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


1
RTI Academic Interventions for
Difficult-to-Teach StudentsJim
Wrightwww.interventioncentral.org
2
Workshop Agenda
3
Workshop PowerPoints and Related Resources
Available at
  • http//www.jimwrightonline.com/esc20.php

4
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.

5
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.
6
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).
7
RTI Pyramid of Interventions
8
Intervention Research Development A Work in
Progress
9
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.
10
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.
11
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.
12
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
13
RTI Intervention Key Concepts
14
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.

15
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.

16
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).

17
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).

18
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..
19
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

20
Improving the Integrity of Academic Interventions
Through a Critical-Components Pre-Flight Check
Jim Wrightwww.interventioncentral.org
21
Academic Interventions Critical Components
Checklist
22
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.

23
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).
24
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,
25
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26
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.
27
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).
28
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?

29
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).
30
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.
31
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.
32
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
33
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).
34
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.
35
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?

36
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.

37
RTI Best Practicesin MathematicsInterventions
pp. Jim Wrightwww.interventioncentral.org
38
National Mathematics Advisory Panel Report13
March 2008
39
Math Advisory Panel Report athttp//www.ed.gov/
mathpanel
40
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
41
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).
42
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

43
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.
46
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
48
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49
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.
50
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.
51
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
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