Axe & Sainato, 2010

MATRIX TRAINING OF PRELITERACY SKILLS WITHPRESCHOOLERS WITH AUTISM

JUDAH B. AXE AND DIANE M. SAINATO

THE OHIO STATE UNIVERSITY

Matrix training is a generative approach to instruction in which words are arranged in a matrix sothat some multiword phrases are taught and others emerge without direct teaching. We taught 4preschoolers with autism to follow instructions to perform actionpicture combinations (e.g.,circle the pepper, underline the deer). Each matrix contained 6 actions on 1 axis and 6 pictureson the other axis. We used most-to-least prompting to train the instructions along the diagonalof each matrix and probed the untrained combinations. For 2 participants, untrained respondingemerged after the minimum amount of training. The other 2 participants required furthertraining before untrained combinations emerged. At the end of the study, 3 of the 4 participantsperformed the trained actions with previously known pictures, letters, and numbers. This studydemonstrated that matrix training is an efficient approach to teaching language and literacy skillsto children with autism.

Key words: letter identification, matrix training, number identification, picture identifica-tion, recombinative generalization

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Children with autism often exhibit delays inthe acquisition of language (Eikeseth & Hay-ward, 2009; Rapin, 2006) and literacy skills(Mirenda, 2003). Educational approaches toincreasing language often involve direct trainingof listener and speaker repertoires (Lovaas,1987; Sundberg & Partington, 1998). In thearea of literacy, many children with autismexhibit delays in reading and basic readinessskills used to maximize academic achievement,such as writing (Katims & Pierce, 1995;Nation, Clarke, Wright, & Williams, 2006).With the No Child Left Behind Act (2001)holding students with autism to grade-levelstandards, researchers must continue to identifyeffective techniques for teaching literacy skills tostudents with autism (Yell, Drasgow, & Low-

rey, 2005). One approach is to target thereading and writing behaviors that precedeliteracy development, such as looking at books,listening to others read books, constructingstories from pictures and writings, scribbling,and writing (Koppenhaver & Erickson, 2003;Teale & Sulzby, 1986). Although most of thisresearch has focused on adolescents with autism,Denton and West (2002) found preschoolchildren with letter-naming skills and letterknowledge performed better on measures ofphonological awareness and word reading infirst grade than did children without letterknowledge. There is clearly, however, a dearthof research on methods of teaching literacy skillsto young children with autism.

Although interventions that target languageand literacy skills with children with autismhave been effective, it is difficult for educationalprograms to address all the individual skillsrequired for children with language delays tomeet the standards of their same-age peers(Mackay, Kotlarchyk, & Stromer, 1997). Onemethod to address this problem is generativeinstruction, which allows educators to directlyteach one set of skills so that others emergewithout direct teaching (Johnson & Layng,

Correspondence concerning this article should beaddressed to Judah B. Axe, who is now at the Departmentof Education, Simmons College, Boston, Massachusetts02115 (e-mail: [email protected]).

doi: 10.1901/jaba.2010.43-635

This research was based on the doctoral dissertation ofthe first author. We thank Ashley Kremer, AlaynaHaberlin, Jessie Chung, Manoel Rodriguez-Neto, Len-wood Gibson, and Ruth DeBar for their assistance withdata collection. We also thank William Heward, NancyNeef, Michael Cameron, and the anonymous reviewers fortheir helpful comments on previous drafts of this article.

JOURNAL OF APPLIED BEHAVIOR ANALYSIS 2010, 43, 635652 NUMBER 4 (WINTER 2010)

635

1992; Layng, Twyman, & Stikeleather, 2004;Rehfeldt & Barnes-Holmes, 2009; Sidman,1994). Matrix training, one form of generativeinstruction, has been used to teach listener skillsand labeling with multicomponent phrases,such as learning to label colorobject combina-tions with children with mental retardation(Goldstein & Mousetis, 1989; Karlan et al.,1982; Remington, Watson, & Light, 1990;Striefel et al., 1978). For example, a 2 3 2matrix can be arranged with two colors on oneaxis and two objects on the other axis, resultingin four colorobject combinations. If two of thefour combinations are trained, the other twomay emerge without direct training. Forexample, if a child is taught to label red carand blue boat, the responses blue car andred boat may emerge without direct training.Goldstein (1983a) termed this outcome recom-binative generalization, because the constituentsof trained combinations are arranged in newcombinations based on environmental require-ments. Arranging targets in a matrix andteaching along the diagonal of the matrix allowsefficient instruction, in that skills are learnedwithout direct teaching.

Goldstein, Angelo, and Mousetis (1987)evaluated matrix training with three individualswith severe mental retardation. They targetedlabeling and instruction following, and arrangedboth known and unknown words in matrices.In the submatrices with known words, Gold-stein et al. taught one combination and probedthe untrained combinations. Once the partici-pants met the performance criterion withknown words, training commenced with un-known words. All correct responses duringprobes received reinforcement, and correctivefeedback was not provided. Results suggestedthat training one combination of known wordsreadily produced responding with the newcombinations with the known words. Resultsalso showed that training one combination withpreviously unknown words produced correctresponding to the other unknown word com-

binations. Goldstein et al. noted that 94% to98% of the learning was untrained.

Two studies have examined matrix trainingspecifically with children on the autism spec-trum. Kinney, Vedora, and Stromer (2003)taught generative spelling using video modelingto a first-grade girl. In the video, an adultmodeled spelling a word on a large sheet ofpaper with videos as rewards. In Phase 1, theparticipant learned to spell 15 words with videomodeling. Phase 2 revealed that she did notexhibit recombinative generalization based onthe words learned in Phase 1. In Phase 3, shewas taught to spell five words and spelled fourother words without training. In Phase 4, shewas taught to spell nine words and learned 18words by recombining initial consonants andword endings. This study extended the researchon matrix training and video modeling to teachgenerative spelling to a child with autism.

In another study, Dauphin, Kinney, andStromer (2004) used video-based activityschedules and matrix training to teach socio-dramatic play to a 3-year-old boy with autismspectrum and attention deficit hyperactivitydisorders. In Phase 1, the participant was taughtto follow video-based activity schedules, sayfour-word phrases (e.g., Dinosaur, want torun?), and perform objectaction combina-tions (e.g., Bear have a bite, Rabbit take adrink) across the diagonals of 3 3 3 matrices.Ten sessions of most-to-least prompting wereeffective in producing 21 of the 28 novelphrases and four of the six novel actions. In afollow-up phase, training of new objectactioncombinations was similar to the first phase, butDauphin et al. tested responses using picturesrather than videos. The participant performedmost of the untrained combinations.

The purpose of the current study was toextend the literature in two ways, first toevaluate matrix training with children withautism (Dauphin et al., 2004; Kinney et al.,2003) and second to extend the research tofocus on the early literacy skills of writing and

636 JUDAH B. AXE and DIANE M. SAINATO

identifying letters and numbers. In addition,whereas least-to-most prompting was employedin most previous matrix-training studies, most-to-least prompting was used in the currentstudy to promote errorless learning (Massey &Wheeler, 2000; Touchette & Howard, 1984).

METHOD

Participants

We recruited preschool children who had adiagnosis of autism; significant delays ininstruction following, writing skills, pictureidentification, and labeling; and mild or nochallenging behavior. Four children (4 to 5 yearsold) participated. All four could make simplerequests, identify letters, and identify numbersunder 20. Matt was a Caucasian boy with a full-scale IQ of 91 on the Leiter InternationalPerformance ScaleRevised (Leiter-R; Roid &Miller, 1995). On the Battelle DevelopmentalInventory (BDI; Newborg, Stock, Wnek,Guidubaldi, & Svinicki, 1994), his age equiv-alent was 21 to 22 months in the receptive,expressive, and total communication subdo-mains. At the time of the study, he spoke inone- to two-word sentences when prompted.He exhibited delays in responding to greetingsand to his name, taking turns with peers,identifying objects and pictures, and answeringyesno questions. Rex was a Caucasian boywhose full-scale IQ on the Leiter-R was 106.On the BDI, he scored in the 30- to 31-monthage equivalent on the receptive communicationsubtest, 43 months on the expressive commu-nication subtest, and 36 months on the totalcommunication subtest. He spoke in complexsentences but exhibited delays with conversationand pragmatic aspects of language. At the timeof the study, his individualized educationprogram goals were to increase his discrimina-tion and classification skills, prewriting andother fine-motor skills, and conversation skills.

Trey was an African American boy with afull-scale IQ of 81. On the BDI, his ageequivalents were 21 to 22 months, 14 months,

and 16 months on the receptive, expressive, andtotal communication subdomains, respectively.He spoke in one- to two-word sentences whenprompted and often needed many reminders tocomply with simple instructions. When he wasgiven instructions that broke routines, he oftenwhined and cried. At the time of the study,Treys educational goals included requestingassistance, following one- to two-step verbaldirections, requesting reinforcers, and tracingletters. Nina was a Caucasian girl with a full-scale IQ of 82. She scored in the 17 to18 months, 27 months, and 22 months ageequivalents on the receptive, expressive, and totalcommunication subdomains of the BDI, respec-tively. She spoke in five-word sentences and wasecholalic. Her educational goals were to completewriting tasks (e.g., make shapes, trace letters),request reinforcers, take turns with adults, use apicture schedule to make smooth transitions, andfollow one-step verbal directives.

Setting and Materials

The study took place at a private inclusivepreschool for children with autism spectrumdisorders. We conducted sessions in a smallprivate room in the school (8 m by 5 m). Theexperimenter sat with each participant at a smalltable next to a video camera. Materials were acup with utensils (pencil, highlighter, stamp,scissors, pen), a timer, toys (books, sensory toys,toy cars, bubbles, balloons), and three types ofprobe sheets (21.6 cm by 28 cm with colorphotographs that were 3 cm by 3 cm). Thetypes of probe sheets included (a) pictures in theprimary matrices (six target photographs and sixdistracter photographs arranged in three rows),(b) previously known pictures (six photographsarranged in two rows), and (c) previouslyknown letters and numbers (16 large-printletters and numbers arranged in four rows).We prepared three versions of each type of sheetto vary the order of pictures for each trial. Thephotographs used in training (see below) werethe same size and style as those in the probesheets.

MATRIX TRAINING 637

Dependent VariableThe dependent variable was percentage of

correct instruction following in each probesession, defined as performing the action withthe picture, letter, or number that matched thespoken words from the experimenter (e.g.,underline the pepper, stamp the deer) within5 s of the instruction. Instruction following wasfurther defined as diagonal trained and non-diagonal untrained. Diagonal trained refers toresponses that were either targeted for training(i.e., on the diagonal of the matrix) or directlytrained (i.e., if more cells other than those onthe diagonal were trained). Nondiagonal un-trained refers to responses that were not targetedfor training (i.e., not on the diagonal) orresponses that were never trained (i.e., if othercells other than those on the diagonal weretrained).

Interobserver AgreementThe experimenter trained graduate students

in special education and applied behavioranalysis on the definition and measurement ofthe dependent variable. The observers indepen-dently scored instruction following from video-tapes across phases and tiers in 29%, 30%,31%, and 30% of sessions for Matt, Rex, Trey,and Nina, respectively. Interobserver agreementof the probes of performing actions withpreviously known pictures, letters, and numberswas measured in 50%, 25%, and 75% ofsessions for Matt, Rex, and Trey, respectively(these probes were not conducted with Nina).Agreement was defined as both observersscoring the response as being correct orincorrect and diagonal trained or nondiagonaluntrained. Interobserver agreement was calcu-lated by dividing the number of agreements bythe sum of the agreements and disagreementsand converting the ratio to a percentage. Meanagreement was 100% for Matt and Trey. Meanagreement for Rex was 100% in the baselineand maintenance phases and 86% (range, 0% to100%) in the training phase. Mean agreementfor Nina was 100% in baseline and mainte-

nance and 99% (range, 92% to 100%) in thetraining phase. In the probes of actions withpreviously known pictures, letters, and num-bers, agreement was 100% for Trey and Rexand 94% for Matt.

Design

A multiple probe design across behaviors wasemployed (Cooper, Heron, & Heward, 2007).For each participant, there were four tiers of themultiple probe design corresponding to the foursubmatrices in the matrix targeted for eachparticipant (Figure 1). That is, the bold lines inFigure 1 separate Submatrices 1 through 4assigned to Tiers 1 through 4 in the multipleprobe design. The three phases were baseline,training, and maintenance. A probe sessionoccurred each time the experimenter met with aparticipant. In baseline and maintenance, only aprobe session occurred. In training, a trainingsession followed the probe session in which theexperimenter trained the cells along the diago-nal of the matrix in accordance with themultiple probe design.

The following criteria were applied to thedesign: Following baseline, training occurred ifresponding was less than 90% correct ondiagonal trained instructions in the probe.Once performance was at 90% correct or higheron one probe of diagonal trained instructions,we administered probes of nondiagonal un-trained instructions. Following three sessions of90% correct or higher on diagonal trainedinstructions and 50% correct or higher onnondiagonal untrained instructions, we con-ducted a series of baseline sessions in the nextsubmatrix to ensure that the participantsresponding was stable. Following three consec-utive sessions of 90% correct or higher ondiagonal trained instructions and less than 50%correct on nondiagonal untrained instructions,we trained a new cell from the submatrix. Weinitially selected a new cell randomly. If a fewextra cells were trained and untrained respond-ing still did not exceed criterion, we selectednew cells for training based on a high


probability of their promoting untrained in-struction following. For example, in Submatrix2 (Figure 1), if we trained three cells with theaction, put an X on, and we trained only onecell with highlight, we trained a newhighlight cell. We probed two other 6 3 6matrices at the beginning and end of the study.One matrix contained the same actions as theprimary matrix with previously known pictures(e.g., animals and foods). The other matrixcontained the same actions as the primarymatrix with randomly selected, previouslyknown letters and numbers (S, V, P, 4, 7, 9).

Procedure

The experimenter met with each participantonce or twice per day, 5 days per week, for 10 to30 min each meeting.

Preassessment. We conducted informal inter-views with the participants teachers to identifypotential reinforcers and target skills. Potentialreinforcers were enthusiastic praise, books, andpreferred toys. Access to these items for 20 s to40 s was used to reinforce compliance and

correct responding during preassessments,warm-ups, probes, and training.

We conducted five 15-min preassessmentsessions over the course of 5 days with eachparticipant to identify actions, pictures, letters,and numbers to use in the study. First, theexperimenter tested 13 actions by presenting theletter A on a sheet of paper and the cup ofutensils and saying, [action] on the A (e.g.,circle the A, stamp the A). Second, theexperimenter tested 30 pictures by presentingseveral sheets of paper with 12 differentrandomly distributed pictures on each paperand asking each participant, Where is the[picture]? Third, the experimenter testedreceptive discrimination of letters and numbersby presenting four letters or numbers at a timeand asking the participant to select a letter ornumber (e.g., point to the 3). We tested allthe letters and numbers up to 20. Correct andincorrect responses did not produce feedback. Ifthe participant did not make a response within5 s, the experimenter repeated the instruction. Ifthe participant did not make a response within

Figure 1. Actionpicture matrix used for Matt, Trey, and Nina. Bold lines separate each submatrix, and eachsubmatrix was assigned to a tier in the multiple probe design.

MATRIX TRAINING 639

another 5 s, the experimenter made a neutralstatement (e.g., okay) and delivered the nextinstruction. After every four to six trials, theexperimenter presented known instructions(e.g., clap your hands, touch your head),and compliance produced a choice of preferreditems (e.g., books, toys).

The preassessment criterion to identifyunknown actions was zero of three trials correct.Criterion to identify unknown pictures was zeroof three presentations correct or less than 20%correct on at least six presentations. Criterion toidentify distracter pictures was 75% correct orless on at least four presentations or 0% correcton two presentations. Criterion to identifyknown pictures, letters, and numbers was100% correct in at least three presentations.As a result of this preassessment, five sets oftargets were identified: unknown actions, un-known pictures, distracter pictures (to bepresented on primary probe sheets with targetpictures), known pictures (to be tested in amatrix at the beginning and end of the study),and known letters and numbers (to be tested ina matrix at the beginning and end of the study).Figure 1 is the primary matrix used by Matt,Trey, and Nina. Based on his performances onpreassessments, Rexs matrix had put a sunon and put a check on instead of stampand circle. In addition, Rexs pictures wereonion, anchor, potato, lettuce, sta-pler, and spinach.

Probes. A probe session occurred first duringeach meeting with a participant. Each probesession began with a warm-up in which theexperimenter presented two to three knowninstructions (e.g., touch your nose, clapyour hands), and compliance resulted in apreferred item or choice of preferred items. Ineach probe trial, the experimenter presented asheet of paper with six target pictures from thematrix, six distracter pictures, and the cup withutensils. The experimenter used three versionsof the probe sheets so that the order of pictureswas different for each trial. The order of

instructions was also randomized, but diagonaltrained instructions occurred before nondiago-nal untrained instructions. After the warm-up,the experimenter presented each instruction toperform an actionpicture combination in theform, get ready, [action] the [picture] withexaggerated and elongated inflection on theaction and picture. Correct responses produceda choice of preferred items. Incorrect responsesresulted in the presentation of the next trial withno feedback. If there was no response after 5 s,the experimenter repeated the instruction. Ifthere was no response following another 5 s, theexperimenter presented the next instruction.Following four to six consecutive incorrectresponses or no responses, the experimenterpresented two to three known instructions (e.g.,touch your head, stomp your feet) and apreferred item contingent on compliance.

Training. In the training phase, a trainingsession immediately followed the probe session.Each training session lasted 11 to 13 min andconsisted of 20 to 40 trials. A training trialconsisted of presenting the pictures, the utensils,giving the instruction, providing prompts,providing the opportunity for the participantto make a response, reinforcing correct respons-es, and re-presenting instructions and promptscontingent on errors (more details below). Eachsession started with the experimenter presentingtwo to three known instructions (e.g., touchyour tummy, touch your ears) and a choiceof preferred items contingent on compliance.Each training trial began with the presentationof the cup with utensils, a picture or pictures,and an instruction, get ready, [action] the[object] with elongated and exaggerated in-flection on the action and picture. Whentraining a new actionpicture combination,the experimenter showed the picture aloneand provided model and physical prompts toperform the action. According to the followingseven steps, the experimenter gradually addeddistracters and faded prompts. Four correctresponses at each step were required to proceed


to the next step. In Step 1, the experimentershowed a picture alone, presented the instruc-tion, modeled the response, re-presented theinstruction, and physically guided the response.Step 2 was the same but the experimenter didnot present the physical prompt. In Step 3, theexperimenter presented a distracter picture withthe target picture. Step 4 was the same as Step3, but the experimenter only used a pointprompt. In Step 5, the experimenter added asecond distracter and did not use the pointprompt. The experimenter used Step 6 onlywhen a participant was learning two newinstructions, as in Submatrices 1 and 2. In thisstep, the experimenter presented two newpictures with one distracter picture and alter-nated between the two target instructions. InStep 7, the experimenter presented the probesheet (i.e., 12 pictures), and training occurredwith the two target instructions. The trainingsession ended when the participant correctlyresponded to the new actionpicture combina-tions in Step 7 or when 13 min had passed.

In training sessions, the experimenter rein-forced all prompted and unprompted responses.If at any step the participant did not respondwithin 5 s or performed an incorrect response,the experimenter immediately re-presented theinstruction and presented the prompt from theprevious step in the sequence (e.g., a modelprompt after an error with a point prompt). Acorrect response with a prompt following anerror was reinforced in Steps 1 through 3. InSteps 4 through 7, the experimenter did notreinforce a correct prompted response followingan error. The experimenter re-presented theinstruction without the prompt and thenreinforced a correct response. After a participantprogressed through Steps 1 through 7 for aparticular actionpicture combination, subse-quent training sessions were slightly different.First, all training trials occurred with the probesheet (i.e., 12 pictures were presented). Second,if a participant was incorrect on a particularinstruction in the probe session, the experi-

menter presented a model prompt in the firsttraining trial for that instruction.

We made procedural modifications for Rex,Trey, and Nina. For Rex, the general proce-dures were ineffective in establishing trianglesand suns. We placed dots on the trainedpictures for Rex to connect, and given correctresponding, we faded the intensity of the dots intwo phases across two sessions. We made threemodifications for Trey. First, Trey resistedphysical prompts, and they were not used.Second, because his underlines were too long,we placed dots under the pictures for him toconnect. Third, when he was given an untrainedinstruction, he reached for the correct utensiland then pointed to the correct picture. Whenhe reached for a utensil in the probes of Sessions46 through 48, the experimenter pointed to itand said, yes, [action] the [picture].

We made seven modifications for Nina: threein the error-correction procedures, three inseparating the components of the instructions,and one in the feedback for correct responses.These seven modifications were added andremoved across training sessions as the experi-menter attempted to bring her respondingunder stimulus control of the instructions.First, in Sessions 8 and 9, the experimenterpresented known instructions (e.g., give mefive, touch your head) between prompted,correct, unreinforced responses and unprompt-ed, correct, reinforced responses. Second, inSessions 8, 10, 11, 40, 43, 44, 45, 48, 49, and54, the experimenter presented training trialswith the same picture but different actions infast alternation without reinforcement untilNina was correct with two different actions intwo consecutive trials. Third, in Sessions 10, 22,44, and 45, the experimenter said, with whichone do you [action]? and reinforcement wascontingent on selecting the utensil that matchedthe action. Fourth, in Sessions 11, 38, and 44,the experimenter gave Nina descriptive feed-back following correct performances (e.g.,thats right, you stamped the deer). Fifth, in

MATRIX TRAINING 641

Sessions 12, 45, 46, and 47, the experimenterseparated instructions according to this proce-dure: The experimenter said the action, Ninaselected the utensil, the experimenter said thename of the picture, and Nina performed theactionpicture combination. Sixth, in Sessions38, 40, and 43, the experimenter did notreinforce prompted responses following errorsand then re-presented the instruction with apreferred item delivered contingent on a correctresponse. Seventh, in Sessions 55 through 58,the experimenter presented a picture of a car(previously known) alone and prompted andreinforced the four actions from Submatrices 1and 2 with the car.

Procedural Integrity

For measurement of procedural integrity,correctly implemented training steps was definedas following the scripted set of proceduresaccording to Steps 1 through 7 in theProcedure. For example, in Step 1 (below),the experimenter presented the picture alone,gave the instruction, modeled the actionresponse, said you do it, presented a cleanpicture and the instruction, physically guidedthe response, and praised and delivered areinforcer contingent on a correct response.Observers also measured correctly implementedsteps in the probe, defined as the experimenterfollowing the script for conducting probesessions. This involved doing warm-up instruc-tions, presenting the probe sheet with thecorrect instruction, reinforcing correct respons-es, and presenting known instructions followingfour to six incorrect responses. A secondobserver independently measured the integrityof the training and probe procedures in 22% to24% of randomly selected probe and trainingsessions across participants. Integrity was calcu-lated by dividing the correctly implementedsteps by the sum of correctly and incorrectlyimplemented steps and converting the ratio to apercentage. Mean integrity was 95% for Mattand 99% for Rex, Trey, and Nina (range acrossparticipants, 91% to 100%). Mean integrity of

implementing the probe procedures as de-scribed was 94% (range, 94% to 100%) acrossparticipants, phases, and submatrices, with theexception of a mean of 50% integrity (range,0% to 100%) for Submatrix 3 of training forRex. This score of 0% occurred when theobservers measured only two responses in asession, and there was disagreement on thesetwo responses.

Social Validity

After the study, data on social validity werecollected from seven respondents: Rexs teacher,Ninas teacher, the participants speechlan-guage pathologist, the principal of the school,Matts and Rexs mothers, and a kindergartenteacher. The experimenter explained the proce-dures and outcomes of the study, and therespondents watched 1- to 2-min video clips ofprobes at the beginning and end of the study aswell as the training procedures. The respon-dents completed a questionnaire with sevenquestions, asking about the procedures using a7-point Likert scale (e.g., How much do youlike the teaching procedures? How confident areyou that the procedures would be effective?How likely would you be to use matrixtraining?). Seven additional questions askedrespondents to rate their agreement withstatements about the outcomes on a 7-pointLikert scale (e.g., the student learned languageskills, the student learned preacademic skills, thestudent is more prepared for kindergarten, theteaching strategies were more efficient thantypical teaching strategies, based on the out-comes I would recommend the teachingstrategies). We also asked open-ended questionsregarding strengths and weaknesses of theprocedures and outcomes. The respondentsrated the procedures a mean of 5.9 andoutcomes a mean of 6.1, where 1 was dontagree or unacceptable and 7 was strongly agree oracceptable. A frequently noted concern was thetransferability of the teaching procedures andmatrix strategy from a one-on-one setting to aclassroom situation.


RESULTSData for correct instruction following in the

probes are displayed in Figures 2 through 5.Matt was 0% correct in baseline in Submatrix

(S) 1 and near 50% correct in S2 through S4(Figure 2). Training consistently produced100% correct responding to diagonal trainedinstructions and 70% to 100% correct respond-

Figure 2. Matts percentage of correct diagonal trained and nondiagonal untrained instruction following across the

36 instructions in the matrix.

MATRIX TRAINING 643

ing to nondiagonal untrained instructions.Maintenance of responding was 80% to100%, with the exception of two probes ofnondiagonal untrained instructions in S1 at50% correct. Results for Rex (Figure 3) were

similar to Matts. Rexs baseline responding wasat or near 0% in S1 and S2, 0% for diagonalinstructions in S3 and S4, and near 50% fornondiagonal instructions in S3 and S4. Herequired a few more training sessions than Matt

Figure 3. Rexs percentage of correct diagonal trained and nondiagonal untrained instruction following across the 36instructions in the matrix.


to meet criterion in S1 and S2. Maintenancewas 100% correct in all but one session.

Trey was 0% correct in baseline in S1 and S2(Figure 4). He received training on all four

instructions from S1 and was 0% correct onnondiagonal untrained instructions. In S2, hemet criterion on the two diagonal instructionsbut his behavior did not generalize, so he was

Figure 4. Treys percentage of correct diagonal trained and nondiagonal untrained instruction following across the36 instructions in the matrix. Vertical dotted lines indicate that a new cell was trained. The asterisk indicates when aprocedural modification was implemented.

MATRIX TRAINING 645

trained on an additional instruction (highlightdeer, represented by a dotted line on thegraph). After meeting criterion on those threeinstructions, the third procedural modification(i.e., pointing to the correct utensil and saying,yes, [action] the [picture]) was employed.This resulted in an initial decrease and then

increase in correct responding to the trainedinstructions (Sessions 46 through 51). After 10instructions received training as part of themodification (four were reinforced only once),the two untrained instructions were 100%correct. Following these performances, Treysresponding to all instructions in S3 and S4

Figure 5. Ninas percentage of correct diagonal trained and nondiagonal untrained instruction following across the36 instructions in the matrix. Vertical dotted lines indicate that a new cell was trained. Asterisks indicate when proceduralmodifications were implemented.


increased to between 80% and 100% correctwithout training. Responding was maintainedat 70% to 100% correct.

For Nina, baseline responding was 0%correct in S1 and S2 (Figure 5). She followedone untrained instruction after training on threeinstructions in S1. In S2, she met criterion onfive trained instructions, and untrained re-sponding was 20% to 50% correct. In S2,criterion was not met for proceeding to a newsubmatrix. Because the untrained response in S1was not maintained, it was retrained followedby 100% correct responding to all instructionsin S1 in the maintenance condition. Respond-ing in S3 and S4 remained at 0% correct, withthe exception of the final probe in S4.

In the two additional 6 3 6 matrices ofactions with previously known pictures andactions with previously known letters andnumbers, Matt, Rex, and Trey were 0% correctprior to training. At the end of the study, Matt,Rex, and Trey were 83%, 97%, and 94%correct on the probes of actions with previouslyknown pictures and 92%, 94%, and 89%correct on the probes of actions with letters andnumbers, respectively. We did not conduct theprobes with Nina because she did not completethe primary matrix.

In terms of overall learning, Matt and Rexwere directly trained on six instructions (i.e., onthe diagonal) and were probed on 102untrained instructions. Matt responded correct-ly to 93 untrained instructions. This represents94% of learning without direct training and 91%correct on untrained instructions (Table 1). Rex

followed 99 untrained instructions correctly,representing 94% of learning without directtraining and 97% correct on untrained instruc-tions. Trey received training on 14 instructionsand followed 89 instructions without directtraining. This represents 86% of learning withoutdirect training and 95% correct on untrainedinstructions.

DISCUSSION

Arranging actions, pictures, letters, andnumbers in matrices and training a subset ofthe actionpicture instructions consistentlyproduced untrained instruction following withthree of four preschoolers with autism. Theseresults are consistent with previous research thatdemonstrated recombinative generalization withinstruction following (Goldstein et al., 1987;Goldstein & Brown, 1989; Goldstein &Mousetis, 1989; Mineo & Goldstein, 1990;Nigam, Schlosser, & Lloyd, 2006; Striefel et al.,1978), labeling (Dauphin et al., 2004; Gold-stein, 1983b; Karlan et al., 1982; Light,Watson, & Remington, 1990; Remington etal., 1990), reading (de Souza et al., 2009;Mueller, Olmi, & Saunders, 2000; Saunders,ODonnell, Vaidya, & Williams, 2003), andspelling (de Rose, de Souza, & Hanna, 1996;Hanna, de Souza, de Rose, & Fonseca, 2004;Melchiori, de Souza, & de Rose, 2000). Theresults extend the literature by demonstratingrecombinative generalization with preschoolerswith autism and by targeting writing andpicture-selection skills. Because the participants

Table 1

Correct Trained and Untrained Responding, Percentages of Learning Without Direct Training, and Percentage Correct

on Untrained Cells

Primary matrixMatrix with

known picturesMatrix with

known letters and numbers% learning

without directtraining

% correcton untrained

cellsTrainedcorrect

Untrainedcorrect

Trainedcorrect

Untrainedcorrect

Trainedcorrect

Untrainedcorrect

Matt 6 30 0 30 0 33 94 91Rex 6 30 0 35 0 34 94 97Trey 14 22 0 35 0 32 86 95

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emitted writing skills in novel ways with lettersand numbers, the results add to the relativelysmall literature on teaching literacy skills tochildren with autism (Koppenhaver & Erick-son, 2003; Teale & Sulzby, 1986).

The largest benefit of matrix training is itsefficiency, which comes primarily from trainingon only the diagonal of the matrix. Goldstein(1983a) recommended training on more thanthe diagonal when the individual componentsare unknown. This recommendation was notsupported by Matts and Rexs data, in thatthese two participants received training on thediagonal only. However, the recommendationwas supported by Treys and Ninas data, inthat these participants required training onmore than the diagonal before untrainedresponding emerged. For Matt, Rex, and Trey,94%, 94%, and 86% of learning occurredwithout direct training, respectively. Theseresults are consistent with Goldstein (1983b),Goldstein et al. (1987), and Goldstein andMousetis (1989) in which untrained respondingaccounted for 56% to 75%, 94% to 98%, and95% to 98% of learning, respectively.

Untrained instruction following can beexplained in terms of establishing stimuluscontrol of each component of the instructionover responding. The two components of theinstruction exerted control in a specific order inthe following way: The action portion of theinstruction evoked selection of a particularutensil, the picture portion of the instructionevoked selection of a particular picture, and theaction portion of the instruction evoked theproduction of a particular action. Once stimu-lus control was established with trained instruc-tions, the terms in the instruction could besubstituted with other trained terms to controlnovel actionpicture responding. Matt and Rexcame under control of instructions with novelcombinations with relative ease, whereas Treyand Nina required extensive training for novelarrangements of terms in the instruction toexert control. Matrix training may be effective

in producing generalized outcomes by sharingfeatures with general case programming (Stokes& Baer, 1977), the technique of exposing anindividual to all the types of stimuli encoun-tered in a generalization setting. Diagonaltraining provides exposure to all stimuliencountered in generalization probes.

It is not clear why the four participantsresponded differently to matrix training. Onelimitation of the study was the absence ofpreassessment data on each childs ability tofollow two-step instructions; this informationcould identify responders and nonresponders totraining two-part instructions. Anecdotally, Rexreadily followed complex instructions and Matt,Trey, and Nina often needed many prompts tocomply with one-step instructions. Whenpresented with an untrained instruction, Treyexhibited rigid responding in that he oftenreached for but did not grasp a writing utensiland then pointed to the picture. It was not untilhe was trained with many exemplars in theprocedural modification that he performeduntrained responses. Nina did not meetcriterion on untrained responding in Tier 2and did not complete training, a clear limitationof the study. Time constraints with the schooldid not allow further training. Ninas errorswere often performing the trained action with apicture when instructed to perform a differentaction with the picture. For example, aftercorrect responding to put X on tape andhighlight onion (trained), she highlighted theonion when instructed to put X on onion.Responding appeared to come more under thecontrol of the picture portion of the instructionthan the action portion, possibly because thepicture portion was in closer proximity to theresponse. This learning problem is similar tostimulus blocking (Fields, 1979; Partington,Sundberg, Newhouse, & Spengler, 1994) andoverselectivity (Dickson, Deutsch, Wang, &Dube, 2006; Lovaas, Koegel, & Schreibman,1979), in which a child with autism focuses onirrelevant features of a stimulus. This error


pattern was the rationale for the proceduralmodifications of having Nina first respond tothe action (by selecting the utensil) and thenrespond to the picture as well as quicklyalternating between trials with different actionswith the same picture.

The correct baseline responding by Matt,Rex, and Trey was another limitation of thestudy, and three sources are possible. First, inS2, S3, and S4, the participants may haveselected the correct picture through learning byexclusion (Ferrari, de Rose, & McIlvane, 1993).That is, they may have selected pictures otherthan those previously trained (e.g., in S1) andother than the distracter pictures, which theycorrectly selected on some preassessment trials.Second, whereas in early probes Trey pointed tothe same picture when presented untrainedinstructions, in S3 and S4 he pointed to avariety of different pictures, and reinforcementmay have facilitated stimulus control. Thecontingent reinforcement in the probes is onepossible limitation of the study. Matrix trainingstudies have been mixed in terms of program-ming contingent reinforcement in probes(Goldstein et al., 1987; Hanna et al., 2004;Saunders et al., 2003; Striefel et al., 1978).Striefel et al. argued that reinforced trial-and-error responding is a stringent control conditionmore closely approximating natural conditionsthan a probe condition with extinction forcorrect responding. A third explanation forbaseline responding is that after the participantslearned to respond correctly to instructions inthe form of do an action on a picture, thetraining may have brought to strength reper-toires that were too weak to be detected inpreassessments or prior baseline probes. Forexample, before the study Trey could not drawa circle, but he could receptively identify acircle. After training with drawing particularshapes on pictures, he was able to draw a circleon pictures without direct training.

Future research should address the limita-tions and further our knowledge of matrix

training. Ninas data suggest the need toexamine techniques for developing complexverbal stimulus control, and there is limitedresearch in this area. General strategies includewithin-stimulus prompting in which eachcomponent of a verbal stimulus is more salient(Summers, Rincover, & Feldman, 1993; Wolfe& Cuvo, 1978) and requiring a differentialobserving response to each component of theverbal stimulus (Dube & McIlvane, 1999;Walpole, Roscoe, & Dube, 2007). Thesestudies primarily used visual stimuli, and moreresearch is needed in applying these techniquesto vocal verbal stimuli. Researchers shouldevaluate verbal stimulus control by manipulat-ing the order of words in two-componentinstructions, because responding may be re-stricted to the second component with somelearners. Strategies for reducing baseline re-sponding in future matrix-training studiesinclude the use of more stringent preassessmentcriteria for unknown responses and not rein-forcing probed responses. Nonsense variablescould be used to minimize learning duringbaseline and would allow further analysis of thestimulus control properties of matrix training.In terms of other repertoires, matrices couldincorporate letters and words with the sameactions used in this study as well as letters andwords on the vertical axis and prepositions onthe horizontal axis (e.g., write bed under thebox, write shoe next to the box). This couldbe reversed so that participants touch underbed and next to shoe. Matrix training hasbeen evaluated solely with instruction follow-ing, labeling, and reading. It could be extrap-olated to requesting or manding by havingparticipants request reinforcers with adjectives(e.g., I want the red candy, I want the bluetruck). Conversation-type repertoires (i.e.,intraverbals; Skinner, 1957) could be analyzedwith matrix training with participants respond-ing to two-component phrases (e.g., What is ared food? What is a yellow drink?). Finally,especially because it was a concern of the

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respondents in the social validity assessment,future researchers should examine trainingteachers and early intensive behavior interven-tion therapists to arrange teaching targets inmatrices to promote efficient teaching.

The current research has practical implica-tions for both students and teachers. Preschoolstudents taught the skills trained in this studywould likely be prepared for elementary schoolworksheets, such as those requiring students tocircle all the As, put a triangle on all theBs, and so on. Further, a respondent on thesocial validity questionnaire suggested that theskills addressed in this study are important forstandardized testing. Providing young childrenwith the skills (e.g., writing, discrimination)required to complete standardized testingcould help to improve their test-taking reper-toires and test scores. For teachers, matrixtraining offers a highly efficient teachingstrategy on which teachers and therapistsshould capitalize. Teachers and therapists whowork with children with autism often have anabundant number of skills they need to target.Arranging skills in matrices with two or moretypes of words taught simultaneously andprogramming learning to emerge withoutdirect teaching must occur to help childrenwith autism gain the language and literacyskills needed to succeed.

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Received January 6, 2009Final acceptance January 28, 2010Action Editor, Jennifer Zarcone


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