The Prevention and Identification of Math Disability Using RTI

11

The Prevention and Identification of The Prevention and Identification of Math Disability Math Disability

Using RTIUsing RTI

Lynn FuchsLynn Fuchs

Vanderbilt UniversityVanderbilt University

September 18, 2008September 18, 2008

22

This PresentationThis Presentation

Part 1Part 1:: Brief Review of RTI FrameworkBrief Review of RTI Framework

Part 2Part 2: : Screening and Progress Monitoring within RTIScreening and Progress Monitoring within RTI

Part 3Part 3: : Example of Secondary Tutoring at First GradeExample of Secondary Tutoring at First Grade

Part 4Part 4: Example of Secondary Tutoring at Third Grade: Example of Secondary Tutoring at Third Grade

33

Responsiveness-To-Intervention Responsiveness-To-Intervention (RTI)(RTI)

RTI integrates assessment and intervention RTI integrates assessment and intervention within a multi-level prevention system to within a multi-level prevention system to identify and reduce risk for academic failure.identify and reduce risk for academic failure.

44

Typical RTI ProcedureTypical RTI ProcedureTypical RTI ProcedureTypical RTI Procedure

• Primary Prevention

• All children receive the universal, core instructional program.

• All children are tested once in the fall to identify students as potentially at-risk for academic failure.

• The progress of potentially at-risk students is monitored for 6-8 weeks to (dis)confirm risk and identify students for secondary prevention.

55

Typical RTI ProcedureTypical RTI Procedure

Secondary Prevention− For at-risk students, a second level of prevention is

implemented using standard research-validated tutoring protocols.

− Student progress is monitored throughout intervention, and students are re-tested following intervention.

− Growth/performance is dichotomized as responsive or unresponsive.

− Students who respond well return to this primary prevention, with ongoing progress monitoring.

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Typical RTI ProcedureTypical RTI Procedure Tertiary Prevention

− Those who do not respond receive a multidisciplinary team evaluation and are identified for individualized programming in special education.

− Tertiary prevention represents a reformed special education where

Individual student goals are set ambitiously. Ongoing progress monitoring is used in a formative and

recursive way to formulate individualized programs that are effective.

Ongoing progress monitoring is also used to identify when students have met benchmarks that permit flexible return to secondary or primary prevention (with progress monitoring so re-entry to tertiary prevention occurs as needed), making special education a flexible service.

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Health Care AnalogyHealth Care Analogy High blood pressure (HBP) can lead to heart attacks or strokes High blood pressure (HBP) can lead to heart attacks or strokes (like (like

academic failure can produce serious long-term negative academic failure can produce serious long-term negative consequences).consequences).

At the annual check-up (primary prevention), HBP screening At the annual check-up (primary prevention), HBP screening (like (like annual fall screening for low reading or math scores).annual fall screening for low reading or math scores).

If screening suggests HBP, then monitoring over 6-8 weeks occurs to If screening suggests HBP, then monitoring over 6-8 weeks occurs to verify HBP verify HBP (like PM to ([dis]confirm risk).(like PM to ([dis]confirm risk).

If HBP is verified, secondary prevention occurs with relatively If HBP is verified, secondary prevention occurs with relatively inexpensive diuretics, which are effective for vast majority, and inexpensive diuretics, which are effective for vast majority, and monitoring continues monitoring continues (like small-group secondary preventive tutoring, (like small-group secondary preventive tutoring, using a standard treatment protocol, with PM to index response).using a standard treatment protocol, with PM to index response).

For patients who fail to respond to secondary prevention (diuretics), For patients who fail to respond to secondary prevention (diuretics), then tertiary prevention occurs—experimentation with more expensive then tertiary prevention occurs—experimentation with more expensive medications (e.g., ACE inhibitors, beta blockers), with ongoing medications (e.g., ACE inhibitors, beta blockers), with ongoing monitoring to determine which drug or combination of drugs is monitoring to determine which drug or combination of drugs is effective effective (like individualized instructional programs inductively (like individualized instructional programs inductively formulated with progress monitoring).formulated with progress monitoring).

88

Part 2:Part 2:Progress Monitoring:Progress Monitoring:

An Essential Form of Assessment An Essential Form of Assessment within RTIwithin RTI

To screen students as at risk for failure.To screen students as at risk for failure.

To determine whether students respond.To determine whether students respond.

For students who fail to respond, to build For students who fail to respond, to build individualized instructional programs.individualized instructional programs.

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Progress MonitoringProgress Monitoring

Teachers assess students’ academic Teachers assess students’ academic performance, using brief measures, on a performance, using brief measures, on a frequent basisfrequent basis

CBM is the scientifically validated form CBM is the scientifically validated form of progress monitoring.of progress monitoring.

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Research ShowsResearch Shows

CBM produces accurate, meaningful CBM produces accurate, meaningful information about students’ academic levels information about students’ academic levels and their rates of improvement.and their rates of improvement.

CBM is sensitive to student improvement.CBM is sensitive to student improvement.

CBM corresponds well with high-stakes tests.CBM corresponds well with high-stakes tests.

When teachers use CBM to inform their When teachers use CBM to inform their instructional decisions, students achieve instructional decisions, students achieve better.better.

1111

Most Progress Monitoring: Most Progress Monitoring: Mastery MeasurementMastery Measurement

CBM is CBM is NOTNOT

Mastery MeasurementMastery Measurement

1212

MASTERY MEASUREMENT MASTERY MEASUREMENT Tracks Mastery of Short-term Tracks Mastery of Short-term

Instructional Objectives Instructional Objectives

Determines the sequence of skills in an Determines the sequence of skills in an instructional hierarchyinstructional hierarchy

For each skill, develops a criterion-For each skill, develops a criterion-referenced testreferenced test

To implement Mastery Measurement, To implement Mastery Measurement, the teacherthe teacher

1313

Hypothetical Fourth-Grade Math Computation Curriculum

1. Multidigit addition with regrouping

2. Multidigit subtraction with regrouping

3. Multiplication facts, factors to 9

4. Multiply 2-digit numbers by a 1-digit number


6. Division facts, divisors to 9

7. Divide 2-digit numbers by a 1-digit number


9. Add/subtract simple fractions, like denominators

10. Add/subtract whole number and mixed number

1414

Name: Date

3 65 216 37 58+

5 34 296 34 21+

8 45 257 56 32+

6 78 425 39 37+

5 63 829 47 42+

5 73 2 14 63 9 1+

3 64 225 75 29+

3 48 246 94 26+

3 24 158 54 39+

4 53 21+ 8 62 74

Adding

Multidigit Addition Mastery Test

1515


1. Multidigit addition with regrouping

2. Multidigit subtraction with regrouping

3. Multiplication facts, factors to 9



6. Division facts, divisors to 9



9. Add/subtract simple fractions, like denominators

10. Add/subtract whole number and mixed number

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Multidigit Subtraction Mastery Test

Name: Date

6 52 13 75

5 42 96 34

8 45 57 56

6 78 29 37

5 68 29 42

7 32 13 91

6 42 25 29

3 48 44 26

2 41 58 54

4 32 18 74

Subtracting

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Problems with Mastery Problems with Mastery MeasurementMeasurement

Hierarchy of skills is logical, not empirical.Hierarchy of skills is logical, not empirical.

Performance on single-skill assessments can be Performance on single-skill assessments can be misleading.misleading.

Assessment does not reflect maintenance or Assessment does not reflect maintenance or generalization.generalization.

Assessment is designed by teachers or sold with Assessment is designed by teachers or sold with textbooks, with unknown reliability and validity.textbooks, with unknown reliability and validity.

SO THAT, the number of objectives mastered does SO THAT, the number of objectives mastered does not relate well to performance on high-stakes tests.not relate well to performance on high-stakes tests.

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CBM was designed to address CBM was designed to address these problems.these problems.

An Example of CBM: An Example of CBM:

Math ComputationMath Computation

1919

Multidigit addition with regrouping

Multidigit subtraction with regrouping

Multiplication facts, factors to 9

Multiply 2-digit numbers by a 1-digit number

Multiply 2-digit numbers by a 2-digit number

Division facts, divisors to 9

Divide 2-digit numbers by a 1-digit number

Divide 3-digit numbers by a 1-digit number

Add/subtract simple fractions, like denominators

Add/subtract whole number and mixed number


2020

41x

98 297

95 22 575 26 8+

24 47x

B C D E

G H I J

L M N O

Q R S T

V W X Y

A

F

K

P

U

64 )37

27 =

61 4444 20

Sheet #1

Password: ARM

Computation 4

Name: Date

67 =31 +

47 =27 -

35

15 =+

786 ) 87 57x

67x

90x 486 ) 205 )

502 ) 3310x

60x

307 )

328 ) 11 5628 24

+ 83

3833x

95x 567 )

• Each weekly test incorporates the same problems types, but problems are not the same and are in a different order.

2121

0

10

20

30

40

50

60

70

Sep Oct Nov Dec Jan Feb Mar Apr May

Donald Ross Computation 4

DIGITS

Donald’s Progress in Digits CorrectDonald’s Progress in Digits CorrectAcross the School YearAcross the School Year

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One page of a 3-page CBM in math concepts and applications (24 total problems)

Column A Column B

Name _______________________________ Date ________________________ Test 4 Page 1

Applications 4

•N

•M

(B)LK••

•Z (A)

(C)

(D)

point

ray

line segment

line

Write the letter in each blank.

(1)

Look at this numbers.:

356.17

Which number is in the hundredths place?

(2)

(3)

Jeff wheels his wheelchair for 33 hoursa week at school and for 28 hours a weekin his neighborhood. About how manyhours does Jeff spend each week wheelinghis wheelchair?

Solve the problem by estimating the sum ordifference to the nearest ten.

(4)

Write the number in each blank.

3 ten thousands, 6 hundreds, 8 ones

2 thousands, 8 hundreds, 4 tens, 6 ones

(5)

Write a number in the blank.

1 week = _____ days

(6) Vacation Plans for Summit School Students

SummerSchool

Camp

Travel

Stay home

0 2010 30 40 50 60 70 80 90 100

Number of Students

The P.T.A. will buy a Summit SchoolT-Shirt for each student who goesto summer school. Each shirt costs$4.00. How much money will theP.T.A. spend on these T shirts?

How many students are planning totravel during the summer?

How many fewer students are planningto go to summer school than planningto stay home?

Use the bar graph to answer the questions.

(A) meters

(B) centimeters

(C) kilometers

To measure the distance of the busride from school to your house youwould use

(7)

$ .00

2323

Sampling performance on year-long Sampling performance on year-long curriculum for each CBMcurriculum for each CBM

Avoids need to specify a skills hierarchyAvoids need to specify a skills hierarchy Avoids single-skill testsAvoids single-skill tests Automatically assesses maintenance/generalizationAutomatically assesses maintenance/generalization Permits standardized procedures for sampling the Permits standardized procedures for sampling the

curriculum, with known reliability and validitycurriculum, with known reliability and validity SO THAT: CBM scores relate well to performance SO THAT: CBM scores relate well to performance

on high-stakes testson high-stakes tests

2424

CBM in RTI:CBM in RTI:Primary PreventionPrimary Prevention

− CBM is used to screen all students in the class to CBM is used to screen all students in the class to identify those potentially at risk for poor identify those potentially at risk for poor outcomes at the end of the year.outcomes at the end of the year.

− For students identified as potentially at risk, CBM For students identified as potentially at risk, CBM is administered weekly. CBM slope (weekly rate is administered weekly. CBM slope (weekly rate of improvement) is used to quantify response to of improvement) is used to quantify response to primary prevention. If slope is inadequate, then primary prevention. If slope is inadequate, then student moves to secondary prevention.student moves to secondary prevention.

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Primary Prevention:Primary Prevention:Screening for Possible Math RiskScreening for Possible Math Risk

GradeGrade Computation Cut-OffComputation Cut-Off Concepts & Applications Cut-OffConcepts & Applications Cut-Off

Grade 1Grade 1 < 5 digits< 5 digits < 5 points< 5 points


Grade 3Grade 3 < 10 digits < 10 digits < 10 points< 10 points




Note: These figures may change pending additional RTI research.

2626

Primary Prevention:Primary Prevention:Confirming Risk Status With PMConfirming Risk Status With PM

At the end of 6 to 8 weeks, student risk status At the end of 6 to 8 weeks, student risk status is confirmed or disconfirmed.is confirmed or disconfirmed.

GradeGrade InadequateInadequateReadingReading

SlopeSlope

Inadequate Inadequate MathMath

ComputationComputationSlopeSlope

Inadequate MathInadequate MathConcepts and Concepts and

Applications SlopeApplications Slope

KindergartenKindergarten < 1 (LSF)< 1 (LSF) < 0.20< 0.20 < 0.20< 0.20

Grade 1Grade 1 < 1.8 (WIF)< 1.8 (WIF) < 0.25< 0.25 < 0.30< 0.30

Grade 2Grade 2 < 1 (PRF)< 1 (PRF) < 0.20< 0.20 < 0.30< 0.30

Grade 3Grade 3 < 0.75 (PRF)< 0.75 (PRF) < 0.20< 0.20 < 0.50< 0.50

Grade 4Grade 4 < 0.25 (Maze)< 0.25 (Maze) < 0.50< 0.50 < 0.50< 0.50

Grade 5Grade 5 < 0.25 (Maze)< 0.25 (Maze) < 0.50< 0.50 < 0.50< 0.50

Grade 6Grade 6 < 0.25 (Maze)< 0.25 (Maze) < 0.50< 0.50 < 0.50< 0.50Note: These figures may change pending additional RTI research.

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CBM in RTI: CBM in RTI: Secondary PreventionSecondary Prevention

− CBM is administered weekly throughout tutoring.CBM is administered weekly throughout tutoring.

− If CBM slope and/or projected year-end level are If CBM slope and/or projected year-end level are adequate, student returns to primary prevention, adequate, student returns to primary prevention, but weekly CBM continues.but weekly CBM continues.

− If CBM neither slope nor projected year-end level If CBM neither slope nor projected year-end level is inadequate, then student moves to tertiary is inadequate, then student moves to tertiary prevention.prevention.

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Secondary Prevention:Secondary Prevention:Determining Response in MathDetermining Response in Math

GradeGrade

ComputationComputation Concepts and ApplicationsConcepts and Applications

< Slope< Slope < End level< End level < Slope< Slope < End level< End level

Grade 1Grade 1 < 0.50< 0.50 < 20 digits< 20 digits < 0.40< 0.40 < 20 points< 20 points






Note: These figures may change pending additional RTI research.

2929

CBM in RTI:CBM in RTI:Tertiary PreventionTertiary Prevention

Set ambitious goalsSet ambitious goals Distinguish the intensity of secondary vs. tertiary prevention Distinguish the intensity of secondary vs. tertiary prevention

− Tertiary prevention is reserved for students who fail to respond Tertiary prevention is reserved for students who fail to respond to standard forms of instruction (i.e., validated, standard tutoring to standard forms of instruction (i.e., validated, standard tutoring protocols) and who therefore need a nonstandard protocols) and who therefore need a nonstandard (individualized) form of instruction.(individualized) form of instruction.

− Begin tertiary prevention with a validated protocol, but Begin tertiary prevention with a validated protocol, but implement more frequently, and/or with longer sessions, with implement more frequently, and/or with longer sessions, with smaller group size. Collect CBM weekly to systematically smaller group size. Collect CBM weekly to systematically experiment with instructional components that individually tailor experiment with instructional components that individually tailor the protocol to match the student’s needs and ensure its the protocol to match the student’s needs and ensure its effectiveness for that student.effectiveness for that student.

Use flexible exit/re-entry decisions, based on student progress, to Use flexible exit/re-entry decisions, based on student progress, to rely on tertiary prevention as needed and to maximize time in rely on tertiary prevention as needed and to maximize time in primary/secondary prevention as possible.primary/secondary prevention as possible.

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Part 3:Part 3:Secondary Tutoring Secondary Tutoring

at First Gradeat First Grade

Lynn Fuchs, Don Compton, Doug Fuchs, Lynn Fuchs, Don Compton, Doug Fuchs, Kim Paulsen, Joan Bryant, and Carol HamlettKim Paulsen, Joan Bryant, and Carol Hamlett


Journal of Educational PsychologyJournal of Educational Psychology, 2005, 2005

Funded by OSEP Funded by OSEP Grant #H324U010004Grant #H324U010004National Research Center on Learning DisabilitiesNational Research Center on Learning Disabilities

3131

SampleSample 41 141 1stst-grade teachers in 6 Title 1 and 4 non-Title 1 schools (92% -grade teachers in 6 Title 1 and 4 non-Title 1 schools (92%

consented students)consented students)

Conducted weekly CBM ComputationConducted weekly CBM Computation

Using CBM Computation level and slope over 5 weeks, identified the Using CBM Computation level and slope over 5 weeks, identified the 139 lowest performing students (21% of 667 consented students) as 139 lowest performing students (21% of 667 consented students) as AR; randomly assigned these AR to control or tutoringAR; randomly assigned these AR to control or tutoring

NAR: NAR: 528 528 remaining students with consentremaining students with consent

Of 528 NAR:Of 528 NAR:

− All weekly CBM ComputationAll weekly CBM Computation

− 180 sampled for individual and group pre/posttesting 180 sampled for individual and group pre/posttesting

− 348 group pre/posttested 348 group pre/posttested

3232

3333

Pretreatment ScoresPretreatment ScoresNAR > AR Control, AR TutoredNAR > AR Control, AR Tutored

IQIQ

Various aspects of mathematics performanceVarious aspects of mathematics performance

Various aspects of reading performanceVarious aspects of reading performance

3434

TutoringTutoring

Small groups of 2-3 Small groups of 2-3

3 times per week outside classrooms for 16 weeks3 times per week outside classrooms for 16 weeks

40 minutes per session40 minutes per session

3535

First 30 MinutesFirst 30 Minutes

Concrete-representational-abstract model, which relies on Concrete-representational-abstract model, which relies on concrete objects to promote conceptual understandingconcrete objects to promote conceptual understanding (e.g., base-10 blocks for place value instruction)(e.g., base-10 blocks for place value instruction)

17 scripted topics addressing number concepts, 17 scripted topics addressing number concepts, numeration, computation, story problems (e.g., numeration, computation, story problems (e.g., notnot geometry, measurement, charts/figures, money)geometry, measurement, charts/figures, money)

Clear rules for mastery of topicsClear rules for mastery of topics Cumulative review as each new topic is introducedCumulative review as each new topic is introduced Each session audiotaped; tapes sampled and coded for Each session audiotaped; tapes sampled and coded for

fidelity, which was highfidelity, which was high

3636

Last 10 MinutesLast 10 Minutes

Two Ways to Answer a Basic Facts ProblemTwo Ways to Answer a Basic Facts Problem

Know itKnow it- Adding and subtracting 1 or 0- Adding and subtracting 1 or 0- Doubles- Doubles- Pulling known facts from long-term memory- Pulling known facts from long-term memory

CountCount- Count in for addition- Count in for addition- Count up for subtraction- Count up for subtraction

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Count In for AdditionCount In for Addition

Terminology: smaller number and bigger number.Terminology: smaller number and bigger number.OpenOpen hand to show smaller number. hand to show smaller number.Say bigger number and count in raised fingers.Say bigger number and count in raised fingers.Answer is last number Answer is last number countedcounted..

3+2=?3+2=? Open hand to show 2 fingers.Open hand to show 2 fingers.

Say 3 and count: 4 (lower 1 finger), 5 (lower 1 Say 3 and count: 4 (lower 1 finger), 5 (lower 1 finger).finger).

Answer: last number counted (5)Answer: last number counted (5)

3838

Count Up for SubtractionCount Up for Subtraction Terminology: minus number and other number.Terminology: minus number and other number. CloseClose hand. hand. Say the minus number and count up to the other Say the minus number and count up to the other

number.number. Answer is number of fingers used to count up.Answer is number of fingers used to count up.

6-2=46-2=4 Say 2 and count: 3 (raise 1 finger), 4 (raise 1 finger) Say 2 and count: 3 (raise 1 finger), 4 (raise 1 finger)

5 (raise 1 finger), 6 (raise 1 finger)5 (raise 1 finger), 6 (raise 1 finger) Answer: number of raised fingers (6)Answer: number of raised fingers (6)

3939

Know It or Count-Up PracticeKnow It or Count-Up Practice

““Round Robin” timed practiceRound Robin” timed practice Shuffle deck of basic fact flashcards (sums 0-Shuffle deck of basic fact flashcards (sums 0-

9; minuends 0-9)9; minuends 0-9) Each student Each student

− Has 1 minute; when errors occur, immediately Has 1 minute; when errors occur, immediately asked to count up (uses time)asked to count up (uses time)

− Has another minute to “beat own score”Has another minute to “beat own score”

4040

Purpose 1: Tutoring EfficacyPurpose 1: Tutoring Efficacy

ImprovementImprovement Weekly Weekly CBM Computation SlopeCBM Computation Slope

− AR tutoredAR tutored = NAR > AR control = NAR > AR control

WJ III CalculationWJ III Calculation− AR tutoredAR tutored > NAR and AR > NAR and AR

Grade 1 Concepts/ApplicationsGrade 1 Concepts/Applications− AR tutoredAR tutored > NAR and > NAR and AR controlAR control

Story ProblemsStory Problems− NAR > NAR > AR tutoredAR tutored > AR control > AR control

First-grade tutoring enhances outcomes.First-grade tutoring enhances outcomes.

4141

Purpose 1: Tutoring EfficacyPurpose 1: Tutoring Efficacy

Did tutoring decrease MD prevalence? Did tutoring decrease MD prevalence? Yes, across identification options,Yes, across identification options,

tutoring substantially decreased prevalence.tutoring substantially decreased prevalence.

e.g., Final Low Achievement (<10e.g., Final Low Achievement (<10thth percentile) percentile) on Grade 1 Concepts/Applications, prevalence went from 9.75% on Grade 1 Concepts/Applications, prevalence went from 9.75%

without tutoring to 5.14% with tutoring.without tutoring to 5.14% with tutoring.~ 2.5 million fewer children identified MD~ 2.5 million fewer children identified MD

One year later, at end of grade 2, AR tutored One year later, at end of grade 2, AR tutored students were half as less likely to qualify as MD students were half as less likely to qualify as MD

(compared to AR control students).(compared to AR control students).

4242

Part 4: Part 4: Secondary Tutoring Secondary Tutoring

at Third Gradeat Third Grade

Lynn Fuchs, Sarah Powell, Pamela Seethaler, Lynn Fuchs, Sarah Powell, Pamela Seethaler, Paul Cirino, Jack Fletcher, Doug Fuchs, Paul Cirino, Jack Fletcher, Doug Fuchs, Carol Hamlett, and Rebecca ZumetaCarol Hamlett, and Rebecca ZumetaVanderbilt University and University of HoustonVanderbilt University and University of Houston

Journal of Educational PsychologyJournal of Educational Psychology, in press, in press

Grant #Grant #P01046261P01046261National Institute of National Institute of

Child Health and Human DevelopmentChild Health and Human Development

4343

ParticipantsParticipants

Screened 924 students in 63 classrooms in 18 Screened 924 students in 63 classrooms in 18 schools at 2 sites on calculations and word schools at 2 sites on calculations and word problem measuresproblem measures

To participate, students had to be low To participate, students had to be low performing on calculations or word problems performing on calculations or word problems

133 students eligible for participation133 students eligible for participation

4444

Examined Efficacy Examined Efficacy of Two Tutoring Protocolsof Two Tutoring Protocols

Both Tutoring ProtocolsBoth Tutoring Protocols

Delivered individuallyDelivered individually 48 sessions: 3 per week for 16 weeks48 sessions: 3 per week for 16 weeks 20-30 minutes per session20-30 minutes per session Scripted lessons, which tutors studied (not read)Scripted lessons, which tutors studied (not read) Motivational system to ensure on-task behavior and Motivational system to ensure on-task behavior and

hard, accurate workhard, accurate work Each session audiotaped; tapes sampled and coded Each session audiotaped; tapes sampled and coded

for fidelity, which was high for both tutoring for fidelity, which was high for both tutoring conditionsconditions

4545

Examined Efficacy Examined Efficacy of Two Tutoring Protocolsof Two Tutoring Protocols

The exclusive focus of Math Flash was The exclusive focus of Math Flash was math math factfact deficits deficits

The primary focus of Pirate Math was The primary focus of Pirate Math was word word problemproblem deficits, but it also addressed deficits, but it also addressed foundational skills (math facts, procedural foundational skills (math facts, procedural calculations, and algebra skills)calculations, and algebra skills)

4646

Math Facts (MF) Tutoring: Math FlashMath Facts (MF) Tutoring: Math Flash First, +/-1, +/-0, doubles 0-6, +/-2First, +/-1, +/-0, doubles 0-6, +/-2

Then, counting strategies: min for adding, missing Then, counting strategies: min for adding, missing addend for subtracting (students taught to “Know It or addend for subtracting (students taught to “Know It or Count Up)Count Up)

Then, MFs families through 18 and doubles through 20Then, MFs families through 18 and doubles through 20

Stay on a MFs category at least 1 day, until mastery or Stay on a MFs category at least 1 day, until mastery or maximum of 4 days (to ensure content coverage)maximum of 4 days (to ensure content coverage)

4747

MF Tutoring: Math FlashMF Tutoring: Math Flash

Activities in Each SessionActivities in Each Session

1.1. Flash card warm up (all 200 MFs): Know It or Flash card warm up (all 200 MFs): Know It or Count UpCount Up

2.2. Conceptual and strategic instructionConceptual and strategic instruction3.3. Lesson-specific MFs “repeated” practice: Know It Lesson-specific MFs “repeated” practice: Know It

or Count Upor Count Up4.4. Computerized practice to build fluency (while Computerized practice to build fluency (while

assessing mastery of lesson-specific MFs)assessing mastery of lesson-specific MFs)5.5. Paper-pencil review (15 lesson-specific MFs; 15 Paper-pencil review (15 lesson-specific MFs; 15

review number MFs)review number MFs)

4848

Word-Problem (WP) TutoringWord-Problem (WP) Tutoring Unit 1: Skills foundational to WPsUnit 1: Skills foundational to WPs

− Counting up (different than 1Counting up (different than 1stst grade) grade)− Double-digit calculationsDouble-digit calculations− Solving X in simple algebraic equationsSolving X in simple algebraic equations− Checking WP workChecking WP work

Unit 2: Total ProblemsUnit 2: Total Problems

Unit 3: Difference ProblemsUnit 3: Difference Problems

Unit 4: Change ProblemsUnit 4: Change Problems

Across Units 2-4, cumulative review; irrelevant information; Across Units 2-4, cumulative review; irrelevant information; charts/graphscharts/graphs

4949

WP TutoringWP Tutoring

Following Unit 1, four activities per sessionFollowing Unit 1, four activities per session

1. Flash-card warm up (identical to MF tutoring): Know 1. Flash-card warm up (identical to MF tutoring): Know It or Count UpIt or Count Up

2. Conceptual/strategic instruction using schema-2. Conceptual/strategic instruction using schema-broadening instructionbroadening instruction

3. Problem-type flash card practice on identifying 3. Problem-type flash card practice on identifying problem typesproblem types

4. Paper/pencil review (10 MFs; 4 double-digit 4. Paper/pencil review (10 MFs; 4 double-digit calculations; one WP)calculations; one WP)

5050

Results: Results: Fluency with MFsFluency with MFs

Both tutoring conditions effected superior Both tutoring conditions effected superior improvement compared to control groupimprovement compared to control group

No difference between tutoring conditionsNo difference between tutoring conditions

Notable, because MF tutoring spent 20-30 minutes Notable, because MF tutoring spent 20-30 minutes per session on MFs whereas WP tutoring spent 4-6 per session on MFs whereas WP tutoring spent 4-6 minutes per session on MFsminutes per session on MFs

5151

Results: Results: Procedural CalculationsProcedural Calculations

Both tutoring conditions effected superior improvement Both tutoring conditions effected superior improvement compared to control groupcompared to control group

Effect size greater for WP tutoring and NC tutoring Effect size greater for WP tutoring and NC tutoring

Only WP tutoring allocated time (although limited) on Only WP tutoring allocated time (although limited) on procedural calculations (1 initial lesson; 2 minutes procedural calculations (1 initial lesson; 2 minutes paper/pencil review; as embedded in WPs)paper/pencil review; as embedded in WPs)

Notable that even without time on procedural calculations, Notable that even without time on procedural calculations, MF tutoring effected better outcomes, indicating transfer.MF tutoring effected better outcomes, indicating transfer.

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Results: AlgebraResults: Algebra

WP tutoring effected superior outcome compared to WP tutoring effected superior outcome compared to control group and MF tutoringcontrol group and MF tutoring

Notable that algebraic cognition improved as a Notable that algebraic cognition improved as a function of tutoring, even though students were function of tutoring, even though students were severely deficient in math and young.severely deficient in math and young.

Given strong focus on algebra in high schools and Given strong focus on algebra in high schools and curricular and/or graduation requirements for curricular and/or graduation requirements for algebra, introducing algebra earlier in the curriculum algebra, introducing algebra earlier in the curriculum may represent a productive innovation.may represent a productive innovation.

5353

Results: Word ProblemsResults: Word Problems

Work on these foundation skills (MFs, procedural Work on these foundation skills (MFs, procedural calculations, algebra), combined with schema-calculations, algebra), combined with schema-broadening instruction, also produced differential broadening instruction, also produced differential growth on WP outcomes compared to MF tutoring growth on WP outcomes compared to MF tutoring group and compared to control group.group and compared to control group.

MF tutoring did not result in improvement on WPs.MF tutoring did not result in improvement on WPs.

5454

ConclusionsConclusions

MF tutoring enhances fluency with MFs with MF tutoring enhances fluency with MFs with transfer to procedural calculations but without transfer to procedural calculations but without transfer to algebra or WPs.transfer to algebra or WPs.

For a comparable amount of tutoring time, For a comparable amount of tutoring time, WP tutoring (with work on foundational WP tutoring (with work on foundational skills) enhances WP skill, fluency with MFs, skills) enhances WP skill, fluency with MFs, procedural calculations, and algebra.procedural calculations, and algebra.

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Tutoring ManualsTutoring Manuals

First-Grade Secondary Prevention Tutoring First-Grade Secondary Prevention Tutoring ManualManual

Third-Grade Pirate Math ManualThird-Grade Pirate Math Manual

Also: Hot Math (Whole Class and Tutoring)Also: Hot Math (Whole Class and Tutoring)

5656

ContactContact

Flora MurrayFlora Murray

[email protected]@vanderbilt.edu


328 Peabody College328 Peabody College

Department of Special EducationDepartment of Special Education

Nashville, TN 37203Nashville, TN 37203

(615) 343-4782(615) 343-4782

mailto:[email protected]

5757

CBM Math MaterialsCBM Math Materials

McGraw-Hill: Web-based math (and reading) McGraw-Hill: Web-based math (and reading) systemssystems

Pro-Ed, Inc.: Math computation and Pro-Ed, Inc.: Math computation and concepts/applications tests (Monitoring Basic concepts/applications tests (Monitoring Basic Skills Progress)Skills Progress)

www.studentprogress.orgwww.studentprogress.org

Documents

The Prevention and Identification of Math Disability Using RTI