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RTI - Mathematics: What do we know and where do we go from here?

Ben Clarke, Ph.D.Scott Baker. Ph.D.

Pacific Institutes for Research

Increasing recognition of the importance of mathematical knowledge

“For people to participate fully in society, they must know basic mathematics. Citizens who cannot reason mathematically are cut off from whole

“For people to participate fully in society, they must know basic mathematics. Citizens who cannot reason mathematically are cut off from wholemathematically are cut off from whole realms of human endeavor. Innumeracy deprives them not only of opportunity but also of competence in everyday tasks”. (Adding it Up, 2001)

mathematically are cut off from whole realms of human endeavor. Innumeracy deprives them not only of opportunity but also of competence in everyday tasks”. (Adding it Up, 2001)

State of Mathematics

Achievement on the NAEP trending upward for 4th/8th grade and steady for 12th grade

Large numbers of students still lacking proficient skillsPersistent income and ethnicity gapsDrop in achievement at the time algebra instruction

Achievement on the NAEP trending upward for 4th/8th grade and steady for 12th grade

Large numbers of students still lacking proficient skillsPersistent income and ethnicity gapsDrop in achievement at the time algebra instructionDrop in achievement at the time algebra instruction begins

TIMS data indicate significant lower levels of achievement between US and other nations

Gap increase over timeJobs requiring intensive mathematics and science knowledge will outpace job growth 3:1 (STEM) and everyday work will require greater mathematical understanding

Drop in achievement at the time algebra instruction begins

TIMS data indicate significant lower levels of achievement between US and other nations

Gap increase over timeJobs requiring intensive mathematics and science knowledge will outpace job growth 3:1 (STEM) and everyday work will require greater mathematical understanding

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High Level of Interest in Mathematics Achievement

National Mathematics Advisory Report

National Council Teachers of Mathematics: Focal Points

National Mathematics Advisory Report

National Council Teachers of Mathematics: Focal PointsMathematics: Focal Points

National Research Council: Adding it Up

Mathematics: Focal Points

National Research Council: Adding it Up

Response to Intervention

Reauthorization of IDEA (2004) allowed for RTI to be included as a component in special education evaluationsPremised on the use of research based

Reauthorization of IDEA (2004) allowed for RTI to be included as a component in special education evaluationsPremised on the use of research based interventions and student response to intervention

Students who respond are not identified as learning disabledStudents who do not respond are referred for a complete evaluation and potential identification as learning disabled

interventions and student response to intervention

Students who respond are not identified as learning disabledStudents who do not respond are referred for a complete evaluation and potential identification as learning disabled

Response to Intervention

Linked closely to an early identification and prevention model of deliveryProvides for the delivery of tiered services across traditional boundaries (e g Special

Linked closely to an early identification and prevention model of deliveryProvides for the delivery of tiered services across traditional boundaries (e g Specialacross traditional boundaries (e.g.Special and General Education)Most often implemented by schools using a schoolwide model of instruction…..

In Reading, but what about Math!

across traditional boundaries (e.g.Special and General Education)Most often implemented by schools using a schoolwide model of instruction…..

In Reading, but what about Math!

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Paucity of Research

A lit search for studies on reading disabilities studies and math disability studies from 1996-2005 found over 600 studies in the area of reading and less than 50 for mathematics (14:1)Meta analysis conducted in the areas of low

A lit search for studies on reading disabilities studies and math disability studies from 1996-2005 found over 600 studies in the area of reading and less than 50 for mathematics (14:1)Meta analysis conducted in the areas of lowMeta analysis conducted in the areas of low achievement and learning disabilties in mathematics consisted of 15, 38, and 58 studies - in comparison to the large number of studies that formed the basis of recommendations for the National Reading Panel Specific RTI mathematics studies for a recent annotated bibliography totaled 9 studies

Meta analysis conducted in the areas of low achievement and learning disabilties in mathematics consisted of 15, 38, and 58 studies - in comparison to the large number of studies that formed the basis of recommendations for the National Reading Panel Specific RTI mathematics studies for a recent annotated bibliography totaled 9 studies

Broad Issues to Consider (RTI)

Levels of Support / LD identification process

Standard prototcol / Problem Solving

Levels of Support / LD identification process

Standard prototcol / Problem SolvingStandard prototcol / Problem SolvingStandard prototcol / Problem Solving

What is Needed for RTI

Primary:Valid system for screening.System for progress monitoring.An array of evidence-base intervention or at least

i i i t ti f b i i Ti 2 t d t

Primary:Valid system for screening.System for progress monitoring.An array of evidence-base intervention or at least

i i i t ti f b i i Ti 2 t d tpromising interventions for beginning Tier 2 students.

Secondary:Diagnostic assessmentsCore instructional program

promising interventions for beginning Tier 2 students.

Secondary:Diagnostic assessmentsCore instructional program

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Tier 1: Components

Screening instruments

Core Curriculum based on expert judgment

Screening instruments

Core Curriculum based on expert judgmentjudgment

Enhancements to the core curriculum

judgment

Enhancements to the core curriculum

Screening1. Measures used in screening vary from short

duration fluency measures to in-depth measures.Short duration: Early Numeracy CBM; CBM computational and conceptual probes.Number Knowledge Test (approx. 15 min).

1. Measures used in screening vary from short duration fluency measures to in-depth measures.

Short duration: Early Numeracy CBM; CBM computational and conceptual probes.Number Knowledge Test (approx. 15 min). Math specific tests such as TEMA, Key Math -also used in diagnostic testing.

2. Goal is to make accurate predictions about who needs and who does not need additional services.

3. Must balance efficiency of screening process with goal of accurate predictions.

Math specific tests such as TEMA, Key Math -also used in diagnostic testing.

2. Goal is to make accurate predictions about who needs and who does not need additional services.

3. Must balance efficiency of screening process with goal of accurate predictions.

Measures for ScreeningEarly Grades

Short duration fluency measures.E.g. Early Magnitude ComparisonMissing Number in a series (strategic

ti ) 7 9 X 10 11

Early GradesShort duration fluency measures.

E.g. Early Magnitude ComparisonMissing Number in a series (strategic

ti ) 7 9 X 10 11counting) e.g.. 7,_9…… X, 10,11Robust Indicators….. But only for one year.For long term prediction: working memory, PA measures show promise (E.g. reverse digit span)…

counting) e.g.. 7,_9…… X, 10,11Robust Indicators….. But only for one year.For long term prediction: working memory, PA measures show promise (E.g. reverse digit span)…

4 1 5 11 9 4

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Example: Number Knowledge Test

Level 1If you had 4 chocolates and someone gave you 3 more, how many chocolates would you have?

Level 1If you had 4 chocolates and someone gave you 3 more, how many chocolates would you have?Which is bigger: 5 or 4?

Level 3What number comes 9 after 999?Which difference is smaller: the difference between 48 and 36 or the difference between 84 and 73?

Which is bigger: 5 or 4?Level 3

What number comes 9 after 999?Which difference is smaller: the difference between 48 and 36 or the difference between 84 and 73?

Upper Grades Screening

Algebra measuresDesigned by Foegen and colleagues assess pre-algebra and basic algebra skills. Administered and scored similar to Math-CBM

Algebra measuresDesigned by Foegen and colleagues assess pre-algebra and basic algebra skills. Administered and scored similar to Math-CBM

Math CBM Computation and Concepts and Applications

Concepts and Applications showed greater valdity in 6th, 7th, and 8th grade

Math CBM Computation and Concepts and Applications

Concepts and Applications showed greater valdity in 6th, 7th, and 8th grade

Core curriculumNational Math Panel

Need to develop understanding and mastery ofWhole number: understand place value, compose/decompose numbers, meaning of operations, algorithms and automaticity with facts, apply to problem solving, use/knowledge of commutative, associative, and distributive properties,

National Math PanelNeed to develop understanding and mastery of

Whole number: understand place value, compose/decompose numbers, meaning of operations, algorithms and automaticity with facts, apply to problem solving, use/knowledge of commutative, associative, and distributive properties, p p ,Rational number: locate +/- fractions on number line, represent/compare fractions, decimals percents, sums, differences products and quotients of fractions are fractions, understand relationship between fractions, decimals, and percents, understand fractions as rates, proportionality, and probability, computational facilityCritical aspects of geometry and measurement:similar triangles, slope of straight line/linear functions, analyze properties of two and three dimensional shapes and determine perimeter, area, volume, and surface area

p p ,Rational number: locate +/- fractions on number line, represent/compare fractions, decimals percents, sums, differences products and quotients of fractions are fractions, understand relationship between fractions, decimals, and percents, understand fractions as rates, proportionality, and probability, computational facilityCritical aspects of geometry and measurement:similar triangles, slope of straight line/linear functions, analyze properties of two and three dimensional shapes and determine perimeter, area, volume, and surface area

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Less is More

US curricula tend to cover more topics with less depth resulting in persistent review across grades versus closure after exposure, development and refinement.

US curricula tend to cover more topics with less depth resulting in persistent review across grades versus closure after exposure, development and refinement.

NCTM Focal PointsEmphasize critical topics at each grade level

(e.g. 2nd grade)Still contains more non-arithmetic coverage than TIMSS

NCTM Focal PointsEmphasize critical topics at each grade level

(e.g. 2nd grade)Still contains more non-arithmetic coverage than TIMSS

Example Tier 1 intervention: VanDerHayden et al. (STEEP)

Entire class is screened on a computation probeIf class is below criterion established by Deno, then entire class receives Tier 1 intervention (i.e. practice in computation and facts for 30 min

Entire class is screened on a computation probeIf class is below criterion established by Deno, then entire class receives Tier 1 intervention (i.e. practice in computation and facts for 30 minpractice in computation and facts for 30 min daily)Students who do not respond to the Tier 1 intervention are provided a similar Tier 2 intervention consisting of peer tutoring on computation problemsLimited scope and duration of the Tier 1 intervention

practice in computation and facts for 30 min daily)Students who do not respond to the Tier 1 intervention are provided a similar Tier 2 intervention consisting of peer tutoring on computation problemsLimited scope and duration of the Tier 1 intervention

Tier 2 and 3 Components

Progress monitoring and diagnostic assessments

Standard protocol interventions

Progress monitoring and diagnostic assessments

Standard protocol interventionsStandard protocol interventions

Instructional design considerations

Standard protocol interventions

Instructional design considerations

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Progress Monitoring Assessments

Progress monitoring measures:Some screening measures have promise as General Outcome Measures but need more research to also be used as progress monitoring measures

Progress monitoring measures:Some screening measures have promise as General Outcome Measures but need more research to also be used as progress monitoring measuresmonitoring measures.Well researched progress monitoring measures are available for grades one and up.These possess weaker criterion-related validity than reading measures. (Foegen et al, in press)

monitoring measures.Well researched progress monitoring measures are available for grades one and up.These possess weaker criterion-related validity than reading measures. (Foegen et al, in press)

Diagnostic Assessments

Deciding when to usePrior to intervention orIf the intervention is not successful

Sources

Deciding when to usePrior to intervention orIf the intervention is not successful

SourcesSourcesCompilation of data from progress monitoringCurriculum-Based Assessment (e.g. Howell)In-depth math specific measure (e.g. TEMA)

SourcesCompilation of data from progress monitoringCurriculum-Based Assessment (e.g. Howell)In-depth math specific measure (e.g. TEMA)

Tier 2/3 (Interventions)

Standard protocol approach

Students maintain in the program for a set duration of time

Standard protocol approach

Students maintain in the program for a set duration of timeduration of time

I.e. Progress monitoring data collected but not used for educational decision-making

Limit scope to critical topicsAvoid low grade dose of the same material and same approach

duration of time I.e. Progress monitoring data collected but not used for educational decision-making

Limit scope to critical topicsAvoid low grade dose of the same material and same approach

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Intervention Content

Wu and Milgram (CA standards) for at-risk 4th to 7th grade studentsRecommend 2 hours of instruction per dayTaught by teacher with content knowledge expertise

Wu and Milgram (CA standards) for at-risk 4th to 7th grade studentsRecommend 2 hours of instruction per dayTaught by teacher with content knowledge expertiseexpertiseTopics

Place Value and Basic Number Skills (1st-3rd grade skills)Fractions and DecimalsRatios, Rates, Percents, and ProportionsThe Core Processes of MathematicsFunctions and EquationsMeasurement

expertiseTopics

Place Value and Basic Number Skills (1st-3rd grade skills)Fractions and DecimalsRatios, Rates, Percents, and ProportionsThe Core Processes of MathematicsFunctions and EquationsMeasurement

Example: Fuchs 1st Grade Small Group Tutoring

41 1st-grade teachers in 6 Title 1 and 4 non-Title 1 schools (92% consented students)Conducted weekly CBM ComputationAR: Using Week 4 CBM Computation, 139 lowest performing (21% of 667 consented students); randomly assigned to control or tutoring

41 1st-grade teachers in 6 Title 1 and 4 non-Title 1 schools (92% consented students)Conducted weekly CBM ComputationAR: Using Week 4 CBM Computation, 139 lowest performing (21% of 667 consented students); randomly assigned to control or tutoringgNAR: 528 remaining students with consent Of 528 NAR:

All weekly CBM Computation180 sampled for individual and group pre/posttesting 348 group pre/posttested

With attrition, samples sizes of:127 AR: 63 control + 64 tutored 437 NAR: 145 individually/group tested + 292 group tested

gNAR: 528 remaining students with consent Of 528 NAR:

All weekly CBM Computation180 sampled for individual and group pre/posttesting 348 group pre/posttested

With attrition, samples sizes of:127 AR: 63 control + 64 tutored 437 NAR: 145 individually/group tested + 292 group tested

Tutoring

Small groups (11 groups of two students and 16 groups of three students)3 times per week outside classrooms

Small groups (11 groups of two students and 16 groups of three students)3 times per week outside classrooms3 times per week outside classrooms Each session:

30 min of tutor-led instruction10 min of student use of practice to improve automatic retrieval of math facts

3 times per week outside classrooms Each session:

30 min of tutor-led instruction10 min of student use of practice to improve automatic retrieval of math facts

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Tutor-Led Instruction

Concrete-representational-abstract model, which relies on concrete objects to promote conceptual understanding (e g

Concrete-representational-abstract model, which relies on concrete objects to promote conceptual understanding (e gpromote conceptual understanding (e.g., base-10 blocks for place value instruction)17 scripted topics addressing number concepts, numeration, computation, story problems (e.g., not geometry, measurement, charts/figures, money)

promote conceptual understanding (e.g., base-10 blocks for place value instruction)17 scripted topics addressing number concepts, numeration, computation, story problems (e.g., not geometry, measurement, charts/figures, money)

Flash Card Activity

Final 10 minutes of each session devoted to practice to improve retrieval of math factsStudents individually presented basic

Final 10 minutes of each session devoted to practice to improve retrieval of math factsStudents individually presented basicStudents individually presented basic addition and subtraction problems and earn points for correct answersStudents receive additional practice for incorrect answers

Students individually presented basic addition and subtraction problems and earn points for correct answersStudents receive additional practice for incorrect answers

17 Scripted TopicsIdentifying and Writing NumbersIdentifying More & Less Objects Sequencing NumbersUsing <, >, and = Skip Counting by 10s, 5s, and 2sIntroduction to Place Value Place Value Identifying Operations

Identifying and Writing NumbersIdentifying More & Less Objects Sequencing NumbersUsing <, >, and = Skip Counting by 10s, 5s, and 2sIntroduction to Place Value Place Value Identifying OperationsIdentifying OperationsWriting Addition and Subtraction SentencesPlace ValueAddition FactsSubtraction FactsAddition and Subtraction Facts ReviewPlace Value Review2-Digit Addition 2-Digit Subtraction Missing Addends

Identifying OperationsWriting Addition and Subtraction SentencesPlace ValueAddition FactsSubtraction FactsAddition and Subtraction Facts ReviewPlace Value Review2-Digit Addition 2-Digit Subtraction Missing Addends

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Tutoring Efficacy

ImprovementWeekly CBM Computation Slope

AR tutored = NAR > AR control WJ III Calculation

AR t t d > NAR d AR

ImprovementWeekly CBM Computation Slope

AR tutored = NAR > AR control WJ III Calculation

AR t t d > NAR d ARAR tutored > NAR and AR Grade 1 Concepts/Applications

AR tutored > NAR and AR control Story Problems

NAR > AR tutored > AR control

First-grade tutoring enhances outcomes.

AR tutored > NAR and AR Grade 1 Concepts/Applications

AR tutored > NAR and AR control Story Problems

NAR > AR tutored > AR control

First-grade tutoring enhances outcomes.

Tutoring Efficacy

Did tutoring decrease MD prevalence at end of 1st grade?

Yes, across identification options, tutoring substantially decreased prevalence.Example

Did tutoring decrease MD prevalence at end of 1st grade?

Yes, across identification options, tutoring substantially decreased prevalence.ExampleExample

Final Low Achievement (<10th percentile) on Gr 1 Concepts/Applications, prevalence went from 9.75% without tutoring to 5.14% with tutoring.

~ 2.5 million fewer children identified MDAt end of 2nd grade, MD prevalence was still twice as high in the untutored group.

ExampleFinal Low Achievement (<10th percentile) on

Gr 1 Concepts/Applications, prevalence went from 9.75% without tutoring to 5.14% with tutoring.

~ 2.5 million fewer children identified MDAt end of 2nd grade, MD prevalence was still twice as high in the untutored group.

Tier 2/3 Instructional Design Previous Syntheses on mathematics interventions

Not LD specific (Xin & Jitendra, 1999; Kroesbergen & Van Luit, 2003; Baker, Gersten, & Lee, 2002)Organized on basis of dependent measure (Swanson, Hoskyn, & Lee, 1999)

Fuchs, Fuchs, Mathes, and Lipsey (2002) meta-analysis in reading: LD vs Low Achieving students

Previous Syntheses on mathematics interventionsNot LD specific (Xin & Jitendra, 1999; Kroesbergen & Van Luit, 2003; Baker, Gersten, & Lee, 2002)Organized on basis of dependent measure (Swanson, Hoskyn, & Lee, 1999)

Fuchs, Fuchs, Mathes, and Lipsey (2002) meta-analysis in reading: LD vs Low Achieving studentsanalysis in reading: LD vs. Low Achieving students

LD lower performing than low achieving (d = .61)Discrepancy between LD and low achieving greater on timed vs. untimed measures -- (automaticity / speed of processing implications)LD vs. low achieving differences were greater when LD determinations based on objective measures vs. more subjective approaches (e.g., team decision making)

analysis in reading: LD vs. Low Achieving studentsLD lower performing than low achieving (d = .61)Discrepancy between LD and low achieving greater on timed vs. untimed measures -- (automaticity / speed of processing implications)LD vs. low achieving differences were greater when LD determinations based on objective measures vs. more subjective approaches (e.g., team decision making)

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Purpose

To synthesize experimental and quasi-experimental research on instructional approaches that enhance the mathematics performance of students with learning

To synthesize experimental and quasi-experimental research on instructional approaches that enhance the mathematics performance of students with learningperformance of students with learning disabilities performance of students with learning disabilities

Method

Review of all published studies and dissertations between 1970 and 2003

Conduct meta analysis to identify trends in

Review of all published studies and dissertations between 1970 and 2003

Conduct meta analysis to identify trends inConduct meta-analysis to identify trends in the literatureConduct meta-analysis to identify trends in the literature

FindingsN of studies in meta-analysis: 38N Intervention Categories: 8

3 clusters of studiesN of Effect Sizes: 59Range of Effect Sizes per category: 4 to 10

N of studies in meta-analysis: 38N Intervention Categories: 8

3 clusters of studiesN of Effect Sizes: 59Range of Effect Sizes per category: 4 to 10Range of Effect Sizes per category: 4 to 10

Effect size range: –0.43 to 2.96Average Unweighted ES: –0.11 to 1.62Average Weighted ES: –0.04 to 1.53

Range of Effect Sizes per category: 4 to 10

Effect size range: –0.43 to 2.96Average Unweighted ES: –0.11 to 1.62Average Weighted ES: –0.04 to 1.53

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Intervention Categories

Feedback to Teachers: N ES = 10 Feedback to students: N ES = 9 Visuals N ES = 9

(including graphic organizers and pictures)

Explicit Instruction: N ES 9

Feedback to Teachers: N ES = 10 Feedback to students: N ES = 9 Visuals N ES = 9

(including graphic organizers and pictures)

Explicit Instruction: N ES 9Explicit Instruction: N ES = 9 Student Verbalizations: N ES = 5Range and sequence of examples N ES = 5Peer Assisted Instruction: N ES = 7Computer Assisted Instruction: N ES = 5

Explicit Instruction: N ES = 9 Student Verbalizations: N ES = 5Range and sequence of examples N ES = 5Peer Assisted Instruction: N ES = 7Computer Assisted Instruction: N ES = 5

Providing Feedback to Teachers

Feedback provided to teachers on the status of student learning resulted in small effects

(10 ESs; d = .31*; range = –0.06 to 0.71)

F db k id d i l d ifi

Feedback provided to teachers on the status of student learning resulted in small effects

(10 ESs; d = .31*; range = –0.06 to 0.71)

F db k id d i l d ifiFeedback provided includes specific information (e.g., instructional recommendations) along with feedback on student performance

(5 ESs; d = .29*; range = –0.06 to 0.71)

Feedback provided includes specific information (e.g., instructional recommendations) along with feedback on student performance

(5 ESs; d = .29*; range = –0.06 to 0.71)

Providing Feedback to Students about their Performance

Overall: Providing students with feedback about their performance

9 ESs; d = 0.21*; range = –0.43 to 0.64f

Overall: Providing students with feedback about their performance

9 ESs; d = 0.21*; range = –0.43 to 0.64fWithout specific goals

5 ESs; d = 0.33*; range = 0.04 to 0.64With specific goals

4 ESs; d = –0.18; range = –0.43 to 0.11

Without specific goals5 ESs; d = 0.33*; range = 0.04 to 0.64

With specific goals4 ESs; d = –0.18; range = –0.43 to 0.11

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Use of VisualsStudent use graphic representations to clarify or solve problems resulted in moderate effect sizes

5 ESs; d = .56*; range = 0.32 to1.5

Student use graphic representations to clarify or solve problems resulted in moderate effect sizes

5 ESs; d = .56*; range = 0.32 to1.5

Teachers using pictures or diagrams to explain how to solve a problem resulted in moderate effects

4 ESs; d = .55*; range = –0.38 to 1.15)

Teachers using pictures or diagrams to explain how to solve a problem resulted in moderate effects

4 ESs; d = .55*; range = –0.38 to 1.15)

Use of Visuals

Teacher had to use the visual representation during her initial teaching/demonstration ORStudents had to use visuals while solving the

bl

Teacher had to use the visual representation during her initial teaching/demonstration ORStudents had to use visuals while solving the

blproblem Could not be an optional stepVisuals were used in solving 1-2 step arithmetic story problems

problem Could not be an optional stepVisuals were used in solving 1-2 step arithmetic story problems

Explicit InstructionExplicit instruction used to teach a single skill resulted in large effects

4 ESs; d = 1.72*; range = 0.88 to 2.49

Explicit instruction used to teach multiple

Explicit instruction used to teach a single skill resulted in large effects

4 ESs; d = 1.72*; range = 0.88 to 2.49

Explicit instruction used to teach multipleExplicit instruction used to teach multiple related skills resulted in equally large effects

5 ESs; d = 1.53*; range = 0.61 to 2.96

Explicit instruction used to teach multiple related skills resulted in equally large effects

5 ESs; d = 1.53*; range = 0.61 to 2.96

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Explicit Instruction

Teacher demonstrated a step-by-step plan (strategy) for solving the problem This step-by-step plan had to be problem-specific and not just a generic, heuristic guide for

Teacher demonstrated a step-by-step plan (strategy) for solving the problem This step-by-step plan had to be problem-specific and not just a generic, heuristic guide for solving problemsStudents had to use the same procedure/steps shown by the teacher to solve the problem

solving problemsStudents had to use the same procedure/steps shown by the teacher to solve the problem

Student VerbalizationsStudent use of verbalizations while solving problems resulted in large effects

5 ESs; d = 1.25*; range = 0.23 to 2.49

In all studies students verbalized the solution while

Student use of verbalizations while solving problems resulted in large effects

5 ESs; d = 1.25*; range = 0.23 to 2.49

In all studies students verbalized the solution while solving problemsIn all but 1 study, focus was narrow -- e.g., single digit addition/subtraction; 1-2 step arithmetic story problems involving addition/subtraction

Students did not have to verbalize a range of solutionsIn most complex verbalization study -- ES = 0.23

solving problemsIn all but 1 study, focus was narrow -- e.g., single digit addition/subtraction; 1-2 step arithmetic story problems involving addition/subtraction

Students did not have to verbalize a range of solutionsIn most complex verbalization study -- ES = 0.23

Range and Sequence of Examples

Controlled range and sequence of instructional examples (e.g., Concrete –Representational – Abstract) resulted in moderate effects

5 ESs; d = 53*; range = 12 to 1 15

Controlled range and sequence of instructional examples (e.g., Concrete –Representational – Abstract) resulted in moderate effects

5 ESs; d = 53*; range = 12 to 1 155 ESs; d = .53 ; range = .12 to 1.155 ESs; d = .53 ; range = .12 to 1.15

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Peer Assisted Learning

Use of same age and cross age peers for learning and extended practice of math content resulted in moderate effects

7 ESs; d = 0.42*; range = –0.27 to 1.19

Use of same age and cross age peers for learning and extended practice of math content resulted in moderate effects

7 ESs; d = 0.42*; range = –0.27 to 1.19

Computer Assisted Instruction

Student use of computers for activities, games, and practice in mathematics resulted in no effect

5 ESs (3 studies); d = –0.04; range = –0.60 to 0 15)

Student use of computers for activities, games, and practice in mathematics resulted in no effect

5 ESs (3 studies); d = –0.04; range = –0.60 to 0 15)0.15)0.15)

LD Vs. Low Achieving Baker, Gersten, & Lee (2002)

Independent VariableCategory

Low Achieve ES

LD ES

Feedback to Teachers 0.66 0.31Feedback to Teachers 0.66 0.31

Feedback to Students 0.51 0.21

Explicit Instruction 0.58 1.53

Peer Assisted 0.66 0.42

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SummaryResults of this meta-analysis suggest that students with learning disabilities benefit from:

Curricula that employ explicit instruction, include a range of examples that are sequenced from concrete to abstract;

Results of this meta-analysis suggest that students with learning disabilities benefit from:

Curricula that employ explicit instruction, include a range of examples that are sequenced from concrete to abstract;Student Verbalization and use of visuals for problem solving;Teacher instruction that uses visuals to demonstrate problem solvingPeer assisted learning particularly for extended practice

Student Verbalization and use of visuals for problem solving;Teacher instruction that uses visuals to demonstrate problem solvingPeer assisted learning particularly for extended practice

Final thoughtsRTI for identification is only possible if tiered support and corresponding elements are in place

Professional Development is critical in enhancing both the teaching of mathematics and data-based instructional decision-making

RTI for identification is only possible if tiered support and corresponding elements are in place

Professional Development is critical in enhancing both the teaching of mathematics and data-based instructional decision-makingg

Districts and schools should think of developing math specialists similar to reading specialists

Our understanding of how best to teach and assess mathematics is rapidly expanding - Stay connected and be flexible in your approach to supporting mathematics achievement

g

Districts and schools should think of developing math specialists similar to reading specialists

Our understanding of how best to teach and assess mathematics is rapidly expanding - Stay connected and be flexible in your approach to supporting mathematics achievement

ResourcesNMAP

http://www.ed.gov/about/bdscomm/list/mathpanel/index.htmlCenter On Instruction - Mathematics

http://www.centeroninstruction.org/resources.cfm?category=math

NCTM focal points

NMAPhttp://www.ed.gov/about/bdscomm/list/mathpanel/index.html

Center On Instruction - Mathematicshttp://www.centeroninstruction.org/resources.cfm?category=math

NCTM focal pointshttp://www.nctm.org/focalpoints.aspx?linkidentifier=id&amp;itemid=270

PIR website (Best Practices/Articles)http://pacificir2.uoregon.edu:8100/

National Center Progress Monitoringhttp://www.studentprogress.org/

CA Intervention Standardshttp://www.cde.ca.gov/ci/ma/im/mathprogramnov2007.asp

http://www.nctm.org/focalpoints.aspx?linkidentifier=id&amp;itemid=270

PIR website (Best Practices/Articles)http://pacificir2.uoregon.edu:8100/

National Center Progress Monitoringhttp://www.studentprogress.org/

CA Intervention Standardshttp://www.cde.ca.gov/ci/ma/im/mathprogramnov2007.asp