Instruction and Interventions within Response to

InterventionJim Wrightwww.interventioncentral.o

rg

Resources from This Workshop Available at

http//www.interventioncentral.org/ES_BOCES.php

Workshop Agenda

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.

Schools Need to Review Tier 1 (Classroom)

Interventions to Ensure That They Are Supported

By Research

- There is a lack of agreement about what is meant

by scientifically validated classroom (Tier I)

interventions. Districts should establish a

vetting processcriteria for judging whether a

particular instructional or intervention approach

should be considered empirically based.

Source Fuchs, D., Deshler, D. D. (2007). What

we need to know about responsiveness to

intervention (and shouldnt be afraid to ask)..

Learning Disabilities Research Practice,

22(2),129136.

What Are Appropriate Content-Area Tier 1

Universal Interventions for Secondary Schools?

- High schools need to determine what constitutes

high-quality universal instruction across content

areas. In addition, high school teachers need

professional development in, for example,

differentiated instructional techniques that will

help ensure student access to instruction

interventions that are effectively implemented.

Source Duffy, H. (August 2007). Meeting the

needs of significantly struggling learners in

high school. Washington, DC National High School

Center. Retrieved from http//www.betterhighschool

s.org/pubs/ p. 9

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.

Core Instruction, Interventions, Accommodations

Modifications Sorting Them Out

- Intervention. An academic intervention is a

strategy used to teach a new skill, build fluency

in a skill, or encourage a child to apply an

existing skill to new situations or settings. An

intervention can be thought of as a set of

actions that, when taken, have demonstrated

ability to change a fixed educational trajectory

(Methe Riley-Tillman, 2008 p. 37).

Core Instruction, Interventions, Accommodations

Modifications Sorting Them Out

- Accommodation. An accommodation is intended to

help the student to fully access and participate

in the general-education curriculum without

changing the instructional content and without

reducing the students rate of learning (Skinner,

Pappas Davis, 2005). An accommodation is

intended to remove barriers to learning while

still expecting that students will master the

same instructional content as their typical

peers. - Accommodation example 1 Students are allowed to

supplement silent reading of a novel by listening

to the book on tape. - Accommodation example 2 For unmotivated

students, the instructor breaks larger

assignments into smaller chunks and providing

students with performance feedback and praise for

each completed chunk of assigned work (Skinner,

Pappas Davis, 2005).

Core Instruction, Interventions, Accommodations

Modifications Sorting Them Out

- Modification. A modification changes the

expectations of what a student is expected to

know or dotypically by lowering the academic

standards against which the student is to be

evaluated. Examples of modifications - Giving a student five math computation problems

for practice instead of the 20 problems assigned

to the rest of the class - Letting the student consult course notes during a

test when peers are not permitted to do so

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

Source Burns, M. K., Gibbons, K. A. (2008).

Implementing response-to-intervention in

elementary and secondary schools. Routledge New

York. Kratochwill, T. R., Clements, M. A.,

Kalymon, K. M. (2007). Response to intervention

Conceptual and methodological issues in

implementation. In Jimerson, S. R., Burns, M. K.,

VanDerHeyden, A. M. (Eds.), Handbook of

response to intervention The science and

practice of assessment and intervention. New

York Springer.

RTI Interventions What If There is No Commercial

Intervention Package or Program Available?

- Although commercially prepared programs and the

subsequent manuals and materials are inviting,

they are not necessary. A recent review of

research suggests that interventions are research

based and likely to be successful, if they are

correctly targeted and provide explicit

instruction in the skill, an appropriate level of

challenge, sufficient opportunities to respond to

and practice the skill, and immediate feedback on

performanceThus, these elements could be used

as criteria with which to judge potential tier 2

interventions. p. 88

Source Burns, M. K., Gibbons, K. A. (2008).

Implementing response-to-intervention in

elementary and secondary schools. Routledge New

York.

Research-Based Elements of Effective Academic

Interventions

- Correctly targeted The intervention is

appropriately matched to the students academic

or behavioral needs. - Explicit instruction Student skills have been

broken down into manageable and deliberately

sequenced steps and providing overt strategies

for students to learn and practice new skills

p.1153 - Appropriate level of challenge The student

experiences adequate success with the

instructional task. - High opportunity to respond The student

actively responds at a rate frequent enough to

promote effective learning. - Feedback The student receives prompt

performance feedback about the work completed.

Source Burns, M. K., VanDerHeyden, A. M.,

Boice, C. H. (2008). Best practices in intensive

academic interventions. In A. Thomas J. Grimes

(Eds.), Best practices in school psychology V

(pp.1151-1162). Bethesda, MD National

Association of School Psychologists.

Interventions Potential Fatal Flaws

- Any intervention must include 4 essential

elements. The absence of any one of the elements

would be considered a fatal flaw (Witt,

VanDerHeyden Gilbertson, 2004) that blocks the

school from drawing meaningful conclusions from

the students response to the intervention - Clearly defined problem. The students target

concern is stated in specific, observable,

measureable terms. This problem identification

statement is the most important step of the

problem-solving model (Bergan, 1995), as a

clearly defined problem allows the teacher or RTI

Team to select a well-matched intervention to

address it. - Baseline data. The teacher or RTI Team measures

the students academic skills in the target

concern (e.g., reading fluency, math computation)

prior to beginning the intervention. Baseline

data becomes the point of comparison throughout

the intervention to help the school to determine

whether that intervention is effective. - Performance goal. The teacher or RTI Team sets a

specific, data-based goal for student improvement

during the intervention and a checkpoint date by

which the goal should be attained. - Progress-monitoring plan. The teacher or RTI Team

collects student data regularly to determine

whether the student is on-track to reach the

performance goal.

Source Witt, J. C., VanDerHeyden, A. M.,

Gilbertson, D. (2004). Troubleshooting behavioral

interventions. A systematic process for finding

and eliminating problems. School Psychology

Review, 33, 363-383.

Team Activity What Are Challenging Issues in

Your School Around the Topic of Academic

Interventions?

- At your tables
- Discuss the task of promoting the use of

evidence-based academic interventions in your

school. - What are enabling factors that should help you to

promote the routine use of such interventions. - What are challenges or areas needing improvement

to allow you to promote use of those

interventions?

RTI Best Practicesin MathematicsInterventionsJ

im Wrightwww.interventioncentral.org

National Mathematics Advisory Panel Report13

March 2008

Math Advisory Panel Report athttp//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/rep

ort/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

- Spatial organization. The student commits errors

such as misaligning numbers in columns in a

multiplication problem or confusing

directionality in a subtraction problem (and

subtracting the original numberminuendfrom the

figure to be subtracted (subtrahend). - Visual detail. The student misreads a

mathematical sign or leaves out a decimal or

dollar sign in the answer. - Procedural errors. The student skips or adds a

step in a computation sequence. Or the student

misapplies a learned rule from one arithmetic

procedure when completing another, different

arithmetic procedure. - Inability to shift psychological set. The

student does not shift from one operation type

(e.g., addition) to another (e.g.,

multiplication) when warranted. - Graphomotor. The students poor handwriting can

cause him or her to misread handwritten numbers,

leading to errors in computation. - Memory. The student fails to remember a specific

math fact needed to solve a problem. (The student

may KNOW the math fact but not be able to recall

it at point of performance.) - Judgment and reasoning. The student comes up with

solutions to problems that are clearly

unreasonable. However, the student is not able

adequately to evaluate those responses to gauge

whether they actually make sense in context.

Source Rourke, B. P. (1993). Arithmetic

disabilities, specific otherwise A

neuropsychological perspective. Journal of

Learning Disabilities, 26, 214-226.

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 averageUsing higher

percentile cutoffs increases the likelihood that

young children who go on to have serious math

problems will be picked up in the screening. p.

295

Source Gersten, R., Jordan, N. C., Flojo, J.

R. (2005). Early identification and interventions

for students with mathematics difficulties.

Journal of Learning Disabilities, 38, 293-304.

The Elements of Mathematical Proficiency What

the Experts Say

(No Transcript)

Five Strands of Mathematical Proficiency

- Understanding Comprehending mathematical

concepts, operations, and relations--knowing what

mathematical symbols, diagrams, and procedures

mean. - Computing Carrying out mathematical procedures,

such as adding, subtracting, multiplying, and

dividing numbers flexibly, accurately,

efficiently, and appropriately. - Applying Being able to formulate problems

mathematically and to devise strategies for

solving them using concepts and procedures

appropriately.

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.

Five Strands of Mathematical Proficiency (Cont.)

- Reasoning Using logic to explain and justify a

solution to a problem or to extend from something

known to something less known. - Engaging Seeing mathematics as sensible, useful,

and doableif you work at itand being willing to

do the work.

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.

Five Strands of Mathematical Proficiency (NRC,

2002)

- Table Activity Evaluate Your Schools Math

Proficiency - As a group, review the National Research Council

Strands of Math Proficiency. - Which strand do you feel that your school /

curriculum does the best job of helping students

to attain proficiency? - Which strand do you feel that your school /

curriculum should put the greatest effort to

figure out how to help students to attain

proficiency? - Be prepared to share your results.

- Understanding Comprehending mathematical

concepts, operations, and relations--knowing what

mathematical symbols, diagrams, and procedures

mean. - Computing Carrying out mathematical procedures,

such as adding, subtracting, multiplying, and

dividing numbers flexibly, accurately,

efficiently, and appropriately. - Applying Being able to formulate problems

mathematically and to devise strategies for

solving them using concepts and procedures

appropriately. - Reasoning Using logic to explain and justify a

solution to a problem or to extend from something

known to something less known. - Engaging Seeing mathematics as sensible, useful,

and doableif you work at itand being willing to

do the work.

Three General Levels of Math Skill Development

(Kroesbergen Van Luit, 2003)

- As students move from lower to higher grades,

they move through levels of acquisition of math

skills, to include - Number sense
- Basic math operations (i.e., addition,

subtraction, multiplication, division) - Problem-solving skills The solution of both

verbal and nonverbal problems through the

application of previously acquired information

(Kroesbergen Van Luit, 2003, p. 98)

Source Kroesbergen, E., Van Luit, J. E. H.

(2003). Mathematics interventions for children

with special educational needs. Remedial and

Special Education, 24, 97-114..

Development of Number Sense

What is Number Sense? (Clarke Shinn, 2004)

- the ability to understand the meaning of

numbers and define different relationships among

numbers. Children with number sense can

recognize the relative size of numbers, use

referents for measuring objects and events, and

think and work with numbers in a flexible manner

that treats numbers as a sensible system. p. 236

Source Clarke, B., Shinn, M. (2004). A

preliminary investigation into the identification

and development of early mathematics

curriculum-based measurement. School Psychology

Review, 33, 234248.

What Are Stages of Number Sense? (Berch, 2005,

p. 336)

- Innate Number Sense. Children appear to possess

hard-wired ability (neurological foundation

structures) to acquire number sense. Childrens

innate capabilities appear also to include the

ability to represent general amounts, not

specific quantities. This innate number sense

seems to be characterized by skills at estimation

(approximate numerical judgments) and a

counting system that can be described loosely as

1, 2, 3, 4, a lot. - Acquired Number Sense. Young students learn

through indirect and direct instruction to count

specific objects beyond four and to internalize a

number line as a mental representation of those

precise number values.

Source Berch, D. B. (2005). Making sense of

number sense Implications for children with

mathematical disabilities. Journal of Learning

Disabilities, 38, 333-339...

Task Analysis of Number Sense Operations (Methe

Riley-Tillman, 2008)

- Counting
- Comparing and Ordering Ability to compare

relative amounts e.g., more or less than ordinal

numbers e.g., first, second, third) - Equal partitioning Dividing larger set of

objects into equal parts - Composing and decomposing Able to create

different subgroupings of larger sets (for

example, stating that a group of 10 objects can

be broken down into 6 objects and 4 objects or 3

objects and 7 objects) - Grouping and place value abstractly grouping

objects into sets of 10 (p. 32) in base-10

counting system. - Adding to/taking away Ability to add and

subtract amounts from sets by using accurate

strategies that do not rely on laborious

enumeration, counting, or equal partitioning. P.

32

Source Methe, S. A., Riley-Tillman, T. C.

(2008). An informed approach to selecting and

designing early mathematics interventions. School

Psychology Forum Research into Practice, 2,

29-41.

Childrens Understanding of Counting Rules

- The development of childrens counting ability

depends upon the development of - One-to-one correspondence one and only one word

tag, e.g., one, two, is assigned to each

counted object. - Stable order the order of the word tags must be

invariant across counted sets. - Cardinality the value of the final word tag

represents the quantity of items in the counted

set. - Abstraction objects of any kind can be

collected together and counted. - Order irrelevance items within a given set can

be tagged in any sequence.

Source Geary, D. C. (2004). Mathematics and

learning disabilities. Journal of Learning

Disabilities, 37, 4-15.

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.

Internal Numberline

- As students internalize the numberline, they are

better able to perform mental arithmetic (the

manipulation of numbers and math operations in

their head).

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

16 17 18 1920 21 22 23 24 25 26 27 28 29

Associative Property

- within an expression containing two or more of

the same associative operators in a row, the

order of operations does not matter as long as

the sequence of the operands is not changed - Example
- (23)510
- 2(35)10

Source Associativity. Wikipedia. Retrieved

September 5, 2007, from http//en.wikipedia.org/wi

ki/Associative

Commutative Property

- the ability to change the order of something

without changing the end result. - Example
- 23510
- 25310

Source Associativity. Wikipedia. Retrieved

September 5, 2007, from http//en.wikipedia.org/wi

ki/Commutative

How much is 3 8? Strategies to Solve

Source Gersten, R., Jordan, N. C., Flojo, J.

R. (2005). Early identification and interventions

for students with mathematics difficulties.

Journal of Learning Disabilities, 38, 293-304.

Math Skills Importance of Fluency in Basic Math

Operations

- A key step in math education is to learn the

four basic mathematical operations (i.e.,

addition, subtraction, multiplication, and

division). Knowledge of these operations and a

capacity to perform mental arithmetic play an

important role in the development of childrens

later math skills. Most children with math

learning difficulties are unable to master the

four basic operations before leaving elementary

school and, thus, need special attention to

acquire the skills. A category of interventions

is therefore aimed at the acquisition and

automatization of basic math skills.

Source Kroesbergen, E., Van Luit, J. E. H.

(2003). Mathematics interventions for children

with special educational needs. Remedial and

Special Education, 24, 97-114.

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 Problem Interspersal Technique

- The teacher first identifies the range of

challenging problem-types (number problems

appropriately matched to the students current

instructional level) that are to appear on the

worksheet. - Then the teacher creates a series of easy

problems that the students can complete very

quickly (e.g., adding or subtracting two 1-digit

numbers). The teacher next prepares a series of

student math computation worksheets with easy

computation problems interspersed at a fixed rate

among the challenging problems. - If the student is expected to complete the

worksheet independently, challenging and easy

problems should be interspersed at a 11 ratio

(that is, every challenging problem in the

worksheet is preceded and/or followed by an

easy problem). - If the student is to have the problems read aloud

and then asked to solve the problems mentally and

write down only the answer, the items should

appear on the worksheet at a ratio of 3

challenging problems for every easy one (that

is, every 3 challenging problems are preceded

and/or followed by an easy one).

Source Hawkins, J., Skinner, C. H., Oliver, R.

(2005). The effects of task demands and additive

interspersal ratios on fifth-grade students

mathematics accuracy. School Psychology Review,

34, 543-555..

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 childs natural sense of

number and order and conceptual learning. - -Chard, D. (n.d.)

Source Chard, D. (n.d.. Vocabulary strategies

for the mathematics classroom. Retrieved November

23, 2007, from http//www.eduplace.com/state/pdf/a

uthor/chard_hmm05.pdf.

Math Vocabulary Classroom (Tier I)

Recommendations

- Preteach math vocabulary. Math vocabulary

provides students with the language tools to

grasp abstract mathematical concepts and to

explain their own reasoning. Therefore, do not

wait to teach that vocabulary only at point of

use. Instead, preview relevant math vocabulary

as a regular a part of the background

information that students receive in preparation

to learn new math concepts or operations. - Model the relevant vocabulary when new concepts

are taught. Strengthen students grasp of new

vocabulary by reviewing a number of math problems

with the class, each time consistently and

explicitly modeling the use of appropriate

vocabulary to describe the concepts being taught.

Then have students engage in cooperative learning

or individual practice activities in which they

too must successfully use the new

vocabularywhile the teacher provides targeted

support to students as needed. - Ensure that students learn standard, widely

accepted labels for common math terms and

operations and that they use them consistently to

describe their math problem-solving efforts.

Source Chard, D. (n.d.. Vocabulary strategies

for the mathematics classroom. Retrieved November

23, 2007, from http//www.eduplace.com/state/pdf/a

uthor/chard_hmm05.pdf.

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.

Promoting Math Vocabulary Other Guidelines

- Create a standard list of math vocabulary for

each grade level (elementary) or course/subject

area (for example, geometry). - Periodically check students mastery of math

vocabulary (e.g., through quizzes, math journals,

guided discussion, etc.). - Assist students in learning new math vocabulary

by first assessing their previous knowledge of

vocabulary terms (e.g., protractor product) and

then using that past knowledge to build an

understanding of the term. - For particular assignments, have students

identify math vocabulary that they dont

understand. In a cooperative learning activity,

have students discuss the terms. Then review any

remaining vocabulary questions with the entire

class. - Encourage students to use a math dictionary in

their vocabulary work. - Make vocabulary a central part of instruction,

curriculum, and assessmentrather than treating

as an afterthought.

Source Adams, T. L. (2003). Reading mathematics

More than words can say. The Reading Teacher,

56(8), 786-795.

Math Instruction Unlock the Thoughts of

Reluctant Students Through Class Journaling

- Students can effectively clarify their knowledge

of math concepts and problem-solving strategies

through regular use of class math journals. - At the start of the year, the teacher introduces

the journaling weekly assignment in which

students respond to teacher questions. - At first, the teacher presents safe questions

that tap into the students opinions and

attitudes about mathematics (e.g., How important

do you think it is nowadays for cashiers in

fast-food restaurants to be able to calculate in

their head the amount of change to give a

customer?). As students become comfortable with

the journaling activity, the teacher starts to

pose questions about the students own

mathematical thinking relating to specific

assignments. Students are encouraged to use

numerals, mathematical symbols, and diagrams in

their journal entries to enhance their

explanations. - The teacher provides brief written comments on

individual student entries, as well as periodic

oral feedback and encouragement to the entire

class. - Teachers will find that journal entries are a

concrete method for monitoring student

understanding of more abstract math concepts. To

promote the quality of journal entries, the

teacher might also assign them an effort grade

that will be calculated into quarterly math

report card grades.

Source Baxter, J. A., Woodward, J., Olson, D.

(2005). Writing in mathematics An alternative

form of communication for academically

low-achieving students. Learning Disabilities

Research Practice, 20(2), 119135.

Teaching Math Symbols

Learning Math Symbols 3 Card Games

- The interventionist writes math symbols that the

student is to learn on index cards. The names of

those math symbols are written on separate cards.

The cards can then be used for students to play

matching games or to attempt to draw cards to get

a pair. - Create a card deck containing math symbols or

their word equivalents. Students take turns

drawing cards from the deck. If they can use the

symbol/word on the selected card to generate a

correct mathematical sentence, the student wins

the card. For example, if the student draws a

card with the term negative number and says

that A negative number is a real number that is

less than 0, the student wins the card. - Create a deck containing math symbols and a

series of numbers appropriate to the grade level.

Students take turns drawing cards. The goral is

for the student to lay down a series of cards to

form a math expression. If the student correctly

solves the expression, he or she earns a point

for every card laid down.

Source Adams, T. L. (2003). Reading mathematics

More than words can say. The Reading Teacher,

56(8), 786-795.

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 solvingThat is,

successful problem solvers, consciously or

unconsciously (depending on task demands), use

self-instruction, self-questioning, and

self-monitoring to gain access to strategic

knowledge, guide execution of strategies, and

regulate use of strategies and problem-solving

performance. p. 231

Source Montague, M. (1992). The effects of

cognitive and metacognitive strategy instruction

on the mathematical problem solving of middle

school students with learning disabilities.

Journal of Learning Disabilities, 25, 230-248.

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 - Reading the problem. The student reads the

problem carefully, noting and attempting to clear

up any areas of uncertainly or confusion (e.g.,

unknown vocabulary terms). - Paraphrasing the problem. The student restates

the problem in his or her own words. - Drawing the problem. The student creates a

drawing of the problem, creating a visual

representation of the word problem. - Creating a plan to solve the problem. The student

decides on the best way to solve the problem and

develops a plan to do so. - Predicting/Estimating the answer. The student

estimates or predicts what the answer to the

problem will be. The student may compute a quick

approximation of the answer, using rounding or

other shortcuts. - Computing the answer. The student follows the

plan developed earlier to compute the answer to

the problem. - Checking the answer. The student methodically

checks the calculations for each step of the

problem. The student also compares the actual

answer to the estimated answer calculated in a

previous step to ensure that there is general

agreement between the two values.

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

Combined Cognitive Metacognitive Elements of

Strategy

Combined Cognitive Metacognitive Elements of

Strategy

Combined Cognitive Metacognitive Elements of

Strategy

Combined Cognitive Metacognitive Elements of

Strategy

Combined Cognitive Metacognitive Elements of

Strategy

Combined Cognitive Metacognitive Elements of

Strategy

Applied Problems Pop Quiz

- Q To move their armies, the Romans built over

50,000 miles of roads. Imagine driving all those

miles! Now imagine driving those miles in the

first gasoline-driven car that has only three

wheels and could reach a top speed of about 10

miles per hour. - For safety's sake, let's bring along a spare

tire. As you drive the 50,000 miles, you rotate

the spare with the other tires so that all four

tires get the same amount of wear. Can you figure

out how many miles of wear each tire accumulates?

Directions As a team, read the following

problem. At your tables, apply the 7-step

problem-solving (cognitive) strategy to complete

the problem. As you complete each step of the

problem, apply the Say-Ask-Check metacognitive

sequence. Try to complete the entire 7 steps

within the time allocated for this exercise.

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

A Since the four wheels of the three-wheeled

car share the journey equally, simply take

three-fourths of the total distance (50,000

miles) and you'll get 37,500 miles for each

tire.

Source The Math Forum _at_ Drexel Critical

Thinking Puzzles/Spare My Brain. Retrieved from

http//mathforum.org/k12/k12puzzles/critical.think

ing/puzz2.html

Finding a Way Out of the Research-Based Maze

A Guide for SchoolsJim Wrightwww.intervention

central.org

Innovations in Education Efficacy vs.

Effectiveness

- A useful distinction has recently emerged

between efficacy and effectiveness (Schoenwald

Hoagwood, 2001). Efficacy refers to intervention

outcomes that are produced by researchers and

program developers under ideal conditions of

implementation (i.e., adequate resources, close

supervision ). In contrast, effectiveness refers

to demonstration(s) of socially valid outcomes

under normal conditions of usage in the target

setting(s) for which the intervention was

developed. Demonstrations of effectiveness are

far more difficult than demonstrations of

efficacy. In fact, numerous promising

interventions and approaches fail to bridge the

gap between efficacy and effectiveness.

Emphasis added

Source Walker, H. M. (2004). Use of

evidence-based interventions in schools Where

we've been, where we are, and where we need to

go. School Psychology Review, 33, 398-407. p. 400

Finding a Way Out of the Research-Based Maze A

Guide for Schools

- Define the Academic or Behavioral Needs Requiring

Intervention in Detail and Using Standard

Terminology. Effective interventions cannot be

reliably identified and matched to student needs

if those needs are loosely or vaguely defined. - Overly broad academic goal statement a student

will know her letters. - More focused goal statement When shown any

letter in uppercase or lowercase form, the

student will accurately identify the letter name

and its corresponding sound without assistance.

- When possible, describe academic behaviors

selected as intervention target using standard

terminology to make it easier to locate

appropriate evidence-based intervention ideas.

Finding a Way Out of the Research-Based Maze A

Guide for Schools

- Develop Consensus in Your School About What is

Meant by Evidence-Based. - Compile a list of trusted professional

organizations and journals. Continue to add to

this list of trusted organizations and journals

over time.

Finding a Way Out of the Research-Based Maze A

Guide for Schools

- Develop Consensus in Your School About What is

Meant by Evidence-Based. - Draft a definition of evidence-based. Example

The International Reading Association (2002)

provides these guidelines Produce

objective dataso that different evaluators

should be able to draw similar conclusions when

reviewing the data from the studies. Have

valid research results that can reasonably be

applied to the kinds of real-world reading tasks

that children must master in actual classrooms.

Yield reliable and replicable findings that would

not be expected to change significantly based on

such arbitrary factors as the day or time that

data on the interventions were collected or who

collected them. - Employ current best-practice methods in

observation or experimentation to reduce the

probability that other sources of potential bias

crept into the studies and compromised the

results. - Checked before publication by independent

experts, who review the methods, data, and

conclusions of the studies.

Finding a Way Out of the Research-Based Maze A

Guide for Schools

- Develop Consensus in Your School About What is

Meant by Evidence-Based. - Adopting a research continuum. It can be useful

for schools to use a research continuum that

establishes categories for interventions in

descending levels of research quality. The

continuum would be used as an aid to judge

whether specific instructional practices or

interventions are supported by research of

sufficient quantity and quality for use in

schools.

Finding a Way Out of the Research-Based Maze A

Guide for Schools

- Use Impartial On-Line Rating Sites to Evaluate

Commercial Intervention Products. Cautions to

keep in mind when using these sites - They typically rely on existing research only.
- There can potential delays / lag time between the

publication of new research and these sites

evaluation of that research.

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Finding a Way Out of the Research-Based Maze A

Guide for Schools

- Know the Research-Based Components That Are

Building Blocks of Effective Interventions.

Research indicates (Burns, VanDerHeyden, Boice,

2008) that, to be maximally effective,

interventions should - be matched to the students academic needs
- be delivered using explicit instruction
- provide the student with adequate success in the

instructional task - give the student a high opportunity to respond
- provide timely performance feedback.

Finding a Way Out of the Research-Based Maze A

Guide for Schools

- Keep Up With Emerging Intervention Research

Through Knowledge Brokers. - Districts first define manageable and sensible

intervention topic areas, such as alphabetics

and reading fluency. - Then district or school staff members are

selected to serve as knowledge brokers based on

their training, experience, and/or interest. - Knowledge brokers regularly read educational

research journals and other publications from

reputable organizations or government agencies to

keep up with emerging research in their

intervention topic area. - They periodically share their expertise with

other district RTI planners to ensure that the

schools are using the best available intervention

strategies.

Defining Academic Problems Get It Right and

Interventions Are More Likely to Be

EffectiveJim Wrightwww.interventioncentral.org

Defining Academic Problems Recommended Steps

- Be knowledgeable of the school academic

curriculum and key student academic skills that

are taught. The teacher should have a good

survey-level knowledge of the key academic skills

outlined in the schools curriculumfor the grade

level of their classroom as well as earlier grade

levels. If the curriculum alone is not adequate

for describing a students academic deficit, the

instructor can make use of research-based

definitions or complete a task analysis to

further define the academic problem area. Here

are guidelines for consulting curriculum and

research-based definitions and for conducting a

task analysis for more global skills.

Defining Academic Problems Recommended Steps

- Curriculum. The teacher can review the schools

curriculum and related documents (e.g.,

score-and-sequence charts curriculum maps) to

select specific academic skill or performance

goals. First, determine the approximate grade or

level in the curriculum that matches the

students skills. Then, review the curriculum at

that alternate grade level to find appropriate

descriptions of the students relevant academic

deficit. For example, a second-grade student

had limited phonemic awareness. The student was

not able accurately to deconstruct a spoken word

into its component sound-units, or phonemes. In

the schools curriculum, children were expected

to attain proficiency in phonemic awareness by

the close of grade 1. The teacher went off

level to review the grade 1 curriculum and found

a specific description of phonemic awareness that

she could use as a starting point in defining the

students skill deficit.

Defining Academic Problems Recommended Steps

- Research-Based Skill Definitions. Even when a

schools curriculum identifies key skills,

schools may find it useful to corroborate or

elaborate those skill definitions by reviewing

alternative definitions published in research

journals or other trusted sources. For example,

a student had delays in solving quadratic

equations. The math instructor found that the

schools math curriculum did not provide a

detailed description of the skills required to

successfully complete quadratic equations. So the

teacher reviewed the National Mathematics

Advisory Panel report (Fennell et al., 2008) and

found a detailed description of component skills

for solving quadratic equations. By combining the

skill definitions from the school curriculum with

the more detailed descriptions taken from the

research-based document, the teacher could better

pinpoint the students academic deficit in

specific terms.

Defining Academic Problems Recommended Steps

- Task Analysis. Students may possess deficits in

more global academic enabling skills that are

essential for academic success. Teachers can

complete an task analysis of the relevant skill

by breaking it down into a checklist of

constituent subskills. An instructor can use the

resulting checklist to verify that the student

can or cannot perform each of the subskills that

make up the global academic enabling

skill.For example, teachers at a middle school

noted that many of their students seemed to have

poor organization skills. Those instructors

conducted a task analysis and determined that--in

their classrooms--the essential subskills of

student organization included (a) arriving to

class on time (b) bringing work materials to

class (c) following teacher directions in a

timely manner (d) knowing how to request teacher

assistance when needed and (e) having an

uncluttered desk with only essential work

materials.

Defining Academic Problems Recommended Steps

- Describe the academic problem in specific,

skill-based terms (Batsche et al., 2008 Upah,

2008). Write a clear, brief description of the

academic skill or performance deficit that

focuses on a specific skill or performance area.

Here are sample problem-identification

statements - John reads aloud from grade-appropriate text much

more slowly than his classmates. - Ann lacks proficiency with multiplication math

problems (double-digit times double-digit with no

regrouping). - Tye does not turn in homework assignments.
- Angela produces limited text on in-class writing

assignments.

Defining Academic Problems Recommended Steps

- Develop a fuller description of the academic

problem to provide a meaningful instructional

context. When the teacher has described the

students academic problem, the next step is to

expand the problem definition to put it into a

meaningful context. This expanded definition

includes information about the conditions under

which the academic problem is observed and

typical or expected level of performance. - Conditions. Describe the environmental conditions

or task demands in place when the academic

problem is observed. - Problem Description. Describe the actual

observable academic behavior in which the student

is engaged. Include rate, accuracy, or other

quantitative information of student performance. - Typical or Expected Level of Performance. Provide

a typical or expected performance criterion for

this skill or behavior. Typical or expected

academic performance can be calculated using a

variety of sources,

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Defining Academic Problems Recommended Steps

- Develop a hypothesis statement to explain the

academic skill or performance problem. The

hypothesis states the assumed reason(s) or

cause(s) for the students academic problems.

Once it has been developed, the hypothesis

statement acts as a compass needle, pointing

toward interventions that most logically address

the student academic problems.

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Activity Defining Academic Interventions

- Consider the structured format that was reviewed

for defining academic interventions. - How can you use this framework to support RTI in

your school?

Tier 1 Case Example Patricia Reading

Comprehension

Case Example Reading Comprehension

- The Problem
- A student, Patricia, struggled in her social

studies class, particularly in understanding the

course readings. Her teacher, Ms. Cardamone,

decided that the problem was significant enough

that the student required some individualized

support.

Case Example Reading Comprehension

- The Evidence
- Student Interview. Ms. Cardamone met with

Patricia to ask her questions about her

difficulties with social studies content and

assignments. Patricia said that when she reads

the course text and other assigned readings, she

doesnt have difficulty with the vocabulary but

often realizes after reading half a page that she

hasnt really understood what she has read.

Sometimes she has to reread a page several times

and that can be frustrating.

Case Example Reading Comprehension

- The Evidence (Cont.)
- Review of Records. Past teacher report card

comments suggest that Patricia has had difficulty

with reading comprehension tasks in earlier

grades. She had received help in middle school in

the reading lab, although there was no record of

what specific interventions were tried in that

setting. - Input from Other Teachers. Ms. Cardamone checked

with other teachers who have Patricia in their

classes. All expressed concern about Patricias

reading comprehension skills. The English

teacher noted that Patricia appears to have

difficulty pulling the main idea from a passage,

which limits her ability to extract key

information from texts and to review that

information for tests.

Case Example Reading Comprehension

- The Intervention
- Ms. Cardamone decided, based on the evidence

collected, that Patricia would benefit from

training in identifying the main idea from a

passage, rather than trying to retain all the

information presented in the text. She selected

two simple interventions Question Generation and

Text Lookback. She arranged to have Patricia meet

with the Reading Lab teacher to learn these two

strategies. Then Ms. Cardamone scheduled time to

meet with Patricia to demonstrate how to use

these strategies effectively with the social

studies course text and other assigned readings.

- Students are taught to boost their comprehension

of expository passages by (1) locating the main

idea or key ideas in the passage and (2)

generating questions based on that information.

QuestionGeneration

http//www.interventioncentral.org/htmdocs/interve

ntions/rdngcompr/qgen.php

- Text lookback is a simple strategy that students

can use to boost their recall of expository prose

by identifying questions that require information

from the text and then looking back in the text

in a methodical manner to locate that

information.

Text Lookback

http//www.interventioncentral.org/htmdocs/interve

ntions/rdngcompr/txtlkbk.php

Case Example Reading Comprehension

- The Outcome
- When the intervention had been in place for 4

weeks, Ms. Cardamone noted that Patricia appeared

to have a somewhat better grasp of course content

and expressed a greater grasp of material from

the text. She shared her intervention ideas with

other teachers working with Patricia. While

Patricias grades did improve in Social Studies,

they were still only borderline passing. Ms.

Cardamone decided to continue her classroom

interventions with Patricia but also to refer the

student to the RTI Team to see if the student

could receive any additional support to build her

reading comprehension skills.

Tier 1 Case Example Justin Non-Compliance

Case Example Non-Compliance

- The Problem
- Justin showed a pattern from the start of the

school year of not complying with teacher

requests in his English class. His teacher, Mr.

Steubin, noted