Response to Intervention An Alignment Guide for Fraction Nation · 2015-11-17 · 4 Fraction Nation Overview FractionNation is an intervention program designed to support students

Response to InterventionAn Alignment Guide for

Fraction Nation

PROFESSIONAL PAPER

Scholastic Inc. has prepared this Alignment Guide to assist Local EducationAgencies (LEAs) and schools that are currently implementing or are consideringadopting a Response to Intervention (RTI) approach. This guide provides key

background information on current educational policy related to RTI, and demonstrateshow Fraction Nation can complement and strengthen the implementation of RTI andultimately raise student achievement. This Alignment Guide provides the followinginformation:

� Response to Intervention Overview

� Fraction Nation Overview

� Alignment of Fraction Nation to RTI Core Components

Fraction Nation is a research-based math intervention program that supports students in4th through 8th grades and above to develop a conceptual understanding and proceduralknowledge of fractions and decimals — two of the most difficult concepts to teach andlearn. With explicit instruction and guided practice, the program teaches studentsfraction and decimal quantity concepts, equivalence, and addition and subtraction.Fraction Nation:

• Is grounded in research-based principles that drive fraction instruction and deliverfraction fluency.

• Focuses and individualizes instruction with an adaptive structure that allows eachstudent to work at his or her own pace and gradually releases instruction to meeteach student’s needs.

• Provides ongoing assessments to track student performance and actionable reportsto help teachers to identify those students in need of additional support.

• Offers essential resources and supplementary materials for teachers to monitor,teach, and intervene to meet all students’ varied needs.

Using the Alignment Guide

Since January 2006, districts are permitted to use up to 15 percent of their Individualswith Disabilities Education Act (IDEA) funds for interventions and measurements to beused within the RTI framework. This Alignment Guide addresses how Fraction Nationsupports the implementation of RTI. For questions regarding Response to Interventionservices, please consult the final IDEA, Part B regulations governing the Assistance toStates for Education of Children with Disabilities Program and the Preschool Grantsfor Children with Disabilities Program. They are found at http://idea.ed.gov/explore/home

The Alignment Guide is informed by the IDEA 2004 Regulations, the National Association of State Directorsof Education (NASDSE) 2005 Report, guidelines provided from the Vaughn Gross Center for Reading andLanguage Arts at the University of Texas at Austin, and consultation with Dr. Joe Witt, author of theiSTEEP model on the core principles and practical implementation of RTI in schools.

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Contents

Response to Intervention (RTI) Overview ..............................................................................................2What Is RTI?..................................................................................................................................2The Multitiered Intervention Model..............................................................................................2

Core Components of RTI ....................................................................................................................3

Fraction Nation Overview ....................................................................................................................4

Fraction Nation Aligns to RTI Core Components................................................................................51) A Multitiered Intervention Model ............................................................................................52) Universal Screening ....................................................................................................................73) Scientifically Validated and Research-based Interventions ........................................................84) Frequent Monitoring of Student Progress ..............................................................................105) Data-based Decision Making ..................................................................................................116) Supplemental Instructional Materials ......................................................................................137) Professional Development ........................................................................................................148) Coordinated Funding ..............................................................................................................15

Summary ............................................................................................................................................16

References ..........................................................................................................................................17

About Scholastic Inc.

Scholastic is committed to providing teachers with effective materials for every stage of instruction to ensure

that students develop the skills and strategies needed to succeed in school. Our reputation is built on an 85-

year history of helping foster and support effective learning for all students. For years, we have worked with

leading researchers to develop scientifically based products that improve student achievement, as well as

meaningful changes in teacher effectiveness.

We look forward to partnering with you to improve math achievement, and would welcome the opportunity

to talk with you about how we can best support your efforts to implement Response to Intervention.

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BackgroundThe reauthorization of the Individuals with Disabilities Education Act (IDEA 2004) changedthe way students are evaluated for special services by encouraging schools to use research-basedinterventions to address diverse students’ needs early on.

What Is RTI?Response to Intervention (RTI) is not a particular program, curriculum, or model. Rather, it is aframework for allocating instructional services that are aligned to students’ individual needs. Itaims to prevent unnecessary assignments to special education through the provision of tiers ofintervention and continuous progress monitoring.

RTI includes:

� Providing tiers of increasingly intensive, research-based intervention matched to students’ needs� Measuring and continually monitoring students’ progress over time� Using resulting data to drive educational decision making

The purpose of RTI is:

� To focus on prevention and early identification of students in need of special services� To better integrate services between the general and special education population

The Multitiered Intervention ModelRTI uses a multitiered model of service delivery to promote efficient response to students’ needs.Each tier provides increasingly intense support structures to ensure that students succeed.

Tier 1: Core Instructional Interventions� General curricula for all students� Proactive interventions based on instructional variables within whole-group instruction

Tier 2: Targeted Group Interventions� Supplemental instruction for students who are not successful in Tier 1� Targeted interventions oriented towards small-group instruction� Explicit instruction, rapid response

Tier 3: Intensive, Individual Interventions� Individualized instruction for students who are not successful in Tier 2� Intensive interventions oriented towards individual students� Diagnostic assessments to determine student need� Higher intensity, longer duration

Response to Intervention (RTI) Overview

Tier 3Intensive

Tier 2Targeted

Tier 1Core

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Core Components of RTI1. A Multitiered Intervention Model

Multiple tiers of intervention allow schools to offer increasingly intense interventions tothose students who are not making adequate progress in the core curriculum (Tier 1).Interventions in Tiers 2 and 3 may be intensified by increasing instructional time,decreasing group size, using materials matched to students’ instructional levels, modifyingmodes of presentation, and providing regular corrective feedback.

2. Universal ScreeningAll students should be screened three times a year to identify those students who are notmaking expected academic progress. Screening measures should be brief, reliable and valid,and appropriately identify those students who require more intense interventions.

3. Scientifically Validated and Research-based InterventionsIDEA 2004 and No Child Left Behind (NCLB) require that interventions be research-based. Interventions should be based on research-based practices and validated by scientificstudies.

4. Frequent Monitoring of Student ProgressThe progress of students receiving interventions must be monitored frequently in orderto determine whether the interventions are producing the desired academic gains. Theprogress monitoring measures should be brief, target specific skills, be administered easily,and be accompanied by decisions to inform instruction.

5. Data-based Decision MakingIn all tiers of intervention, data from screening and progress monitoring measures shouldbe used to make educational decisions for individual students.

6. Professional DevelopmentA high-quality professional development plan should be used to support teachersimplementing RTI. The plan should allow for coaching, e-learning courses, and otheropportunities.

7. Supplemental Instructional MaterialsThe use of supplemental materials, where appropriate, strengthens the efficacy of thecomprehensive core curriculum and supports student learning in Tier 1.

8. Coordinated FundingComponents of RTI funded by IDEA may be coordinated with activities funded by,and carried out under, the Elementary and Secondary Education Act (ESEA).

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Fraction Nation Overview

Fraction Nation is an intervention program designed to support students in 4th through 8thgrades and above to develop the critical foundations of fraction fluency. Through the use ofadaptive computer-based instruction and ongoing assessments, students gain a conceptualunderstanding and procedural knowledge of fractions and decimals. The research-basedFraction Nation offers explicit instruction with an adaptive structure that allows individualstudents to work at their own pace and gradually releases instruction to meet every student’sneeds.

The National Mathematics Advisory Panel concluded in 2008 that “fluency with fractions” isone of the critical foundations for algebra success. They noted that a strong grounding in alge-bra “correlates powerfully with access to college, graduation from college, and earning in thetop quartile of income from employment.” The panel also stated that students’ performancewith fractions is “severely underdeveloped,” and that students’ difficulties with fractions beginto emerge in elementary school and “persist through middle school, high school, and intoadulthood, extending beyond those with learning disabilities in mathematics” (NMAPLearning Processes Task Group, 2008).

Fraction Nation focuses on the key areas of fraction and decimal quantity, equivalence, andaddition and subtraction to give students a firm foundation in fraction and decimal concepts.Placement and ongoing assessments, adaptive instruction, guided practice, continuous progressmonitoring, and actionable reports work together to assist teachers in meeting all learnersprecisely where they are. For students who are struggling to gain a conceptual understandingand procedural knowledge of fractions and decimals, Fraction Nation offers the lessons,practice, and assessments they need to attain fraction fluency.

Response to Intervention

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The following information outlines how Fraction Nation addresses the Core Components of aResponse to Intervention (RTI) Model.

Fraction Nation Aligns toResponse to Intervention Core Components

Fraction Nation has the capacity to support diverse learners who require any one of the three tiersof service delivery – Tier 1, Tier 2, or Tier 3. The program can be used flexibly by educatorswithin a variety of instructional models that address all three of the tiers.

In Tier 1, students receive core grade-level instruction designed to be preventive and proactive,and ensure that students continue to perform at or above grade level and not fall behind. FractionNation supplements core classroom instruction that teaches grade-level standards for fractionsand decimals by providing students with explicit instruction and supported practice on topicssuch as fraction and decimal quantity, equivalence, and addition and subtraction. Tier 1 studentscan participate independently in 15-minute daily instructional sessions during, before, or afterschool to complete 64 lessons that complement in-class instruction. Teachers also have theoption of utilizing interactive whiteboards to teach the lessons and key concepts within whole orsmall-group settings.

Tier 2 is characterized by targeted interventions for students who are performing at approximatlya year below grade level, or who do not respond to the core instructional interventions in Tier 1.Students’ progress is monitored frequently to adjust instruction according to individual students’needs. As students move through the 64 lessons, they take performance assessments that deter-mine whether they will be promoted to the next lesson and/or topic or guided through additionalinstruction and practice.

When students are identified as needing additional instruction and practice, the software adaptsto provide them with new practice problems and different assessments. The additional practiceaims to address the needs of students who typically lack the conceptual understanding andprocedural knowledge of fractions and decimals, such as rational number comparison, estimation,equivalence, and addition and subtraction. If the student engages in the additional practice andtakes the new assessment and still does not master the content presented in the lesson, he or sheis provisionally promoted to the next lesson. However, the Scholastic Achievement Manager(SAM) alerts teachers so they can immediately offer targeted support. Using the assessmentresults presented on actionable reports, teachers can choose to form small, flexible groups ofstudents in need of help with similar concepts, and provide teacher-directed support using thelesson overviews and resources located in the Fraction Nation Teacher’s Guide.

Tier 3 is comprised of individual students who do not respond to the interventions provided byTiers 1 and/or 2, and/or are performing two or more years below grade level as determined by

A multitiered intervention model with intensity of servicesincreasing as students move up the tiersRTI 1

An Alignment Guide for Fraction Nation

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their level of mastery of state grade-level standards. When students in Tier 2 receive additionalteacher-led, small group support and still are not mastering the content and being provisionallypromoted to the next lesson, teachers can continue to use the lesson overviews and suggestionslocated in the Fraction Nation Teacher’s Guide to work with individual students one-on-one. Theyalso can use the program’s Lesson Review Library, which provides on-demand access to all of theprogram’s 64 lessons and practice sets, to sit down with a student one-on-one to review previouslessons or preview upcoming lessons. Additional modifications that teachers and students canutilize include a glossary of terms, closed captioning on the software, the play-by-play mode, andthe scaffolded supports embedded in the guided practice.

Fraction Nation supports differentiated instruction and addresses the diverse learning needs ofthe students in all three tiers by providing the following built-in supports:

• Adaptive practice to support each student in the specific areas where he orshe is having trouble

• Scaffolded feedback to guide the student to the correct answer during practice

• Access to an instructional animation during a practice so that the student canreview the skill or concept, if needed

• Feedback for incorrect answers during performance assessments to help thestudent understand why the answer was incorrect

• The option to repeat a lesson that a student has not passed and review all ofthe “Learns” previously completed

• The ability to review any previous lesson in the program (Learn and Practiceactivities only)

• Design features embedded in the technology, such as caption text that canbe shown or hidden; playback controls to pause, play, and rewind; progressindicators that help students with self-monitoring; and play-by-play modewhich slows down the pace of instruction

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Fraction Nation presents ongoing opportunities for teachers to identify students who are in needof intervention and continually assess whether and how they are progressing. When students firstlog into the program, they must take a placement assessment that determines their fractionproficiency level and starting point in the program. Their scores indicate whether they shouldstart at the very beginning at Lesson 1, which focuses on unit fractions, or at Lesson 28, whichfocuses on equivalence. Teachers can use the results from the placement assessment to determinestudents’ overall readiness for participating in the program. Some students will require additionalsupport before they can begin to participate in the program; others already may have achievedfluency in fractions.

The placement assessment consists of two parts: 1) a math fact fluency screener that screensstudents’ fluency with addition and multiplication math facts; and, 2) a test designed to evaluatestudents’ facility with fraction and decimal quantity, equivalence, and addition and subtraction.Fluency with math facts – particularly multiplication math facts – is an important skill thatcontributes to gaining an understanding and procedural knowledge of fraction equivalence andoverall fraction proficiency. The screener helps to identify those students who may have difficultywith math fact recall and would benefit from a thorough assessment and additional instruction toattain math fact fluency. The untimed fraction assessment consists of 20 questions and screensstudents’ level of readiness and starting point in the program.

RTI 2Universal screening measures that are brief, reliable, valid,and appropriately identify students for Tier 2 intervention

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Fraction Nation is informed by an extensive body of research on best practices for providingexplicit instruction and meaningful practice to achieve fraction fluency. These best practices andthe research that identifies them include:

Visual representations: Each of the program’s 64 lessons begins with a multimediatutorial that introduces and extends fraction and decimal concepts through the use ofvisual representations, which include fraction strips, number lines, circles, rectangles, andsets. According to research, visual representations can provide a bridge between concreteobjects, real-world experiences, and the highly abstract symbol system of rationalnumbers (National Research Council, 2001). In addition, research has found the use of“visual models or manipulatives” to be especially valuable when teaching “students at riskfor special-education or students with learning disabilities” (Woodward & Brown, 2006)– students who typically qualify for Tiers 2 and 3.

The primary visual representation in Fraction Nation is the number line. Instructionacross many of the different lessons begins concretely with fraction strips and carefullymoves to the more abstract number line to help students see connections betweendifferent types of numbers, including whole numbers and fractions and decimals.Research and expert opinion suggest that a “length model” has several advantages as acentral explanatory model (Milgram & Wu, 2006; Fuson & Kalchman, 2002), and pointto the number line as an effective means for integrating “all the number systems of pre-Kto grade 8 mathematics,” including whole numbers, negative numbers, fractions, anddecimals (National Research Council, 2001).

Worked examples: Worked examples, as defined in the research literature, typicallyinclude “a problem statement and a [step-by-step] procedure for solving the problem;together these are meant to show how other similar problems might be solved”(Atkinson et al., 2000). Each of the 64 lessons in Fraction Nation combines workedexamples with practice to help students to master key skills and strategies. In theinstructional part of each lesson, animations that integrate text, audio, visual images, anddynamic motion demonstrate at least two worked examples for a given objective, and inthe practice activities, students work through three to eight problems within ascaffolded environment that closely follows the instruction. Research has found thatworked examples, when paired with practice problems, are more effective than practicealone (Cooper & Sweller, 1987; Sweller & Cooper, 1985), and have been shown toincrease instructional efficiency and promote flexible transfer in problem solving. Thisinstructional device is particularly effective among students who are in the “initial statesof cognitive skill acquisition” (Atkinson et al., 2000), thus supporting students in all threeTiers (1, 2, and 3) to achieve fraction fluency.

Computation with understanding: The program links visual representations with fractionsymbols and procedures with the goal of promoting the integration of students’conceptual and procedural understanding of fractions and decimals. Among researchers

RTI 3 Scientifically validated and research-based interventions

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and practitioners, “there is a strong consensus that both computational skill andconceptual understanding are important goals of mathematics learning and instruction,and indeed they are interdependent” (Sophian, 2007). Successful curricula emphasize“working with concrete representations of fractions…and connecting them with fractionsymbols…before introducing purely symbolic work” (Sophian, 2007; Cramer et al., 2002;Moss & Case, 1999). The scope and sequence of Fraction Nation gradually releasescontent so that in earlier lessons, students are exposed to visual representations andmodels that support fraction equivalence, and addition and subtraction tasks before theymove to exclusive use of symbolic procedures.

Support for cognitive processing: The program provides an environment that takes intoaccount the cognitive processing demands associated with the development of fractionfluency. This proves crucial, as there is general agreement about the “complexity of theinformation processing entailed in reasoning about fractions” (Sophian, 2007). Throughthe use of adaptive technology, the program avoids cognitive overload because itsequences the presentation of content in digestible steps; limits the number ofrepresentations and definitions; provides targeted instruction, lots of practice, and regularassessments; offers self-pacing for each individual student; and gives real-time feedbackaimed to build confidence and competence. It is especially important for students inTiers 2 and 3 to receive instruction in small, manageable chunks that progressively buildunderstanding through extensive practice.

For more information on the research-based principles that support the approach of FractionNation, see:

• Research Foundation Paper for Fraction Nation (2010). New York: Scholastic Inc.

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Continuous progress monitoring is necessary to determine whether interventions are workingand supporting teachers to differentiate instruction. Each lesson in Fraction Nation ends with aperformance assessment that determines on a lesson-by-lesson basis whether students havemastered the targeted skill or concept presented during the Learn and Practice activities. Thereare different types of performance assessments that measure students’ capabilities in sixfraction and decimal skill categories. They include: estimating quantity, comparing numbers,using different representations, using number lines, expressing equivalence, and solving problemsby adding and subtracting.

Each performance assessment includes two rounds of problems. If a student demonstrates aperfect or near-perfect performance on the first round of problems, the program offers thestudent an option to move on to the next lesson. If, however, a student demonstrates poor per-formance on the first round of problems, the program immediately determines whether the stu-dent should complete another round. Students must achieve a score above 75% to pass alesson and pass all lessons within a topic to be promoted to the next topic. If a student does notpass a lesson, another opportunity to pass it will be presented before moving on to the next topic.

The program tracks students’ performance on all lessons, and determines the sequence of lessonsfor each student. Teachers receive messages on SAM when a student is provisionally promoted,indicating that the student might be in need of additional support on a particular skill orconcept. Teachers also can use one of the many actionable reports available in SAM to identifystudents who are struggling with similar lessons or concepts, and group them for teacher-led,small group instruction that targets their needs.

Use of frequent and brief progress monitoring assessmentswith decision rules that inform instructionRTI 4

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Data-based Decision Making

Fraction Nation supplies a series of actionable reports that present regular information onindividual student, class or group performance, and software usage. Data from the periodicassessments housed on the software are fed into the Scholastic Achievement Manager (SAM).With assistance from SAM, teachers can continuously monitor and assess learning gains forevery student in order to target instruction to meet each student’s needs and identify individualstudents in need of additional intervention.

RTI 5

The reports include:

� The Student Performance Report shows the detailed performance of an individualstudent in current and completed lessons. Individual students’ scores at or below expectedperformance (75%) are flagged. Teachers are alerted when a student receives a provisionalpromotion so they know which students are in need of additional intervention on certainconcepts.

� The Student Mastery Report displays an individual student’s mastery (a score of 75% orabove on performance assessments) of fractions and decimals by skill category. Teacherscan use the report to review the lessons that students have and have not mastered, andthe amount of time that it took them to master each one so they know the skillcategories in which the student needs additional intervention.

� The Student Activity Report presents an individual student’s login times for each daythat he or she participates in the program and the work completed during that time.Teachers can use the report to examine students’ lesson activity during a selected timeperiod to gauge whether students are completing activities within a reasonable amount oftime and whether intervention is required.

� The Placement and Final Assessment Report shows students’ performance on theplacement assessment, which includes a math fact screener, and the final assessment.Teachers can use this report quarterly to review the overall progress on the program for aclass or group of students, and/or individual students. Results on the Math Fact Screeneridentify students in need of intervention.

� The Progress Report summarizes student performance data for a class or group ofstudents. Teachers can use this report every month to review students’ status, usage, andcumulative performance by skill category, and identify those students who may bestruggling with a particular skill category and/or not using the software adequately. Theycan then use the Student Performance and Mastery reports for more detailedinformation about an individual student’s performance.

reports continued on following page

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� The Response to Intervention Report indicates the mastery of a class or group ofstudents (a score of 75% or above on performance assessments) on the lessons in theprogram, and the amount of time each student has spent in the program. Teachers canuse this report to monitor and compare students over time by using the Median RTI asa benchmark for each student’s mastery relative to his or her peers, and identify thosestudents whose progress is slow and consistently below the Median RTI in order toprovide them with additional instruction and practice.

� The Fraction Proficiency Growth Report graphs the proficiency levels of the totalnumber of students enrolled in the program according to their performance on theplacement and final assessments. Teachers can use this report to monitor the overallgrowth of students who have completed the program, and identify those students who,after participating in the program, remain in need of intervention.

� The Program Usage Report provides data on how each school or grade is using theprogram. Administrators can use the report quarterly to review the percentages andactual numbers of students by school or grade who have taken the placement assessmentonly, are in progress, or have completed the program.

PROGRESSMONITORING

Progress Report

CLASS: PARKER MATH 1

School: Lincoln Middle School

Teacher: Margaret Parker

Grade: 6

Time Period: 09/10/10 - 01/03/11

™

Using This Report

Purpose: Run this report every month for a progress monitoring overview of

all students’ status, usage, and cumulative performance.

Follow-up: Use this report to identify students who may be struggling with

a particular topic and/or not using the software adequately. Review individual

Student Performance Reports for underperforming students.

Copyright © Scholastic Inc. All rights reserved.

STATUSAVERAGE SCORE BY SKILL CATEGORY

STUDENT NAME LESS

ON

ENTR

Y

CU

RR

ENT

LESS

ON

LESS

ON

SR

EMAI

NIN

G

TOTA

LN

UM

BER

OF

SESS

ION

STO

DAT

E

ESTI

MAT

ING

QU

ANTI

TY

CO

MPA

RIN

G

NU

MBE

RS

USI

NG

DIF

FER

ENT

REP

RES

ENTA

TIO

NS

USI

NG

NU

MBE

RLI

NES

EXPR

ESSI

NG

EQU

IVAL

ENC

E

ADD

ING

AND

SUBT

RAC

TIN

G

Bravo, Carol

Clark, Leslie

Cordova, Anna

Estes, Matthew

Flores, Tania

Haley, Eric

Hughes, Marc

Jensen, Nick

McGuire, Maggie

Simpson, Curtis

Williams, Alyson

Vitkova, Iana

L1

L1

L28

L1

L1

L1

L1

L1

L1

L1

L1

L1

DONE

L51

DONE

L57

DONE

L46

DONE

L55

L15

DONE

L52

DONE

0

14

0

8

0

19

0

10

50

0

13

0

60

66

36

52

34

55

69

59

29

59

56

68

94%

85%

91%

77%

100%

60%

90%

90%

63%

80%

94%

96%

89%

95%

93%

76%

100%

85%

85%

92%

61%

81%

85%

91%

92%

81%

85%

76%

100%

65%

88%

86%

66%

76%

77%

93%

100%

83%

83%

76%

100%

81%

92%

91%

N/A

76%

89%

94%

80%

77%

95%

51%

94%

80%

83%

88%

N/A

70%

86%

89%

91%

N/A

90%

59%

92%

N/A

86%

89%

N/A

76%

N/A

90%

Indicates lower than expected performance at or below 75%, which may require teacher attention.

PROGRESSMONITORING

Fraction Proficiency Growth ReportSCHOOL: LINCOLN MIDDLE SCHOOL

Time Period: 09/10/09 - 03/30/10

Total Students Enrolled in Program: 50Total Students with Completed Placement Assessment: 45Total Students with Completed Final Assessment: 40

™

Using This ReportPurpose: Use this report to review the proficiency of students enrolled in theprogram, as measured at the placement assessment and final assessment.Follow-up: Monitor the overall growth in proficiency of students who havecompleted the program.


FRACTION PROFICIENCY LEVEL

%O

FS

TU

DE

NT

S(N

UM

BE

RO

FS

TU

DE

NT

S)

Underperforming

100%

90%

80%

70%

60%

50%

40%

30%

20%

10%

0%

Developing Near Fluent Fluent

25%(10)

12%(5)

38%(15)

25%(10)

25%(10)

25%(10)

12%(5)

38%(15)

Placement Assessment Final AssessmentFraction proficiency scores:Underperforming 0-60% Developing 61-80% Near Fluent 81-94% Fluent 95-100%


PROGRESSMONITORING

Response to Intervention Report

CLASS: PARKER MATH 1School: Lincoln Middle School

Teacher: Margaret ParkerGrade: 6

Time Period: 09/10/10 - 01/03/11

™

Using This ReportPurpose: Use this report to monitor and compare your students’ response

to the program intervention over time. Use the Median RTI as a benchmark

for each student’s mastery relative to his/her peers. Mastery is credited for

performance scores above 75%.

Follow-up: Provide teacher-led instruction and provide additional practice

for students whose progress is slow, who haven’t had adequate time on the

software, or whose mastery is consistently below the Median RTI.


STUDENT NAME

AVERAGE SCORE TO DATE

TOTALTIME(MIN.)LESSONSNOTMASTERED

LESSONSREMAINING(64 TOTAL)

PROGRAMSTART DATE

AVERAGETIME PERLESSON(MIN.)

LESSONSMASTEREDTO DATE(64 TOTAL)

MEDIAN RESPONSETO INTERVENTION

Bravo, CarolClark, Leslie

Cordova, AnnaEstes, Matthew

Flores, TaniaHaley, Eric

Hughes, MarcJensen, Nick

McGuire, MaggieSimpson, Curtis

Williams, AlysonVitkova, Iana

09/15/10

09/10/10

09/10/10

10/01/10

09/10/10

09/10/10

09/15/10

09/15/10

09/10/10

09/10/10

10/01/10

09/10/10

720

1320

468

884

442

935

1104

944

638

708

714

1020

802

12

20

13

17

13

17

16

16

22

12

14

15

16

64

50

64

51

64

37

64

54

4

60

48

64

57

0

0

0

6

0

8

0

0

10

4

3

0

0

0

14

0

7

0

19

0

10

50

0

13

0

4

91%

84%

90%

65%

95%

74%

86%

89%

63%

77%

86%

92%

86%

Indicates mastery credit from placement assessment.

*

*

*

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The Fraction Nation Teacher’s Guide provides supplemental resources designed to complement andstrengthen the software instruction. These include:

� Fraction Nation Lesson Overviews: Provides comprehensive overviews of each ofthe 64 lessons in the program to support teachers in conducting teacher-led interventionfor those students who are in need of extra help. In addition to a description of theLearn, Practice, and Perform parts of a lesson, each overview includes the summary andobjective of the lesson, suggestions for activating prior knowledge, highlightedvocabulary, specific tips for teachers to correct and re-direct, and ways to extend students’understanding of the content. Suggestions for extension include ways for students to talk,write, and think about the concepts presented in each lesson and aim to address theneeds of students in all three tiers.

� Further Reinforcement: Gives recommendations for further reinforcement at the end ofeach topic that include instructions for hands-on activities, as well as for small-group andindividual instruction using the Lesson Review Library.

� Scenarios for Students Needing Support: Presents four distinct scenarios centered onindividual students who are performing at different levels and exhibiting various issues.Outlines steps that teachers can implement and resources they can use to address a rangeof students’ diverse needs.

� Suggestions for Organizing Students for Teacher-Directed Intervention: Offers suggestionsfor how teachers can provide teacher-directed intervention within individual and small-group instruction settings to support students who are not showing progress or meetingperformance benchmarks.

� Additional Resources: Include a comprehensive glossary of terms, reproducibles oflabeled and unlabeled fraction strips, and letters that describe the program and explain itsaim to parents in English and in Spanish.

Supplemental instructional materials, where appropriate, tostrengthen the efficacy of a comprehensive core curriculumand support student learning

RTI 6

Fraction Nation Teacher’s Guide Fraction Nation Lesson Review Library


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A strong professional development plan to supportteachers implementing RTI

Fraction Nation offers a customizable training and professional development plan to ensureeffectiveness of the program. It includes:

Implementation Trainings that teach teachers how to:� Integrate Fraction Nation into existing mathematics curriculum.� Implement Fraction Nation effectively to provide instruction and practice on a daily basis.� Assess student’s progress using Fraction Nation and the program’s management system(Scholastic Achievement Manager).

Administrator Trainings that teach school and district leaders how to:� Monitor and assess fidelity of Fraction Nation implementation.� Monitor and communicate student progress within the school, district, and home.� Modify program use as needed based on student outcomes and teacher knowledge.� Support teachers who are using Fraction Nation.

The program also presents a variety of professional development solutions, which include teacherguides, workshops, and professional papers. They are:

� Fraction Nation Teacher’s Guide provides strategies for effectively implementing theprogram and the assessments, and using the software-generated reports to monitorand manage student progress.

� Research Foundation Paper for Fraction Nation presents the essential research-basedprinciples underlying the development of the program.

� Fraction Nation specialized professional development workshops address:� Fraction Nation Leadership Training� In-Classroom Support for Integrating Technology into Your Curriculum

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IDEA RTI funding in coordination with activities funded by,and carried out under, the ESEA

Fraction Nation can be integrated with funds from states, local districts, private foundations,and other sources. The federal funding programs for which it qualifies include:

� Title I, Part A—Improving Basic Programs� Title I, Part A—Supplemental Educational Services� Title V, Part A—Innovative Programs� 21st Century Community Learning Centers� Enhancing Education Through Technology

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Fraction Nation strengthens and complements the implementation of RTI in schools. Theadaptive computer-based program provides an intervention that proactively improves a rangeof young students’ access to core math curriculum. By supporting the development of fractionfluency for all students (Tier 1); by differentiating and targeting intervention for groups ofstudents in need of additional support (Tier 2); and by providing diagnostic assessments and tar-geted interventions for individual students who have not yet acquired a foundationalunderstanding of fractions and decimals (Tier 3), Fraction Nation serves to support studentswho require any one of the three tiers of service delivery for RTI instruction.

Fraction Nation delivers explicit instruction and guided practice that address the diverse needsof learners. With adaptive structure that allows each student to work at his or her own pace andgradually releases instruction, Fraction Nation targets the gaps in each student’s understanding.Placement and diagnostic performance assessments and actionable reports also promote RTIpractices, such as screening students to identify and monitor those in need of additional support,and providing the targeted instruction that each one needs. Finally, professional developmentresources and supplementary materials further assist practitioners to use the program effectivelyto meet the goals of RTI.

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Atkinson, R., Derry, S., Renkl, A., & Wortham, D. (Summer, 2000). Learning from Examples:Instructional Principles from the Worked Examples Research. Review of Educational Research, 70,(2), pp. 181-214. (Published by American Educational Research Association).

Cooper, G., & Sweller, J. (1987). Effects of schema acquisition and rule automation on mathe-matical problem-solving transfer. Journal of Educational Psychology, 79, 347-362.

Cramer, K.A., Post, T.R., & del Mas, R.C. (2002). Initial fraction learning by fourth- and fifth-grade students: A comparison on the effects of using commercial curricula with the effects ofusing the Rational Number Project Curriculum. Journal for Research in Mathematics Education,33, 111–144.

Fuson, K., & Kalchman, M. (2002). A length model of fractions puts multiplication of fractionsin the learning zone of fifth graders. In D. L. Haury (Ed.). Proceedings of the twenty-fourthannual meeting of the North American chapter of the International Group of the Psychology ofMathematics Education (pp. 1641-1649). Columbus, OH: ERIC Clearinghouse for Science,Mathematics, and Environmental Education.

Milgram, J.R., & Wu, H. (2006). The Key Topics in a Successful Math Curriculum. Retrievedfrom http://math.berkeley.ed/-wu/six-topics1.pdf Department of Mathematics, StanfordUniversity & University of California, Berkeley.

Moss, J., & Case, R. (1999). Developing children’s understanding of rational numbers: A newmodel and experimental curriculum. Journal for Research in Mathematics Education, 30, 122 –147.

National Mathematics Advisory Panel. Foundations for Success: The Final Report of theNational Mathematics Advisory Panel, U.S. Department of Education: Washington, D.C., 2008.

National Mathematics Advisory Panel. Foundations for Success: Report of the NationalMathematics Advisory Panel, U.S. Department of Education: Washington, D.C., 2008. Chapter4: Report of the Task Group on Learning Processes.

National Research Council (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick,J. Swafford, & B. Findell (Eds.). Mathematics Learning Study Committee, Center forEducation, Division of Behavioral and Social Sciences and Education. Washington, D.C.:National Academy Press.

Sophian, C. (2007). The origins of mathematical knowledge in childhood. Studies in mathemati-cal thinking and learning. New York: Lawrence Erlbaum Associates.

Sweller, J., & Cooper, G.A. (1985). The use of worked examples as a substitute for problem solv-ing in learning algebra. Cognition and Instruction, 2, 59-89.

Woodward, J. & Brown, C. (2006). Meeting the curricular needs of academically low-achievingstudents in middle grade mathematics. The Journal of Special Education, 40(3), 151–159.

References



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Response to Intervention An Alignment Guide for Fraction Nation · 2015-11-17 · 4 Fraction Nation Overview FractionNation is an intervention program designed to support students