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Teaching coin equivalences via matching to sample1
Applied Printed
Research IR Menral Rerordorion. i the USA. All rights reserved.
Teaching
Vol. 5. pp. 177-197.
1984 Copyright
Coin Equivalences to Sample’
0
0270-3092/84 1984 Pergamon
53.00+ .w Press Ltd.
Via Matching
E. C. McDonagh Walter
E. Fernald
State
School
W. J. Mcllvane Eunice
Kennedy
Shiver
Center
1. T. Stoddard for Mental
Retardation,
Inc.
and
Northeastern
University
A moderately mentally retarded woman learned coin equivalences (with 5. IO-, and 15cent values) via matching to sample. When taught to match two different coin stimuli to a printed price of equal value, she could then match the coin stimuli to each other and state their values without further training. Additional coin-matching and naming performances emerged after establishing the equivalence between a new coin stimulus and one member of an existing class of equivalent stimuli. The study extends research on stimulus classformation by examining its usefulness in a new application, in teaching a skill repertoire that requires mastery of large numbers of individual performances- monetary equivalences. Further, the study suggests efficient strategies for teaching functional money skills to developmentally limited populations.
Using matching-to-sample methods, a number of recent studies have examined the spontaneous emergence of new matching performances which require no direct instruction. If subjects are taught to match two stimuli (B and C) to a third common stimulus (A), they may then be capable of matching B to C and C to B without having been directly taught to do so. To illustrate: Sidman (1971) and Sidman and Cresson (1973) taught severely mentally retarded boys to match pictures (B) to their dictated picture names (A), and then to match the corresponding printed words (C) to the same dictated names (A). After demonstrating A-B and A-C matching, the subjects could also
Requests for reprints may be addressed to Dr. Lawrence T. Stoddard, Behavioral Neurology Department, E. K. Shriver Center for Mental Retardation, Inc., 200 Trapelo Road, Waltham, MA 02254 177
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match the pictures to their printed names (B-C) and the printed names to the pictures (C-B) for the first time. In a related study, Sidman, Cresson, and Willson-Morris (1974) taught A-B and B-C matching, and subjects then demonstrated A-C matching without further training. The emergence of untrained matching performances has been interpreted as reflecting the formation of classes of equivalent stimuli; the stimuli become interchangeable in a given situation (Sidman, 1977; Spradlin, 1977). For example, in the illustration, the subject could match either the picture or the printed name to the corresponding spoken name, and to each other. Similar results have been obtained with a variety of different teaching stimuli (Spradlin, Cotter, & Baxley, 1973; Spradlin & Dixon, 1976; Dixon & Spradlin, 1976; VanBiervleit, 1977; Stromer & Osborne, 1982; Mackay & Sidman, in press). In teaching situations, use of the stimulus equivalence paradigm has the advantages of simplicity and efficiency.2 If a subject is taught the equivalence between a new stimulus and any member of an existing class, the new stimulus will become equivalent to all the other class members without further instruction; with each successive addition of a new member in this manner, an increasing number of equivalence relations will emerge as the class expands (Sidman & Tailby, 1982). Also, if a stimulus class is first established in receptive matching, and the subject can name one of the stimuli or is taught to do so, the subject may then be able to give that name to each of the other class members without additional teaching (Sidman, 1971; Sidman, et al., 1974; Spradlin & Dixon, 1976; Sidman & Tailby, 1982). The present study systematically replicated and extended the stimulus class formation paradigm, to demonstrate ways for establishing the equivalences among groups of coins and printed prices. No attempt was made to teach general use of money. Rather, the study explored this extension of the stimulus equivalence paradigm in ways that would, if successful, give guidance for more comprehensive practical training. Overall
Design
Figure 1 shows the logic of the first experiment. Boxes represent the stimuli; the lines connecting the stimuli indicate potential stimulus equivalences to be measured by matching-to-sample procedures; line numbers designate the sequence of teaching and testing. Solid lines indicate matching relations to be taught or which the subject demonstrated prior to the study; broken lines show relations which might subsequently emerge without direct teaching. To illustrate: After the subject learns to match a nickel (N) to a 5-cent printed-price (5e) (Task l), and a group of 5 pennies (5P) to the same price (Task 2), then a new skill- matching the nickel with five pennies-may emerge (Task 3), thus showing that a three-member stimulus class had been formed. The nickel
I I : I 6: i : I
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j 11 I
1oc I f 10
I i I I I I i I I I. ’ 13
I I
I I
i
5P5P ---
I
i I I I I I I I
i I I I
i i I
i
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.-.-
--__-
--.-.-.-+-.-.._._. -.-_-_ N N u----_----_
---.____
14 -_--_
1-j
I I I I .i
16
ii ___.( N5P 111: 1:,, I _ __:
FIGURE 1. Schematic summary of Experiment 1. Boxes represent stimuli: SC and 1OCare printed prices; SP is five pennies; N is nickel; D is dime. Solid lines indicate matching relations tbaf were taught directly (if necessary); broken lines show additional matching relations that were tested for emergence, without further training. Numbers designate the sequence of teaching and testing. 179
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and five pennies had become equivalent by virtue of their common equivalence with the 5e price. Similar logic directed the investigation of performances involving IO-cent stimuli. In Figure 1, there are two sets of lo-cent relations represented as triangles. Stimuli in the first set were a lo-cent printed price (lOC), a dime (D), and two groups of five pennies (SPSP). In the second set, they were all combinations of j-cent stimuli-two j-cent price signs (5C5e), two nickels (NN), and again 5P5P. As before, matching coins with prices was a requirement (Tasks 4, 5; and 7, 8) before examining coin to coin matching (6; 9). Only the first set of IO-cent relations provided a conclusive test of stimulus class formation, by examining the emergence of D:5PSP matching (Task 6). The second set could be performed by matching individual j-cent components; for example, to do NN:5P5P matching, the subject could match 5P with N twice (considering five pennies as a unit). .4 stimulus class with the combination stimuli need not have been formed, only the class involving the j-cent components. However, the two IO-cent sets shared a common stimulus, 5PSP. If 5P5P had become equivalent to each of the other four stimuli, then the subject might be capable of matching the other combination stimuli - 5C5c and NN- with 100 and D (Tasks lo-13), tasks that could not be done by component matching. This outcome would suggest that a five-member stimulus class had been formed. The remaining IO-cent stimulus-a nickel and five pennies (NSP) -was examined last. This stimulus could potentially become the sixth member of the class as follows: First, the subject might be able to match N5P to other combination stimuli on the basis of components (Figure 1, Tasks 14-16). Then, matching it with other class members - 100: and D-might emerge (Tasks 17 and 18). Study of 15-cent equivalences followed similar logic and will be described in Experiment 2. All training stimuli were visual. Nonetheless, since the subject could state the value of some of the stimuli prior to the study (see Subject, below), oral naming was periodically examined, but never directly trained. EXPERIMENT
1A
This experiment addressed Tasks l-9 in Figure 1, which involved the initial 5- and IO-cent matching performances. A note on terminology in this report: A matching-to-sample performancefor example, matching a nickel to (or with) five pennies-always includes the reverse-matching five pennies to a nickel (unless otherwise specified). Hence, each numbered task in Figure 1 is comprised of two matching relations; either of the stimuli connected by a line can be the sample or the choice on a given trial.3
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Method Subject. The subject was a 28-year-old, moderately mentally retarded, institutionalized woman. She had good receptive and expressive oral language skills but could not read or write. She could travel independently to a sheltered workshop via public transportation; however, she could not count change (for bus fares, pay telephones, vending machines, etc.). During the first part of the study (Experiment lA, lB), the subject received .07 mg/kg/ day of haloperidcl(4 mg @ 60.5 kg). However, an unanticipated 9 kg weight gain prior to Experiment 2 effectively reduced the dosage to .06 mg/kg/day for that aspect of the study. Entry skills. Preliminary testing revealed that the subject could: (1) count 1 to 15 objects by ones; (2) count out 1 to 10 objects from a larger group; (3) name the printed prices: le, 5e, lOQ, 15C, 2OC, and 25C; (4) name the coins: “Penny, ))“Nickel,” “ Dime,” and “Quarter”; (5) state the value of each coin: “One cent,” “5 cents,” “ 10 cents,” and “25 cents”; (6) match each coin to its corresponding dictated and printed price; and (7) match stimuli that were identical (e.g., 5 nickels to 5 nicke!s). Of critical importance to the present study, the subject was unable to match correctly when either the sample or the correct comparison stimulus contained two or more coins (excluding identity matches). For example, she could not: (1) match two or more coins with corresponding dictated or printed-prices (e.g., 2 nickels with a 1OCprinted price; l/5 correct, with a four-choice display); or (2) match two or more coins with one or more different coins having the same monetary value (e.g., 2 nickels with a dime, 10 pennies with a dime or 2 nickels, etc.; l/18 correct). The subject could not do any type of arithmetic.
General Procedures Setting. Sessions were conducted in a small office or a private area of the subject’s residence. The subject sat at a table facing the experimenter. Sessions lasted from 45 to 60 minutes. Stimuli and apparatus. Stimuli were real coins and printed prices-digits 2.5 cm high plus a cent sign. The subject sat facing a display panel placed flat on the table. Figure 2 schematically illustrates the display on four representative trials early in training. The sample stimulus was presented on a card at the top, and comparison stimuli on the lower four cards. Each card was 7.6 x 12.7 cm. The subject was required to discriminate coin stimuli on the basis of number and kind of coins. For example, as illustrated in Fig. 2A,
l-l P P PPP
FIGURE 2. A, B, C, and D show arrangements of sample (upper card) and comparison (lower four cnrds) stimuli on four representative trial displays: P =Penny; N = Nickel; D = Dime; lC, SC, 1OC = printed prices. 182
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she must select five pennies (choice 4) in response to the printed-price sample, 50. She had to reject comparison stimuli that had only the correct number of coins (e.g., five dimes; choice l), or only the correct type of coins (e.g., six pennies; choice 2). Further, she had to ignore irrelevant spatial characteristics of coin arrangements (e.g., Fig. 2C, five nickels; choice 4). The sample, comparisons, spatial configurations of coin stimuli, head and tail positions of the coins, and the position of the correct comparison varied unsystematically from trial to trial. Trialsequence. Each trial began with the presentation of a sample alone, and the subject had to touch it. Then, the four comparisons were uncovered, and the subject touched one to indicate her choice. Every correct choice was followed by delivery of a token and praise; at the end of each session, tokens were exchanged for various reinforcers (e.g., food, going to lunch with the experimenter). An incorrect choice ended the trial without any token. The experimenter covered all stimuli after each choice. During intertrial intervals (approximately 20 to 60 seconds), the subject held a cardboard screen to conceal data recording and arrangement of stimuli for the next trial. To start a trial, the experimenter lowered the screen to expose the next sample. Teaching and Testing Procedures Baseline and review trials. At least half the trials in each session reviewed pre-
viously mastered performances: (1) groups of coins, and matching single 7; see above); and (2) newly acquired ing and test trials were interspersed trials.
identity matching of prices, coins, and coins with their prices (entry skills 6 and performances, added for review. Trainirregularly among baseline and review
Matching performances were pretested prior to teaching. Procedures were the same as tests for emergent performances (see below).
Pretests.
Teaching. A delayed cue procedure (Touchette, 197 1; Sidman, 1977) was used to teach the required coin-to-price relations. The sample stimulus initially included both the price and, below it, coins identical to the correct coin comparison. The coins in this composite sample permitted the subject to respond correctly on the basis of visual identity. The price could come also to control correct selections if the subject observed and learned the relation between the price and the coins. Learning was encouraged by presenting the priceportion of the sample first and then adding the coin-portion (the delayed cue) after progressively longer times. If the subject learned the new coin-to-price
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matching relation, she could respond prior to the presentation of the delayed cue; if not, she could still respond correctly by waiting for it. Teaching continued until the subject correctly responded to the price alone on eight successive teaching trials. During teaching (and testing), each comparison stimulus was presented as the correct choice on some trials and the incorrect choice on others, to verify and maintain differential responding to the sample. Post-tests for emergent performances. After the subject could match two different coin stimuli to their corresponding printed price, the untrained cointo-coin matching was tested. On half of the 8 to 16 test trials, one stimulus of a pair to be matched was the sample and the other was the correct comparison; on the remaining trials, these roles were reversed. Further procedural details will accompany the results. Oral naming tests. Naming tests were given at the end of Experiment 1A to evaluate the effect of visual matching training on labeling the coin and price stimuli. Each sample was presented on three trials. The subject had to label each 5- and lo-cent stimulus by saying its name. The tests also included entry skills-labeling the le and 25e printed prices, and the penny and quarter. Correct responses did not produce tokens or praise. RESULTS
AND
DISCUSSION
Table 1 shows the percent correct scores and the sequence of teaching and testing phases (numbers in parentheses) in Experiments 1A and IB. The results omit the subject’s performances on baseline trials, which were virtually errorless. (Henceforth, monetary designations will be the abbreviated terms used in Figure 1 and Table 1, and matching tasks will be identified only by the task number.) Pretests. In Phases 1 and 7, the critical coin-to-coin matching tasks were pretested (3, 6, 9, 13, 15, and 18; omitting 16). The subject was never correct; she selected incorrect comparison stimuli that contained either the same type or number of coins as the sample. Other pretest data follow. Tasks 1-3 (phases I-3). Pretests of the 5-cent tasks confirmed that the subject could do only the first coin-to-price matching task (Table 1, 1, 5e:N; 93%), and not the second (2, 5Q:5P; 20%). When Task 2 was taught, the subject learned it in a single session, without errors, by means of the delayed cue procedure (subsequent teaching was equally effective, as well, unless noted). Having learned to match both N and 5P with the 5Q price, she was tested for emergence of coin-to-coin matching (3, N:5P); she scored 75% (3/4), a marked improvement over her pretest score. After Task 2 was reviewed in a second
Teaching
Coin Equivalences TABLE 1 Scores with S-Cent and IO-Cent Stimuli. phases is shown by numbers in parentheses.
Percent Correct Matching-to-Sample The sequence of teaching and testing
STIMULlaeb
PRETEST
Experiment IA I. 50 :N 2. 50 : 5P 3. N : 5P 4. IOQ : D 5. 100 : 5P5P 6. D : 5P5P 7. 5050 : NN 8. 5C5C : 5P5P 9. NN : 5PSP Experiment IL3 lo. 100 : 5454 ii. 5a5a : D 12. 100 : NN 13. D : NN 14. N5P : 5a5a 15. N5P : NN 16. N5P : 5P5P 17. N5P : loa 18. N5P : D
185
TEACH
TEST
TEACH
TEST
93 (1)
20(1) 0 100 0 0
100 (2)
100 (3B)
(1) (1) (1) (1)
15
(3A)
0 (4)
loo (3C) 100 (5) 94 (6)
100 63) 100 (8)
0 (7) 0 (7)
100 (9)
0 (1,7)
75 38 88 60 0
(10) (10) (10) (10) (10)
100 89 100 100 89 88 94 100 loo
0 (7) 0 (7)
0 (10)
(12.14)’ (12,14) (12.14) (12,14) (14) (14) (14) (14) (14)
REVIEW 97 98 96 99 96 97 96 98 97 98 95 100 97 94 97 93 96 94
a5P = 5 Pennies; N = Nickel; D = Dime; 5Q, 100 = Printed Prices bEach member of the listed pairs of stimuli served as the sample on some trials, with the other member as the correct comparison stimulus; on other trials, these roles were reversed. ‘See text for description of Phases 11 and 13.
teaching session, the subject then achieved a score of 100% (4/4) on Task 3. Training appeared to have established a class of five-cent stimuli. Tasks 4-6 (phases 1 and 4-6). With the first set of lo-cent stimuli, pretests again confirmed that the subject could match a single coin to its price (4, lOC:D, lOO%), but not a coin combination (5, 100:5PSP, 0%). After she was taught this task, she was then able to match the coins (6, D:5PSP); she scored
Constructed
TABLE 2 Response Test Scores
Session Matching Tasksa
l-5 (Phase ll)b .91 (49/54)C .OO(0/32)d
6-12 (Phase 13)
.96 (54/56) 10-13 .91 (96/106) 14-18 aNumbers refer to performances specified in Figure 1 and Table 1. bSee text for phase descriptions. CNumbers in parentheses are total responses/total opportunities. dPrior to presentation of N5P as a sample.
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94% on the untrained task, making only one incorrect response (on the sixth test trial). The subject appeared to have learned a second three-member class. Tasks 7-9 (phases 7-9). After learning Tasks 1-6, the subject failed pretests of Tasks 8 and 9, thus showing that she was not capable of matching these combinations of 5-cent stimuli at this stage; due to oversight, Task 7 was not pretested. Once again, the subject was taught coin-to-price matching-55cSQ: NN (7) and 505Q:5P5P (8). Without further teaching, she matched the coins - NN and SPSP - perfectly (9, 100%). This emergent performance did not necessarily show that the stimuli in the third set were equivalent, even though composed of equivalent 5-cent stimuli; the subject might have merely learned to match components. Further tests were required (see Experiment 1B). Oralnaming tests. After mastering Tasks l-9, the subject consistently labeled the N, 5P, and 50: samples as “five cents” and the D, NN, 5PSP, lOe, and 5C5e samples as “10 cents”; thus, she proved able to state the value of the combination coin stimuli for the first time, without any direct training with the names. She labeled N5P, pretested for the first time, as “five cents, five cents.” Review performances. The review column summarizes scores from all later trials that tested previously established performances. Throughout Experiments 1 and 2, the subject maintained high accuracy on Task l-9 (96%-99% correct). The number of review trials for each performance ranged from 93 to 200. EXPERIMENT
1B
The two IO-cent stimulus sets each contained 5P5P. If this stimulus had become equivalent to 5e5e and NN (not merely on the basis of components), and since it had already been shown to be equivalent to 1OCand D, then the five stimuli should comprise a five-member class. To test this possibility, the subject was asked to do the remaining tasks with these stimuli, that is, to match 1OCwith 5eSC, 5C5e with D, 10e with NN, and D with NN (Figure 1, 10-13). The remaining lo-cent stimulus - NSP - provided the opportunity for an explicit test of whether the subject had learned to match individual components. If she had learned this skill with N and 5P in combinations that contained identical components, could she now match the new mixed combination of these stimuli with the uniform ones (Figure 1, 14-16). For example, could she match NSP with 5e5C by matching N with one 5C price and 5P with the other 5e price? If successful, would she then be capable of matching N5P
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with 109 and with D-tasks that did not permit component matching (Figure 1, 17 and 18). She could do so only if N5P had joined the other combination stimuli in forming a class with 1OQand D. For these considerations, N5P was tested last (except for limited pretests), and no direct teaching with this stimulus would be conducted unless it proved necessary. Tasks lo-13 and 14-18 were tested by the matching-to-sample method and by a second method devised in the course of Experiment 1B. This experiment also began preliminary study of the importance of direct token reinforcement of matching performances when they emerged. Method Pretests. Of Tasks 10-13, only the last was pretested in Experiment lA, in conjunction with pretests of Tasks 8 and 9 (Table 1, Phases 1 and 7). A more limited study had been planned initially, and relevant training precluded later pretests. Tasks 14-18 were pretested selectively. Reinforcementprocedures. Initial tests of Tasks lo-13 were conducted with continuous reinforcement (Phase 10). Later (Phases 1 l-14), responses on selected tasks were not reinforced with tokens or praise. The subject was first adapted to an intermittent schedule of reinforcement on baseline tasks; on the average, every other correct response produced a token (variable ratio 2; range l-5). Test trials were then interspersed. Some correct test performances, including all initial responses on Tasks 14-18, were followed only by the next trial. Further details will accompany the results. Tasks 10-13: Matching-to-sample test 1 (phase 10). Tasks lo-13 were first tested eight to ten times each, using the standard matching-to-sample procedure. Also, probe tests of Tasks 14 and 18 were given in this phase. Tasks 10-13: Constructed response test (phase II). Based on the initial results, an alternative testing method was devised. The subject was shown a sample and an unsorted pool of different coins and printed prices. Her task was to select from the pool all coins, coin combinations, and prices that might correspond to the sample. She placed each selection on a 7.6 x 12.7 cm card. Each pool permitted selections based on previously demonstrated performances, including identity matching, and also gave opportunities to make at least one novel (potentially emergent) match. The choice pool often presented multiple opportunities for a given selection, such as two dimes when 1OCwas the sample. As the subject constructed her selections, the experimenter recorded each one. If the subject made the same selection more than once on a trial, it was scored simply as one response. The sample remained present
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until the subject said, “No more.” The experimenter then examined the choice pool and recorded any missed opportunities to construct matches; for example, leaving two nickels in the pool when the sample was the 1OCprice was recorded as a missed opportunity to do Task 12. The next trial began with the presentation of a different sample and a new choice pool. Trials that reviewed previously learned and entry performances were included, such as those with 5- and 25cent samples, and some trials permitted only identity selections (e.g., five dimes). Each 5-cent and IO-cent stimulus was presented as a sample at least once per session, except N5P during this phase; however, there were opportunities to select NSP as a potential choice. Unlike standard matching to sample, the constructed response test did not ask the subject to attempt a novel match before she was able to make it. Instead of potentially being “forced” to make an error, she could now simply say “No More.” Tasks 10-13: Matching-to-sample test 2 (phase 12). After tests that used the new procedure, matching-to-sample tests were repeated (8 or 9 trials each). Tasks 14-18 (phases I3 and 14). With NSP, constructed response tests were given first, by adding this stimulus as one of the samples. Then Tasks 14-18 were extensively tested in standard matching to sample (at least 14 trials each). Also, tests of Tasks lo-13 continued in both these phases. Review of Tasks I-18 and oral naming tests followed. Results and Discussion Tasks 10-13. On the first matching-to-sample test of Tasks 10-13, the subject achieved scores of 75%, 3890, 88%, and 60%, respectively (Phase 10); all scores were better than chance performance (25% on these 4-choice tests), but none conclusively demonstrated mastery. In view of the subject’s accurate naming of these lo-cent stimuli at the end of Experiment lA, these results were difficult to interpret (see Sidman & Tailby [1982] for a discussion of the distinction between stimulus classes defined by common responses [naming] and by equivalence relations). Other studies have shown that stimulus class formation apparently can sometimes occur gradually, with initially imperfect performance followed by greater accuracy during repeated testing, even if the tests are conducted in extinction (Spradlin, et al., 1973; Lazar, 1977). Did our subject’s intermediate accuracy reflect incomplete formation of the five-member class? Also, would the early test errors affect later performance? The constructed response procedure was an attempt to answer these questions. The task reviewed previously mastered performances, especially the prerequisite Tasks 4-9; at the same time it gave the subject numer-
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ous opportunities to show whether she was capable of Tasks 10-13, without forcing her to make errors. The constructed response testing was conducted over 12 sessions. Given the opportunity to demonstrate Tasks lo-13 in the new format, the subject often did so immediately. Token reinforcement was withheld for Tasks 12 and 13 until the subject’s fifth and eighth correct selections, respectively. No differences in performance were observed; hence, data on Tasks lo-13 are combined. The upper row of Table 2 shows her constructed response scores for these tasks (total selections/total selections -I- missed opportunities; percent correct scores would not reflect missed opportunities). Over the 12 sessions, the subject’s mean score for these tasks was 0.94. Scores for individual performances ranged from 0.86 (11) to 1.OO (13). In the first five sessions (Phase 1 l), the subject missed slightly more opportunities than later; however, she performed Tasks lo-13 about as often as the previously established IO-cent ones (4-9)-making 49 and 50 matching selections, respectively. In matching-to-sample tests after the 5th constructed response session (Phase 12) and after the 12th (Phase 14), the subject’s scores on Tasks lo-13 showed marked improvement (Table 1, second test). Only her score on Task 11 was imperfect (89%). The data seemed to support the formation of a fivemember class of IO-cent stimuli. Adding the sixth stimulus - NSP - provided a critical test. Tusks 14-18. During the first five constructed response sessions (Phase 1l), the subject had 32 opportunities to select NSP in response to each of the other lo-cent samples; NSP was not presented as a sample. However, she made no NSP selections, thereby failing to do Tasks 14-18 immediately (Table 2, lower row, Sessions l-5). In the sixth session (Phase 13), NSP was given as a sample for the first time: Not only did the subject select all the other IO-cent stimuli to this sample (score 1.00; 12 responses/l2 opportunities), but she then began to choose the NSP match for other lo-cent samples (score .80, 415). In Sessions 7-12, her scores were 0.93 (68/73) with N5P as the sample, and 0.85 (28/33) when it was a possible choice; both scores were 1 .OOin the last four sessions. The subject demonstrated each NSP performance at least five times before it was reinforced with tokens. (The reinforcement issue is discussed after Experiment 2.) Performances with NSP appeared to come about by matching it first with other two-component stimuli; NN and 5954 were the subject’s first two selections to the N5P sample. The test format may have encouraged such matching, since she could select individual components in sequence while constructing her response. However, her third and fourth selections to a NSP sample were 1OCand D, showing rapid emergence of new performances not achievable by component matching. Subsequent matching-to-sample scores on Tasks 14-18 ranged from 88%
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to 100% correct (Table 1, Phase 14), and confirmed the good constructed response results. Thus, the subject appeared to have learned a six-member class of IO-cent stimuli. Review trials and oral naming tests. During review of Tasks lo-18 (41 to 84 trials each), the subject’s scores were 93%-100% correct. On oral naming tests (identical to those at the end of Experiment lA), the subject correctly labeled each 5 and lo-cent stimulus, saying “five cents” or “ten cents.” Having labeled NSP as “five cents, five cents” on the pretest, she now gave it the same name as the other IO-cent stimuli, again showing an emergent skill without direct training. EXPERIMENT
2
The purpose of this experiment was to investigate the establishment of matching performances with nine 15cent stimuli, through extensions of the stimulus class formation methods used in Experiments 1A and IB. In Figure 3, the two printed-price stimuli at the left and the six coin stimuli show all possible combinations of the 5- and lo-cent stimuli that total 15 cents. The ninth stimulus- the 15Q printed price- was new. In Experiment lB, the subject seemed initially to have matched NSP with other IO-cent stimuli by matching components. Perhaps now she would prove capable of doing so with 15-cent combinations, most of which were also mixed combinations. However, the subject had not previously matched a two-component stimulus with a three-component one, for example, lOc5c or DN with 5PSPSP (again considering a group of five pennies as a unit). This somewhat different skill might have to be taught directly. If so, teaching one such performance might permit her to do the others. This outcome would provide additional evidence of stimulus class formation, by confirming that the individual components formed classes, as in matching DSP with NNN. A test of whether the eight 15-cent combination stimuli became a stimulus class would be (1) to teach the matching relations between one of them and the ninth stimulus - the 15Q price- and then (2) to examine the relations of the other seven with the price. To investigate reinforcement variables in stimulus class formation further, no programmed consequences would follow any test trial. Method Generalprocedures. Matching-to-sample procedures were the same as before, except that stimuli were attached to large white cards (12.5 x 20 cm), in prearranged displays. Reinforcement was a token delivered approximately every five minutes, after a correct response on a task with 5- and lo-cent stimuli.
I D5p I DN II I I I I
5P 5P5P ’
15c
1 5c 5c 5c
I NNN I 1 NN5P
1
FIGURE 3. Schematic diagram of the nine printed-price and coin stimuli in the 36 possible Scent equivalences. Thin solid lines indicate some of tbe performances that the subject demonstrated after Experiment 1; wider solid lines indicate performances taught directly in Experiment 2. The dashed line shows one performance which might emerge after training. The remaining 29 performances are not shown by lines (for clarity). 191
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Responses on all intervening baseline trials and all test trials were not reinforced, thus making these events less discriminable on the basis of non-reinforcement. Every two tokens were exchanged later for a quarter. Pretests. The subject was given a test battery that presented 18 of the 36 possible matching tasks with U-cent stimuli. The left column of Table 3 lists the stimuli for these and other selected tasks. A second pretest evaluated the six matching relations shown by lines in Figure 3 (omitting the one with the 15c price; Table 3, 19-24). These six tasks were tested selectively for the following reasons: (1) The lOC5e-DN task presented stimulus components that the subject could match individually prior to the study (1OO:D; 5C:N), and she might match the components; (2) the other three stimuli were uniform combinations (5C5C5e, NNN, 5P5PSP) that might prove easier to match than mixed combinations that included one or two groups of pennies; and (3) these tests could set the stage for teaching as in the design of Experiment 1A-to teach the relations between a price and a uniform combination of pennies (lOQ5C:5PSP5P). To follow the same design, a third pretest was required prior to teaching the 15C price-matching 156 with 5PSPSP (Table 3, 36). Pretests typically included 12 trials of each task, interspersed among a greater number of baseline trials. Teaching procedures and post tests. Teaching the coin-to-price relations, when necessary, was conducted with the delayed cue procedure as in Experiment 1A. After training, two types of post tests were conducted: (1) Matchingto-sample tests were identical to pretests and were given first; (2) constructed response tests then followed - identical to those in Experiment 1B except for the addition of 15-cent samples; these tests examined the emergence of the 14 previously untested 15-cent performances (Appendix A), as well as the 22 already measured by standard matching to sample. Naming tests followed. (See Results for further details.) Results and Discussion First pretest. The results at the left of Table 3 show that the subject often could match 15-cent stimulus combinations, when comprised of equal numbers of components (20 and 25-30; mean score of 72% correct). On the other hand, she matched unequal numbers of components much less well (23, 24, 31-35; mean score of 27% correct); typically, she scored 25% or less (e.g., 23, matching lOe50: with 5P5P5P). Thus, a possible prerequisite skill seemed lacking; the subject had difficulty matching two components with three components. Secondpretest. When Tasks 19-24 were tested separately, the subject’s scores supported the predictions and initial findings (Table 3, column 2): (1) match-
Teaching Coin Equivalences
Percent STIMULIB*b 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40.
505Q5Q 5Q5Q50 NNN lOQ5Q 10eW DN 10050 505450 NNN NNN NNSP NNSP loa 5uSU5U DN D5P D5P 15Q 15a 150 Isa Isa
Correct
TABLE Matching-to-Sample
PRETEST : : : : : : : : : : : : : : : : : : : : : :
NNNC 5P5P5P 5PSPSP DN 5P5P5Pd 5PSPSPd D5P NNSP NNSP N5P5P N5PSP SPSPSP N5P5Pd D5Pd NN5Pd N5P5Pd NNNd 5P5P5P NNSP N5P5P DSP ioe5a
92
25 25 19 69 83 75 83 42 75 9 50 17 8
PRETEST
TEACH
100 92 95 100 8 8
94
17 17 17 33
a*bSee notes, Table 1. ‘Task numbers continue from Table 1. dTasks that require matching two components ponent).
3 Scores
with
witb
193
15Cent TEST 100 95 100 100 9-l 98 100 92 100 100 92 100 100 92 92 92 92 0 25 8 25 25
three components
Stimuli. TEACH
TEST
100
97 92 100 92 100
(5P treated
as one com-
ing lOC5C with DN - a test of combined entry skills - was performed at 100% accuracy (22); (2) also, on tasks with equal numbers of components, her scores with uniform combinations (19-21) were 92% correct or better, consistently higher than her scores had been with mixed penny-combinations on the initial test (25-30); (3) she continued to do poorly with unequal numbers of components (23, 24). Teaching. When taught to match a two-component price - 10~5Q- with a uniform three-component penny combination - 5PSPSP - the subject learned with only two errors (23; 94% correct). tests. The subject received the post test of Tasks 19-24, followed by the test battery. The combined scores showed (Table 3, column 4): (1) performance on Tasks 19-23 was maintained; (2) on tasks that required her to match unequal numbers of components (24 and 31-35) she scored 92% or better; thus, having learned one such performance-matching lOC5C with 5PSPSP-she was then able to do others of a similar type, without direct teaching; (3) on tasks with mixed penny combinations, but equal numbers
Initialpost
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E. C. McDonagh, W. J. Mcllvane, and L. T. Stoddard
of components, her scores became virtually perfect (25-30); and (4) performances with the 1% price did not improve. On the constructed response test that followed, the subject demonstrated all previously untested relations between 15cent combinations (Appendix A, 41-51; data not shown). She made matching selections on 77 of 78 opportunities, at least 6 with each of the 11 new tasks. With previously tested tasks, she also missed only 1 of 109 opportunities. She made only four incorrect selections to 15-cent samples. The 15C price was not presented as a sample or potential choice. !n summary, the subject now was able to match any of the eight 15cent combination stimuli to any other, but possibly only on the basis of matching components. The next phase examined whether they comprised a stimulus class. Teaching the 154price. The subject was taught to match the 150 price with one of the eight 15cent combinations -5PSPSP. When this task was pretested, the subject had not responded correctly. On all teaching trials, she was correct (Table 3, 36, columns 4 and 5). Post tests with the ISprice. On matching-to-sample tests with the 15e price, the subject scored 92Vo correct or better (last column in Table 3). On subsequent constructed response tests, she missed no opportunities to select each of the nine 15-cent stimuli, including the 15C price, in response to each of them as a sample. The 135 total opportunities included 6 with each of the three previously untested tasks, matching the 1% price with DN, NNN, and 5e5C5U (Appendix A, 52-54). These data provide evidence that a nine-member stimulus class had been formed. Naming tests. The subject was able to state the value of all stimuli used in the study, correctly labeling them as “five cents,” “ten cents,” or “fifteen cents”. Prior to the study, the subject could give the name “fifteen cents” to the 150 printed price, but could not match the price to any coin (or price) combination. When taught to match the price with one 1S-cent combination 5PSPSP-not only was she able then to match it with the remaining seven, but also to name each of them. GENERAL
DISCUSSION
In Experiments 1 and 2 combined, the subject was tested on a total of 54 matching relations involving 18 visual stimuli, 13 of which were the critical 5-, lo-, and 15-cent coin and price combinations. Of the 54 relations, 2 were entry performances, 6 were directly taught, and 46 emerged without direct teaching. All matching relations were bidirectional, in that either stimulus of a given pair could be the sample or choice. Also, the subject could both point
Teaching Coin Equivalences
195
to choices in a fixed array and select (construct) choices from an unsorted array. Further, the subject was able, also without direct teaching, to state the value of each of the 13 combination stimuli for the first time. Subsequent tests revealed that she could also match each of them with its corresponding dictated price. Although the subject could have performed many new relations by matching components, the components themselves must have formed classes in any given instance, in order for her to do so. For example, to match DSP with NNN by components must depend on the prior establishment of the 5- and IO-cent classes. Moreover, matching by components is a significant accomplishment in itself, especially when considering the increased complexity of two- and three-component matching in many 15-cent relations. The data are relevant to the question: “Is direct reinforcement of individual performances necessary in their emergence without direct training?” (cf., Spradlin et al., 1973; Sidman, 1981). Withholding tokens as consequences for some performances did not seem to retard or disrupt their reliable emergence: all 15cent equivalences, all naming and visual-to-auditory relations, and some emergent relations in the lo-cent class. These outcomes could have depended on reinforcement of other class members (Sidman & Tailby, 1982). However, in face-to-face teaching, it is impossible to rule out other reinforcing factors like differential attention, even though the teacher strives to remain neutral (as was done in this study). Additional research is needed to determine whether all features of the procedures are necessary in practical teaching situations. It would probably not be necessary, for example, to conduct the extensive baseline training, testing, and reinforcement-schedule pretraining that were required to provide experimental verification of stimulus class formation. Also, the question of general usefulness of these procedures remains. Our subject began the study with entry skills (e.g., generalized identity matching, coin identification) which less advanced students would have to acquire. Notably, stimulus class formation has been achieved with less capable subjects (Sidman & Cresson, 1973), and helpful methods for teaching such entry skills to moderately and severely mentally retarded individuals have been developed (cf., Sidman, 1977). On a methodological note, the constructed response method may be an especially benign and helpful way to test potential stimulus equivalences, since the subject need make no errors if a new performance has not been established. The method allows the subject to show newly emergent and directly trained performances in any order, and to do so with equal facility, as our subject demonstrated in Experiment 2. Where the order of emergence seemed to matter, the subject can freely show that fact as well, as with the N5P relations in Experiment 1B. Further, the test format -selecting actual coins from an unsorted array - resembles real monetary transactions and may promote generalization of new skills to community settings. In conclusion, the study contributes to research on stimulus class for-
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mation by providing systematic replication of the procedures and general outcome of the stimulus equivalence paradigm. The data from a mentally retarded subject add support to the findings of other studies with this population, which show the capacity to acquire stimulus classes through similar procedures (see Introduction). As this study illustrates, such procedures require no special setting or equipment, and might eventually be adapted for use by teachers with minimal training. Further, the study employs stimulus class methodology with a different type of stimuli, thereby illustrating strategies for addressing the practical problem of teaching skill repertoires that require mastery of large numbers of individual performances. Inclusion of such methods may enhance other successful programs for teaching money skills (e.g., Wunderlich, 1972; Bellamy & Buttars, 1975; Lowe & Cuvo, 1976; Trace, Cuvo, & Criswell, 1977; Cuvo, Veitch, Trace, & Konke, 1978), by reducing the number of performances that have to be taught directly. REFERENCE
NOTES
1. This paper is based on a thesis submitted by the first author to the Department of Psychology, Northeastern University, in partial fulfillment of the requirements for the Master of Arts degree. The research was supported in part by NICHHD Grant HD10210 to the Eunice Kennedy Shriver Center for Mental Retardation, by the University Affiliated Facility Training Grant, BCHS, MCH (HHS) Grant No. MCT-000906, and by the Administration of Developmental Disabilities, Office of Human Developmental Services, Grant No. 59-P-05424. The authors wish to thank Branko J. Gerovac for indispensable contributions and Leila R. Cohen, Harry A. Mackay, and Barbara Ray, for their valuable comments on an earlier version of the manuscript. 2. Historically, the method has been termed mediated transfer (cf., Sidman, et al., 1974). 3. Sample-choice reversibility is a test for symmetry in matching relations, one of three logical properties that the relations must possess to be called equivalence relations (Sidman, et al., 1982; Sidman & Tailby, 1982).
REFERENCES Bellamy, T. & Buttars, K. L. Teaching trainable level retarded students to count money: Toward personalized independence through academic instruction. Education and Training of the Mentally Retarded, 1975, 10, 18-26. Cuvo, A. J., Veitch, V. D., Trace, M. W., & Konke, J. L. Teaching change computation to the mentally retarded. Behavior Modification, 1978, 2, 531-548. Dixon, M. H. & Spradlin, J. E. Establishing stimulus equivalences among retarded adolescents. Journal of Experimental Child Psychology, 1976, 21, 144-164. Lazar, R. Extending sequence-class membership with matching to sample. Journal of the Experimental Analysis of Behavior, 1971, 27, 381-392. Lowe, M. L., & Cuvo, A. J. Teaching coin summation to the mentally retarded. Journalof Applied Behavior Analysis. 1976, 9, 483-489. Mackay, H. A. & Sidman, M. Teaching new behavior via equivalence relations. In R. Sperber, C. McCauley, and P. H. Brooks (eds.), Language and Cognition in the Mentally Retarded, Baltimore: University Park Press, in press.
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Sidman, M. Reading and auditory-visual equivalences.. Journal of Speech and Hearing Research, 1971,14,5-13. Sidman, M. Teaching some basic prerequisites for reading. In P. Mittler (Ed.), Research fo Prucrice in Mental Returdafion, Vol. II. Baltimore: University Park Press, 1977, Pp. 350-360. 350-360. Sidman, M. Remarks. Behaviorism, 1981, 9, 127-129. Sidman, M. & Cresson, 0. Reading and crossmodal transfer of stimulus equivalences in severe retardation. American Journal of Menlo1 Deficiency, 1973, 77, 515-523. Sidman, M., Cresson, O., & Willson-Morris, M. Acquisition of matching-to-sample via mediated transfer. Journal of the Experimental Analysis of Behavior, 1974, 22, 261-273. Sidman, M., Rauzin, R., Lazar, R., Cunningham, S., Tailby, W., & Carrigan, P. A search for symmetry in the conditional discriminations of rhesus monkeys, baboons, and children. Journal of fhe Experimenlul
Analysis
of Behavior,
1982, 37, 23-44.
Sidman, M. & Tailby, W. Conditional discriminations vs. matching to sample: An expansion of the testing paradigm. Journal of the Experimental Analysis of Behavior, 1982.37,5-22. Spradlin, J. E. Language and emergent behavior. In P. Mittler (Ed.), Research fo Practice in Mental Retardation, Vol. II. Baltimore: University Park Press, 1977, Pp. 253-260. Spradlin, J. E., Cotter, V. W., & Baxley, N. Establishing a conditional discrimination without direct training: a study of transfer with retarded adolescents. American Journul of Menfal Deficiency,
1973, 77, 556-566.
Spradlin, J. E. & Dixon, M. H. Establishing conditional discriminations without direct training: Stimulus classesand labels. American Journul of Mentul Deficiency, 1976, 80, 555-561. Stromer, R. &Osborne, J. G. Control of adolescents’arbitrary matching-to-sample by positive and negative stimulus relations. Journul of the Experimental Analysis of Behavior, 1982, 37, 329-348. Touchette, P. E. Transfer of stimulus control: Measuring the moment of transfer. Journal of the Experimental Analysis of Behavior, 1911, 15, 347-354. Trace, M. W., Cuvo, A. J. & Criswell, J. L. Teaching coin equivalence to the mentally retarded. Journal of Applied Behavior Analysis, 1977, 10, 85-92. VanBiervliet, A. Establishing words and objects as functionally equivalent through manual sign training. American Journal of Menful Deficiency. 1971, 82, 178-186. Wunderlich, R. A. Programmed instruction: Teaching coinage to retarded children. Mental Retardation, 1972, 10, 21-23.
APPENDIX
A
Fourteen matching tasks involving 15cent stimuli; not pretested and examined only in constructed response tests (task numbers continue from Table 3): (41) lOQ5Q-5~5C50;(42) IOCSC-NNN; (43) lOCS’LNN5P; (44) 505C5CN5P5P; (45) 5C5CSO-DN; (46) DN-NNN; (47) DN-NSPSP; (48) DN-DSP; (49) D5P-5P5P5P; (50) DSP-NNSP; (5 1) 5P5P5P-NSP5P; (52) 150-5@5C5C; (53) ISQ-NNN; (54) 15GDN.
Research IR Menral Rerordorion. i the USA. All rights reserved.
Teaching
Vol. 5. pp. 177-197.
1984 Copyright
Coin Equivalences to Sample’
0
0270-3092/84 1984 Pergamon
53.00+ .w Press Ltd.
Via Matching
E. C. McDonagh Walter
E. Fernald
State
School
W. J. Mcllvane Eunice
Kennedy
Shiver
Center
1. T. Stoddard for Mental
Retardation,
Inc.
and
Northeastern
University
A moderately mentally retarded woman learned coin equivalences (with 5. IO-, and 15cent values) via matching to sample. When taught to match two different coin stimuli to a printed price of equal value, she could then match the coin stimuli to each other and state their values without further training. Additional coin-matching and naming performances emerged after establishing the equivalence between a new coin stimulus and one member of an existing class of equivalent stimuli. The study extends research on stimulus classformation by examining its usefulness in a new application, in teaching a skill repertoire that requires mastery of large numbers of individual performances- monetary equivalences. Further, the study suggests efficient strategies for teaching functional money skills to developmentally limited populations.
Using matching-to-sample methods, a number of recent studies have examined the spontaneous emergence of new matching performances which require no direct instruction. If subjects are taught to match two stimuli (B and C) to a third common stimulus (A), they may then be capable of matching B to C and C to B without having been directly taught to do so. To illustrate: Sidman (1971) and Sidman and Cresson (1973) taught severely mentally retarded boys to match pictures (B) to their dictated picture names (A), and then to match the corresponding printed words (C) to the same dictated names (A). After demonstrating A-B and A-C matching, the subjects could also
Requests for reprints may be addressed to Dr. Lawrence T. Stoddard, Behavioral Neurology Department, E. K. Shriver Center for Mental Retardation, Inc., 200 Trapelo Road, Waltham, MA 02254 177
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E. C. McDonagh,
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and L. T. Stoddard
match the pictures to their printed names (B-C) and the printed names to the pictures (C-B) for the first time. In a related study, Sidman, Cresson, and Willson-Morris (1974) taught A-B and B-C matching, and subjects then demonstrated A-C matching without further training. The emergence of untrained matching performances has been interpreted as reflecting the formation of classes of equivalent stimuli; the stimuli become interchangeable in a given situation (Sidman, 1977; Spradlin, 1977). For example, in the illustration, the subject could match either the picture or the printed name to the corresponding spoken name, and to each other. Similar results have been obtained with a variety of different teaching stimuli (Spradlin, Cotter, & Baxley, 1973; Spradlin & Dixon, 1976; Dixon & Spradlin, 1976; VanBiervleit, 1977; Stromer & Osborne, 1982; Mackay & Sidman, in press). In teaching situations, use of the stimulus equivalence paradigm has the advantages of simplicity and efficiency.2 If a subject is taught the equivalence between a new stimulus and any member of an existing class, the new stimulus will become equivalent to all the other class members without further instruction; with each successive addition of a new member in this manner, an increasing number of equivalence relations will emerge as the class expands (Sidman & Tailby, 1982). Also, if a stimulus class is first established in receptive matching, and the subject can name one of the stimuli or is taught to do so, the subject may then be able to give that name to each of the other class members without additional teaching (Sidman, 1971; Sidman, et al., 1974; Spradlin & Dixon, 1976; Sidman & Tailby, 1982). The present study systematically replicated and extended the stimulus class formation paradigm, to demonstrate ways for establishing the equivalences among groups of coins and printed prices. No attempt was made to teach general use of money. Rather, the study explored this extension of the stimulus equivalence paradigm in ways that would, if successful, give guidance for more comprehensive practical training. Overall
Design
Figure 1 shows the logic of the first experiment. Boxes represent the stimuli; the lines connecting the stimuli indicate potential stimulus equivalences to be measured by matching-to-sample procedures; line numbers designate the sequence of teaching and testing. Solid lines indicate matching relations to be taught or which the subject demonstrated prior to the study; broken lines show relations which might subsequently emerge without direct teaching. To illustrate: After the subject learns to match a nickel (N) to a 5-cent printed-price (5e) (Task l), and a group of 5 pennies (5P) to the same price (Task 2), then a new skill- matching the nickel with five pennies-may emerge (Task 3), thus showing that a three-member stimulus class had been formed. The nickel
I I : I 6: i : I
I
r.-.-;-.I I I I i12 I i I I I I
.I
j 11 I
1oc I f 10
I i I I I I i I I I. ’ 13
I I
I I
i
5P5P ---
I
i I I I I I I I
i I I I
i i I
i
I
I I ‘-
.-.-
--__-
--.-.-.-+-.-.._._. -.-_-_ N N u----_----_
---.____
14 -_--_
1-j
I I I I .i
16
ii ___.( N5P 111: 1:,, I _ __:
FIGURE 1. Schematic summary of Experiment 1. Boxes represent stimuli: SC and 1OCare printed prices; SP is five pennies; N is nickel; D is dime. Solid lines indicate matching relations tbaf were taught directly (if necessary); broken lines show additional matching relations that were tested for emergence, without further training. Numbers designate the sequence of teaching and testing. 179
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E. C. McDonagh,
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and L. T. Stoddard
and five pennies had become equivalent by virtue of their common equivalence with the 5e price. Similar logic directed the investigation of performances involving IO-cent stimuli. In Figure 1, there are two sets of lo-cent relations represented as triangles. Stimuli in the first set were a lo-cent printed price (lOC), a dime (D), and two groups of five pennies (SPSP). In the second set, they were all combinations of j-cent stimuli-two j-cent price signs (5C5e), two nickels (NN), and again 5P5P. As before, matching coins with prices was a requirement (Tasks 4, 5; and 7, 8) before examining coin to coin matching (6; 9). Only the first set of IO-cent relations provided a conclusive test of stimulus class formation, by examining the emergence of D:5PSP matching (Task 6). The second set could be performed by matching individual j-cent components; for example, to do NN:5P5P matching, the subject could match 5P with N twice (considering five pennies as a unit). .4 stimulus class with the combination stimuli need not have been formed, only the class involving the j-cent components. However, the two IO-cent sets shared a common stimulus, 5PSP. If 5P5P had become equivalent to each of the other four stimuli, then the subject might be capable of matching the other combination stimuli - 5C5c and NN- with 100 and D (Tasks lo-13), tasks that could not be done by component matching. This outcome would suggest that a five-member stimulus class had been formed. The remaining IO-cent stimulus-a nickel and five pennies (NSP) -was examined last. This stimulus could potentially become the sixth member of the class as follows: First, the subject might be able to match N5P to other combination stimuli on the basis of components (Figure 1, Tasks 14-16). Then, matching it with other class members - 100: and D-might emerge (Tasks 17 and 18). Study of 15-cent equivalences followed similar logic and will be described in Experiment 2. All training stimuli were visual. Nonetheless, since the subject could state the value of some of the stimuli prior to the study (see Subject, below), oral naming was periodically examined, but never directly trained. EXPERIMENT
1A
This experiment addressed Tasks l-9 in Figure 1, which involved the initial 5- and IO-cent matching performances. A note on terminology in this report: A matching-to-sample performancefor example, matching a nickel to (or with) five pennies-always includes the reverse-matching five pennies to a nickel (unless otherwise specified). Hence, each numbered task in Figure 1 is comprised of two matching relations; either of the stimuli connected by a line can be the sample or the choice on a given trial.3
Teaching Coin Equivalences
181
Method Subject. The subject was a 28-year-old, moderately mentally retarded, institutionalized woman. She had good receptive and expressive oral language skills but could not read or write. She could travel independently to a sheltered workshop via public transportation; however, she could not count change (for bus fares, pay telephones, vending machines, etc.). During the first part of the study (Experiment lA, lB), the subject received .07 mg/kg/ day of haloperidcl(4 mg @ 60.5 kg). However, an unanticipated 9 kg weight gain prior to Experiment 2 effectively reduced the dosage to .06 mg/kg/day for that aspect of the study. Entry skills. Preliminary testing revealed that the subject could: (1) count 1 to 15 objects by ones; (2) count out 1 to 10 objects from a larger group; (3) name the printed prices: le, 5e, lOQ, 15C, 2OC, and 25C; (4) name the coins: “Penny, ))“Nickel,” “ Dime,” and “Quarter”; (5) state the value of each coin: “One cent,” “5 cents,” “ 10 cents,” and “25 cents”; (6) match each coin to its corresponding dictated and printed price; and (7) match stimuli that were identical (e.g., 5 nickels to 5 nicke!s). Of critical importance to the present study, the subject was unable to match correctly when either the sample or the correct comparison stimulus contained two or more coins (excluding identity matches). For example, she could not: (1) match two or more coins with corresponding dictated or printed-prices (e.g., 2 nickels with a 1OCprinted price; l/5 correct, with a four-choice display); or (2) match two or more coins with one or more different coins having the same monetary value (e.g., 2 nickels with a dime, 10 pennies with a dime or 2 nickels, etc.; l/18 correct). The subject could not do any type of arithmetic.
General Procedures Setting. Sessions were conducted in a small office or a private area of the subject’s residence. The subject sat at a table facing the experimenter. Sessions lasted from 45 to 60 minutes. Stimuli and apparatus. Stimuli were real coins and printed prices-digits 2.5 cm high plus a cent sign. The subject sat facing a display panel placed flat on the table. Figure 2 schematically illustrates the display on four representative trials early in training. The sample stimulus was presented on a card at the top, and comparison stimuli on the lower four cards. Each card was 7.6 x 12.7 cm. The subject was required to discriminate coin stimuli on the basis of number and kind of coins. For example, as illustrated in Fig. 2A,
l-l P P PPP
FIGURE 2. A, B, C, and D show arrangements of sample (upper card) and comparison (lower four cnrds) stimuli on four representative trial displays: P =Penny; N = Nickel; D = Dime; lC, SC, 1OC = printed prices. 182
Teaching Coin Equivalences
183
she must select five pennies (choice 4) in response to the printed-price sample, 50. She had to reject comparison stimuli that had only the correct number of coins (e.g., five dimes; choice l), or only the correct type of coins (e.g., six pennies; choice 2). Further, she had to ignore irrelevant spatial characteristics of coin arrangements (e.g., Fig. 2C, five nickels; choice 4). The sample, comparisons, spatial configurations of coin stimuli, head and tail positions of the coins, and the position of the correct comparison varied unsystematically from trial to trial. Trialsequence. Each trial began with the presentation of a sample alone, and the subject had to touch it. Then, the four comparisons were uncovered, and the subject touched one to indicate her choice. Every correct choice was followed by delivery of a token and praise; at the end of each session, tokens were exchanged for various reinforcers (e.g., food, going to lunch with the experimenter). An incorrect choice ended the trial without any token. The experimenter covered all stimuli after each choice. During intertrial intervals (approximately 20 to 60 seconds), the subject held a cardboard screen to conceal data recording and arrangement of stimuli for the next trial. To start a trial, the experimenter lowered the screen to expose the next sample. Teaching and Testing Procedures Baseline and review trials. At least half the trials in each session reviewed pre-
viously mastered performances: (1) groups of coins, and matching single 7; see above); and (2) newly acquired ing and test trials were interspersed trials.
identity matching of prices, coins, and coins with their prices (entry skills 6 and performances, added for review. Trainirregularly among baseline and review
Matching performances were pretested prior to teaching. Procedures were the same as tests for emergent performances (see below).
Pretests.
Teaching. A delayed cue procedure (Touchette, 197 1; Sidman, 1977) was used to teach the required coin-to-price relations. The sample stimulus initially included both the price and, below it, coins identical to the correct coin comparison. The coins in this composite sample permitted the subject to respond correctly on the basis of visual identity. The price could come also to control correct selections if the subject observed and learned the relation between the price and the coins. Learning was encouraged by presenting the priceportion of the sample first and then adding the coin-portion (the delayed cue) after progressively longer times. If the subject learned the new coin-to-price
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matching relation, she could respond prior to the presentation of the delayed cue; if not, she could still respond correctly by waiting for it. Teaching continued until the subject correctly responded to the price alone on eight successive teaching trials. During teaching (and testing), each comparison stimulus was presented as the correct choice on some trials and the incorrect choice on others, to verify and maintain differential responding to the sample. Post-tests for emergent performances. After the subject could match two different coin stimuli to their corresponding printed price, the untrained cointo-coin matching was tested. On half of the 8 to 16 test trials, one stimulus of a pair to be matched was the sample and the other was the correct comparison; on the remaining trials, these roles were reversed. Further procedural details will accompany the results. Oral naming tests. Naming tests were given at the end of Experiment 1A to evaluate the effect of visual matching training on labeling the coin and price stimuli. Each sample was presented on three trials. The subject had to label each 5- and lo-cent stimulus by saying its name. The tests also included entry skills-labeling the le and 25e printed prices, and the penny and quarter. Correct responses did not produce tokens or praise. RESULTS
AND
DISCUSSION
Table 1 shows the percent correct scores and the sequence of teaching and testing phases (numbers in parentheses) in Experiments 1A and IB. The results omit the subject’s performances on baseline trials, which were virtually errorless. (Henceforth, monetary designations will be the abbreviated terms used in Figure 1 and Table 1, and matching tasks will be identified only by the task number.) Pretests. In Phases 1 and 7, the critical coin-to-coin matching tasks were pretested (3, 6, 9, 13, 15, and 18; omitting 16). The subject was never correct; she selected incorrect comparison stimuli that contained either the same type or number of coins as the sample. Other pretest data follow. Tasks 1-3 (phases I-3). Pretests of the 5-cent tasks confirmed that the subject could do only the first coin-to-price matching task (Table 1, 1, 5e:N; 93%), and not the second (2, 5Q:5P; 20%). When Task 2 was taught, the subject learned it in a single session, without errors, by means of the delayed cue procedure (subsequent teaching was equally effective, as well, unless noted). Having learned to match both N and 5P with the 5Q price, she was tested for emergence of coin-to-coin matching (3, N:5P); she scored 75% (3/4), a marked improvement over her pretest score. After Task 2 was reviewed in a second
Teaching
Coin Equivalences TABLE 1 Scores with S-Cent and IO-Cent Stimuli. phases is shown by numbers in parentheses.
Percent Correct Matching-to-Sample The sequence of teaching and testing
STIMULlaeb
PRETEST
Experiment IA I. 50 :N 2. 50 : 5P 3. N : 5P 4. IOQ : D 5. 100 : 5P5P 6. D : 5P5P 7. 5050 : NN 8. 5C5C : 5P5P 9. NN : 5PSP Experiment IL3 lo. 100 : 5454 ii. 5a5a : D 12. 100 : NN 13. D : NN 14. N5P : 5a5a 15. N5P : NN 16. N5P : 5P5P 17. N5P : loa 18. N5P : D
185
TEACH
TEST
TEACH
TEST
93 (1)
20(1) 0 100 0 0
100 (2)
100 (3B)
(1) (1) (1) (1)
15
(3A)
0 (4)
loo (3C) 100 (5) 94 (6)
100 63) 100 (8)
0 (7) 0 (7)
100 (9)
0 (1,7)
75 38 88 60 0
(10) (10) (10) (10) (10)
100 89 100 100 89 88 94 100 loo
0 (7) 0 (7)
0 (10)
(12.14)’ (12,14) (12.14) (12,14) (14) (14) (14) (14) (14)
REVIEW 97 98 96 99 96 97 96 98 97 98 95 100 97 94 97 93 96 94
a5P = 5 Pennies; N = Nickel; D = Dime; 5Q, 100 = Printed Prices bEach member of the listed pairs of stimuli served as the sample on some trials, with the other member as the correct comparison stimulus; on other trials, these roles were reversed. ‘See text for description of Phases 11 and 13.
teaching session, the subject then achieved a score of 100% (4/4) on Task 3. Training appeared to have established a class of five-cent stimuli. Tasks 4-6 (phases 1 and 4-6). With the first set of lo-cent stimuli, pretests again confirmed that the subject could match a single coin to its price (4, lOC:D, lOO%), but not a coin combination (5, 100:5PSP, 0%). After she was taught this task, she was then able to match the coins (6, D:5PSP); she scored
Constructed
TABLE 2 Response Test Scores
Session Matching Tasksa
l-5 (Phase ll)b .91 (49/54)C .OO(0/32)d
6-12 (Phase 13)
.96 (54/56) 10-13 .91 (96/106) 14-18 aNumbers refer to performances specified in Figure 1 and Table 1. bSee text for phase descriptions. CNumbers in parentheses are total responses/total opportunities. dPrior to presentation of N5P as a sample.
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94% on the untrained task, making only one incorrect response (on the sixth test trial). The subject appeared to have learned a second three-member class. Tasks 7-9 (phases 7-9). After learning Tasks 1-6, the subject failed pretests of Tasks 8 and 9, thus showing that she was not capable of matching these combinations of 5-cent stimuli at this stage; due to oversight, Task 7 was not pretested. Once again, the subject was taught coin-to-price matching-55cSQ: NN (7) and 505Q:5P5P (8). Without further teaching, she matched the coins - NN and SPSP - perfectly (9, 100%). This emergent performance did not necessarily show that the stimuli in the third set were equivalent, even though composed of equivalent 5-cent stimuli; the subject might have merely learned to match components. Further tests were required (see Experiment 1B). Oralnaming tests. After mastering Tasks l-9, the subject consistently labeled the N, 5P, and 50: samples as “five cents” and the D, NN, 5PSP, lOe, and 5C5e samples as “10 cents”; thus, she proved able to state the value of the combination coin stimuli for the first time, without any direct training with the names. She labeled N5P, pretested for the first time, as “five cents, five cents.” Review performances. The review column summarizes scores from all later trials that tested previously established performances. Throughout Experiments 1 and 2, the subject maintained high accuracy on Task l-9 (96%-99% correct). The number of review trials for each performance ranged from 93 to 200. EXPERIMENT
1B
The two IO-cent stimulus sets each contained 5P5P. If this stimulus had become equivalent to 5e5e and NN (not merely on the basis of components), and since it had already been shown to be equivalent to 1OCand D, then the five stimuli should comprise a five-member class. To test this possibility, the subject was asked to do the remaining tasks with these stimuli, that is, to match 1OCwith 5eSC, 5C5e with D, 10e with NN, and D with NN (Figure 1, 10-13). The remaining lo-cent stimulus - NSP - provided the opportunity for an explicit test of whether the subject had learned to match individual components. If she had learned this skill with N and 5P in combinations that contained identical components, could she now match the new mixed combination of these stimuli with the uniform ones (Figure 1, 14-16). For example, could she match NSP with 5e5C by matching N with one 5C price and 5P with the other 5e price? If successful, would she then be capable of matching N5P
Teaching Coin Equivalences
187
with 109 and with D-tasks that did not permit component matching (Figure 1, 17 and 18). She could do so only if N5P had joined the other combination stimuli in forming a class with 1OQand D. For these considerations, N5P was tested last (except for limited pretests), and no direct teaching with this stimulus would be conducted unless it proved necessary. Tasks lo-13 and 14-18 were tested by the matching-to-sample method and by a second method devised in the course of Experiment 1B. This experiment also began preliminary study of the importance of direct token reinforcement of matching performances when they emerged. Method Pretests. Of Tasks 10-13, only the last was pretested in Experiment lA, in conjunction with pretests of Tasks 8 and 9 (Table 1, Phases 1 and 7). A more limited study had been planned initially, and relevant training precluded later pretests. Tasks 14-18 were pretested selectively. Reinforcementprocedures. Initial tests of Tasks lo-13 were conducted with continuous reinforcement (Phase 10). Later (Phases 1 l-14), responses on selected tasks were not reinforced with tokens or praise. The subject was first adapted to an intermittent schedule of reinforcement on baseline tasks; on the average, every other correct response produced a token (variable ratio 2; range l-5). Test trials were then interspersed. Some correct test performances, including all initial responses on Tasks 14-18, were followed only by the next trial. Further details will accompany the results. Tasks 10-13: Matching-to-sample test 1 (phase 10). Tasks lo-13 were first tested eight to ten times each, using the standard matching-to-sample procedure. Also, probe tests of Tasks 14 and 18 were given in this phase. Tasks 10-13: Constructed response test (phase II). Based on the initial results, an alternative testing method was devised. The subject was shown a sample and an unsorted pool of different coins and printed prices. Her task was to select from the pool all coins, coin combinations, and prices that might correspond to the sample. She placed each selection on a 7.6 x 12.7 cm card. Each pool permitted selections based on previously demonstrated performances, including identity matching, and also gave opportunities to make at least one novel (potentially emergent) match. The choice pool often presented multiple opportunities for a given selection, such as two dimes when 1OCwas the sample. As the subject constructed her selections, the experimenter recorded each one. If the subject made the same selection more than once on a trial, it was scored simply as one response. The sample remained present
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and L. T. Stoddard
until the subject said, “No more.” The experimenter then examined the choice pool and recorded any missed opportunities to construct matches; for example, leaving two nickels in the pool when the sample was the 1OCprice was recorded as a missed opportunity to do Task 12. The next trial began with the presentation of a different sample and a new choice pool. Trials that reviewed previously learned and entry performances were included, such as those with 5- and 25cent samples, and some trials permitted only identity selections (e.g., five dimes). Each 5-cent and IO-cent stimulus was presented as a sample at least once per session, except N5P during this phase; however, there were opportunities to select NSP as a potential choice. Unlike standard matching to sample, the constructed response test did not ask the subject to attempt a novel match before she was able to make it. Instead of potentially being “forced” to make an error, she could now simply say “No More.” Tasks 10-13: Matching-to-sample test 2 (phase 12). After tests that used the new procedure, matching-to-sample tests were repeated (8 or 9 trials each). Tasks 14-18 (phases I3 and 14). With NSP, constructed response tests were given first, by adding this stimulus as one of the samples. Then Tasks 14-18 were extensively tested in standard matching to sample (at least 14 trials each). Also, tests of Tasks lo-13 continued in both these phases. Review of Tasks I-18 and oral naming tests followed. Results and Discussion Tasks 10-13. On the first matching-to-sample test of Tasks 10-13, the subject achieved scores of 75%, 3890, 88%, and 60%, respectively (Phase 10); all scores were better than chance performance (25% on these 4-choice tests), but none conclusively demonstrated mastery. In view of the subject’s accurate naming of these lo-cent stimuli at the end of Experiment lA, these results were difficult to interpret (see Sidman & Tailby [1982] for a discussion of the distinction between stimulus classes defined by common responses [naming] and by equivalence relations). Other studies have shown that stimulus class formation apparently can sometimes occur gradually, with initially imperfect performance followed by greater accuracy during repeated testing, even if the tests are conducted in extinction (Spradlin, et al., 1973; Lazar, 1977). Did our subject’s intermediate accuracy reflect incomplete formation of the five-member class? Also, would the early test errors affect later performance? The constructed response procedure was an attempt to answer these questions. The task reviewed previously mastered performances, especially the prerequisite Tasks 4-9; at the same time it gave the subject numer-
Teaching Coin Equivalences
I89
ous opportunities to show whether she was capable of Tasks 10-13, without forcing her to make errors. The constructed response testing was conducted over 12 sessions. Given the opportunity to demonstrate Tasks lo-13 in the new format, the subject often did so immediately. Token reinforcement was withheld for Tasks 12 and 13 until the subject’s fifth and eighth correct selections, respectively. No differences in performance were observed; hence, data on Tasks lo-13 are combined. The upper row of Table 2 shows her constructed response scores for these tasks (total selections/total selections -I- missed opportunities; percent correct scores would not reflect missed opportunities). Over the 12 sessions, the subject’s mean score for these tasks was 0.94. Scores for individual performances ranged from 0.86 (11) to 1.OO (13). In the first five sessions (Phase 1 l), the subject missed slightly more opportunities than later; however, she performed Tasks lo-13 about as often as the previously established IO-cent ones (4-9)-making 49 and 50 matching selections, respectively. In matching-to-sample tests after the 5th constructed response session (Phase 12) and after the 12th (Phase 14), the subject’s scores on Tasks lo-13 showed marked improvement (Table 1, second test). Only her score on Task 11 was imperfect (89%). The data seemed to support the formation of a fivemember class of IO-cent stimuli. Adding the sixth stimulus - NSP - provided a critical test. Tusks 14-18. During the first five constructed response sessions (Phase 1l), the subject had 32 opportunities to select NSP in response to each of the other lo-cent samples; NSP was not presented as a sample. However, she made no NSP selections, thereby failing to do Tasks 14-18 immediately (Table 2, lower row, Sessions l-5). In the sixth session (Phase 13), NSP was given as a sample for the first time: Not only did the subject select all the other IO-cent stimuli to this sample (score 1.00; 12 responses/l2 opportunities), but she then began to choose the NSP match for other lo-cent samples (score .80, 415). In Sessions 7-12, her scores were 0.93 (68/73) with N5P as the sample, and 0.85 (28/33) when it was a possible choice; both scores were 1 .OOin the last four sessions. The subject demonstrated each NSP performance at least five times before it was reinforced with tokens. (The reinforcement issue is discussed after Experiment 2.) Performances with NSP appeared to come about by matching it first with other two-component stimuli; NN and 5954 were the subject’s first two selections to the N5P sample. The test format may have encouraged such matching, since she could select individual components in sequence while constructing her response. However, her third and fourth selections to a NSP sample were 1OCand D, showing rapid emergence of new performances not achievable by component matching. Subsequent matching-to-sample scores on Tasks 14-18 ranged from 88%
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to 100% correct (Table 1, Phase 14), and confirmed the good constructed response results. Thus, the subject appeared to have learned a six-member class of IO-cent stimuli. Review trials and oral naming tests. During review of Tasks lo-18 (41 to 84 trials each), the subject’s scores were 93%-100% correct. On oral naming tests (identical to those at the end of Experiment lA), the subject correctly labeled each 5 and lo-cent stimulus, saying “five cents” or “ten cents.” Having labeled NSP as “five cents, five cents” on the pretest, she now gave it the same name as the other IO-cent stimuli, again showing an emergent skill without direct training. EXPERIMENT
2
The purpose of this experiment was to investigate the establishment of matching performances with nine 15cent stimuli, through extensions of the stimulus class formation methods used in Experiments 1A and IB. In Figure 3, the two printed-price stimuli at the left and the six coin stimuli show all possible combinations of the 5- and lo-cent stimuli that total 15 cents. The ninth stimulus- the 15Q printed price- was new. In Experiment lB, the subject seemed initially to have matched NSP with other IO-cent stimuli by matching components. Perhaps now she would prove capable of doing so with 15-cent combinations, most of which were also mixed combinations. However, the subject had not previously matched a two-component stimulus with a three-component one, for example, lOc5c or DN with 5PSPSP (again considering a group of five pennies as a unit). This somewhat different skill might have to be taught directly. If so, teaching one such performance might permit her to do the others. This outcome would provide additional evidence of stimulus class formation, by confirming that the individual components formed classes, as in matching DSP with NNN. A test of whether the eight 15-cent combination stimuli became a stimulus class would be (1) to teach the matching relations between one of them and the ninth stimulus - the 15Q price- and then (2) to examine the relations of the other seven with the price. To investigate reinforcement variables in stimulus class formation further, no programmed consequences would follow any test trial. Method Generalprocedures. Matching-to-sample procedures were the same as before, except that stimuli were attached to large white cards (12.5 x 20 cm), in prearranged displays. Reinforcement was a token delivered approximately every five minutes, after a correct response on a task with 5- and lo-cent stimuli.
I D5p I DN II I I I I
5P 5P5P ’
15c
1 5c 5c 5c
I NNN I 1 NN5P
1
FIGURE 3. Schematic diagram of the nine printed-price and coin stimuli in the 36 possible Scent equivalences. Thin solid lines indicate some of tbe performances that the subject demonstrated after Experiment 1; wider solid lines indicate performances taught directly in Experiment 2. The dashed line shows one performance which might emerge after training. The remaining 29 performances are not shown by lines (for clarity). 191
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E. C. McDonagh, W. J. Mcllvane, and L. T. Stoddard
Responses on all intervening baseline trials and all test trials were not reinforced, thus making these events less discriminable on the basis of non-reinforcement. Every two tokens were exchanged later for a quarter. Pretests. The subject was given a test battery that presented 18 of the 36 possible matching tasks with U-cent stimuli. The left column of Table 3 lists the stimuli for these and other selected tasks. A second pretest evaluated the six matching relations shown by lines in Figure 3 (omitting the one with the 15c price; Table 3, 19-24). These six tasks were tested selectively for the following reasons: (1) The lOC5e-DN task presented stimulus components that the subject could match individually prior to the study (1OO:D; 5C:N), and she might match the components; (2) the other three stimuli were uniform combinations (5C5C5e, NNN, 5P5PSP) that might prove easier to match than mixed combinations that included one or two groups of pennies; and (3) these tests could set the stage for teaching as in the design of Experiment 1A-to teach the relations between a price and a uniform combination of pennies (lOQ5C:5PSP5P). To follow the same design, a third pretest was required prior to teaching the 15C price-matching 156 with 5PSPSP (Table 3, 36). Pretests typically included 12 trials of each task, interspersed among a greater number of baseline trials. Teaching procedures and post tests. Teaching the coin-to-price relations, when necessary, was conducted with the delayed cue procedure as in Experiment 1A. After training, two types of post tests were conducted: (1) Matchingto-sample tests were identical to pretests and were given first; (2) constructed response tests then followed - identical to those in Experiment 1B except for the addition of 15-cent samples; these tests examined the emergence of the 14 previously untested 15-cent performances (Appendix A), as well as the 22 already measured by standard matching to sample. Naming tests followed. (See Results for further details.) Results and Discussion First pretest. The results at the left of Table 3 show that the subject often could match 15-cent stimulus combinations, when comprised of equal numbers of components (20 and 25-30; mean score of 72% correct). On the other hand, she matched unequal numbers of components much less well (23, 24, 31-35; mean score of 27% correct); typically, she scored 25% or less (e.g., 23, matching lOe50: with 5P5P5P). Thus, a possible prerequisite skill seemed lacking; the subject had difficulty matching two components with three components. Secondpretest. When Tasks 19-24 were tested separately, the subject’s scores supported the predictions and initial findings (Table 3, column 2): (1) match-
Teaching Coin Equivalences
Percent STIMULIB*b 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40.
505Q5Q 5Q5Q50 NNN lOQ5Q 10eW DN 10050 505450 NNN NNN NNSP NNSP loa 5uSU5U DN D5P D5P 15Q 15a 150 Isa Isa
Correct
TABLE Matching-to-Sample
PRETEST : : : : : : : : : : : : : : : : : : : : : :
NNNC 5P5P5P 5PSPSP DN 5P5P5Pd 5PSPSPd D5P NNSP NNSP N5P5P N5PSP SPSPSP N5P5Pd D5Pd NN5Pd N5P5Pd NNNd 5P5P5P NNSP N5P5P DSP ioe5a
92
25 25 19 69 83 75 83 42 75 9 50 17 8
PRETEST
TEACH
100 92 95 100 8 8
94
17 17 17 33
a*bSee notes, Table 1. ‘Task numbers continue from Table 1. dTasks that require matching two components ponent).
3 Scores
with
witb
193
15Cent TEST 100 95 100 100 9-l 98 100 92 100 100 92 100 100 92 92 92 92 0 25 8 25 25
three components
Stimuli. TEACH
TEST
100
97 92 100 92 100
(5P treated
as one com-
ing lOC5C with DN - a test of combined entry skills - was performed at 100% accuracy (22); (2) also, on tasks with equal numbers of components, her scores with uniform combinations (19-21) were 92% correct or better, consistently higher than her scores had been with mixed penny-combinations on the initial test (25-30); (3) she continued to do poorly with unequal numbers of components (23, 24). Teaching. When taught to match a two-component price - 10~5Q- with a uniform three-component penny combination - 5PSPSP - the subject learned with only two errors (23; 94% correct). tests. The subject received the post test of Tasks 19-24, followed by the test battery. The combined scores showed (Table 3, column 4): (1) performance on Tasks 19-23 was maintained; (2) on tasks that required her to match unequal numbers of components (24 and 31-35) she scored 92% or better; thus, having learned one such performance-matching lOC5C with 5PSPSP-she was then able to do others of a similar type, without direct teaching; (3) on tasks with mixed penny combinations, but equal numbers
Initialpost
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E. C. McDonagh, W. J. Mcllvane, and L. T. Stoddard
of components, her scores became virtually perfect (25-30); and (4) performances with the 1% price did not improve. On the constructed response test that followed, the subject demonstrated all previously untested relations between 15cent combinations (Appendix A, 41-51; data not shown). She made matching selections on 77 of 78 opportunities, at least 6 with each of the 11 new tasks. With previously tested tasks, she also missed only 1 of 109 opportunities. She made only four incorrect selections to 15-cent samples. The 15C price was not presented as a sample or potential choice. !n summary, the subject now was able to match any of the eight 15cent combination stimuli to any other, but possibly only on the basis of matching components. The next phase examined whether they comprised a stimulus class. Teaching the 154price. The subject was taught to match the 150 price with one of the eight 15cent combinations -5PSPSP. When this task was pretested, the subject had not responded correctly. On all teaching trials, she was correct (Table 3, 36, columns 4 and 5). Post tests with the ISprice. On matching-to-sample tests with the 15e price, the subject scored 92Vo correct or better (last column in Table 3). On subsequent constructed response tests, she missed no opportunities to select each of the nine 15-cent stimuli, including the 15C price, in response to each of them as a sample. The 135 total opportunities included 6 with each of the three previously untested tasks, matching the 1% price with DN, NNN, and 5e5C5U (Appendix A, 52-54). These data provide evidence that a nine-member stimulus class had been formed. Naming tests. The subject was able to state the value of all stimuli used in the study, correctly labeling them as “five cents,” “ten cents,” or “fifteen cents”. Prior to the study, the subject could give the name “fifteen cents” to the 150 printed price, but could not match the price to any coin (or price) combination. When taught to match the price with one 1S-cent combination 5PSPSP-not only was she able then to match it with the remaining seven, but also to name each of them. GENERAL
DISCUSSION
In Experiments 1 and 2 combined, the subject was tested on a total of 54 matching relations involving 18 visual stimuli, 13 of which were the critical 5-, lo-, and 15-cent coin and price combinations. Of the 54 relations, 2 were entry performances, 6 were directly taught, and 46 emerged without direct teaching. All matching relations were bidirectional, in that either stimulus of a given pair could be the sample or choice. Also, the subject could both point
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195
to choices in a fixed array and select (construct) choices from an unsorted array. Further, the subject was able, also without direct teaching, to state the value of each of the 13 combination stimuli for the first time. Subsequent tests revealed that she could also match each of them with its corresponding dictated price. Although the subject could have performed many new relations by matching components, the components themselves must have formed classes in any given instance, in order for her to do so. For example, to match DSP with NNN by components must depend on the prior establishment of the 5- and IO-cent classes. Moreover, matching by components is a significant accomplishment in itself, especially when considering the increased complexity of two- and three-component matching in many 15-cent relations. The data are relevant to the question: “Is direct reinforcement of individual performances necessary in their emergence without direct training?” (cf., Spradlin et al., 1973; Sidman, 1981). Withholding tokens as consequences for some performances did not seem to retard or disrupt their reliable emergence: all 15cent equivalences, all naming and visual-to-auditory relations, and some emergent relations in the lo-cent class. These outcomes could have depended on reinforcement of other class members (Sidman & Tailby, 1982). However, in face-to-face teaching, it is impossible to rule out other reinforcing factors like differential attention, even though the teacher strives to remain neutral (as was done in this study). Additional research is needed to determine whether all features of the procedures are necessary in practical teaching situations. It would probably not be necessary, for example, to conduct the extensive baseline training, testing, and reinforcement-schedule pretraining that were required to provide experimental verification of stimulus class formation. Also, the question of general usefulness of these procedures remains. Our subject began the study with entry skills (e.g., generalized identity matching, coin identification) which less advanced students would have to acquire. Notably, stimulus class formation has been achieved with less capable subjects (Sidman & Cresson, 1973), and helpful methods for teaching such entry skills to moderately and severely mentally retarded individuals have been developed (cf., Sidman, 1977). On a methodological note, the constructed response method may be an especially benign and helpful way to test potential stimulus equivalences, since the subject need make no errors if a new performance has not been established. The method allows the subject to show newly emergent and directly trained performances in any order, and to do so with equal facility, as our subject demonstrated in Experiment 2. Where the order of emergence seemed to matter, the subject can freely show that fact as well, as with the N5P relations in Experiment 1B. Further, the test format -selecting actual coins from an unsorted array - resembles real monetary transactions and may promote generalization of new skills to community settings. In conclusion, the study contributes to research on stimulus class for-
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and L. T. Stoddard
mation by providing systematic replication of the procedures and general outcome of the stimulus equivalence paradigm. The data from a mentally retarded subject add support to the findings of other studies with this population, which show the capacity to acquire stimulus classes through similar procedures (see Introduction). As this study illustrates, such procedures require no special setting or equipment, and might eventually be adapted for use by teachers with minimal training. Further, the study employs stimulus class methodology with a different type of stimuli, thereby illustrating strategies for addressing the practical problem of teaching skill repertoires that require mastery of large numbers of individual performances. Inclusion of such methods may enhance other successful programs for teaching money skills (e.g., Wunderlich, 1972; Bellamy & Buttars, 1975; Lowe & Cuvo, 1976; Trace, Cuvo, & Criswell, 1977; Cuvo, Veitch, Trace, & Konke, 1978), by reducing the number of performances that have to be taught directly. REFERENCE
NOTES
1. This paper is based on a thesis submitted by the first author to the Department of Psychology, Northeastern University, in partial fulfillment of the requirements for the Master of Arts degree. The research was supported in part by NICHHD Grant HD10210 to the Eunice Kennedy Shriver Center for Mental Retardation, by the University Affiliated Facility Training Grant, BCHS, MCH (HHS) Grant No. MCT-000906, and by the Administration of Developmental Disabilities, Office of Human Developmental Services, Grant No. 59-P-05424. The authors wish to thank Branko J. Gerovac for indispensable contributions and Leila R. Cohen, Harry A. Mackay, and Barbara Ray, for their valuable comments on an earlier version of the manuscript. 2. Historically, the method has been termed mediated transfer (cf., Sidman, et al., 1974). 3. Sample-choice reversibility is a test for symmetry in matching relations, one of three logical properties that the relations must possess to be called equivalence relations (Sidman, et al., 1982; Sidman & Tailby, 1982).
REFERENCES Bellamy, T. & Buttars, K. L. Teaching trainable level retarded students to count money: Toward personalized independence through academic instruction. Education and Training of the Mentally Retarded, 1975, 10, 18-26. Cuvo, A. J., Veitch, V. D., Trace, M. W., & Konke, J. L. Teaching change computation to the mentally retarded. Behavior Modification, 1978, 2, 531-548. Dixon, M. H. & Spradlin, J. E. Establishing stimulus equivalences among retarded adolescents. Journal of Experimental Child Psychology, 1976, 21, 144-164. Lazar, R. Extending sequence-class membership with matching to sample. Journal of the Experimental Analysis of Behavior, 1971, 27, 381-392. Lowe, M. L., & Cuvo, A. J. Teaching coin summation to the mentally retarded. Journalof Applied Behavior Analysis. 1976, 9, 483-489. Mackay, H. A. & Sidman, M. Teaching new behavior via equivalence relations. In R. Sperber, C. McCauley, and P. H. Brooks (eds.), Language and Cognition in the Mentally Retarded, Baltimore: University Park Press, in press.
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Sidman, M. Reading and auditory-visual equivalences.. Journal of Speech and Hearing Research, 1971,14,5-13. Sidman, M. Teaching some basic prerequisites for reading. In P. Mittler (Ed.), Research fo Prucrice in Mental Returdafion, Vol. II. Baltimore: University Park Press, 1977, Pp. 350-360. 350-360. Sidman, M. Remarks. Behaviorism, 1981, 9, 127-129. Sidman, M. & Cresson, 0. Reading and crossmodal transfer of stimulus equivalences in severe retardation. American Journal of Menlo1 Deficiency, 1973, 77, 515-523. Sidman, M., Cresson, O., & Willson-Morris, M. Acquisition of matching-to-sample via mediated transfer. Journal of the Experimental Analysis of Behavior, 1974, 22, 261-273. Sidman, M., Rauzin, R., Lazar, R., Cunningham, S., Tailby, W., & Carrigan, P. A search for symmetry in the conditional discriminations of rhesus monkeys, baboons, and children. Journal of fhe Experimenlul
Analysis
of Behavior,
1982, 37, 23-44.
Sidman, M. & Tailby, W. Conditional discriminations vs. matching to sample: An expansion of the testing paradigm. Journal of the Experimental Analysis of Behavior, 1982.37,5-22. Spradlin, J. E. Language and emergent behavior. In P. Mittler (Ed.), Research fo Practice in Mental Retardation, Vol. II. Baltimore: University Park Press, 1977, Pp. 253-260. Spradlin, J. E., Cotter, V. W., & Baxley, N. Establishing a conditional discrimination without direct training: a study of transfer with retarded adolescents. American Journul of Menfal Deficiency,
1973, 77, 556-566.
Spradlin, J. E. & Dixon, M. H. Establishing conditional discriminations without direct training: Stimulus classesand labels. American Journul of Mentul Deficiency, 1976, 80, 555-561. Stromer, R. &Osborne, J. G. Control of adolescents’arbitrary matching-to-sample by positive and negative stimulus relations. Journul of the Experimental Analysis of Behavior, 1982, 37, 329-348. Touchette, P. E. Transfer of stimulus control: Measuring the moment of transfer. Journal of the Experimental Analysis of Behavior, 1911, 15, 347-354. Trace, M. W., Cuvo, A. J. & Criswell, J. L. Teaching coin equivalence to the mentally retarded. Journal of Applied Behavior Analysis, 1977, 10, 85-92. VanBiervliet, A. Establishing words and objects as functionally equivalent through manual sign training. American Journal of Menful Deficiency. 1971, 82, 178-186. Wunderlich, R. A. Programmed instruction: Teaching coinage to retarded children. Mental Retardation, 1972, 10, 21-23.
APPENDIX
A
Fourteen matching tasks involving 15cent stimuli; not pretested and examined only in constructed response tests (task numbers continue from Table 3): (41) lOQ5Q-5~5C50;(42) IOCSC-NNN; (43) lOCS’LNN5P; (44) 505C5CN5P5P; (45) 5C5CSO-DN; (46) DN-NNN; (47) DN-NSPSP; (48) DN-DSP; (49) D5P-5P5P5P; (50) DSP-NNSP; (5 1) 5P5P5P-NSP5P; (52) 150-5@5C5C; (53) ISQ-NNN; (54) 15GDN.