response to intervention rti at middle and high schools: academic interventions for difficult-...

Response to Intervention

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RTI at Middle and High Schools: Academic Interventions for Difficult-to-Teach Students

Jim Wrightwww.interventioncentral.org


www.interventioncentral.org 2

Secondary Students: Unique Challenges…

Struggling learners in middle and high school may:• Have significant deficits in basic academic skills• Lack higher-level problem-solving strategies and

concepts• Present with issues of school motivation• Show social/emotional concerns that interfere with

academics• Have difficulty with attendance• Are often in a process of disengaging from learning

even as adults in school expect that those students will move toward being ‘self-managing’ learners…



Why Do Students Drop Out of School?: Student Survey

• Classes were not perceived as interesting (47 percent)• Not motivated by teachers to ‘work hard’ (69 percent)• Failing in school was a major factor in dropping out (35 percent)• Had to get a job (32 percent)• Became a parent (26 percent)• Needed to care for a family member (22 percent)

Source: Bridgeland, J. M., DiIulio, J. J., & Morison, K. B. (2006). The silent epidemic: Perspectives of high school dropouts. Seattle, WA: Gates Foundation. Retrieved on May 4, 2008, from http://www.gatesfoundation.org/nr/downloads/ed/TheSilentEpidemic3-06FINAL.pdf



Overlap Between ‘Policy Pathways’ & RTI Goals: Recommendations for Schools to Reduce Dropout Rates• A range of high school learning options matched to the needs of

individual learners: ‘different schools for different students’• Strategies to engage parents• Individualized graduation plans• ‘Early warning systems’ to identify students at risk of school

failure• A range of supplemental services/’intensive assistance strategies’

for struggling students• Adult advocates to work individually with at-risk students to

overcome obstacles to school completionSource: Bridgeland, J. M., DiIulio, J. J., & Morison, K. B. (2006). The silent epidemic: Perspectives of high school dropouts. Seattle, WA: Gates Foundation. Retrieved on May 4, 2008, from http://www.gatesfoundation.org/nr/downloads/ed/TheSilentEpidemic3-06FINAL.pdf



School Dropout as a Process, Not an Event

“It is increasingly accepted that dropout is best conceptualized as a long-term process, not an instantaneous event; however, most interventions are administered at a middle or high school level after problems are severe.”

Source: Jimerson, S., Reschly, A.L., & Hess, R. (2008). Best practices in increasing the likelihood of school completion. In A. Thomas & J. Grimes (Eds). Best Practices in School Psychology - 5th Ed (pp. 1085-1097). Bethesda, MD: National Association of School Psychologists.. p.1090



Universal Screening at Secondary Schools: Using Existing Data Proactively to Flag ‘Signs of Disengagement’

“Across interventions…, a key component to promoting school completion is the systematic monitoring of all students for signs of disengagement, such as attendance and behavior problems, failing courses, off track in terms of credits earned toward graduation, problematic or few close relationships with peers and/or teachers, and then following up with those who are at risk.”

Source: Jimerson, S., Reschly, A.L., & Hess, R. (2008). Best practices in increasing the likelihood of school completion. In A. Thomas & J. Grimes (Eds). Best Practices in School Psychology - 5th Ed (pp. 1085-1097). Bethesda, MD: National Association of School Psychologists.. p.1090



Student Motivation & The Need for Intervention“A common response to students who struggle in sixth grade is to wait and hope they grow out of it or adapt, to attribute early struggles to the natural commotion of early adolescence and to temporary difficulties in adapting to new organizational structures of schooling, more challenging curricula and assessment, and less personalized attention. Our evidence clearly indicates that, at least in high-poverty urban schools, sixth graders who are missing 20% or more of the days, exhibiting poor behavior, or failing math or English do not recover. On the contrary, they drop out. This says that early intervention is not only productive but absolutely essential.”

Source: Balfanz, R., Herzog, L., MacIver, D. J. (2007). Preventing student disengagement and keeping students on the graduation path in urban middle grades schools: Early identification and effective interventions. Educational Psychologist,42, 223–235. .



Mining Archival Data: What Are the ‘Early Warning Flags’ of Student Drop-Out?

A sample of 13,000 students in Philadelphia were tracked for 8 years. These early warning indicators were found to predict student drop-out in the sixth-grade year:

• Failure in English• Failure in math• Missing at least 20% of school days• Receiving an ‘unsatisfactory’ behavior rating from at least one

teacher




What is the Predictive Power of These Early Warning Flags?


Number of ‘Early Warning Flags’ in Student Record

Probability That Student Would Graduate

None 56%

1 36%

2 21%

3 13%

4 7%



Five Core Components of RTI Service Delivery

1. Student services are arranged in a multi-tier model 2. Data are collected to assess student baseline levels

and to make decisions about student progress 3. Interventions are ‘evidence-based’4. The ‘procedural integrity’ of interventions is measured5. RTI is implemented and developed at the school- and

district-level to be scalable and sustainable over time

Source: Glover, T. A., & DiPerna, J. C. (2007). Service delivery for response to intervention: Core components and directions for future research. School Psychology Review, 36, 526-540.



RTI ‘Pyramid of Interventions’

Tier 1

Tier 2

Tier 3

Tier 1: Universal interventions. Available to all students in a classroom or school. Can consist of whole-group or individual strategies or supports.

Tier 2 Individualized interventions. Subset of students receive interventions targeting specific needs.

Tier 3: Intensive interventions. Students who are ‘non-responders’ to Tiers I & II are referred to the building RTI Problem-Solving Team.



Tier I Instruction/InterventionsTier I instruction/interventions:

• Are universal—available to all students.• Can be delivered within classrooms or throughout the school. • Are likely to be put into place by the teacher at the first sign that a student is struggling.

All children have access to Tier 1 instruction/interventions. Teachers have the capability to use those strategies without requiring outside assistance.

Tier 1 instruction/interventions encompass:

• The school’s core curriculum and all published or teacher-made materials used to deliver that curriculum.

• Teacher use of ‘whole-group’ teaching & management strategies.• Teacher use of individualized strategies with specific students.

Tier I instruction/interventions attempt to answer the question: Are routine classroom instructional strategies sufficient to help the student to achieve academic success?



Complementary RTI Models: Standard Treatment & Problem-Solving Protocols

“The two most commonly used RTI approaches are (1) standard treatment and (2) problem-solving protocol. While these two approaches to RTI are sometimes described as being very different from each other, they actually have several common elements, and both fit within a problem-solving framework. In practice, many schools and districts combine or blend aspects of the two approaches to fit their needs.”

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.betterhighschools.org/pubs/ p. 5



RTI Interventions: Standard-Treatment vs. Problem-SolvingThere are two different vehicles that schools can use to deliver RTI interventions:

Standard-Protocol (Standalone Intervention). Programs based on scientifically valid instructional practices (‘standard protocol’) are created to address frequent student referral concerns. These services are provided outside of the classroom. A middle school, for example, may set up a structured math-tutoring program staffed by adult volunteer tutors to provide assistance to students with limited math skills. Students referred for a Tier II math intervention would be placed in this tutoring program. An advantage of the standard-protocol approach is that it is efficient and consistent: large numbers of students can be put into these group interventions to receive a highly standardized intervention. However, standard group intervention protocols often cannot be individualized easily to accommodate a specific student’s unique needs.

Problem-solving (Classroom-Based Intervention). Individualized research-based interventions match the profile of a particular student’s strengths and limitations. The classroom teacher often has a large role in carrying out these interventions. A plus of the problem-solving approach is that the intervention can be customized to the student’s needs. However, developing intervention plans for individual students can be time-consuming.



Tier 2: Supplemental (Group-Based) Interventions(Standard Treatment Protocol)

Tier 2 interventions are typically delivered in small-group format. About 15% of students in the typical school will require Tier 2/supplemental intervention support.

Group size for Tier 2 interventions is limited to 4-7 students.

Students placed in Tier 2 interventions should have a shared profile of intervention need.

The progress of students in Tier 2 interventions are monitored at least 1-2 times per month.

Source: Burns, M. K., & Gibbons, K. A. (2008). Implementing response-to-intervention in elementary and secondary schools. Routledge: New York.



Tier 3: Intensive Individualized Interventions(Problem-Solving Protocol)

Tier 3 interventions are the most intensive offered in a school setting.

Students qualify for Tier 3 interventions because:– they are found to have a large skill gap when compared to their class or grade

peers; and/or– They did not respond to interventions provided previously at Tiers 1 & 2.

Tier 3 interventions are provided daily for sessions of 30 minutes. The student-teacher ratio is flexible but should allow the student to receive intensive, individualized instruction.

The progress of students in Tier 3 interventions is monitored at least weekly.




Middle & High School: Lack of Consensus on an RTI Model

“Because RTI has thus far been implemented primarily in early elementary grades, it is not clear precisely what RTI might look like at the high school level.”




At the Federal Level: A ‘Hands-Off Approach to RTI Implementation

“There are many RTI models and the regulations are written to accommodate the many different models that are currently in use. The Department does not mandate or endorse any particular model. Rather, the regulations provide States with the flexibility to adopt criteria that best meet local needs. Language that is more specific or prescriptive would not be appropriate. For example, while we recognize that rate of learning is often a key variable in assessing a child’s response to intervention, it would not be appropriate for the regulations to set a standard for responsiveness or improvement in the rate of learning.” p. 46653

Source: U.S. Department of Education. (2006). Assistance to States for the education of children with disabilities and preschool grants for children with disabilities; final rule. 71 Fed. Reg. (August 14, 2006) 34 CFR Parts 300 and 301.



The Purpose of RTI in Secondary Schools: What Students Should It Serve?

Early Identification. As students begin to show need for academic support, the RTI model proactively supports them with early interventions to close the skill or performance gap with peers.

Chronically At-Risk. Students whose school performance is marginal across school years but who do not qualify for special education services are identified by the RTI Team and provided with ongoing intervention support.

Special Education. Students who fail to respond to scientifically valid general-education interventions implemented with integrity are classified as ‘non-responders’ and found eligible for special education.



Intervention Research & Development: A Work in

Progress



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.



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.



There is a lack of agreement about what is meant by ‘scientifically validated’ classroom (Tier I) interventions. Districts should establish a ‘vetting’ process—criteria 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 shouldn’t be afraid to ask).. Learning Disabilities Research & Practice, 22(2),129–136.

Schools Need to Review Tier 1 (Classroom) Interventions to Ensure That They Are Supported

By Research



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.”




RTI & Intervention: Key Concepts



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.



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.




• 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).




• 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 student’s 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).



“ ”“Teaching is giving; it isn’t 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..




• Modification. A modification changes the expectations of what a student is expected to know or do—typically 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



Big Ideas: The Four Stages of Learning Can Be Summed Up in the ‘Instructional Hierarchy’ pp. 2-3

(Haring et al., 1978)

Student learning can be thought of as a multi-stage process. The universal stages of learning include:

• Acquisition: The student is just acquiring the skill.• Fluency: The student can perform the skill but

must make that skill ‘automatic’.• Generalization: The student must perform the skill

across situations or settings.• Adaptation: The student confronts novel task

demands that require that the student adapt a current skill to meet new requirements.

Source: Haring, N.G., Lovitt, T.C., Eaton, M.D., & Hansen, C.L. (1978). The fourth R: Research in the classroom. Columbus, OH: Charles E. Merrill Publishing Co.



Increasing the Intensity of an Intervention: Key Dimensions

Interventions can move up the RTI Tiers through being intensified across several dimensions, including:

• Type of intervention strategy or materials used• Student-teacher ratio• Length of intervention sessions• Frequency of intervention sessions• Duration of the intervention period (e.g., extending an intervention

from 5 weeks to 10 weeks)• Motivation strategies


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.



RTI Interventions: What If There is No Commercial Intervention Package or Program Available?

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




Research-Based Elements of Effective Academic Interventions

• ‘Correctly targeted’: The intervention is appropriately matched to the student’s academic or behavioral needs.

• ‘Explicit instruction’: Student skills have been broken down “into manageable and deliberately sequenced steps and providing overt strategies for students to learn and practice new skills” p.1153

• ‘Appropriate level of challenge’: The student experiences adequate success with the instructional task.

• ‘High opportunity to respond’: The student actively responds at a rate frequent enough to promote effective learning.

• ‘Feedback’: The student receives prompt performance feedback about the work completed.

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



Interventions: Potential ‘Fatal Flaws’Any intervention must include 4 essential elements. The absence of any one of the elements would be considered a ‘fatal flaw’ (Witt, VanDerHeyden & Gilbertson, 2004) that blocks the school from drawing meaningful conclusions from the student’s response to the intervention:

1. Clearly defined problem. The student’s target concern is stated in specific, observable, measureable terms. This ‘problem identification statement’ is the most important step of the problem-solving model (Bergan, 1995), as a clearly defined problem allows the teacher or RTI Team to select a well-matched intervention to address it.

2. Baseline data. The teacher or RTI Team measures the student’s academic skills in the target concern (e.g., reading fluency, math computation) prior to beginning the intervention. Baseline data becomes the point of comparison throughout the intervention to help the school to determine whether that intervention is effective.

3. Performance goal. The teacher or RTI Team sets a specific, data-based goal for student improvement during the intervention and a checkpoint date by which the goal should be attained.

4. Progress-monitoring plan. The teacher or RTI Team collects student data regularly to determine whether the student is on-track to reach the performance goal.

Source: Witt, J. C., VanDerHeyden, A. M., & Gilbertson, D. (2004). Troubleshooting behavioral interventions. A systematic process for finding and eliminating problems. School Psychology Review, 33, 363-383.



‘Elbow Group’ Activity: Key Intervention Concepts • Discuss the introductory concepts and resources

presented in the workshop and how they might be useful in intervention planning in your school or district: • Teacher intervention planning form (p. 2)

• Intervention script builder (p. 3)

• Instructional Hierarchy (pp. 5-6)

• Increasing intervention intensity (p. 7)

• Research-based elements of effective interventions (p. 8)

• Definitions of core instruction, intervention, accommodation, and modification (p. 9)

• Potential ‘fatal flaws’ in intervention planning (p. 11)



RTI: Best Practicesin MathematicsInterventionsJim Wrightwww.interventioncentral.org



National Mathematics Advisory Panel Report13 March 2008



Math Advisory Panel Report at:

http://www.ed.gov/mathpanel



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/report/final-factsheet.html



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).



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



Profile of Students With Significant Math Difficulties 1. 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 number—minuend—from the figure to be subtracted (subtrahend).

2. Visual detail. The student misreads a mathematical sign or leaves out a decimal or dollar sign in the answer.

3. 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.

4. Inability to ‘shift psychological set’. The student does not shift from one operation type (e.g., addition) to another (e.g., multiplication) when warranted.

5. Graphomotor. The student’s poor handwriting can cause him or her to misread handwritten numbers, leading to errors in computation.

6. 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’.)

7. 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.



“Mathematics is made of 50 percent formulas, 50 percent proofs, and 50 percent imagination.”

–Anonymous



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 average…Using 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.



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..



The Elements of Mathematical Proficiency: What the Experts Say…



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.

5 Strands of Mathematical Proficiency

1. Understanding

2. Computing

3. Applying

4. Reasoning

5. Engagement

5 Big Ideas in Beginning Reading

1. Phonemic Awareness

2. Alphabetic Principle

3. Fluency with Text

4. Vocabulary

5. ComprehensionSource: Big ideas in beginning reading. University of Oregon. Retrieved September 23, 2007, from http://reading.uoregon.edu/index.php



Five Strands of Mathematical Proficiency1. 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.




Five Strands of Mathematical Proficiency (Cont.)

4. Reasoning: Using logic to explain and justify a solution to a problem or to extend from something known to something less known.

5. Engaging: Seeing mathematics as sensible, useful, and doable—if you work at it—and being willing to do the work.




Five Strands of Mathematical

Proficiency (NRC, 2002)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.

4. Reasoning: Using logic to explain and justify a solution to a problem or to extend from something known to something less known.

5. Engaging: Seeing mathematics as sensible, useful, and doable—if you work at it—and being willing to do the work.

Table Activity: Evaluate Your School’s Math Proficiency…

• As a group, review the National Research Council ‘Strands of Math Proficiency’.

• Which strand do you feel that your school / curriculum does the best job of helping students to attain proficiency?

• Which strand do you feel that your school / curriculum should put the greatest effort to figure out how to help students to attain proficiency?

• Be prepared to share your results.



Math Computation: Building FluencyJim Wrightwww.interventioncentral.org



"Arithmetic is being able to count up to twenty without taking off your shoes."

–Anonymous



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.



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 children’s 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.



Big Ideas: Learn Unit (Heward, 1996)

The three essential elements of effective student learning include:1. 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.

2. Active Student Response. The student answers the item, solves the problem presented, or completes the academic task. Answering the teacher’s 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.

3. Performance Feedback. The student receives timely feedback about whether his or her response is correct—often 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, CA:Brooks/Cole.



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 day’s 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, CA:Brooks/Cole.



Self-Administered Arithmetic Combination Drills…

No Reward

Reward GivenReward GivenReward Given

No RewardNo Reward

Reward Given



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.



Math Computation: Motivate With ‘Errorless Learning’ Worksheets

In this version of an ‘errorless learning’ approach, the student is directed to complete math facts as quickly as possible. If the student comes to a number problem that he or she cannot solve, the student is encouraged to locate the problem and its correct answer in the key at the top of the page and write it in.

Such speed drills build computational fluency while promoting students’ ability to visualize and to use a mental number line.

TIP: Consider turning this activity into a ‘speed drill’. The student is given a kitchen timer and instructed to set the timer for a predetermined span of time (e.g., 2 minutes) for each drill. The student completes as many problems as possible before the timer rings. The student then graphs the number of problems correctly computed each day on a time-series graph, attempting to better his or her previous score.

Source: Caron, T. A. (2007). Learning multiplication the easy way. The Clearing House, 80, 278-282



Math Computation: Problem Interspersal Technique• The teacher first identifies the range of ‘challenging’ problem-types

(number problems appropriately matched to the student’s 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 1:1 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..



Teaching Math Vocabulary



Comprehending Math Vocabulary: The Barrier of Abstraction

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

Source: Chard, D. (n.d.. Vocabulary strategies for the mathematics classroom. Retrieved November 23, 2007, from http://www.eduplace.com/state/pdf/author/chard_hmm05.pdf.



Math Vocabulary: Classroom (Tier I) Recommendations• Preteach math vocabulary. Math vocabulary provides students with the

language tools to grasp abstract mathematical concepts and to explain their own reasoning. Therefore, do not wait to teach that vocabulary only at ‘point of use’. Instead, preview relevant math vocabulary as a regular a part of the ‘background’ information that students receive in preparation to learn new math concepts or operations.

• Model the relevant vocabulary when new concepts are taught. Strengthen students’ grasp of new vocabulary by reviewing a number of math problems with the class, each time consistently and explicitly modeling the use of appropriate vocabulary to describe the concepts being taught. Then have students engage in cooperative learning or individual practice activities in which they too must successfully use the new vocabulary—while the teacher provides targeted support to students as needed.

• Ensure that students learn standard, widely accepted labels for common math terms and operations and that they use them consistently to describe their math problem-solving efforts.

Source: Chard, D. (n.d.. Vocabulary strategies for the mathematics classroom. Retrieved November 23, 2007, from http://www.eduplace.com/state/pdf/author/chard_hmm05.pdf.



Promoting Math Vocabulary: Other Guidelines– Create a standard list of math vocabulary for each grade level (elementary)

or course/subject area (for example, geometry).– Periodically check students’ mastery of math vocabulary (e.g., through

quizzes, math journals, guided discussion, etc.).– Assist students in learning new math vocabulary by first assessing their

previous knowledge of vocabulary terms (e.g., protractor; product) and then using that past knowledge to build an understanding of the term.

– For particular assignments, have students identify math vocabulary that they don’t understand. In a cooperative learning activity, have students discuss the terms. Then review any remaining vocabulary questions with the entire class.

– Encourage students to use a math dictionary in their vocabulary work.– Make vocabulary a central part of instruction, curriculum, and assessment

—rather than treating as an afterthought.Source: Adams, T. L. (2003). Reading mathematics: More than words can say. The Reading Teacher, 56(8), 786-795.



Math Instruction: Unlock the Thoughts of Reluctant Students Through Class Journaling

Students can effectively clarify their knowledge of math concepts and problem-solving strategies through regular use of class ‘math journals’.

• At the start of the year, the teacher introduces the journaling weekly assignment in which students respond to teacher questions.

• At first, the teacher presents ‘safe’ questions that tap into the students’ opinions and attitudes about mathematics (e.g., ‘How important do you think it is nowadays for cashiers in fast-food restaurants to be able to calculate in their head the amount of change to give a customer?”). As students become comfortable with the journaling activity, the teacher starts to pose questions about the students’ own mathematical thinking relating to specific assignments. Students are encouraged to use numerals, mathematical symbols, and diagrams in their journal entries to enhance their explanations.

• The teacher provides brief written comments on individual student entries, as well as periodic oral feedback and encouragement to the entire class.

• Teachers will find that journal entries are a concrete method for monitoring student understanding of more abstract math concepts. To promote the quality of journal entries, the teacher might also assign them an effort grade that will be calculated into quarterly math report card grades.

Source: Baxter, J. A., Woodward, J., & Olson, D. (2005). Writing in mathematics: An alternative form of communication for academically low-achieving students. Learning Disabilities Research & Practice, 20(2), 119–135.



Building Student Skills inApplied Math Problems




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 children’s

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..



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 < 2’) Difficulty ‘extracting’ underlying math operations from word/story

problems Difficulty identifying and ignoring extraneous information included in

word/story problems



Math Intervention Ideas for Higher-Level Math ProblemsJim Wrightwww.interventioncentral.org



Applied Problems



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.



Applied Problems: Encourage Students to ‘Draw’ the ProblemMaking a drawing of an applied, or ‘word’, problem is one easy heuristic tool that students can use to help them to find the solution and clarify misunderstandings.

• The teacher hands out a worksheet containing at least six word problems. The teacher explains to students that making a picture of a word problem sometimes makes that problem clearer and easier to solve.

• The teacher and students then independently create drawings of each of the problems on the worksheet. Next, the students show their drawings for each problem, explaining each drawing and how it relates to the word problem. The teacher also participates, explaining his or her drawings to the class or group.

• Then students are directed independently to make drawings as an intermediate problem-solving step when they are faced with challenging word problems. NOTE: This strategy appears to be more effective when used in later, rather than earlier, elementary grades.

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..



Applied Problems: Individualized Self-Correction ChecklistsStudents 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 don’t 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.



Interpreting Math Graphics: A Reading Comprehension Intervention



Housing Bubble Graphic:

New York Times23 September 2007

Housing Price Index = 100 in 1987

Housing Price Index = 171 in 2005



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, 21–27.



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.




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.





2. 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 > tables > bar graphs > charts > 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?”





3. 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.





4. 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:

A. Read the question,

B. Review the graphic,

C. Reread the question,

D. Choose a QAR,

E. Answer the question, and

F. 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 don’t short-circuit their inquiry.




Developing Student Metacognitive Abilities



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 solving…That 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.



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.



Combining Cognitive & Metacognitive Strategies to Assist Students With Mathematical Problem Solving

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



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:

1. 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).

2. Paraphrasing the problem. The student restates the problem in his or her own words.3. ‘Drawing’ the problem. The student creates a drawing of the problem, creating a

visual representation of the word problem.4. 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.5. 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.

6. Computing the answer. The student follows the plan developed earlier to compute the answer to the problem.

7. 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.



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’).



Combined Cognitive & Metacognitive Elements of Strategy



RTI: Writing Interventions Jim Wrightwww.interventioncentral.org



Defining Student Writing Problems



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



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



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 negative…Such 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.



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: Writer’s 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.



5-Step Writing Process: (Items in bold are iterative):1. Planning. The student carries out necessary pre-writing

planning activities, including content, format, and outline.

2. Drafting. The student writes or types the composition.

3. 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.

4. Editing. The student looks over the composition and corrects any mechanical mistakes (capitalization, punctuation, etc.).

5. Publication: The student submits the composition in finished form.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.

Domains of writing to be assessed (Robinson & Howell, 2008):



Elements of effective writing instruction for adolescents:

1. Writing Process (Effect Size = 0.82): Students are taught a process for planning, revising, and editing.

2. Summarizing (Effect Size = 0.82): Students are taught methods to identify key points, main ideas from readings to write summaries of source texts.

3. Cooperative Learning Activities (‘Collaborative Writing’) (Effect Size = 0.75): Students are placed in pairs or groups with learning activities that focus on collaborative use of the writing process.

4. Goal-Setting (Effect Size = 0.70): Students set specific ‘product goals’ for their writing and then check their attainment of those self-generated goals.

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. Retrieved from http://www.all4ed.org/files/WritingNext.pdf




5. Writing Processors (Effect Size = 0.55): Students have access to computers/word processors in the writing process.

6. Sentence Combining (Effect Size = 0.50): Students take part in instructional activities that require the combination or embedding of simpler sentences (e.g., Noun-Verb-Object) to generate more advanced, complex sentences.

7. Prewriting (Effect Size = 0.32): Students learn to select, develop, or organize ideas to incorporate into their writing by participating in structured ‘pre-writing’ activities.

8. Inquiry Activities (Effect Size = 0.32): Students become actively engaged researchers, collecting and analyzing information to guide the ideas and content for writing assignments.





9. Process Writing (Effect Size = 0.32): Writing instruction is taught in a ‘workshop’ format that “ stresses extended writing opportunities, writing for authentic audiences, personalized instruction, and cycles of writing” (Graham & Perin, 2007; p. 4).

10. Use of Writing Models (Effect Size = 0.25): Students read and discuss models of good writing and use them as exemplars for their own writing.

11. Writing to Learn Content (Effect Size = 0.23): The instructor incorporates writing activities as a means to have students learn content material.




Origins of the Latin Alphabet:Early Greek Alphabet

Source: http://www.translexis.demon.co.uk/new_page_2.htm

Boustrophedon: ‘ox trail’: Script alternates between left-to-right and right-to-left



"The difference between the right word and the almost right word is the difference between lightning and the lightning bug."– Mark Twain



"Your manuscript is both good and original. But the part that is good is not original, and the part that is original is not good."– Samuel Johnson



[If lost on an island] I woud drink water from the ocean and I woud eat the fruit off of the trees. Then I woud bilit a house out of trees, and I woud gather firewood to stay warm. I woud try and fix my boat in my spare time.

Writing SampleDetermine the 1 or 2 most important features in this writing that should be targeted for intervention.



Determine the 1 or 2 most important features in this writing that should be targeted for intervention.

Existing is being unique. Existence, reality, essence, cause, or truth is uniqueness. The geometric point in the center of the sphere is nature’s symbol of the immeasurable uniqueness within its measurable effect. A center is always unique; otherwise it would not be a center. Because uniqueness is reality, or that which makes a thing what it is, everything that is real is based on a centralization.



Selected Writing Interventions



Fluency: Have Students Write Every Day Short daily writing assignments can build student writing fluency and make writing a more motivating activity. Poor writers gradually develop into better writers when they are prompted to write daily--and receive rapid feedback and encouragement about that writing. The teacher can encourage daily writing by:

• giving short writing assignments• allowing time for students to journal about their learning

activities• requiring that they correspond daily with pen pals via email• even posting a question on the board as a bell-ringer activity that students can respond to in writing for extra credit.

Source: Graham, S., Harris, K. R., & Larsen, L. (2001). Prevention and intervention of writing difficulties for students with learning disabilities. Learning Disabilities Research & Practice, 16, 74-84.



Writing Support in the Classroom: Essentials of Effective Instruction Teachers are most successful in reaching students with writing delays when they:

• Build their written expression lessons around the 3 stages of writing –planning, writing, and revision— and make those stages clear and explicit.

• Provide students with ‘think sheets’ that outline step-by-step strategies for tackle the different phases of a writing assignment (e.g., taking concise notes from research material; building an outline; proofreading a draft).

• Expose students to different kinds of expressive text, such as persuasive, narrative, and expository writing-- good prose models that the student can review when completing a writing assignment.

• Give supportive and timely feedback to students about their writing. When teachers or classmates offer writing feedback to the student, they are honest but also maintain an encouraging tone.

Source: Gersten, R., Baker, S., & Edwards, L. (1999). Teaching expressive writing to students with learning disabilities: A meta-analysis. New York: National Center for Learning Disabilities.



Integrated Writing Instruction (MacArthur, Graham, & Schwarz, 1993 )

The instructor follows a uniform daily instructional framework for writing instruction.

1. Status-checking. At the start of the writing session, the instructor quickly goes around the room, asking each student what writing goal(s) he or she plans to accomplish that day. The instructor records these responses for all to see.

2. Mini-Lesson. The instructor teaches a mini-lesson relevant to the writing process. Mini-lessons are a useful means to present explicit writing strategies (e.g., an outline for drafting an opinion essay) as well as a forum for reviewing the conventions of writing. Mini-lessons should be kept short (e.g.,5-10 minutes) to hold the attention of the class.



Integrated Writing Instruction Cont. (MacArthur, Graham, & Schwarz, 1993 )

3. Student Writing. During the session, substantial time is set aside for students to write. Their writing assignment might be one handed out that day or part of a longer composition (e.g., story, extended essay) that the student is writing and editing across multiple days. When possible, student writers are encouraged to use computers as aids in composing and editing their work.

4. Peer & Teacher Conferences. At the end of the daily writing block, the student may sit with a classmate to review each other's work, using a structured peer editing strategy. During this discussion time, the teacher also holds brief individual conferences with students to review their work, have students evaluate how successfully they completed their writing goals for the day, and hear writers' thoughts about how they might plan to further develop a writing assignment.



Integrated Writing Instruction Cont. (MacArthur, Graham, & Schwarz, 1993 )

5. Group Sharing or Publishing. At the end of each session, writing produced that day is shared with the whole class. Students might volunteer to read passages aloud from their compositions. Students are encouraged to choose more polished work and post it on the classroom wall or bulletin board, have their work displayed in a public area of the school, publish the work in an anthology of school writings, read it aloud at school assemblies, or publish it on a school Internet site.



Monitoring to Increase Writing Fluency (Rathvon, 1999)

Students gain motivation to write through daily monitoring and charting of their own and classwide rates of writing fluency. – Assign timed freewriting several times per week. – After each freewriting period, direct each student to count up the

number of words he or she has written in their daily journal entry (whether spelled correctly or not).

– Have students to record their personal writing-fluency score in their journal and also chart the score on their own time-series graph for visual feedback.

– Collect the day’s writing-fluency scores of all students in the class, sum those scores, and chart the results on a large time-series graph posted at the front of the room.

– Raise the class goal by five percent per week.



Organization: Build an Outline by Talking Through the Topic

Students who struggle to organize their notes into a coherent outline can tell others what they know about the topic—and then capture the informal logical structure of that conversation to create a working outline.

• The student studies notes from the topic and describes what he or she knows about the topic and its significance to a listener. (The student may want to audio-record this conversation for later playback.)

• After the conversation, the student jots down an outline from memory to capture the structure and main ideas of the discussion.

• This outline ‘kernel’ can then be expanded and refined into the framework for a paper.

Source: The Writing Center, University of North Carolina at Chapel Hill (n.d.). Reorganizing your draft. Retrieved December 23, 2006, from http://www.unc.edu/depts/wcweb/handouts/organization.html



Organization: ‘Reverse Outline’ the Draft

Students can improve the internal flow of their compositions through ‘reverse outlining’.

• The student writes a draft of the composition. • Next, the student reads through the draft, jotting notes in the margins that

signify the main idea of each paragraph or section. • Then the student organizes the margin notes into an outline to reveal the

organizational structure of the paper. • This ‘reverse outline’ allows the student to note whether sections of the

draft are repetitious, are out of order, or do not logically connect with one another.

Source: The Writing Center, University of North Carolina at Chapel Hill (n.d.). Reorganizing your draft. Retrieved December 23, 2006, from http://www.unc.edu/depts/wcweb/handouts/organization.html



A Memory Device for Proofreading: SCOPE (Bos & Vaughn, 2002)

When students regularly use a simple, portable, easily memorized plan for proofreading, the quality of their writing improves significantly. – Create and have students refer to a classroom with the SCOPE

proofreading elements: Spelling: Are my words spelled correctly; Capitalization: Have I capitalized all appropriate words, including first words of sentences, proper nouns, and proper names?; Order of words: Is my word order (syntax) correct?; Punctuation: Did I use end punctuation and other punctuation marks appropriately? Expression of complete thoughts: Do all of my sentences contain a noun and verb to convey a complete thought?



Cover-Copy-Compare (Murphy, Hern, Williams, & McLaughlin, 1990)

Students increase their spelling knowledge by copying a spelling word from a correct model and then recopying the same word from memory. Give students a list of 10-20 spelling words, an index card, and a blank sheet of paper. For each word on the spelling list, the student:1. copies the spelling list item onto a sheet of paper, 2. covers the newly copied word with the index card, 3. writes the spelling word again on the sheet (spelling it from

memory), and 4. uncovers the copied word and checks to ensure that the word

copied from memory is spelled correctly. Repeat as necessary.



Use Selective Proofreading With Highlighting of Errors

To prevent struggling writers from becoming overwhelmed by teacher proofreading corrections, select only 1 or 2 proofreading areas when correcting a writing assignment.1. Create a student ‘writing skills checklist’ that inventories key writing

competencies (e.g., grammar/syntax, spelling, vocabulary, etc.). 2. For each writing assignment, announce to students that you will

grade the assignment for overall content but will make proofreading corrections on only 1-2 areas chosen from the writing skills checklist. (Select different proofreading targets for each assignment matched to common writing weaknesses in your classroom.)



Use Selective Proofreading With Highlighting of Errors: Cont.

3. To prevent cluttering the student’s paper with potentially discouraging teacher comments and editing marks:a. underline problems in the student’ text with a highlighter and b. number the highlighted errors sequentially at the left margin of

the student paper. c. write teacher comments on a separate feedback sheet to

explain the writing errors. Identify each comment with the matching error-number from the left margin of the student’s worksheet.

TIP: Have students use this method when proofreading their own text.



1

1 Rewrite this run-on sentence as two separate sentences.

2

2 Not clear. Rewrite. Consider starting the sentence with ‘The concept of …’

Spelling; Run-on and incomplete

sentences

Mrs. Richman

Jimmy Smith Dec 1, 2006Selective Proofreading With Highlighting of Errors



"A ratio of failures is built into the process of writing. The wastebasket has evolved for a reason."– Margaret Atwood



Sentence CombiningStudents with poor writing skills often write sentences that lack ‘syntactic maturity’. Their sentences often follow a simple, stereotyped format. A promising approach to teach students use of diverse sentence structures is through sentence combining.

In sentence combining, students are presented with kernel sentences and given explicit instruction in how to weld these kernel sentences into more diverse sentence types either – by using connecting words to combine multiple sentences into one

or – by isolating key information from an otherwise superfluous

sentence and embedding that important information into the base sentence.

Sources: Saddler, B. (2005). Sentence combining: A sentence-level writing intervention. The Reading Teacher, 58, 468-471.

Strong, W. (1986). Creative approaches to sentence combining. Urbana, OL: ERIC Clearinghouse on Reading and Communication Skill & National Council of Teachers of English.



Formatting Sentence Combining Examples



Interventionist TIP: Don’t Forget That…Writing Interventions Are Embedded in a

Larger Web of Potential Academic Intervention Strategies

Writing

Homework

Note-TakingReading

Comprehension

Reading Fluency

Time Management

Test Taking



Team Activity: Use of Sentence Combining as a Writing Strategy Across Content Areas…

: • Discuss the sentence-combining strategy

discussed in this workshop.

• Brainstorm ways that schools can promote the use of this strategy across content areas to encourage students to write with greater ‘syntactic maturity’.



Curriculum-Based Measurement: Writing

Jim Wright




• Assesses preselected objectives from local curriculum

• Has standardized directions for administration• Is timed, yielding fluency, accuracy scores• Uses objective, standardized, ‘quick’ guidelines for

scoring• Permits charting and teacher feedback

Curriculum-Based Measurement/Assessment : Defining Characteristics:



CBM Writing: Preparation



CBM Writing Assessment: Preparation

• Select a story starter• Create a CBM writing

probe: a lined sheet with the story starter at the top



CBM Writing Assessment: Preparation

• Create or collect story starters that students will find motivating to write about. (And toss out starters that don’t inspire much enthusiasm!)

• Avoid story starters that allow students simply to generate long lists: e.g., “What I want for my birthday is…”

Story Starter Tips:



CBM Writing Probes: Administration



CBM Writing Probes: Scoring



CBM Writing Assessment: Scoring

I woud drink water from the ocean and I woud eat the fruit off of the trees. Then I woud bilit a house out of trees, and I woud gather firewood to stay warm. I woud try and fix my boat in my spare time.

Total Words:

Total Words = 45Total Words = 45




Total Words: Useful for tracking a student’s fluency in writing (irrespective of spelling, punctuation, etc.)




CBM Writing Assessment: ScoringCorrectly Spelled Words:

Correctly Spelled Words = 39Correctly Spelled Words = 39




Correctly Spelled Words: Permits teachers to (a) monitor student spelling skills in context of writing assignments, and (b) track student vocabulary usage.




Correct Writing Sequences: Most global CBM measure. Looks at quality of writing in context.





Correct Writing Sequences:

Correct Writing Sequences = 37Correct Writing Sequences = 37



Tier 1 (Classroom) Literacy Interventions for Middle & High Schools




“ ”“Risk for reading failure always involves the interaction of a particular set of child characteristics with specific characteristics of the instructional environment. Risk status is not entirely inherent in the child, but always involves a “mismatch” between child characteristics and the instruction that is provided.” (Foorman & Torgesen, 2001; p. 206).

Source: Foorman, B. R., & Torgesen, J. (2001). Critical elements of classroom and small-group instruction promote reading success in all children. Learning Disabilities Research & Practice, 16, 203-212.



‘Fifteen Elements of Effective Adolescent Literacy Programs’

1. Direct, explicit comprehension instruction

2. Effective instructional principles embedded in content

3. Motivation and self-directed learning

4. Text-based collaborative learning

5. Formative student assessment6. Strategic tutoring7. Diverse texts8. Intensive writing9. Technology component

Source: Biancarosa, C., & Snow, C. E. (2006). Reading next—A vision for action and research in middle and high school literacy: A report to Carnegie Corporation of New York (2nd ed.).Washington, DC: Alliance for Excellent Education. Retrieved from http://www.all4ed.org/files/ReadingNext.pdf

10. Extended time for literacy across classes

11. Professional development12. Ongoing summative assessment of

students and programs13. Teacher teams (interdisciplinary

with a student problem-solving focus)

14. Leadership15. Comprehensive and coordinated

literacy program (interdisciplinary, interdepartmental)



Promoting Literacy in Middle & High School Classrooms: Three Elements

• Explicit vocabulary instruction• Reading comprehension• Extended discussion

Source: Kamil, M. L., Borman, G. D., Dole, J., Kral, C. C., Salinger, T., & Torgesen, J. (2008). Improving adolescent literacy: Effective classroom and intervention practices: A practice guide (NCEE #2008-4027). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from http://ies.ed.gov/ncee/wwc.



RTI & Secondary Literacy:Explicit Vocabulary Instruction



Vocabulary: Why This Instructional Goal is Important

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

Students may require 12 to 17 meaningful exposures to a word to learn it.



Provide Dictionary Training

The student is trained to use an Internet lookup strategy to better understand dictionary or glossary definitions of key vocabulary items.

– The student first looks up the word and its meaning(s) in the dictionary/glossary.

– If necessary, the student isolates the specific word meaning that appears to be the appropriate match for the term as it appears in course texts and discussion.

– The student goes to an Internet search engine (e.g., Google) and locates at least five text samples in which the term is used in context and appears to match the selected dictionary definition.



Enhance Vocabulary Instruction Through Use of Graphic Organizers or Displays: A Sampling

Teachers can use graphic displays to structure their vocabulary discussions and activities (Boardman et al., 2008; Fisher, 2007; Texas Reading Initiative, 2002).



4-Square Graphic Display

The student divides a page into four quadrants. In the upper left section, the student writes the target word. In the lower left section, the student writes the word definition. In the upper right section, the student generates a list of examples that illustrate the term, and in the lower right section, the student writes ‘non-examples’ (e.g., terms that are the opposite of the target vocabulary word).



Semantic Word Definition Map

The graphic display contains sections in which the student writes the word, its definition (‘what is this?’), additional details that extend its meaning (‘What is it like?’), as well as a listing of examples and ‘non-examples’ (e.g., terms that are the opposite of the target vocabulary word).



Word Definition Map Example



Semantic Feature Analysis

A target vocabulary term is selected for analysis in this grid-like graphic display. Possible features or properties of the term appear along the top margin, while examples of the term are listed ion the left margin. The student considers the vocabulary term and its definition. Then the student evaluates each example of the term to determine whether it does or does not match each possible term property or element.



Semantic Feature Analysis Example

• VOCABULARY TERM: TRANSPORTATION



Comparison/Contrast (Venn) Diagram

Two terms are listed and defined. For each term, the student brainstorms qualities or properties or examples that illustrate the term’s meaning. Then the student groups those qualities, properties, and examples into 3 sections:

A. items unique to Term 1B. items unique to Term 2C. items shared by both terms



Promote ‘Wide Reading’

Students read widely in the content area, using texts that supplement and extend information supplied by the textbook. ‘Wide reading’ results in substantial increases in student vocabulary over time due to incidental learning. To strengthen the positive impact of wide reading on vocabulary development, have student texts available that vary in difficulty and that are of high interest. Discuss readings in class. Experiment with ways to document student independent reading and integrate that ‘wide reading’ into an effort grade for the course. If needed, build time into the student’s school schedule for supervised ‘wide reading’ time.



Hold ‘Read-Alouds’

Select texts that supplement the course textbook and that illustrate central concepts and contain important vocabulary covered in the course. Read those texts aloud for 3 to 5 minutes per class session--while students follow along silently. Read-alouds provide students with additional exposure to vocabulary items in context. They can also lower the threshold of difficulty: Students may be more likely to attempt to read an assigned text independently if they have already gotten a start in the text by listening to a more advanced reader read the first few pages aloud. Read-alouds can support other vocabulary-building activities such as guided discussion, vocabulary review, and wide reading.



Provide Regular In-Class Instruction and Review of Vocabulary Terms, Definitions

Present important new vocabulary terms in class, along with student-friendly definitions. Provide ‘example sentences’ to illustrate the use of the term. Assign students to write example sentences employing new vocabulary to illustrate their mastery of the terms.



Generate ‘Possible Sentences’ The teacher selects 6 to 8 challenging new vocabulary terms and 4 to 6 easier, more familiar vocabulary items relevant to the lesson. Introduce the vocabulary terms to the class. Have students write sentences that contain at least two words from the posted vocabulary list. Then write examples of student sentences on the board until all words from the list have been used. After the assigned reading, review the ‘possible sentences’ that were previously generated. Evaluate as a group whether, based on the passage, the sentence is ‘possible’ (true) in its current form. If needed, have the group recommend how to change the sentence to make it ‘possible’.



RTI & Secondary Literacy:Extended Discussion



Extended Discussions: Why This Instructional Goal is Important

Extended, guided group discussion is a powerful means to help students to learn vocabulary and advanced concepts. Discussion can also model for students various ‘thinking processes’ and cognitive strategies (Kamil et al. 2008, p. 22). To be effective, guided discussion should go beyond students answering a series of factual questions posed by the teacher: Quality discussions are typically open-ended and exploratory in nature, allowing for multiple points of view (Kamil et al., 2008).

When group discussion is used regularly and well in instruction, students show increased growth in literacy skills. Content-area teachers can use it to demonstrate the ‘habits of mind’ and patterns of thinking of experts in various their discipline: e.g., historians, mathematicians, chemists, engineers, literacy critics, etc.



Use a ‘Standard Protocol’ to Structure Extended Discussions

Good extended classwide discussions elicit a wide range of student opinions, subject individual viewpoints to critical scrutiny in a supportive manner, put forth alternative views, and bring closure by summarizing the main points of the discussion. Teachers can use a simple structure to effectively and reliably organize their discussions…



‘Standard Protocol’ Discussion FormatA. Pose questions to the class that require students to explain their

positions and their reasoning .B. When needed, ‘think aloud’ as the discussion leader to model

good reasoning practices (e.g., taking a clear stand on a topic).C. Supportively challenge student views by offering possible

counter arguments.D. Single out and mention examples of effective student reasoning.E. Avoid being overly directive; the purpose of extended

discussions is to more fully investigate and think about complex topics.

F. Sum up the general ground covered in the discussion and highlight the main ideas covered.



RTI & Secondary Literacy:Reading Comprehension



Reading Comprehension: Why This Instructional Goal is Important

Students require strong reading comprehension skills to succeed in challenging content-area classes.

At present, there is no clear evidence that any one reading comprehension instructional technique is clearly superior to others. In fact, it appears that students benefit from being taught any self-directed practice that prompts them to engage more actively in understanding the meaning of text (Kamil et al., 2008).



Assist Students in Setting ‘Content Goals’ for Reading

Students are more likely to be motivated to read--and to read more closely—if they have specific content-related reading goals in mind. At the start of a reading assignment, for example, the instructor has students state what questions they might seek to answer or what topics they would like to learn more about in their reading. The student or teacher writes down these questions. After students have completed the assignee reading, they review their original questions and share what they have learned (e.g., through discussion in large group or cooperative learning group, or even as a written assignment).



Teach Students to Monitor Their Own Comprehension and Apply ‘Fix-Up’ Skills

Teachers can teach students specific strategies to monitor their understanding of text and independently use ‘fix-up’ skills as needed. Examples of student monitoring and repair skills for reading comprehension include encouraging them to:

• Stop after every paragraph to summarize its main idea• Reread the sentence or paragraph again if necessary• Generate and write down questions that arise during

reading• Restate challenging or confusing ideas or concepts from

the text in the student’s own words



Collect a Bank of ‘Intervention Scripts’ to Teach Specific Comprehension Strategies

Teachers can collect ‘intervention scripts’ to address different comprehension issues that arise in their classrooms.



Paired Reading

The student reads aloud in tandem with an accomplished reader. At a student signal, the helping reader stops reading, while the student continues on. When the student commits a reading error, the helping reader resumes reading in tandem.



RepeatedReading

The student reads through a passage repeatedly, silently or aloud, and receives help with reading errors. The goal is to read the passage a certain number of times or to reach a target reading speed in the passage.



QuestionGeneration

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



Text Lookback

Text lookback is a simple strategy that students can use to boost their recall of expository prose by looking back in the text for important information.



Secondary-Level Academic Tier 1 Intervention: Case ExampleJim Wrightwww.interventioncentral.org



Tier 1 Case Example: Patricia: Reading Comprehension



Case Example: Reading ComprehensionThe Problem• A student, Patricia, struggled in her social studies class,

particularly in understanding the course readings. Her teacher, Ms. Cardamone, decided that the problem was significant enough that the student required some individualized support.

188



Case Example: Reading ComprehensionThe Evidence• Student Interview. Ms. Cardamone met with Patricia to ask her

questions about her difficulties with social studies content and assignments. Patricia said that when she reads the course text and other assigned readings, she doesn’t have difficulty with the vocabulary but often realizes after reading half a page that she hasn’t really understood what she has read. Sometimes she has to reread a page several times and that can be frustrating.

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Case Example: Reading ComprehensionThe Evidence (Cont.)• Review of Records. Past teacher report card comments suggest that

Patricia has had difficulty with reading comprehension tasks in earlier grades. She had received help in middle school in the reading lab, although there was no record of what specific interventions were tried in that setting.

• Input from Other Teachers. Ms. Cardamone checked with other teachers who have Patricia in their classes. All expressed concern about Patricia’s reading comprehension skills. The English teacher noted that Patricia appears to have difficulty pulling the main idea from a passage, which limits her ability to extract key information from texts and to review that information for tests.

•

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Case Example: Reading ComprehensionThe Intervention• Ms. Cardamone decided, based on the evidence collected, that

Patricia would benefit from training in identifying the main idea from a passage, rather than trying to retain all the information presented in the text. She selected two simple interventions: Question Generation and Text Lookback. She arranged to have Patricia meet with her during an open period to review these two strategies. During that meeting, Ms. Cardamone demonstrated how to use these strategies effectively with the social studies course text and other assigned readings.

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QuestionGeneration

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

http://www.interventioncentral.org/htmdocs/interventions/rdngcompr/qgen.php



Text Lookback

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

http://www.interventioncentral.org/htmdocs/interventions/rdngcompr/txtlkbk.php



Case Example: Reading ComprehensionDocumentation and Goal-Setting• Ms Cardamone filled out a Tier 1 intervention plan for the

student. On the plan, she listed interventions to be used, a checkup date (4 instructional weeks), and data to be used to assess student progress.

• Data: Ms. Cardamone decided that she would rate the student’s grasp of text content in two ways: – Student self-rating (1-3 scale; 1=don’t understand; 3 = understand

well)– Quiz grades.

• She collected baseline on both and set a goal for improvement.

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Case Example: Reading ComprehensionThe Outcome• When the intervention had been in place for 4 weeks, Ms.

Cardamone noted that Patricia appeared to have a somewhat better grasp of course content and expressed a greater grasp of material from the text.

• She shared her intervention ideas with other teachers working with Patricia. Because Patricia’s self-ratings of reading comprehension and quiz grades met the goals after 4 weeks, Ms. Cardamone decided to continue the intervention plan with the student without changes.

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response to intervention rti at middle and high schools: academic interventions for difficult-...

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