conditions. Describe the environmental conditions
  or task demands in place when the academic
  problem is observed.
• Problem Description. Describe the actual
  observable academic behavior in which the student
  is engaged. Include rate, accuracy, or other
  quantitative information of student performance.
• Typical or Expected Level of Performance. Provide
  a typical or expected performance criterion for
  this skill or behavior. Typical or expected
  academic performance can be calculated using a
  variety of sources,

91
(No Transcript)
92
Defining Academic Problems Recommended Steps

1. Develop a hypothesis statement to explain the
   academic skill or performance problem. The
   hypothesis states the assumed reason(s) or
   cause(s) for the students academic problems.
   Once it has been developed, the hypothesis
   statement acts as a compass needle, pointing
   toward interventions that most logically address
   the student academic problems.

93
(No Transcript)
94
Activity Defining Academic Interventions

• Consider the structured format that was reviewed
  for defining academic interventions.
• How can you use this framework to support RTI in
  your school?

95
Tier 1 Case Example Patricia Reading
Comprehension
96
Case Example Reading Comprehension

• The Problem
• A student, Patricia, struggled in her social
  studies class, particularly in understanding the
  course readings. Her teacher, Ms. Cardamone,
  decided that the problem was significant enough
  that the student required some individualized
  support.

97
Case Example Reading Comprehension

• The Evidence
• Student Interview. Ms. Cardamone met with
  Patricia to ask her questions about her
  difficulties with social studies content and
  assignments. Patricia said that when she reads
  the course text and other assigned readings, she
  doesnt have difficulty with the vocabulary but
  often realizes after reading half a page that she
  hasnt really understood what she has read.
  Sometimes she has to reread a page several times
  and that can be frustrating.

98
Case Example Reading Comprehension

• The Evidence (Cont.)
• Review of Records. Past teacher report card
  comments suggest that Patricia has had difficulty
  with reading comprehension tasks in earlier
  grades. She had received help in middle school in
  the reading lab, although there was no record of
  what specific interventions were tried in that
  setting.
• Input from Other Teachers. Ms. Cardamone checked
  with other teachers who have Patricia in their
  classes. All expressed concern about Patricias
  reading comprehension skills. The English
  teacher noted that Patricia appears to have
  difficulty pulling the main idea from a passage,
  which limits her ability to extract key
  information from texts and to review that
  information for tests.
•  

99
Case Example Reading Comprehension

• The Intervention
• Ms. Cardamone decided, based on the evidence
  collected, that Patricia would benefit from
  training in identifying the main idea from a
  passage, rather than trying to retain all the
  information presented in the text. She selected
  two simple interventions Question Generation and
  Text Lookback. She arranged to have Patricia meet
  with the Reading Lab teacher to learn these two
  strategies. Then Ms. Cardamone scheduled time to
  meet with Patricia to demonstrate how to use
  these strategies effectively with the social
  studies course text and other assigned readings.

100

• Students are taught to boost their comprehension
  of expository passages by (1) locating the main
  idea or key ideas in the passage and (2)
  generating questions based on that information.

QuestionGeneration
http//www.interventioncentral.org/htmdocs/interve
ntions/rdngcompr/qgen.php
101

• Text lookback is a simple strategy that students
  can use to boost their recall of expository prose
  by identifying questions that require information
  from the text and then looking back in the text
  in a methodical manner to locate that
  information.

Text Lookback
http//www.interventioncentral.org/htmdocs/interve
ntions/rdngcompr/txtlkbk.php
102
Case Example Reading Comprehension

• The Outcome
• When the intervention had been in place for 4
  weeks, Ms. Cardamone noted that Patricia appeared
  to have a somewhat better grasp of course content
  and expressed a greater grasp of material from
  the text. She shared her intervention ideas with
  other teachers working with Patricia. While
  Patricias grades did improve in Social Studies,
  they were still only borderline passing. Ms.
  Cardamone decided to continue her classroom
  interventions with Patricia but also to refer the
  student to the RTI Team to see if the student
  could receive any additional support to build her
  reading comprehension skills.

103
Tier 1 Case Example Justin Non-Compliance
104
Case Example Non-Compliance

• The Problem
• Justin showed a pattern from the start of the
  school year of not complying with teacher
  requests in his English class. His teacher, Mr.
  Steubin, noted