The Effects of a Direct Instruction Program on theFraction Performance of Middle School Students

At-risk for Failure in Mathematics

Margaret M. Flores and Maria Kaylor

The current exploratory study investigated the effects of a Direct Instruction pro-gram implemented with middle school students identified as at-risk for failure inmathematics. Direct Instruction has typically been implemented with students withdisabilities in separate special education settings. However, this study examined theextent to which this kind of instruction could be integrated into a general educationsetting. The study took place in a rural middle school in which the majority of thestudents were from culturally and linguistically diverse backgrounds. The participantswere seventh grade students who had failed the state-mandated annual assessment atleast twice and who were identified as at-risk for failure. The students participatedin fourteen lessons of the Direct Instruction fraction program. Student progress wasassessed using curriculum-based pre and post-tests and the data were analyzed us-ing a t-test. Participation in the program resulted in significant increases in fractionskills. The students also demonstrated increases in appropriate and on-task behaviorduring the intervention.

According to the National Council ofTeachers of Mathematics (NCTM, 2000),students are expected to be proficient in com-putation and estimation. According to NCTMstandards, middle level students will: (a) workflexibly with fractions, decimals, and percentsto solve problems; and (b) compare, order,fractions, decimals, percents efficiently andfind their equivalent locations on a number.Students who struggle in mathematics haveparticular difficulty with fraction concepts(McLeod & Armstrong, 1982; Toumiare &Pulos, 1985). Students have difficulty un-derstanding that numbers and symbols, suchas those used in fraction problems, relate toreal-world situations (Hiebert, 1985). Other

Margaret M. Flores, Assistant Professor.Maria Kaylor, Assistant Professor, University ofTexas at San Antonio.

Correspondence concerning this article shouldbe addressed to Dr. Margaret M. Flores, Depart-ment of Interdisciplinary Leaming and Teaching,University of Texas at San Antonio, One UTSACircle, San Antonio, TX 78249; Email: margaret.flores@usta.edu.

factors may also lead to poorly developedunderstanding of fraction concepts. Accord-ing to Kelly, Gersten, and Carnine (1990),student's poor performance in this area maybe due to curriculum design. Traditional basalcurricula lack the components of effectivecurriculum design such as systematic prac-tice in discriminating among problem types;separation of confusing problems and termi-nology; and use of a wide range of examplesto illustrate each problem type.

The research in the area of math regard-ing specific interventions for students at-riskfor math failure is small compared to what isknown about other academic areas such asreading (National Research Council, 2002).However, there are several studies in whichinterventions in the area of fractions weresuccessful for students at-risk for failure inmathematics. These include instruction usingstrategies and mnemonic devices (Joseph &Hunter, 2000; Test & Ellis, 2005), manipu-latives and pictures (Bulter, Miller, Crehan,Babbitt, & Pierce, 2003), and the use of theDirect Instruction model (Scarlato & Burr,2002).

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An effective mathematics interventionfor students at risk for failure in mathematicsis the use of strategies and mnemonic devices.Joseph and Hunter (2000) provided middleschool students with leaming disabilities withdifferent strategies for solving addition andsubtraction of fractions with like and unlikedenominators on a series of cue cards. Theuse of cue cards fostered independent problemsolving rather than reliance on the teacher.The use of the cue cards was faded and thestudents maintained their performance.Test and Ellis (2005) extended Joseph andHunter's findings by providing similar frac-tion solving strategies, but provided studentswith a mnemonic device that increased thelikelihood that students would remember thestrategies. Middle school students with highincidence disabilities used the mnemonicdevice, LAP, which involved the followingsteps. The first step was "look at the sign anddenominator." If the denominator was thesame, the students proceeded to solve theproblems. The next step was; "Ask yourselfthe question, 'Will the smallest denominatordivide into the largest denominator an evennumberoftimes'?Ifthe student's answer was"yes", the student followed specific steps forthat type of problem. If the student's answerwas "no", the student would follow specificsteps for that particular type of problem. Allof the students participating in the study madegains in their performance, and five of the sixparticipants mastered addition and subtractionof fractions with like and unlike fractionsafter six weeks of instruction.

The use of manipulatives and pictures hasalso been shown to be an effective mathemat-ics intervention for students at risk for failurein mathematics. Jordan, Miller, and Mercerstudied the effects of the concrete-represen-tational-abstract (CRA) instruction sequenceon fraction performance of elementary stu-dents with and without disabilities in generaleducation classrooms. CRA involves threelevels of instruction and each includes teachermodeling, guided practice and independent

practice. The levels are as follows: (a) theconcrete level includes the sue of manipula-tives to foster understanding of the concept;(b) the representational level involves theuse of pictures, fading the students' depen-dence on manipulatives; and (c) the abstractlevel involves numbers only. Jordan, Miller,and Mercer found that the use of the CRAsequence resulted to improved performancein fraction problem solving when comparedto traditional basal instruction.

Bulter, Miller, Crehan. Babbitt, & Pierce,(2003) investigated the need for the concretelevel of instruction for teaching fractionequivalency. The researchers comparedinstruction using the CRA sequence and in-struction using only the representational andabstract levels of instruction. Middle schoolstudents with disabilities participated in theinvestigation and the researchers found thatalthough both the CRA and RA sequencesresulted in increased understanding, studentswho participated in the CRA sequence per-formed at a higher level.

Direct Instruction has also been dem-onstrated as an effective method of teachingmath to students in general education and spe-cial education (Hasselbring, et al., 1987; Kelly,Camine, Gersten, & Grossen, 1986; Kelly,Gersten, & Camine, 1990; Kitz & Thorpe,1995;Tarver& Jung, 1995; Woodward,etal.,1986; Hastings, Raymond, & McLaughlin,1989; Rivera & Smith, 1988; Wilson & Sinde-lar, 1999). The premise of Direct Instructionis that all students can leam with appropriateinstructional design and implementation. Theefficiency ofthis methodology is particularlybeneficial for students with disabilities, whohave many leaming needs but little time toaddress them. Watkins and Slocum (2004)describe the major components of DirectInstruction as follows. Direct Instructionis designed in a way to ensure efficientstudent leaming through: (a) organizingcentral concepts and strategies in ways thatallow application across multiple contexts;(b) providing clear and systematic methods

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of teacher communication, decreasing thelikelihood of student misunderstanding orconfusion; (c) the use of formats involvingstructured verbal exchanges between studentsand teachers, allowing for increased studentengagement, ongoing progress monitoring,and repeated verbal practice; (d) strategicallyintegrating skills to ensure efficient leam-ing and understanding; and (e) arrangingInstructional concepts into tracks in whichleaming develops across the length of theprogram while providing ongoing reviewand generalization.

With regard to fraction instruction, Kelly,Gersten, and Camine (1990) compared tradi-tional basal instruction and with instructionusing a videodisc program based on DirectInstruction methodology. The program wasused to teach fractions to high school studentsenrolled in remedial mathematics classes,half of which were identified as havingleaming disabilities. The researchers foundthat students performed at a higher level afterparticipating in the Direct Instruction video-disc instruction compared to students whoparticipated in instruction from a traditionalbasal curriculum.

Scarlato and Burr (2002) comparedtraditional instmction in fractions to instruc-tion based on the Direct Instruction model.Students with leaming disabilities servedin a resource setting participated in twentyweeks of instruction. One group participatedin fraction instruction using formats outlinedin the book. Designing effective mathematicsinstruction: A Direct Instruction Approach(Stein, Silbert, & Camine, 1997). Theteacher used modeling, guided practice, andindependent practice and cumulative review.Example selection guidelines were followedincluding the use ofvaried systematic practicein discriminating among examples; separationof confusing examples and terminology; anduse of a wide range of examples to illustrateeach problem type. The students receivedimmediate feedback and there were specificmastery criteria for guided and independent

practice. The students who participated inDirect Instruction lessons outperformed theirpeers on informal and formal measures.

Although these investigations demon-strated effective interventions for fractioninstruction, the majority of theses studiesinvolved students with disabilities receivinginstruction outside of the general educationclassroom. The studies that involved DirectInstruction used the principles and proceduresby modifying instructional procedures orusing videodisc program. However, noneinvolved existing published teacher-directedprograms. It is not known whether or howsuch as program could be implemented in ageneral education setting. The purpose of thecurrent study was to investigate the effectsof a Direct Instruction program on the per-formance of middle school students withoutdisabilities who were at-risk for math failurewithin the general education setting.

MethodResearch Design •

This was an exploratory study designedto investigate the following question. Whatare the effects of a Direct Instruction programon the performance of middle school studentswithout disabilities who were at-risk for mathfailure within the general education setting?The students' performance was measuredbefore and after participation in the DirectInstruction intervention and the data wereanalyzed using a t-test.

ParticipantsThe participants were seventh grade

students attending a school in a rural districtoutside of a large southwestem city. Noneof the students had been identified as hav-ing a disability; however, all students hadbeen identified as being at risk for failurein mathematics. The students had failedthe annual state-designated assessment inthe area of mathematics two or more times.With regard to fractions, the test from theprevious year included the following skills:

Direct Instruction.. / B7

(a) modeling of addition and subtractionsituations involving fractions with objects,pictures, words, and numbers; (b) equivalentforms of rational numbers including wholenumbers and fractions; and (c) the applica-tion of addition and subtraction of fractionsin word problems. As a result, the studentswere enrolled in a remedial math course asan elective. Thirty students participated inthe study, ranging in age from 12 to 14 yearsof age, eleven females and nineteen males.Eighteen of the students were Hispanic, sixof the students were white, and six of thestudents were African American. All of thestudents had demonstrated deficits in the areaof basic fractions as demonstrated on districtprogress assessments. The district designedquarterly assessments to monitor students'progress through the state curriculum. Theassessments are administered during thelast 2-weeks of each grading period. Eachassessment includes three components: per-formance assessment, open-ended questions,and multiple-choice items. The performancecomponent requires students to explaintheir learning in writing. The open-endedcomponent requires a brief written responseto a question. With regard to fractions, thequarterly assessment included the follow-ing: (a) representation of multiplication anddivision situations involving fractions withconcrete models, pictures, words, and num-bers; and (b) usage of addition, subtraction,multiplication, and division to solve problemsinvolving fractions and decimals.

The decisions about the instructionalcontent and procedures were made basedon the needs of the individual classroom.The instructional content was chosen basedon the students' needs. The teacher whoseclassroom was used for this study identi-fied basic fractions as an area of significantneed for his students. The teacher had taughtand reviewed basic fraction skills with thestudents earlier in the semester. However,the students' performance in this area hadnot changed after instruction as evidenced

on recent district progress assessments. Theteacher reported concerns about the amountof content that needed to be taught as wellas concerns about the lack of achievementdemonstrated by the students. The instruc-tional procedures were designed to provide aneffective intervention that would not interferewith the existing classroom structure andallow for previously planned instruction tooccur without too much disruption. Instruc-tion took place in three sections of a generaleducation remedial math course over a pe-riod of seven weeks. The students enrolledin this course as an elective, in addition totheir regular seventh grade math course.There were 10-12 students enrolled in eachclass. Through the course of the study, fourstudents moved away or transferred, so 30students participated throughout the entireseven-week study.

Pre-testThe pre-test consisted of a curricu-

lum-based assessment that was includedin the program. It included the following:(a) translating a whole number into a frac-tion; (b) translating a fraction into a wholenumber; (c) multiplication of fractions withlike denominators; (d) addition/subtractionof fractions with like denominators; (e) ad-dition/subtraction of mixed numbers withlike denominators; and (0 multiplication ofwhole numbers and fractions. On the first dayof the second nine-week grading period, thepre-test was administered at the beginning ofeach remedial class period. The assessmentwas administered to students in a wholegroup format. There was no time limit forcompleting the assessment.

Materials for InstructionThe instructional materials consisted

of a published Direct Instruction program.Corrective mathematics, basic fractions(Engelmann & Steely, 2005). The teacher'smaterials included a manual with scripted les-sons. Each lesson began with the introduction

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of a new skill, demonstrated and modeledby the teacher. The students participated inguided practice of the new skill. The studentswere actively involved in the lesson throughfrequent group verbal responses. The teacherprovided a signal to ensure responding inunison. The students chose their own signalin which the teacher said, "OK." Incorrectresponses were corrected immediately.Correction procedures involved three steps:teacher modeling of the correct response,guided practice with the students respondingwith the teacher, and independent studentresponse. Students independently practicedskills only after they demonstrated masterythroughout guided practice with the teacher.This decreased the likelihood that studentswould practice or leam error pattems dur-ing independent practice. Instruction waspresented systematically, providing a widerange of examples, separated confusingskills and concepts, and provided systematicpractice. Instruction facilitated systematicunderstanding of fraction concepts. Under-standing of concepts was developed throughthe use of pictures and drawings rather thanan emphasis on procedures only. Instructionmoved at a quick pace to ensure frequentresponding and increased engagement. Thepresentation of skills and concepts allowedfor the increased pace because skills werebroken down into small units that were mas-tered quickly and systematically combinedto form more complex tasks. The studentsdid not engage in independent practice untilthey had demonstrated mastery of those skillsin previous guided practice with the teacher.This decreased the likelihood of studenterrors or the practice of error pattems. Theprogram design led to high levels of studentsuccess throughout instruction and practiceactivities. The students' materials consistedof workbooks, including lesson worksheetswith guided practice as well as independentpractice problems.

InstructionPrior to the study, each 50-minute class

period had been divided, twenty minutes forreview of difficult concepts, and thirty min-utes of new material. Each class was dividedinto two groups consisting of 6-7 students.For this study, the first twenty minutes ofeach class period continued to be devoted toreview. However, groups altemated betweenparticipation in Direct Instruction, and tradi-tional instruction led by the classroom teacher.For example one group participated in DirectInstruction on Mondays and Wednesdays andtraditional instruction on Tuesdays and Thurs-days and vice-versa. Teacher-led instructiondid not include any of the skills or conceptsincluded in the Direct Instruction program.Traditional instruction involved teacherdemonstration of skills and procedures andstudent practice through remedial skills work-books tailored to the state-mandated annualassessment. University pre-service teacherswere assigned to this classroom to completea field requirement for a practicum course.The pre-service teachers received profes-sional development in Direct Instructionmethodology through a university course anddemonstrated proficiency before beginningthis field placement. The pre-service teachersled the Direct Instruction groups.

Procedural ReliabilitySince pre-service teachers led the Di-

rect Instruction groups. It was important toensure that instruction was carried out withprocedural fidelity. The first author checked50% of the instructional lessons. Thesechecks were conducted through the use of achecklist. The checklist included items such asappropriate pacing of lesson, useof correctionprocedures, appropriate and engaging use oflesson script, organization of materials, anduse of reinforcement for student success. Theprocedural fidelity was 90% for all lessonsacross all three classes.

Direct Instruction .. / 89

PosttestThe post-test consisted of a curriculum

based assessment that was included in the pro-gram. It included the following: (a) translatinga whole number into a fraction; (b) translatinga fraction into a whole number; (c) multipli-cation of fractions with like denominators;(d) addition/subtraction of fractions withlike denominators; (e) addition/subtractionof mixed numbers with like denominators;and (f) multiplication of whole numbers andfractions. The post-test was given during theeighth week of the second grading period atthe beginning of each remedial class period.The assessment was administered to studentsin a whole group format. There was no timelimit for completing the assessment.

ResultsPre-test Results

The students were not given feedbackon their pre-test performance. The meanperformance for the pre-test was 20%, withscores ranging from 0-57%. The students'performance on the different items on thepre-test are as follows: (a) 4% items correcttranslating a whole number into a fraction; (b)22% items correct translating a fraction into awhole number; (c) 30% items correct multi-plication of fractions with like denominators;(d) 14% items correct addition/subtractionof fractions with like denominators; (e) 3%items correct addition/subtraction of mixednumbers with like denominators; and (f)0.02% items correct multiplication of wholenumbers and fractions. The most commonerrors across students were misunderstand-ing of fractions and their relationship towhole numbers (i.e. '^1^^=12, %=12, 7=V^),adding denominators (i.e. M + 14 = '*/g) andthe incorrect usage of cross multiplication

Post-test ResultsThe mean performance for the post-test

was 77%, with scores ranging from 36-100%.The majority of the students' post-tests were

above 75%; howeverthere were three studentswith lower scores. The students' performanceon the different items on the pre-test are asfollows: (a) 80% items correct translating awhole number into a fraction; (b) 90% itemscorrect translating a fraction into a wholenumber; (c) 93% items correct multiplicationof fractions with like denominators; (d) 84%items correct addition/subtraction of fractionswith like denominators; (e) 57% items correctaddition/subtraction of mixed numbers withlike denominators; and (f) 67% items correctmultiplication of whole numbers and frac-tions. Common errors across students wereerrors in multiplication and addition ratherthan procedural errors, and disregard forthe whole number when adding/multiplyingmixed numbers (i.e. 2/1/4 \VA-2 3/16).

Comparison of Pre-test and Post-testPerformance

A paired samples t-test was performedon the overall performance data. A t-score of16.224 was obtained, which was significantat the 0.005 level. The probability that thisscore was obtained by chance was very small(<0.01). Although there was a statisticallysignificant difference between the pre-testsand post-tests, it is more important to examinethe educational significance of the students'performance. Data regarding the student'soverall performance on the pre-test and post-test are visually depicted in figure one.

One third of the students performedbelow 50% on the pre-test and performedabove 90% on the post-test. Twenty-six of thethirty students perfonned above 75% on thepost-test, many improving their performanceby 50% or more. The pre-test and post-testperformances were compared by item typeand the results are as follows: (a) 76% increasein translating a whole number into a fraction;(b) 68% increase in translating a fraction intoa whole number; (c) 63% increase in multi-plication of fractions with like denominators;(d) 70% increase in addition/subtraction offractions with like denominators; (e) 54%

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1009080706050403020100 ill

• pre-test

I • post-test

students

iliJiJincrease in addition/subtraction of mixednumbers with like denominators; and (f)66.08% increase in multiplication of wholenumbers and fractions. Data regarding thestudent's performance by item type are visu-ally depicted in figure one.

Anecdotal resultsAlthough formal data were not collected,

the researchers observed changes in behaviorsduring the intervention. Since the studentsalternated between traditional instructionand Direct Instruction, there was an op-portunity to observe the same students andtheir behavior in each instructional setting.The students appeared to be more engaged in

fraction instruction using Direct Instruction.This increase in engagement was observedthrough the following: the amount of studentresponse and number of correct responses; theamount of on-task behavior such as visuallytracking the movements of the instructor, andcompeting tasks within several seconds ofreceiving directions; and the amount of dis-ruptive or off-task behavior such as talking topeers suing instruction, making inappropriatecomments, out-of-seat behavior etc... Therewere more instances of student responding,correct responses and on-task behavior andfewer instances of off-task behavior whenstudents participated in the Direct Instruc-tion group than when participating in the

Direct instaiction .. / 91

traditional instructional group.

DiscussionThe purpose of the current study was to

investigate the effects of a Direct Instructionprogram on the performance of middle schoolstudents without disabilities who were at-riskfor math failure within the general educationsetting. Previous studies have included mostlystudents with disabilities taught within sepa-rate settings such as a resource room (Butleret al., 2003; Scarlato & Burr, 2002; Test &Ellis, 2005). There is a lack of literature re-garding interventions studied with studentswith disabilities used for the benefit of allstudents with learning needs regardless ofdisability status. The program used in thisstudy was implemented with minor changesin the stiiicture and existing procedures withinthe classroom. The students demonstratedsignificant improvement in skills as a resultof their participation in the fraction program.The results were statistically significant aswell as educationally significant. The studentsmastered basic fraction skills over the courseof 7 weeks of instruction. An effective andefficient method of instruction was includedwithout taking away from the existing struc-ture and content of the classroom. Studentperformance increased in a short amount oftime (7 weeks of instruction) with few (14)instructional lessons. This study extended theliterature in the area of intensive mathematicsinterventions such as Direct Instruction toinclude the general education setting, ratherthan separate settings for students with dis-abilities. This study demonstrated how suchan intervention could be included withouttaking away from the existing structurewhile still resulting in improved studentperformance.

This particular instructional programwas chosen based on the needs identifiedby the teacher. The teacher identified basicfractions as an area of need because this hadbeen a topic previously taught and reviewedin the class. However, the data gathered from

district progress assessments showed thatthe students' performance in this area hadnot changed as a result of instruction. Afterseven weeks of instruction (14 instructionallessons), the students' performance changedsignificantly. These results are consistentwith previous research demonstrating DirectInstruction as a powerful instructional model(Hasselbring, et al.,1987; Kelly, Camine,Gersten, & Grossen, 1986; Kelly, et al.,1990; Kitz & Thorpe, 1995; Tarver & Jung,1995; Wood ward, et al., 1986; Hastings,Raymond, & McLaughlin, 1989; Rivera &Smith, l988;Wilson & Sindelar, 1999).

The Corrective Mathematics programconsists of modules for specific skills suchas addition, subtraction, multiplication, ba-sic fractions, advanced fractions, decimals,percents, and ratios and equations. Modulescould be chosen based on students' needs.Students could be grouped according toindividual needs and different concepts andskillscould be mastered in an efficient manner.Middle school is a critical time in student'sacademic careers, preparing them for moreadvanced studies critical thinking. There aremay be gaps in student's understanding ofcertain mathematical concepts that could beaddressed in an efficient individualized waythrough the use of these modules. Modulescould supplement existing curriculum andallow for intervention without encroachingon the current curriculum or consuming greatamounts of instructional time. It is importantto view the use of such interventions assupplements to existing curriculum. The useof these interventions should not encompassall mathematics instruction, making deficitareas the sole focus. Addressing deficit areasin this way has the potential for impedingstudents' progress through the curriculum.This is an issue in the field of special educa-tion, in which there are instances of studentsin middle and high school resource roomsworking mostly on basic fact instructionand the gap between their performance andtheir grade-level peers' performance becomes

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wider and wider (Cawley, et al., 1978; Caw-ley & Miller, 1989; Jones & Thomas, 2003;Warner, et al., 1980). This is problematic andthe current study has no intent of promotingsuch a model. However, if gaps in skills andunderstanding can be addressed in an efficientmanner without taking over the entire cur-riculum, students will benefit and perhapsprogress more successfully into advancedmathematical understanding.

The effect of Direct Instruction on thestudents' behavior was another interestingfinding. This is consistent with previousresearch that demonstrated decreases inoff-task behavior and increases in studentengagement (Grossen, 2002). The studentsparticipated in each type of instruction on al-ternate days, providing for observation of thesame groups of students in each instructionalsetting. Even though on-task behaviors andevidence of engaged leaming occurred oneday, the same group of students behaved in acontrary way the next day when participatingin the traditional instructional format.

There may be concerns about the in-structional intervention consisting of anexisting published program. The availabilityand accessibility of these resources may belimited for classroom teachers. There arecomponents of Direct Instruction that donot require the use of published materials.Theses include: use of frequent responding;systematic teaching of component skills;immediate feedback; scaffolded instructionthrough modeling, guiding, and providingindependent practice; and including criteriafor mastery before proceeding to the nextlevel of instruction. These practices could beused to teach any concept or skill in a waythat would increase the likelihood that stu-dents would participate actively. Any groupof existing curriculum standards could beorganized and taught in this way, given timeand expertise in the content area.

Another informal observation was stu-dent interest in the program. One a numberof occasions, the students would ask if they

could participate in Direct Instruction ondays when they were scheduled to partici-pate in the traditional instruction group. Thestudents appeared to like the program andmost reported that they were surprised bytheir progress. The students performed fewerrors and completed independent practiceactivities with at least 90% accuracy. Perhapstheir experience with success led to increaseddesire to participate. The students enrolledin these remedial courses had experiencedfailure in mathematics and f)erhaps were notaccustomed to success. At the beginning ofthe study, students reported that they werenot skilled in math and that it was their leastfavorite subject. When the fractions programwas introduced, none of the students appearedenthused, reporting that fractions were thehardest parts of math. Despite these feelingsand perceptions about math, the students weresuccessful and their perceptions of fractionsappeared to change throughout the interven-tion. During most of the lessons, at least onestudent would comment that fractions wereeasy, contrary to previous beliefs.

Although the intervention was successfulfor all of the students, there are limitationsto this study. The classroom teacher did notimplement the Direct Instruction program.Very few general education classrooms in-clude more than one instructor to carry outthe interventions in this manner. However,other instructional arrangements could bemade to deal with this issue. The use of peertutoring has been shown to be an effectiveway for students to leam and practice mathskills without dependence on the teacher(Calhoon & Fuchs, 2003; Maheady, Sacca, &Harper, 1987). Another way in which DirectInstmction could be implemented is withwhole group instruction. The setting withinthis study is not typical of general educationsettings that have twice the number of stu-dents. Whole group instruction with this typeof intervention may be difficult to manage.

Another limitation of this study is thatan individual who implements a Direct

Direct Instmction .. / 93

Instruction program should also engage inprofessional development prior to using theprogram to ensure that instructional proce-dures are followed with fidelity. The resourcesneeded for that sort of preparation may alsobe limited. Therefore the ability to generalizethese findings is decreased. Future researchis needed on how Direct Instruction, such asthe use of Corrective Mathematics modules,could be used in a general education settingwith one teacher. Future research is alsoneeded to study how some of the componentsof Direct Instruction could be used to enhancean existing curriculum and the effects of thosemethods on student achievement. Perhapsexisting curriculum modified with DirectInstruction methodology could be comparedto traditional instruction as well as existingDirect Instruction programs to study the ef-fects of each on student performance.

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