RTI: Academic Interventions for Difficult-to-Teach Students Jim Wright www.interventioncentral.org

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RTI Academic Interventions for
Difficult-to-Teach StudentsJim
Wrightwww.interventioncentral.org
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Workshop Agenda
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Workshop PowerPoints and Related Resources
Available at

• http//www.jimwrightonline.com/esc20.php

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RTI Assumption Struggling Students Are Typical
Until Proven Otherwise

• RTI logic assumes that
• A student who begins to struggle in general
  education is typical, and that
• It is general educations responsibility to find
  the instructional strategies that will unlock the
  students learning potential
• Only when the student shows through
  well-documented interventions that he or she has
  failed to respond to intervention does RTI
  begin to investigate the possibility that the
  student may have a learning disability or other
  special education condition.

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Essential Elements of RTI (Fairbanks, Sugai,
Guardino, Lathrop, 2007)

1. A continuum of evidence-based services available
   to all students" that range from universal to
   highly individualized intensive
2. Decision points to determine if students are
   performing significantly below the level of their
   peers in academic and social behavior domains"
3. Ongoing monitoring of student progress"
4. Employment of more intensive or different
   interventions when students do not improve in
   response" to lesser interventions
5. Evaluation for special education services if
   students do not respond to intervention
   instruction"

Source Fairbanks, S., Sugai, G., Guardino, S.,
Lathrop, M. (2007). Response to intervention
Examining classroom behavior support in second
grade. Exceptional Children, 73, p. 289.
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School Instructional Time The Irreplaceable
Resource

• In the average school system, there are 330
  minutes in the instructional day, 1,650 minutes
  in the instructional week, and 56,700 minutes in
  the instructional year. Except in unusual
  circumstances, these are the only minutes we have
  to provide effective services for students. The
  number of years we have to apply these minutes is
  fixed. Therefore, each minute counts and schools
  cannot afford to support inefficient models of
  service delivery. p. 177

Source Batsche, G. M., Castillo, J. M., Dixon,
D. N., Forde, S. (2008). Best practices in
problem analysis. In A. Thomas J. Grimes
(Eds.), Best practices in school psychology V
(pp. 177-193).
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RTI Pyramid of Interventions
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Intervention Research Development A Work in
Progress
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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.
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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.
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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.
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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
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RTI Intervention Key Concepts
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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.

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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.

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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).

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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).

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Teaching is giving it isnt taking away.
(Howell, Hosp Kurns, 2008 p. 356).


Source Howell, K. W., Hosp, J. L., Kurns, S.
(2008). Best practices in curriculum-based
evaluation. In A. Thomas J. Grimes (Eds.), Best
practices in school psychology V (pp.349-362).
Bethesda, MD National Association of School
Psychologists..
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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

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Improving the Integrity of Academic Interventions
Through a Critical-Components Pre-Flight Check
Jim Wrightwww.interventioncentral.org
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Academic Interventions Critical Components
Checklist
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Academic Interventions Critical Components
Checklist

• This checklist summarizes the essential
  components of academic interventions. When
  preparing a students Tier 1, 2, or 3 academic
  intervention plan, use this document as a
  pre-flight checklist to ensure that the
  academic intervention is of high quality, is
  sufficiently strong to address the identified
  student problem, is fully understood and
  supported by the teacher, and can be implemented
  with integrity. NOTE While the checklist refers
  to the teacher as the interventionist, it can
  also be used as a guide to ensure the quality of
  interventions implemented by non-instructional
  personnel, adult volunteers, parents, and peer
  (student) tutors.

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Allocating Sufficient Contact Time Assuring Appropriate Student-Teacher Ratio Allocating Sufficient Contact Time Assuring Appropriate Student-Teacher Ratio Allocating Sufficient Contact Time Assuring Appropriate Student-Teacher Ratio
The cumulative time set aside for an intervention and the amount of direct teacher contact are two factors that help to determine that interventions strength (Yeaton Sechrest, 1981). The cumulative time set aside for an intervention and the amount of direct teacher contact are two factors that help to determine that interventions strength (Yeaton Sechrest, 1981). The cumulative time set aside for an intervention and the amount of direct teacher contact are two factors that help to determine that interventions strength (Yeaton Sechrest, 1981).
Critical Item? Intervention Element Notes
? Time Allocated. The time set aside for the intervention is appropriate for the type and level of student problem (Burns Gibbons, 2008 Kratochwill, Clements Kalymon, 2007). When evaluating whether the amount of time allocated is adequate, consider Length of each intervention session. Frequency of sessions (e.g.., daily, 3 times per week) Duration of intervention period (e.g., 6 instructional weeks)
? Student-Teacher Ratio. The student receives sufficient contact from the teacher or other person delivering the intervention to make that intervention effective. NOTE Generally, supplemental intervention groups should be limited to 6-7 students (Burns Gibbons, 2008).
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Matching the Intervention to the Student Problem p. 15 expanded handout Matching the Intervention to the Student Problem p. 15 expanded handout Matching the Intervention to the Student Problem p. 15 expanded handout
Academic interventions are not selected at random. First, the student academic problem(s) is defined clearly and in detail. Then, the likely explanations for the academic problem(s) are identified to understand which intervention(s) are likely to helpand which should be avoided. Academic interventions are not selected at random. First, the student academic problem(s) is defined clearly and in detail. Then, the likely explanations for the academic problem(s) are identified to understand which intervention(s) are likely to helpand which should be avoided. Academic interventions are not selected at random. First, the student academic problem(s) is defined clearly and in detail. Then, the likely explanations for the academic problem(s) are identified to understand which intervention(s) are likely to helpand which should be avoided.
Critical Item? Intervention Element Notes
? Problem Definition. The student academic problem(s) to be addressed in the intervention are defined in clear, specific, measureable terms (Bergan, 1995 Witt, VanDerHeyden Gilbertson, 2004). The full problem definition describes 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,
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Matching the Intervention to the Student Problem (Cont.) Matching the Intervention to the Student Problem (Cont.) Matching the Intervention to the Student Problem (Cont.)
Critical Item? Intervention Element Notes
? Appropriate Target. Selected intervention(s) are appropriate for the identified student problem(s) (Burns, VanDerHeyden Boice, 2008). TIP Use the Instructional Hierarchy (Haring et al., 1978) to select academic interventions according to the four stages of learning Acquisition. The student has begun to learn how to complete the target skill correctly but is not yet accurate in the skill. Interventions should improve accuracy. Fluency. The student is able to complete the target skill accurately but works slowly. Interventions should increase the students speed of responding (fluency) as well as to maintain accuracy. Generalization. The student may have acquired the target skill but does not typically use it in the full range of appropriate situations or settings. Or the student may confuse the target skill with similar skills. Interventions should get the student to use the skill in the widest possible range of settings and situations, or to accurately discriminate between the target skill and similar skills. Adaptation. The student is not yet able to modify or adapt an existing skill to fit novel task-demands or situations. Interventions should help the student to identify key concepts or elements from previously learned skills that can be adapted to the new demands or situations.
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Matching the Intervention to the Student Problem (Cont.) Matching the Intervention to the Student Problem (Cont.) Matching the Intervention to the Student Problem (Cont.)
Critical Item? Intervention Element Notes
? Cant Do/Wont Do Check. The teacher has determined whether the student problem is primarily a skill or knowledge deficit (cant do) or whether student motivation plays a main or supporting role in academic underperformance (wont do). If motivation appears to be a significant factor contributing to the problem, the intervention plan includes strategies to engage the student (e.g., high interest learning activities rewards/incentives increased student choice in academic assignments, etc.) (Skinner, Pappas Davis, 2005 Witt, VanDerHeyden Gilbertson, 2004).
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Activity Matching the Intervention to the
Student Problem

• Consider these critical aspects of academic
  intervention
• Clear and specific problem-identification
  statement (Conditions, Problem Description,
  Typical/Expected Level of Performance).
• Appropriate intervention target (e.g., selected
  intervention is appropriately matched to
  Acquisition, Fluency, Generalization, or
  Adaptation phase of Instructional Hierarchy).
• Cant Do/Wont Do Check (Clarification of whether
  motivation plays a significant role in student
  academic underperformance).
• What questions do you have about applying any of
  these concepts when planning classroom
  interventions?

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Incorporating Effective Instructional Elements Incorporating Effective Instructional Elements Incorporating Effective Instructional Elements
These effective building blocks of instruction are well-known and well-supported by the research. They should be considered when selecting or creating any academic intervention. These effective building blocks of instruction are well-known and well-supported by the research. They should be considered when selecting or creating any academic intervention. These effective building blocks of instruction are well-known and well-supported by the research. They should be considered when selecting or creating any academic intervention.
Critical Item? Intervention Element Notes
? Explicit Instruction. Student skills have been broken down into manageable and deliberately sequenced steps and the teacher provided overt strategies for students to learn and practice new skills (Burns, VanDerHeyden Boice, 2008, p.1153).
? Appropriate Level of Challenge. The student experienced sufficient success in the academic task(s) to shape learning in the desired direction as well as to maintain student motivation (Burns, VanDerHeyden Boice, 2008).
? Active Engagement. The intervention ensures that the student is engaged in active accurate responding (Skinner, Pappas Davis, 2005).at a rate frequent enough to capture student attention and to optimize effective learning.
? Performance Feedback. The student receives prompt performance feedback about the work completed (Burns, VanDerHeyden Boice, 2008).
? Maintenance of Academic Standards. If the intervention includes any accommodations to better support the struggling learner (e.g., preferential seating, breaking a longer assignment into smaller chunks), those accommodations do not substantially lower the academic standards against which the student is to be evaluated and are not likely to reduce the students rate of learning (Skinner, Pappas Davis, 2005).
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Activity Incorporating Effective Instructional
Elements

• Think about the effective instructional elements
  reviewed in this workshop.
• How can teachers ensure that all effective
  instructional elements are included in academic
  interventions?

Incorporating Effective Instructional Elements Incorporating Effective Instructional Elements Incorporating Effective Instructional Elements
Critical Item? Intervention Element Notes
? Explicit Instruction.
? Appropriate Level of Challenge.
? Active Engagement..
? Performance Feedback.
? Maintenance of Academic Standards.
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Verifying Teacher Understanding Providing Teacher Support Verifying Teacher Understanding Providing Teacher Support Verifying Teacher Understanding Providing Teacher Support
The teacher is an active agent in the intervention, with primary responsibility for putting it into practice in a busy classroom. It is important, then, that the teacher fully understands how to do the intervention, believes that he or she can do it, and knows whom to seek out if there are problems with the intervention. The teacher is an active agent in the intervention, with primary responsibility for putting it into practice in a busy classroom. It is important, then, that the teacher fully understands how to do the intervention, believes that he or she can do it, and knows whom to seek out if there are problems with the intervention. The teacher is an active agent in the intervention, with primary responsibility for putting it into practice in a busy classroom. It is important, then, that the teacher fully understands how to do the intervention, believes that he or she can do it, and knows whom to seek out if there are problems with the intervention.
Critical Item? Intervention Element Notes
? Teacher Responsibility. The teacher understands his or her responsibility to implement the academic intervention(s) with integrity.
? Teacher Acceptability. The teacher states that he or she finds the academic intervention feasible and acceptable for the identified student problem.
? Step-by-Step Intervention Script. The essential steps of the intervention are written as an intervention script--a series of clearly described stepsto ensure teacher understanding and make implementation easier (Hawkins, Morrison, Musti-Rao Hawkins, 2008).
? Intervention Training. If the teacher requires training to carry out the intervention, that training has been arranged.
? Intervention Elements Negotiable vs. Non-Negotiable. The teacher knows all of the steps of the intervention. Additionally, the teacher knows which of the intervention steps are non-negotiable (they must be completed exactly as designed) and which are negotiable (the teacher has some latitude in how to carry out those steps) (Hawkins, Morrison, Musti-Rao Hawkins, 2008).
? Assistance With the Intervention. If the intervention cannot be implemented as designed for any reason (e.g., student absence, lack of materials, etc.), the teacher knows how to get assistance quickly to either fix the problem(s) to the current intervention or to change the intervention.
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Activity Verifying Teacher Understanding
Providing Teacher Support

• In your teams
• Review the checklist for verifying that teachers
  understand all elements of the intervention and
  actively support its use.
• How will your school ensure that teachers will
  understand and support academic interventions
  designed to be implemented in the classroom?

Verifying Teacher Understanding Providing Teacher Support
Critical Item? Intervention Element
? Teacher Responsibility
? Teacher Acceptability.
? Step-by-Step Intervention Script.
? Intervention Training.
? Intervention Elements Negotiable vs. Non-Negotiable
? Assistance With the Intervention
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Documenting the Intervention Collecting Data Documenting the Intervention Collecting Data Documenting the Intervention Collecting Data
Interventions only have meaning if they are done within a larger data-based context. For example, interventions that lack baseline data, goal(s) for improvement, and a progress-monitoring plan are fatally flawed (Witt, VanDerHeyden Gilbertson, 2004). Interventions only have meaning if they are done within a larger data-based context. For example, interventions that lack baseline data, goal(s) for improvement, and a progress-monitoring plan are fatally flawed (Witt, VanDerHeyden Gilbertson, 2004). Interventions only have meaning if they are done within a larger data-based context. For example, interventions that lack baseline data, goal(s) for improvement, and a progress-monitoring plan are fatally flawed (Witt, VanDerHeyden Gilbertson, 2004).
Critical Item? Intervention Element Notes
? Intervention Documentation. The teacher understands and can manage all documentation required for this intervention (e.g., maintaining a log of intervention sessions, etc.).
? Checkup Date. Before the intervention begins, a future checkup date is selected to review the intervention to determine if it is successful. Time elapsing between the start of the intervention and the checkup date should be short enough to allow a timely review of the intervention but long enough to give the school sufficient time to judge with confidence whether the intervention worked.
? Baseline. Before the intervention begins, the teacher has collected information about the students baseline level of performance in the identified area(s) of academic concern (Witt, VanDerHeyden Gilbertson, 2004).
? Goal. Before the intervention begins, the teacher has set a specific goal for predicted student improvement to use as a minimum standard for success (Witt, VanDerHeyden Gilbertson, 2004). The goal is the expected student outcome by the checkup date if the intervention is successful.
? Progress-Monitoring. During the intervention, the teacher collects progress-monitoring data of sufficient quality and at a sufficient frequency to determine at the checkup date whether that intervention is successful (Witt, VanDerHeyden Gilbertson, 2004).
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Activity Documenting the Intervention
Collecting Data

• In your teams
• Consider the elements of intervention
  documentation, data collection, and data
  interpretation discussed here.
• What steps can your school take to make sure
  that data have a central focus when
  interventionsare planned and implemented?

Documenting the Intervention Collecting Data Documenting the Intervention Collecting Data Documenting the Intervention Collecting Data
Critical Item? Intervention Element Notes
? Intervention Documentation.
? Checkup Date.
? Baseline.
? Goal.
? Progress-Monitoring.
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Activity Using the Critical Components
Checklist

• In your teams
• Discuss the Academic Interventions Critical
  Components Checklist.
• What are ways that your school or district might
  use this checklist?

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References

• Bergan, J. R. (1995). Evolution of a
  problem-solving model of consultation. Journal of
  Educational and Psychological Consultation, 6(2),
  111-123.
• Burns, M. K., Gibbons, K. A. (2008).
  Implementing response-to-intervention in
  elementary and secondary schools. Routledge New
  York.
• 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.
• 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.
• Hawkins, R. O., Morrison, J. Q., Musti-Rao, S.,
  Hawkins, J. A. (2008). Treatment integrity for
  academic interventions in real- world settings.
  School Psychology Forum, 2(3), 1-15.
• 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.
• 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.
• 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. 
• Yeaton, W. M. Sechrest, L. (1981). Critical
  dimensions in the choice and maintenance of
  successful treatments Strength, integrity, and
  effectiveness. Journal of Consulting and Clinical
  Psychology, 49, 156-167.

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RTI Best Practicesin MathematicsInterventions
pp. Jim Wrightwww.interventioncentral.org
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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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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).
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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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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.
44
Mathematics is made of 50 percent formulas, 50
percent proofs, and 50 percent imagination.
Anonymous
45
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..
47
The Elements of Mathematical Proficiency What
the Experts Say
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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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Math Computation Building FluencyJim
Wrightwww.interventioncentral.org
52
"Arithmetic is being able to count up to twenty
without taking off your shoes." Anonymous
53
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.
54
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.
55
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.
56
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.
57
Self-Administered Arithmetic Combination Drills
58
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.
59
Math Computation Problem Interspersal Technique
p.42

• 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..
60
Building Student Skills inApplied Math
ProblemsJim Wrightwww.interventioncentral.org
61
How Do We Reach Low-Performing Math Students?
Instructional Recommendations

• Important elements of math instruction for
  low-performing students
• Providing teachers and students with data on
  student performance
• Using peers as tutors or instructional guides
• Providing clear, specific feedback to parents on
  their childrens mathematics success
• Using principles of explicit instruction in
  teaching math concepts and procedures. p. 51

Source Baker, S., Gersten, R., Lee, D.
(2002).A synthesis of empirical research on
teaching mathematics to low-achieving students.
The Elementary School Journal, 103(1), 51-73..
62
Potential Blockers of Higher-Level Math
Problem-Solving A Sampler

• Limited reading skills
• Failure to master--or develop automaticity in
  basic math operations
• Lack of knowledge of specialized math vocabulary
  (e.g., quotient)
• Lack of familiarity with the specialized use of
  known words (e.g., product)
• Inability to interpret specialized math symbols
  (e.g., 4 lt 2)
• Difficulty extracting underlying math
  operations from word/story problems
• Difficulty identifying and ignoring extraneous
  information included in word/story problems

63
Math Intervention Ideas for Higher-Level Math
ProblemsJim Wrightwww.interventioncentral.org
64
Applied Math Problems Rationale

• Applied math problems (also known as story or
  word problems) are traditional tools for having
  students apply math concepts and operations to
  real-world settings.

65
Applied Problems Individualized Self-Correction
Checklists

• Students can improve their accuracy on
  particular types of word and number problems by
  using an individualized self-instruction
  checklist that reminds them to pay attention to
  their own specific error patterns.
• The teacher meets with the student. Together they
  analyze common error patterns that the student
  tends to commit on a particular problem type
  (e.g., On addition problems that require
  carrying, I dont always remember to carry the
  number from the previously added column.).
• For each type of error identified, the student
  and teacher together describe the appropriate
  step to take to prevent the error from occurring
  (e.g., When adding each column, make sure to
  carry numbers when needed.).
• These self-check items are compiled into a single
  checklist. Students are then encouraged to use
  their individualized self-instruction checklist
  whenever they work independently on their number
  or word problems.

Source Pólya, G. (1945). How to solve it.
Princeton University Press Princeton, N.J.
66
Interpreting Math Graphics A Reading
Comprehension Intervention
67
Housing Bubble GraphicNew York Times23
September 2007
68
Classroom Challenges in Interpreting Math Graphics

• When encountering math graphics, students may
• expect the answer to be easily accessible when in
  fact the graphic may expect the reader to
  interpret and draw conclusions
• be inattentive to details of the graphic
• treat irrelevant data as relevant
• not pay close attention to questions before
  turning to graphics to find the answer
• fail to use their prior knowledge both to extend
  the information on the graphic and to act as a
  possible check on the information that it
  presents.

Source Mesmer, H.A.E., Hutchins, E.J. (2002).
Using QARs with charts and graphs. The Reading
Teacher, 56, 2127.
69
Using Question-Answer Relationships (QARs) to
Interpret Information from Math Graphics

• Students can be more savvy interpreters of
  graphics in applied math problems by applying the
  Question-Answer Relationship (QAR) strategy. Four
  Kinds of QAR Questions
• RIGHT THERE questions are fact-based and can be
  found in a single sentence, often accompanied by
  'clue' words that also appear in the question.
• THINK AND SEARCH questions can be answered by
  information in the text but require the scanning
  of text and making connections between different
  pieces of factual information.
• AUTHOR AND YOU questions require that students
  take information or opinions that appear in the
  text and combine them with the reader's own
  experiences or opinions to formulate an answer.
• ON MY OWN questions are based on the students'
  own experiences and do not require knowledge of
  the text to answer.

Source Mesmer, H.A.E., Hutchins, E.J. (2002).
Using QARs with charts and graphs. The Reading
Teacher, 56, 2127.
70
Using Question-Answer Relationships (QARs) to
Interpret Information from Math Graphics 4-Step
Teaching Sequence

1. DISTINGUISHING DIFFERENT KINDS OF GRAPHICS.
   Students are taught to differentiate between
   common types of graphics e.g., table (grid with
   information contained in cells), chart (boxes
   with possible connecting lines or arrows),
   picture (figure with labels), line graph, bar
   graph. Students note significant differences
   between the various graphics, while the teacher
   records those observations on a wall chart. Next
   students are given examples of graphics and asked
   to identify which general kind of graphic each
   is. Finally, students are assigned to go on a
   graphics hunt, locating graphics in magazines
   and newspapers, labeling them, and bringing to
   class to review.

Source Mesmer, H.A.E., Hutchins, E.J. (2002).
Using QARs with charts and graphs. The Reading
Teacher, 56, 2127.
71
Using Question-Answer Relationships (QARs) to
Interpret Information from Math Graphics 4-Step
Teaching Sequence

1. INTERPRETING INFORMATION IN GRAPHICS. Students
   are paired off, with stronger students matched
   with less strong ones. The teacher spends at
   least one session presenting students with
   examples from each of the graphics categories.
   The presentation sequence is ordered so that
   students begin with examples of the most concrete
   graphics and move toward the more abstract
   Pictures gt tables gt bar graphs gt charts gt line
   graphs. At each session, student pairs examine
   graphics and discuss questions such as What
   information does this graphic present? What are
   strengths of this graphic for presenting data?
   What are possible weaknesses?

Source Mesmer, H.A.E., Hutchins, E.J. (2002).
Using QARs with charts and graphs. The Reading
Teacher, 56, 2127.
72
Using Question-Answer Relationships (QARs) to
Interpret Information from Math Graphics 4-Step
Teaching Sequence

1. LINKING THE USE OF QARS TO GRAPHICS. Students are
   given a series of data questions and correct
   answers, with each question accompanied by a
   graphic that contains information needed to
   formulate the answer. Students are also each
   given index cards with titles and descriptions of
   each of the 4 QAR questions RIGHT THERE, THINK
   AND SEARCH, AUTHOR AND YOU, ON MY OWN. Working
   in small groups and then individually, students
   read the questions, study the matching graphics,
   and verify the answers as correct. They then
   identify the type question being asked using
   their QAR index cards.

Source Mesmer, H.A.E., Hutchins, E.J. (2002).
Using QARs with charts and graphs. The Reading
Teacher, 56, 2127.
73
Using Question-Answer Relationships (QARs) to
Interpret Information from Math Graphics 4-Step
Teaching Sequence

• USING QARS WITH GRAPHICS INDEPENDENTLY. When
  students are ready to use the QAR strategy
  independently to read graphics, they are given a
  laminated card as a reference with 6 steps to
  follow
• Read the question,
• Review the graphic,
• Reread the question,
• Choose a QAR,
• Answer the question, and
• Locate the answer derived from the graphic in the
  answer choices offered.
• Students are strongly encouraged NOT to read the
  answer choices offered until they have first
  derived their own answer, so that those choices
  dont short-circuit their inquiry.

Source Mesmer, H.A.E., Hutchins, E.J. (2002).
Using QARs with charts and graphs. The Reading
Teacher, 56, 2127.
74
Developing Student Metacognitive Abilities
75
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.
76
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.
77
Combining Cognitive Metacognitive Strategies to
Assist Students With Mathematical Problem Solving
p. 44

• 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).

78
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.

79
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).

80
Combined Cognitive Metacognitive Elements of
Strategy
81
Combined Cognitive Metacognitive Elements of
Strategy
82
Combined Cognitive Metacognitive Elements of
Strategy
83
Combined Cognitive Metacognitive Elements of
Strategy
84
Combined Cognitive Metacognitive Elements of
Strategy
85
Combined Cognitive Metacognitive Elements of
Strategy
86
Combined Cognitive Metacognitive Elements of
Strategy
87
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
88
RTI Writing Interventions Jim
Wrightwww.interventioncentral.org
89
(No Transcript)
90
Defining Student Writing Problems
91

• "If all the grammarians in the world were placed
  end to end, it would be a good thing."
• Oscar Wilde

92
Graham, S., Perin, D. (2007). Writing next
Effective strategies to improve writing of
adolescents in middle and high schools A report
to Carnegie Corporation of New York. Washington,
DC Alliance for Excellent Education. Retrieved
from http//www.all4ed.org/files/WritingNext.pdf
93
The Effect of Grammar Instruction as an
Independent Activity

• Grammar instruction in the studies reviewed
  for the Writing Next report involved the
  explicit and systematic teaching of the parts of
  speech and structure of sentences. The
  meta-analysis found an effect for this type of
  instruction for students across the full range of
  ability, but surprisingly, this effect was
  negativeSuch findings raise serious questions
  about some educators enthusiasm for traditional
  grammar instruction as a focus of writing
  instruction for adolescents.Overall, the
  findings on grammar instruction suggest that,
  although teaching grammar is important,
  alternative procedures, such as sentence
  combining, are more effective than traditional
  approaches for improving the quality of students
  writing. p. 21

Source Graham, S., Perin, D. (2007). Writing
next Effective strategies to improve writing of
adolescents in middle and high schools A report
to Carnegie Corporation of New York. Washington,
DC Alliance for Excellent Education.
94

• Domains of writing to be assessed (Robinson
  Howell, 2008)
• Fluency/Text Generation Facility in getting text
  onto paper or typed into the computer. (NOTE
  This element can be significantly influenced by
  student motivation.)
• Syntactic Maturity This skill includes the
• Ability to discern when a word string meets
  criteria as a complete sentence
• Ability to write compositions with a diverse
  range of sentence structures
• Semantic Maturity Writers use of vocabulary of
  range and sophistication

Source Robinson, L. K., Howell, K. W. (2008).
Best practices in curriculum-based evaluation
written expression. In A. Thomas J. Grimes
(Eds.), Best practices in school psychology V
(pp. 439-452). Bethesda, MD National Association
of School Psychologists.
95
Domains of writing to be assessed (Robinson
Howell, 2008)

• 5-Step Writing Process (Items in bold are
  iterative)
• Planning. The student carries out necessary
  pre-writing planning activities, including
  content, format, and outline.
• Drafting. The student writes or types the
  composition.
• Revision. The student reviews the content of the
  composition-in-progress and makes changes as
  needed. After producing an initial written draft,
  the student considers revisions to content before
  turning in for a grade or evaluation.
• Editing. The student looks over