HARRISON STREET INTERVENTION · Created Date: 1/5/2012 1:44:43 PM

Education and Training in Autism and Developmental Disabilities, 2011, 46(4), 544-555© Division on Autism and Developmental Disabilities

Teaching Money Computation Skills to High School Students

with Mild Intellectual Disabilities via the TouchMath©

Program: A Multi-Sensory Approach

Hugh E. Waters and Richard T. BoonThe University of Georgia

Abstract: This study investigated the effects of the TouchMath© program (Bullock, Pierce, & McClellan, 1989)to teach students with mild intellectual disabilities to subtract 3-digit money computational problems withregrouping. Three students with mild intellectual disabilities in high school received instruction in a specialeducation mathematics self-contained classroom. A multiple-probe across participants design (Alberto &Troutman, 2009) was used to evaluate the effectiveness of the TouchMath© program using the "touch-points"strategy to facilitate the student's mathematics performance. The results revealed the TouchMath© programimproved all three of the students' ability to subtract 3-digit mathematics operations using money applications;however, maintenance results were mixed, as the students exhibited difficulty with maintaining the necessaryskills once the intervention was withdrawn. Limitations, recommendations for classroom teachers and futureresearch directions are presented.

With the growing trend of providing proven,scientifically-validated practices in the class-room, teaching students' mathematics instruc-don at the secondary-level, especially thosevnth intellectual disabilities, can be a challeng-ing and often overwhelming task. With recentmandates from federal policies like, the NoChild Left Behind Act of 2001 (NCLB, 2001)and the Individuals with Disabilities Educa-tion Improvement Act (IDEA, 2004), schoolsare now mandated that aZ/students have equalaccess to the general education academic cur-riculum and national and state standards (Na-tional Council of Teachers of Mathematics,2000; U. S. Department of Education, 2007).Thus, an increasing number of students withmild intellectual disabilities are now receivinginstruction and being placed into general ed-ucation clEissrooms where they are not onlyexpected to succeed in the classroom, but alsoon high-stakes assessments such as the Geor-gia End of Course Test (EOCT) and the Geor-

Correspondence concerning this article shouldbe addressed to Richard T. Boon, The University ofGeorgia, Department of Communication Sciences& Special Education, 557 Aderhold Hall, Athens,GA 30602-7153. E-mail: [email protected]

gia High School Graduation Test (GHSGT).These new classroom rigors include movingaway from functional academics and replacingthem with more traditional academic skills.While this is a positive move toward allowingall students regardless of their disability theopportunity to graduate with a high schooldiploma and prepare them to attend furthereducational and occupational prospects, thisdoes not allow students with mild intellectualdisabilities the chance to learn the essentiallife skills (e.g., money computation) that arecrucial for their survival in the community asindependent members of society.

Students with mild intellectual disabilitiesoften exhibit deficits in basic mathematics in-struction, especially in the area of money com-putation (e.g., purchasing skills), which hasbeen well documented (Browder & Grasso,1999; Browder, Spooner, Ahlgrim-Delzell,Harris, & Wakeman, 2008; Butler, Miller, Kit-hung, & Pierce, 2001; Jitendra & Xin, 1997;Kroesbergen & Van Luit, 2003; Mastropieri,Bakken, & Scruggs, 1991; Miller, Butler, &Lee, 1998; Swanson & Jerman, 2006, Xin &Jitendra, 1999). In 2000, the National Councilof Teachers of Mathematics (NCTM, 2000) statedin a comprehensive report five main compo-nents of mathematics instruction standards

544 / Education and Training in Autism and Developmental Disabilities-December 2011

that all students are required to achieve, oneof which focuses explicitly on the ability tomeasure attributes of objects such as time andmoney applications, which is commonly prob-lematic for a large number of students withmild intellectual disabilities. Fortunately, agrowing research-base of new and innovativeinterventions, like the TouchMath© program,has been developing in the literature and hasshown some promising results to be effectivein increasing students with and without dis-abilities mathematics performance.

The TouchMath© program (Bullock et al.,1989), a multi-sensory "dot-notation" system,previously employed by Kramer and Krug(1973) was used to teach mathematics skills tostudents with disabilities. The TouchMath©program uses "dot-notations" often referredto as "touch-points" either with one dot, fornumbers 1 to 5, or a dot-notation with a circlearound them, to indicate two or double touch-points to assist students with and without dis-abilities with basic counting and computationskills. The TouchMath© program using thetouch-points strategy, has been shown in pre-vious research to be effective for students withmathematical disabilities in basic mathematicsinstruction (e.g., adding single, double-digitmathematics problems with and without re-grouping) at the elementary level for studentswith specific learning disabilities and moder-ate intellectual disabilities (Scott, 1993; Simon& Hanrahan, 2004), autism spectrum disor-ders (Cihak & Foust, 2008), and more re-centiy, at the middle school level includingstudents with autism spectrum disorders andmoderate intellectual disabilities (Fletcher,Boon, & Cihak, 2010). However, no studies todate have attempted to explore the effective-ness of the TouchMath© program, usingmoney computation skills, with students withmild intellectual disabilities in a high schoolclassroom setting.

Therefore, the purpose of this study was toexamine the effects of the TouchMath!© pro-gram on the acquisition of subtracting 3-digitmoney computational problems with regroup)-ing for three students with mild intellectualdisabilities in a high school special educationself-contained clcissroom. Prior research onthe efficacy of the TouchMath© program hasfocused only on students vrith specific learningdisabilities, moderate intellectual disabilities.

and autism spectrum disorders at the elemen-tary and middle school grade levels, and hasnot addressed the benefits of such a strategyfor students with mild intellectual disabilitiesat the high school level. Although previousstudies have investigated the use of the touch-points strategy to teach basic addition usingsingle and double-digit mathematics prob-lems; no studies have explored the benefits ofthe touch-points strategy on money applica-tions.

Research Questions

Thus, the two main research questions posedwere: (a) What are the effects of the Touch-Math© program on the mathematics perfor-mance of solving subtraction 3-digit moneycomputational problems with regrouping forstudents vnth mild intellectual disabilities atthe high school grade level? And (b) What arethe students, teachers, and parents percep)-tions of the TouchMath© program to improv-ing students with mild intellectual disabilitiesmathematics performance?

Method

Participants

Three students with mild intellectual disabili-ties, two of which had a dual-diagnosis of au-tism as well, from the same special educationhigh school self-contained classroom partici-pated in the study. The students' ages rangedfrom 14 to 16 years-old, with a mean of 14.75and intellectual quotients (IQ) scores variedfrom 61 to 64, with a meari of 63. All of thestudents were classified with a disability basedon the county, state, and federal criteria,which indicated having below average intellec-tual ability, deficits in adaptive behaviorscores, which both negatively affected theiracademic performance. Demographic and ed-ucational information is depicted in Table 1.All of the students received special educationservices since entering high school where theywere in a self-contained special educationclassroom setting for three block periods a dayand participated in only one general educa-tion course elective. The students were taughtall of their academic subjects including math-ematics instruction in the same self-contained

Touchmath© and Money Skills / 545

TABUE 1

Student Demographic Information

Chronological AgeGradeSex

IQ*Adaptive Behavior

Score Composite**Math Composite***

(Grade Equivalent)Primary Eligibility

Trent

15-0gth

Male6483

5.1

Mild IntellectualDisabilities/Autism

Michael

14-11gth

Male6154

4.2

Mild IntellectualDisabilities

Alex

16-110"̂Male

6471

2.8

Mild IntellectualDisabilities/Asperger's Syndrome

* mSC-III COG = Wechsler Intelligence Scale for Children (3"" ed.) by D. Wechsler. Copyright 1991 by PsychobgicalCorp, San Antonio, TX.

** ABAS-II = Adaptive Behavior Assessment System (2"^ ed.) by P. Harrison & T. Oakland. Copyright 2003 byPsychological Corp, San Antonio, TX.

*** MBA = Mini-Battery of Achievement by R Woodcock, K. McGrew, & J. Werder. Copyright 1994 by RiversidePublishing, Chicago, IL.

classroom from tbe same teacher for all threeblock periods. Finally, all three studentsscored well-below grade level in mathemadcs,based on tbe Woodcock-McGretv-Werder Mini-Bat-tery of Achievement (MBA; 1994) test results.Students were selected based on their grade-level, special education classification andmathematical ability. All of the students wereunable to properly and accurately subtract nu-merical or monetary values without a calcula-tor. The classroom instructor had previouslytaught the students to use calculators to deter-mine purchcise price in order to facilitate ac-curacy and fluency in tbe classroom and com-munity-based setting.

Trent. Trent was a ninth grader and was15 years, 10 months old at tbe outset of thestudy. Trent had received special educationservices for ten years for a mild intellectualdisability and autism. Placement was sup-ported with a Full Scale IQ score of 64 fromthe MSC-///(Wechsler, 1991) and the ABAS-II(Harrison & Oakland, 2003), with a 72 con-ceptual score; 75 social score; 91 practicalscore, and a general adaptive composite scoreof 83. Trent's IEP (Individualized EducationalPlan) goals covered several academic and lifeskill areas, as he had a mathematics academicgoal of becoming more proficient in basicmathematics skills. His teacher said that he is

consistendy willing to work bard to completehis assignments and complies with directionsfrom the classroom teacher and paraprofes-sionals.

Michael. Michael entered his first year ofhigh school as a ninth grader during the studyat 14 years, 11 months old and turned 15witbin the study's span. He struggles with allacademic subjects as evident by his instruc-tors' observations during the daily educationsessions and receives one to four instructionsdaily for his academics. Micbael has receivedspecial education services since bis entranceinto the school system in self-contained class-rooms for students with mild intellectual dis-abilities. According to the WISC-III (Wechsler,1991) Michael had a Full Scale IQ score of 61,with a 53 conceptual score; 70 social score; 53practical score, and a general adaptive com-posite score of 54. The results from theABAS-II (Harrison & Oakland, 2003) instru-ment determined Michael lacked adaptive be-havior skills and met criterion for classifica-tion for a mild intellectual disability.Increasing basic mathematics skills was one ofbis academic (IEP) goals. His teacher statedthat he is cooperative during instruction andputs forth much effort towards his classroomwork.


Alex. Alex was a tenth grade student beingserved in the same self-contained special edu-cation classroom as Trent and Michael. Hewas 16 years, 1 month at the beginning of thestudy and has received special education ser-vices for thirteen years with an eligibility of amild intellectual disability and Asperger's Syn-drome. Alex's placement was determined by aWISGIII (Wechsler, 1991) Full Scale IQ scoreof 64 and on the ABAS-II (Harrison & Oak-land, 2003) he had a 70 conceptual score, 77social score, 75 practical score, and a generaladaptive composite score of 71. He had twomoney mathematics skills goals on his (IEP),which included adding and subtracting twoand three-digit mathematics problems withouta calculator and to write checks, make depos-its, and balance a checkbook. He had demon-strated a lack of restraint and cooperationwith teachers in the past, but has not shownthese behaviors since entering high school, ashis teachers have stated that he has been veryobliging and receptive to instruction.

Setting and Arrangements

The public high school consisted of approxi-mately 1,500 students, with grades ninethrough twelfth, and was located in a south-eastern region of the United States. Thecounty school system population was consid-ered low-income, with a low socio-economicstatus (SES) with manufacturing as the majoremployer in the area. Data collection, train-ing, and intervention procedures were con-ducted in that same self-contained special ed-ucation mathematics classroom. Theclassroom dimensions were 3 m X 6.5 m andthe room consisted of 12 student desks andtwo teacher desks. The teacher desks faced thestudent desks located to the side of the stu-dent desks and immediately in front of oneteacher desk, was a podium. The studentswere instructed at a distance of 1 meter, facingthe teacher, and two student desks were di-rectly in front of the teacher. The TouchMath©poster displaying the touch-points for thenumbers 1 to 9 was placed on the wall betweentbe student and teacher desks as a reminderand visual cue during the training and inter-vention phases. No other students were in theclassroom during the block period and allphases of the study.

Materials

The TouchMatl^ program (Bullock et al.,1989) was the intervention utilized during theintervention phase to teach students to sub-tract 3-digit money computational problemsvnth regrouping. The researcher and class-room teacher collected the data for all phasesof the study. The researcher and classroomteacher were trained to use the TouchMath©program via the teacher training DVD andinstructional materials, that were sent by thepublisber. Tbe TouchMath© system is based onthe placement of dots (e.g., dot-notations) onnumbers (1 to 9). For example, the studentwould be asked to state the number aloudthen the student was expected to count aloudas he made contact on the touch-points; how-ever, for subtraction problems, the studentsmust be able to count backwards from 20.When regrouping, the students were expectedto be able to mark tbrough the number bor-rowed from and tben place a 1 next to theprevious number and subtract the numbers.TouchMath© made a point of ensuring thenumber borrowed was the same size as theother digits. Worksheets were provided by thepublisher that the researcher and classroomteacher utilized to introduce, instruct, prac-tice, and assess all of the students. The work-sheets were designed based on the specificsteps previously mentioned above and con-sisted of examples on how to count forwardand add with and vrithout regrouping. Aposter with the touch-points for each of thenumbers 1 to 9 was posted on the wall in theclassroom. In addition, mini-posters were pro-vided to the students and laminated on theirdesktop as a reference, while learning thetouch-points strategy (see Figure 1 for an ex-ample of the mini-posters).

Assessment Materials

Researcher developed worksheets with thesame font and size as the publisher's wereemployed as the probe during the interven-tion and maintenance phases (see Figure 2 foran example of the worksheets). The measuresserved as permanent products to collect data.These worksheets consisted of 10 subtraction3-digit money computational problems withregrouping. All probes consisted of different


I

7

25

3

Figure L Example of the mini-poster that was pro-vided to the students and laminated ontheir desktop as a reference, while learn-ing the touch-points strategy. Touch-Math® TouchPoints. By permission of J.Bullock and Innovative Learning Con-cepts Inc., Colorado Springs, CO. Allrights reserved.

mathematics problems so the students wouldnot be able to memorize the answers.

Procedure

General procedure. All instruction, trainingsessions, observations and probes occurredduring the regular school day during the first

block period from 8:30-10:00 a.m. Therewere five sessions per week for ten weeks andeach student received instruction in the self-contained special education classroom. Thetraining and intervention sessions lasted induration from 10 to 15 minutes on the Touch-Math© procedures to subtract numbers withregrouping and probes were designed to takeno longer than 10 to 15 minutes. Maintenancesessions extended long enough to completethe probe (10 to 15 minutes). These sessionswere held concurrentiy with the last three in-tervention sessions of subsequent student'ssessions. The intervention was introduced tosubsequent students based on the studentreaching criterion, which was established asthe students' average score increase to beabove 40% of the average baseline score for80% of the sessions. Baseline stability followedthe 80/30 guideline to establish a trend be-fore the intervention was implemented.

Intervention began with identifying each ofthe numbers (1 to 9) and where the touch-points were located on the numbers. Next, thestudents were taught how to count the touch-points in a certain order, as described in thepublisher's manual. According to the Touch-Math© procedures, the students are to countaloud during instruction, while learning thetouch-points on each of the numbers. In ad-dition, counting backwards was also taughtand practiced while utilizing the touch-pointsstrategy. Once these skills had been mastered.

Name: Date:

%7.6-0 .5

$6.83-2.14

$3.07 $4.52- Î . 3 2 - 8 .

$3.19-2.50

%bM7 $7.09 $1.29- Î .5Î - I.¿0 - 0 .

$0.53-0.2¿

Figure 2. Example of the subtraction 3-digit money computational problems with regrouping worksheet usedduring the intervention and maintenance phases.


the students could move on to actual subtrac-tion problems vnth regrouping. With the sub-traction problems, the students were taughtto: (a) state the problem aloud, (b) state thefirst number aloud, (c) count backwards usingthe touch-points on the second number (ifthe student reaches 0 before finishing count-ing the bottom number, then regroup), (d)mark-out the number borrowed from, writelowered number above on the line, (e) place a1 next to the number on the right makingsure it is the same size, (f) count backwardsusing the touch-points on the second number,(g) place the difference in the answer blank,and finally (h) repeat the problem aloud withthe answer.

Experimental Procedures

Baseline. Before baseline probes were de-livered, prerequisite skills were taught until100% of the students' mastery was achieved.The student had to be able to learn to countbackwards, place the touch-points on thenumbers 1 to 9, and count those touch-pointsin a proper pattern. The first student was ad-ministered a minimum of three probes to es-tablish trend stability, which consisted of 10subtraction 3-digit money computationalproblems with regrouping without the use ofthe touch-points strategy. Once stability wasestablished, the touch-points intervention be-gan. Subsequent students were probed con-currentiy with the last three intervention ses-sions of the previous student. Verbal cues andpraise were offered for correct and/or incor-rect behaviors.

Intervention. First, the TouchMath© strategywas introduced to each of the students, whichconsisted of the instructor modeling how tocount the "dot-notations" on each of the num-bers 1 to 9 to solve a subtraction problem. Thestudents were then given an opportunity topractice one problem along with the specialeducation teacher using the touch-pointsstrategy. Second, the teacher demonstratedthe proper steps and verbal cues to solve asubtraction problem. Afterwards, the studentwas asked to carry out the task independentlyas performed by the teacher. During the prob-lem-solving procedures, the instructor pro-vided positive verbal corrective feedback toredirect any operational errors performed by

the student. The student then practiced thesteps a minimum of five times. Third, theinstructor modeled the proper steps of theTouchMath© program and verbal cues to solvea subtraction problem. The student was thenasked to perform the task as modeled. Duringthe problem-solving procedures, the instruc-tor provided positive verbal corrective feed-back to redirect any operational errors per-formed by the student for the first twopractice problems and then was asked to solvea minimum of five problems independentiy.And finally, in the fourth step, the instructormodeled the proper steps and verbal cues tosolve a subtraction problem. The student wasthen expected to solve 10 3-digit money sub-traction computational problems witb re-grouping using the touch-points interventionindependently.

Maintenance. During the maintenancephase, the students were provided no instruc-tion or visual cues from the TouchMath© ma-terials to perform the operational steps to sub-tract a 3-digit money computational problemwith regrouping. After the student hadreached criteria for three consecutive days, aminimum of two sessions without instructionlapsed before a maintenance probe was given.These probes consisted of 10 3-digit subtrac-tion problems with regrouping following thesame format as those mentioned in the base-line and intervention sessions. Concurrentwith subsequent students being presentedtheir last two intervention probes, each previ-ous student was given a minimum of onemaintenance probe every five days until theconclusion of the study with the last student.These probes indicated whether the touch-point system could be maintained for otherproblem sets. Generalization was monitoredthroughout the study with subtraction prob-lems at the end of each probe. These prob-lems also accompanied maintenance sessions.These three problems, consisting of the sameskills addressed during the intervention phasewere presented to the students from differentstimuli, workbooks and instructor made work-sheets. This measure determined if the stu-dents could generalize TouchMath© tech-niques and procedures to the same mathbebaviors from different stimuli.


Experimental Design

This study employed a multiple-probe acrossparticipants design (Alberto & Troutman,2009) to examine the effectiveness of thetouch-points strategy to teach students withmild intellectual disabilities to subtract 3-digitmoney computational problems with regroup-ing.

Reliability

Inter-observer agreement. Inter-observer reli-ability data was collected across all conditionsusing a point-by-point agreement formula.The special education teacher's paraprofes-sional was a second observer and was asked toindependentiy score the probes and evaluatethe procedural fidelity measures. The para-professional was familiar with the training ma-terials in conjunction with the special educa-tion teacher and researcher and was presentduring a minimum of 20% of the sessions.Inter-observer agreement was calculatedbased on the point-by-point reliability and cal-culated by counting the number of agree-ments between tbe special education teacherand the paraprofessional and dividing thisnumber by the total number of agreementsand disagreements and then multiplied by100% (Cooper, Heron, & Heward, 2007).

Procedural reliability. Procedural reliabilitywas assessed by the special education class-room teacher and paraprofessional in the self-contained special education classroom with awritten procedural protocol checklist and wasset for a minimum of 90%. Procedural reliabil-ity data was collected during the same sessionsas the inter-observer agreement data weretaken by both teachers on a minimum of 20%of the sessions. A point-by-point agreementformula (Cooper et al., 2007) was again usedand was calculated by counting the number oftimes the special education teacher and/orparaprofessional agreed that a behavior eitheroccurred or did not occur during the sessions.This number was then divided by the totalnumber of agreements and disagreementsand multiplied by 100%. Finally, for each ofthe three students their percentage agree-ment was recorded for each behavior on theprocedural checklist.

Social Validity

A 10-item survey was administered to the stu-dents, teachers, and parents to determine thesocial validity (Wolf, 1978) of the TouchMath©program using the touch-points strategy inmathematics instruction. The items in the so-cial validity survey were rated on a 5-pointLikert scale ranging from 1 (strongly dis-agree) to 5 (strongly agree). The social valid-ity data was collected upon conclusion of thestudy and the survey was completed by thestudents and teachers (e.g., special educationteacher and paraprofessional) in the highschool classroom, while another version of thesurvey for the parents was mailed to theirresidence to compete and return back to thespecial education teacher. The social validitysurvey consisted of the following items: (1)TouchMath© is a beneficial strategy to help mewith my subtraction problems; (2) Subtractionis an important skill to have for real-life situa-tions; (3) Subtraction is an important skill tolearn before leaving high school; (4) I wouldrecommend this strategy to someone else; (5)I understood the TouchMath© strategy andwhat was expected of me; (6) TouchMath© waseasy to use; (7) TouchMath© was an effectivestrategy to subtract money values; (8) Thetarget skills are necessary for grade level re-quirements; (9) The target skills are necessaryfor classroom requirements; and (10) The tar-get skills are necessary for community-life re-quirements.

Results

Reliability

Inter-observer and procedural reliability wascollected during 7 (20%) of the 35 sessions.Of the 49 probes graded, two were found tohave different scores between the scorers, thespecial education teacher and paraprofes-sional. On the two probes, eacb had one re-sponse in conflict between the scorers due todisagreement over identifying a particulardigit in the response. The mean percent ofagreements for each student was as follows:Trent, 100%; Michael, 93.3%; and Alex, 95%.The mean procedural reliability was 100% forall researcher behaviors across all experimen-tal conditions. Of the observed sessions, 56%


00 -

80 -

60 -

40 •

20 -

0 -

Base line

V

TouchMaÜiStrategy

hiil/

Nlainteiiance

•

A *

A

Trent

11 16 21 26 31 36 41 46 51 56 61

Figure 3. Percentage of subtraction 3-digit money computational problems with regrouping using the touch-points strategy answered correctly by Trent, Michael, and Alex.

were conducted during the training phase,while 44% were completed in the probe ses-sions. The inter-observer agreement was100%.

Effectiveness of the Intervention

Figure 3 illustrates the percentage of correctresponses the students received on the sub-traction problems v«th regrouping using

money computations during the basehne, in-tervention, and maintenance phases.

Trent. Trent's baseline mean score was6.66% across all 3 sessions, which demon-strates a stable trend in the data. A substantialimmediate positive score increase was ob-served when the intervention probes were is-sued, which showed the touch-points strategywas an effective intervention for acquiringsubtraction problems witb regrouping usingmoney values. The average score across all

Touchmath® and Money Skills / 551

intervention sessions was 75.55% demonstrat-ing a continual, stable, and maintained acqui-sition of the target skills set needed to calcu-late the correct answers, which was a 68.88%increase from the baseline phase. Trentreached criteria within the preset number ofsessions, which was established when 80% ofthe probe scores were 40% bigher than thebaseline scores. There was no data point over-lap observed from the baseline to the inter-vention phases signifying an immediate posi-tive increase that was maintained throughoutthe intervention. The trend from the interven-tion through the maintenance phase was pos-itive and the data points within the trend werereasonably stable. Trent's mean score duringintervention was 75.55% and increased to83% during the maintenance phase, indicat-ing a continual improvement in skill level withadditional opportunities to utilize the strategy.There was an 83% overlap between tbe inter-vention and maintenance phase, thoughTrent was able to increase his mean scoresduring maintenance. This indicates that Trentwas able to prolong his ability to solve thesubtraction problems with regrouping and,based on his scores during the maintenancephase, improve his scores over time. The in-tervention strategy was successful initially andin sustaining Trent's ability to solve subtrac-tion problems with regrouping.

Michael. Michael's mean score during thebaseline phase was 5% indicating that he hadestablished a flat and stable baseline measure.However, Michael's mean score during theintervention phase increased to 88%, whichwas an 83% increase from the baseline pbase.This abrupt level change and 0% overlappingdata points from baseline to intervention sub-stantiated tbat the touch-points interventionstrategy was effective for Michael in acquiringthe subtraction skills witb regrouping. Mi-cbael met criteria after only four sessions.There was a level trend after the abrupt levelchange from the baseline to the interventionphase indicating a consistent calculation skillaptitude. The mean maintenance score forMichael was 45% with a median score of 35%.There was 100% data point overlap from in-tervention to the maintenance phase. A con-tinual decreasing trend occurred during themaintenance phase ending in a 20% score on

the final probe session. Michael did not revertto his previous baseline scores, but furtherprobes would be needed to determine sus-tained skill retention. The intervention strat-egy was confirmed to be effective over a rela-tively sbort period of time, as furtber strategyinstruction may prove beneficial for Michael'scontinued success.

Alex. Alex's baseline pbase extended for 9sessions, while maintaining a flat and stabletrend with a mean score of 2.22%. However,during the intervention phase, Alex demon-strated a positive level change with the firstintervention probe session. The second probescore increased significandy from 20% to70%, then faltering back to 30% causing anunstable level change with the first four ses-sions. The fifth session established the start ofan observable stable level change. Due to be-ginning unstable scores, Alex required thegreatest time to meet criteria. Criteria weremet after ten sessions with an average score of76% and a 90% median score, which was a73.77% increase from the baseline measures.The touch-points intervention strategy was ef-fective for Alex to subtract 3-digit money prob-lems with regrouping. Between the baselineand intervention pbases there was 0% datapoint overlap, demonstrating a positive levelchange though five additional sessions wererequired until stability and criteria were met.There was 100% overlap frond intervention tomaintenance phase. The mean maintenancescore for Michael was 100%. From the begin-ning of the baseline to the end of the main-tenance phase, there was a steady increasingdata score trend and overall the touch-pointsintervention strategy proved to be effective forAlex.

Social Validity Survey

In general, the students, teachers, and parentsindicated in the social validity survey that theTouchMath© program using the touch-pointsintervention was beneficial. Tbe studentsstated that the strategy was easy to use andunderstand and improved their ability to solvesubtraction problems with regrouping involv-ing money computations. The teachers re-ported they appreciated the students' abilitiesto quickly acquire and successfully follow thenumber of steps needed to solve tbe subtrac-


tion problems with regrouping. All involvedagreed that others would benefit from expo-sure to the TouchMath© program and that itwas easy to learn and use in the classroom.The ease of use was also evaluated and thestudents stated that once they understood thesteps and sequence (e.g., counting the dot-notations on the numbers, etc.), the touch-points strategy was a fun, and an easy way tolearn how to solve subtraction problems. Inaddition, all of the groups indicated that theyagreed or strongly agreed that the skillsgained were necessary for the students to havebefore leaving high school to prepare themfor real-life situations. All involved agreed thatthe skill was grade appropriate and necessaryfor classroom requirements. The students re-ported that they were neutral when consider-ing the skills crucial for grade-level require-ments; however, they all agreed that thetouch-points strategy was helpful to learningmathematics and would recommend the strat-egy to their peers. Finally, all of the respon-dents agreed that money computation skillsare an important and critical skill essential forindependent living in the community.

Discussion

The purpose of this study was to examine theeffects of the TouchMath© program on theacquisition of subtracting 3-digit money com-putational problems vnth regrouping forthree students with mild intellectual disabili-ties in a high school special education self-contained classroom. The findings indicatedthat the use of the touch-point strategy waseffective for all three students in acquiring3-digit money computational problems withregrouping. Findings from this study not onlyadd to the previous literature base on theTouchMath® program, but also provide newinsights into applications to teach money com-putational skills to students at the high schoollevel. As previous studies have suggested, thetouch-points strategy procedures have beenshown to be effective to increase the mathe-matics performance for elementary-age studentswith specific learning disabilities, moderateintellectual disabilities, and autism spectrumdisorders (Cihak & Foust, 2008; Scott, 1993;Simon & Hanrahan, 2004), and at the middleschool level including students with autism

spectrum disorders and moderate intellectualdisabilities (Fletcher et al.). Thus far, no re-search has been conducted on the use of theTouchMath© program with money values, in-cluding students with mild intellectual disabil-ities at the high school level.

During the baseline phase, all three of thestudents demonstrated an inability to solve3-digit subtraction problems with regrouping.There was an abrupt level change for all threestudents with no overlapping data points indi-cating an increase in performance and contin-ued level of competence. An ascending trendwas observed for the students during the in-tervention phase exhibiting marked perfor-mance when the intervention was employed.These observations provide evidence that theintervention was effective in teaching the stu-dents via the touch-points strategy to subtract3-digit money values with regrouping. Duringthe intervention probes phase, two of thethree students, Trent and Michael, showeddramatic increases in their mathematics per-formance and reached criterion in the allot-ted amount of time, five sessions. However,the third student, Alex, required a total of 10sessions to reach criterion. During the secondsession, Alex scored well on the second probebut only scored 30% on the following probe.This low score caused Alex not to reach crite-rion in the allotted amount of time. On sub-sequent probe scores, Alex averaged 91.4%over the last seven probes. If the one probewere erased then Alex would have reachedcriterion in five sessions. Finally, during themaintenance phase, all three of the students'mathematics performance showed great vari-ability. For example, Trent sustained an as-cending trend throughout the study. After sixsessions, Trent retained the necessary targetskill set to solve the subtraction problems withregrouping. Michael demonstrated a descend-ing trend across four of the maintenance ses-sions with a median score of 35%. After theminimum two-day period, Alex completedone maintenance session with a score of 100%before the conclusion of the study. Clearly,further research is needed to determine theability for students with mild intellectual dis-abilities to sustain the skills necessary to sub-tract 3-digit money values with regrouping. To


help continue maximum skill proficiency overtime, refresher sessions to review the steps andprocedures of the touch-points method wouldbe required and additional maintenanceprobes may need to be conducted.

Limitations of the Study

The following limitations need to be consid-ered to interpret the findings of this study.First, the number of students, only three stu-dents, makes it difficult to support argumentsfor generalization of the touch-points strategyto all students at the high school level. Also,the sample only included students with mildintellectual disabilities and/or autism spec-trum disorders and does not represent thecharacteristics of typical school-age popula-tions. So, the findings cannot be generalizedto other disability categories, age, grade, race,and/or other genders. For instance, all threeof the students were male in ninth and tenthgrade levels. Second, the instructional proce-dures were conducted on a one-to-one basisand would need to be modified for groupinstruction. Third, during the interventionand maintenance phases, the students wereprovided the "dot-notations" on the numbersand a line to vmte the lowered number forregrouping on the worksheets; however, thislimits their ability to fully apply and generalizethe strategy to novel situations. Also, the pro-cedures included only one specific target skillset (e.g., 3-digit subtraction problems with re-grouping with money values) limiting the abil-ity to generalize these findings to other math-ematical skills. Fourth, due to studentcapability levels, addition and subtractionwithout regrouping were not considered norwere higher skill level problems. Maintenancedata was inconsistent and only one probe wasgathered from the last student, Alex, due to aholiday and conclusion of the project, as fur-ther investigations are obviously warranted ex-amining maintenance capacities of the touch-points strategy.

Implications

Based on the results of this study and previousfindings, there are a number of implicationsfor classroom teachers, both general and spe-

cial education to consider. The TouchMath©program is an easy, simple, and teacher-friendly method to employ as a component ofthe instructional lesson in a self-contained,remedial and/or inclusive classroom setting.The results support a promising and growingresearch-base for the use of the TouchMath©strategy to help students not only with mildintellectual disabilities and/or autism, butother disability categories, as well as studentswithout disabilities, that exhibit difficulties inbasic mathematics instruction. Also, the pro-gram allows teachers to adapt their instruc-tion, at a developmentally appropriate level,to meet the student's individual needs andlearning styles. More recentiy, TouchMath©has developed a variety of new products toteach such concepts as money applications,coins and counting, mathematics manipula-tives (e.g., math fans), and a software programknown as TouchMath Tutor©, that can easily bemodified for students to teach functional skillsin a variety of clcissroom and community-based settings.

Future Research

In the current research literature base, nopublished, empirical studies have examinedthe effectiveness of the TouchMath© strategyto teach students with mild intellectual disabil-ities to subtract money values, in fact, evenmore noteworthy, no studies have exploredthis technique with high school populations,as much of the limited research-base focusesalmost exclusively on elementary-age popula-tions. Future research should address the useof the touch-points method with not only ad-dition and subtraction problems, but withmultiplication and division problems, with twoand three-digits, with and without regrouping,for students with different types of disabilitiesin the secondary grade levels. Also, futurestudies should employ experimental groupdesigns to determine if the strategy can beimplemented on a larger scale to reach morethan one student at a time. Further consider-ation towards fading the intervention and pro-viding students additional training time tomemorize and independentiy mark the touch-points properly on the numbers before solv-ing the problem is necessary to determine theefficacy of the strategy. Finally, the probe


problems employed in this study presentedone instance of regrouping within the prob-lem; therefore, generalization to more diffi-cult skills such as multiple regrouping oppor-tunities or regrouping with zero in theproblem should be examined.

References

Alberto, P. A., & Troutman, A. C. (2009). Appliedbehavior analysis for teachers (8* ed.). Upper SaddleRiver, NJ: Pearson Education, Inc.

Browder, D. M., & Grasso, E. (1999). Teachingmoney skills to individuals with mental retarda-tion: A research review with practical applica-tions. Remedial and Special Education, 20, 297-308.

Browder, D. M., Spooner, F., Ahlgrim-Delzell, L.,Harris, A., & Wakeman, S. Y. (2008). A meta-analysis on teaching mathematics to students withsignificant cognitive disabilities. Exceptional Chil-dren, 74, 407-432.

Bullock, J., Pierce, S., & McClellan, L. (1989). TouchMath. Colorado Springs, Go: Innovative LearningConcepts.

Buder, F. M., Miller, S. P., Kit-hung, L., & Pierce, T.(2001). Teaching mathematics to students withmild-to-moderate mental retardation: A review ofthe literature. Mental Retardation, 39, 20-31.

Cihak, D., & Foust, J. (2008). Comparing numberlines and touch points to teach addition facts tostudents with autism. Focus on Autism and OtherDevelopmental Disabilities, 23, 131-137.

Cooper, J. O., Heron, T. E., & Heward, W. L.(2007). Applied behavior analysis (2^ ed.). UpperSaddle River, NJ: Merrill.

Fletcher, D., Boon, R., & Cihak, D. (2010). Effects ofthe TouchMath program compared to a numberline strategy to teach addition facts to middleschool students with moderate intellectual dis-abilities. Education and Training in Autism and De-velopmental Disabilities, 45, 449-458.

Harrison, P. L., & Oakland, T. (2003), Adaptive Be-havior Assessment System (2nd ed.). San Antonio,TX: The Psychological Corporation.

Individuals with Disabilities Education Improve-ment Act of 2004, 20 U. S. C. §§ 1400-1485 (2004supp. IV), Pub. L. No. 108-446 (2004), 108*Congress, Second Session.

Jitendra, A. K., & Xin, Y. (1997). Mathematicalproblem solving instruction for students withmild disabilities and students at risk for mathfailure: A research synthesis. The Journal of SpecialEducation, 30, 412-438.

Kramer, T., & Krug, D. A. (1973). A rationale and

procedure for teaching addition. Education andTraining of the Mentally Retarded, 8, 140-145.

Kroesbergen, E. H., & Van Luit, J. (2003). Mathe-matics interventions for children with special ed-ucational needs: A meta-analysis. Remedial and Spe-cial Education, 24, 97-114.

Mastropieri, M. A., Bakken, J. P., & Scruggs, T. E.(1991). Mathematics instruction for individualswith mental retardation: A perspective and re-search synthesis. Education and Training in MentalRetardation, 26, 115-129.

Miller, S. P., Butler, F. M., & Lee, K (1998). Vali-dated practices for teaching mathematics to stu-dents with learning disabilities: A review of liter-ature. Focus on Exceptional Children, 31, 1-24.

National Council of Teachers of Mathematics.(2000). Principles and NCTM Standards for schoolmathematics. Reston, VA: The National Council ofTeachers of Mathematics, Inc.

No Child Left Behind Act of 2001, Public Law 107-110, 107"' Congress, First Session.

Scott, K S. (1993). Multisensory mathematics forchildren with mild disabilities. Exceptionality, 4,97-111.

Simon, R., & Hanrahan, J. (2004). An evaluation ofthe touch math method for teaching addition tostudents with learning disabilities in mathematics.European Journal of Special Needs Education, 19,191-209.

Swanson, H. L., &Jerman, O. (2006). Math disabil-ities: A selective meta-analysis of the literature.Review of Educational Research, 76, 249-274.

U. S. Department of Education. (2007). Twenty-ninth annual report to Congress on the implementationof the Individuals with Disabilities Education Act(IDEA). Washington, DC: Author.

Wechsler, D. (1991). Wechsler Intelligence Scale forChildren-Third Edition. San Antonio, TX: Psycho-logical Corporation.

Wolf, M. M. (1978). Social validity: The case forsubjective measurement or how applied behav-ioral analysis is finding its heart. Journal of AppliedBehavior Analysis, 11, 203-214.

Woodcock, R. W., McGrew, K S., & Werder, J. K.(1994). Woodcock-McOrew-Werder Mini-Battery ofAchievement. Chicago, IL: Riverside Publishing.

Xin, Y. P., & Jitendra, A. K (1999). The effects ofinstruction in solving mathematical word prob-lems for students with learning problems: A meta-analysis. The foumal of Special Education, 32, 207-225.

Received: 7 September 2010Initial Acceptance: 2 November 2010Final Acceptance: 23 February 2011


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TITLE: Teaching Money Computation Skills to High SchoolStudents with Mild Intellectual Disabilities via theTouchMath© Program: A Multi-Sensory Approach

SOURCE: Educ Train Autism Dev Disabil 46 no4 D 2011

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HARRISON STREET INTERVENTION · Created Date: 1/5/2012 1:44:43 PM

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