Efficiently Forming Equivalence Classes: Strategies and Applications
http://www.rapidshare.com.cn/8qhxdHC
Colleen Yorlets RCS Behavioral & Educational Consulting & Simmons College
Christina KingRCS Learning Center & Simmons College
Megan BreaultRCS Learning Center & Simmons College
Goals and Objectives
• Define stimulus equivalence and the three major properties
– Reflexivity, symmetry, and transitivity (Sidman & Tailby, 1982)
• Provide examples of applications for teaching specific skills
• Identify and arrange stimulus-stimulus relations to be taught/emerge
Sidman, 1971
• Participant: 17 year old male diagnosed with mental retardation and microcephaly
• Demonstrated 60 emergent relations after being taught only 20 auditory-visual conditional discriminations
Tests of Equivalence - Reflexivity
•Reflexivity – “Each stimulus bears the relation to itself” (Sidman & Tailby, 1982, p. 6) •“if R is the conditional relation, reflexivity requires, “if a, then a, if b, then b, etc.” (Sidman, Rauzin, Lazar, Cunningham, Tailby, & Carrigan, 1982, p. 24) •Tested by generalized identity matching –A=A
Identity Matching-To-Sample (MTS)
Tests of Equivalence – Symmetry •Symmetry - “Symmetry requires the relation R to hold bi-directionality between two different stimuli” (Sidman et al., 1982, p. 24) •Requires functional sample-comparison interchangeability of stimuli (Sidman et al., 1982; Sidman, Willson-Morris, & Kirk, 1986) •Symmetry – must show if A=B then B=A without any additional training (Sidman and Tailby, 1982)
Symmetry
Tests of Equivalence – Transitivity
•Transitivity - Relation amongst three stimuli (Sidman et al., 1982) •Transitivity – a derived relation that develops following other trained relations (Sidman & Tailby, 1982) –If A=B and A=C then B=C and C=B
Transitivity
Equivalence Triangle
Applied Studies Math Skills• Coin Equivalence (McDonagh, McIlvane, &
Stoddard 1984)• Fraction, decimal relations (Lynch & Cuvo, 1995)• Multiplication and Division relations (Persson,
Maguire, & Cameron, 2009)• Geometry relations (Sumner, Maguire, &
Cameron, 2010)Geography• Geography relations (LeBlanc, Miguel, Cummings,
Goldsmith, & Carr, 2003)Reading Comprehension• Reading skills (Mackay, 1985)
Match-to-Sample
• Match-to-sample: In the presence of a conditional or sample stimulus, the participant selects the S+ from an array of comparison stimuli.
• Common format for equivalence-based instruction.
Country Music Hall
of Fame
Johnny Cash Nirvana Easy E
Country Music Hall
of Fame
Johnny Cash Nirvana Run DMC
Sample Stimulus
S+ S- S-
Demonstration of Equivalence
• Refer to your packet
• Demonstration
http://www.rapidshare.com.cn/8qhxdHC
Stimulus Class Table
Experimental Schematic
Demonstration Slides
Data Sheet
A-B Pre-Test
Johnny CashRun DMC Nirvana
Country Music Hall of Fame
Nirvana Johnny Cash Run DMC
Rock and Roll Hall of Fame
NirvanaJohnny Cash Run DMC
Hip Hop Hall of Fame
A-C Pre-Test
Cleveland Nashville New York City
Rock and Roll Hall of Fame
ClevelandNashville New York City
Hip Hop Hall of Fame
NashvilleNew York City Cleveland
Country Music Hall of Fame
B-A Pre-Test
Rock and Roll
Hall of FameCountry Music
Hall of FameHip Hop
Hall of Fame
Run DMC
Country Music
Hall of Fame
Hip Hop
Hall of FameRock and Roll
Hall of Fame
Johnny Cash
Rock and Roll
Hall of Fame
Country Music
Hall of Fame
Hip Hop
Hall of Fame
Nirvana
B-C Pre-Test
NashvilleNew York City Cleveland
Johnny Cash
Cleveland Nashville New York City
Nirvana
ClevelandNashville New York City
Run DMC
C-A Pre-Test
Rock and Roll
Hall of Fame
Country Music
Hall of Fame
Hip Hop
Hall of Fame
Cleveland
Rock and Roll
Hall of FameCountry Music
Hall of FameHip Hop
Hall of Fame
New York City
Country Music
Hall of Fame
Hip Hop
Hall of FameRock and Roll
Hall of Fame
Nashville
C-B Pre-Test
NirvanaJohnny Cash Run DMC
New York City
Johnny CashRun DMC Nirvana
Nashville
Nirvana Johnny Cash Run DMC
Cleveland
A-B Training Step 1
Johnny CashRun DMC Nirvana
Country Music Hall of Fame
Correct!
Johnny Cash Run DMC Nirvana
Hip Hop Hall of Fame
Correct!
Run DMCNirvana Johnny Cash
Rock and Roll Hall of Fame
Correct!
A-B Training Step 2
Johnny Cash Run DMC Nirvana
Hip Hop Hall of Fame
Correct!
Johnny CashRun DMC Nirvana
Country Music Hall of Fame
Correct!
Run DMCNirvana Johnny Cash
Rock and Roll Hall of Fame
Correct!
A-B Training Step 3
Run DMCNirvana Johnny Cash
Rock and Roll Hall of Fame
Correct!
Johnny Cash Run DMC Nirvana
Hip Hop Hall of Fame
Correct!
Johnny CashRun DMC Nirvana
Country Music Hall of Fame
Correct!
A-C Training Step 1
NashvilleNew York City Cleveland
Country Music Hall of Fame
Correct!
Nashville New York City Cleveland
Hip Hop Hall of Fame
Correct!
New York CityCleveland Nashville
Rock and Roll Hall of Fame
Correct!
A-B Training Step 2
Nashville New York City Cleveland
Hip Hop Hall of Fame
Correct!
NashvilleNew York City Cleveland
Country Music Hall of Fame
Correct!
New York CityCleveland Nashville
Rock and Roll Hall of Fame
Correct!
A-B Training Step 3
New York CityCleveland Nashville
Rock and Roll Hall of Fame
Correct!
Nashville New York City Cleveland
Hip Hop Hall of Fame
Correct!
NashvilleNew York City Cleveland
Country Music Hall of Fame
Correct!
Post-Test Intermixed Relations
Johnny CashRun DMC Nirvana
Country Music Hall of Fame
Cleveland Nashville New York City
Rock and Roll Hall of Fame
Rock and Roll
Hall of FameCountry Music
Hall of FameHip Hop
Hall of Fame
Run DMC
NashvilleNew York City Cleveland
Johnny Cash
Rock and Roll
Hall of Fame
Country Music
Hall of Fame
Hip Hop
Hall of Fame
Cleveland
NirvanaJohnny Cash Run DMC
New York City
Nirvana Johnny Cash Run DMC
Rock and Roll Hall of Fame
ClevelandNashville New York City
Hip Hop Hall of Fame
Country Music
Hall of Fame
Hip Hop
Hall of FameRock and Roll
Hall of Fame
Johnny Cash
Cleveland Nashville New York City
Nirvana
Rock and Roll
Hall of FameCountry Music
Hall of FameHip Hop
Hall of Fame
New York City
Johnny CashRun DMC Nirvana
Nashville
NirvanaJohnny Cash Run DMC
Hip Hop Hall of Fame
NashvilleNew York City Cleveland
Country Music Hall of Fame
Rock and Roll
Hall of Fame
Country Music
Hall of Fame
Hip Hop
Hall of Fame
Nirvana
ClevelandNashville New York City
Run DMC
Country Music
Hall of Fame
Hip Hop
Hall of FameRock and Roll
Hall of Fame
Nashville
Nirvana Johnny Cash Run DMC
Cleveland
Stimulus Class Table
Experimental Schematic
Reflexivity slide
A-B Training
A-C Training
Symmetry Post-Test
Transitivity Post-Test
Experimental Schematic
Scoring and Reporting on Results
Scoring Pretest Results
Scoring Pretest Results
Hypothetical Pretest Results
Hypothetical Pretest Results
Scoring Posttest Results
Hypothetical Posttest Results
Reflexivity
Trained Relations
Symmetry
Transitivity
Various Visual Displays
Keintz, Miguel, Kao, & Finn (2011)
Various Visual Displays
Keintz, Miguel, Kao, & Finn (2011)
Various Visual Displays
Keintz, Miguel, Kao, & Finn (2011)
Visual Analysis
Cowley, Green & Braunling-McMorrow
(1992)
Tests for Delayed Emergence
Evaluating Individual Relations
Evaluating Individual Relations
•A-A = A1-A1, A2-A2, A3-A3
•B-B= B1-B1, B2-B2, B3-B3
•C-C= C1-C1, C2-C2, C3-C3
•A-B = A1-B1, A1-B2, A3-B3
•A-C= A1-C1, A2-C2, A3-C3
•B-A= B1-A1, B2-A2, B3-A3
•C-A= C1-A1, C2-A2, C3-A3
•B-C= B1-C1, B2-C2, B3-C3
•C-B= C1-B1, C2-B2, C3-B3
Individual Relations
Pre-Test Results• A-C = 49% correct• B-C= 66% correct• C-B= 55% correct
• Criteria was less than 66% correct at baseline
• Student had stimulus class 1 already in their repertoire
Designing Equivalence-Based Instruction
1. Evaluate pre-requisite skills
2. Identify target skills
3. Determine stimulus class size and number of classes
4. Decide training structure and identify trained/emergent relations
5. Identify training and test acquisition criteria
6. Determine number of training and test trials
7. Decide mode of presentation
8. Identify prompting procedures
9. Arrange stimuli within design structure
10. Pre-test all possible relations
11. Data analysis
12. Train specified relations to criteria
13. Post-test all possible relations
14. Data analysis
1. Evaluate pre-requisite skills
• Identity matching-to-sample
• Arbitrary matching-to-sample
• Attending duration
elm oak fir
2. Identify Target Skills
• Identify specific skills to be demonstrated and target stimuli
• Consider prior history
• Avoid faulty stimulus control• Irrelevant features can control responding, so need to
plan for this• Size of stimuli• Color• Length of word/phrase• Initial letter
Degas
Degas
Jaguar
Jaguar
alpaca
cria cygnetchrysalis
alpaca
cria cribcrow
tick track truck
tick
tick tier tint
tick
3. Stimulus Class Size and Number of Classes
• Minimum class size is 3
• Can have larger classes
• Determine number of classes to be demonstrated
Experimental Schematic
Stimulus Class Table
Figure 1. Schematic of potential three, 3-member stimulus classes to be formed. Solid lines
denote relations to be trained. Dashed lines denote potential emergent relations.
A- AUDITORY STIMULI
A1 “Truck” A2 “Tick”
A3 “Track”
C – PRINTED WORDC1 Truck
C2 Tick
C3 Track
B -PICTURE OF ITEM
B1
B2
B3
D - Spelling
D1
D2
D3
Black Line = Established Relations Prior to the StudyRed Line = Taught RelationsDashed Line = Potential Emergent Relations
(Breault, 2015)
B
"flower" C "flower"
D
*Solidlineswithintheschematicrepresenttrainedrelations
*Dashedlineswithintheschematicrepresentemergent(untrained)relations
LISTENER TACT
(King, 2015)
4. Training Structures
• One to many (OTM)
• Many to one (MTO)
• Linear series (LS)
Linear Series (Arntzen, 2012)
cranberry
bog Ocean Spray
A
CB
One to Many (Arntzen, 2012)
cranberry
bog Ocean Spray
A
CB
Many to One (Arntzen, 2012)
cranberry
bog Ocean Spray
A
CB
Linear Series
OTM
MTO
Which is best?
• Overall, research indicates Linear Series is the least effective (Arntzen, 2012)
• Varied results comparing MTO and OTM in terms of which is most effective
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
A-B A-C B-A C-A B-C C-B
Perc
ent
Corr
ect
Relation
Figure 2. Percent correct during pretesting for one hypothetical participant.
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
A-B A-C B-A C-A B-C C-B
Perc
ent
Corr
ect
Relation
Figure 3. Percent correct during pretesting for one hypothetical participant.
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
A-B A-C B-A C-A B-C C-B
Perc
ent
Corr
ect
Relation
Figure 4. Percent correct during pretesting for one hypothetical participant.
5. Training and Testing Criteria
• Establish acquisition criteria for training and testing phases
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
A-B A-C B-A C-A B-C C-B
Perc
ent
Corr
ect
Relation
Figure 5. Percent correct during pretesting for one hypothetical participant.
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
A-B A-C
Perc
ent
Corr
ect
Relation
Figure 6. Percent correct per trained relation for one hypothetical participant.
6. Decide number of training and test trials
•During testing, need to present all sample stimuli and comparison stimuli an equal number of times
• No rule as to how many times need to present - too few - could be by chance; too many - could see effects of fatigue
# classes # stimuli within
class
# presentations
per stimulus
Total # trials
2 3 3 18
2 3 6 36
3 3 3 27
3 3 6 54
3 4 6 72
4 3 6 72
7. Decide Mode of Presentation
•Low tech–present on paper–respond to Sd by: pointing, circle, stamp
(benefits of permanent product)
• Computer-based–may be preferred mode for student–can efficiently incorporate stimulus prompting
and differential reinforcement–some softwares will collect data
(King, 2015)
(King, 2015)
8. Prompting Procedures
• Errorless instruction (Terrace, 1963a)• Stimulus fading
• Stimulus highlighting
• Positional prompting
• Exaggeration
• Time delay
• Stimulus shaping
• Response prompts
Stimulus Highlighting
Popsicles
Chicken Nuggets
Pizza
Toothpaste
Soap
Deodorant
Milk
Cheese
Eggs
Stimulus Highlighting
Popsicles
Chicken Nuggets
Pizza
Toothpaste
Soap
Deodorant
Milk
Cheese
Eggs
Stimulus Highlighting
Popsicles
Chicken Nuggets
Pizza
Toothpaste
Soap
Deodorant
Milk
Cheese
Eggs
Exaggeration
GENIUSMEDIOCRE
SKINNER
AMATEUR
Exaggeration
GENIUSMEDIOCRE
SKINNER
AMATEUR
Exaggeration
GENIUSMEDIOCRE
SKINNER
AMATEUR
Superimposition
PENGUIN
Superimposition
PENGUIN
Superimposition
Positional Prompts
A=A
Symmetry
Reflexivity
Transitivity
Positional Prompts
A=A
Symmetry
Reflexivity
Transitivity
Positional Prompts
A=A
Symmetry ReflexivityTransitivity
Hocus PocusScreamPoltergeist
9. Arrange stimuli within design
• Each trial will have the same number of comparison stimuli – at least 2 comparison stimuli per trial
• Counterbalancing rules
Counterbalancing Rules
• Each stimulus presented in linear array in each position an equal number of times.
• Comparison stimuli presented as discriminative stimuli and stimulus deltas an equal number of times.
• If discriminative stimuli occur more than once in the same position for consecutive trials, this should occur for all other positions as well.
• Counterbalance presentation of sample stimuli across trials.
(Green, 2001)
10. Pre-test all relations
•Referencing schematic, identify all possible trained and emergent stimulus-stimulus relations
•Pre-test identity matching-to-sample
• No feedback for any test trials
• If needed, can intersperse known trials to be reinforced
cranberry
bog Ocean Spray
A
CB
11. Data Analysis
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
A-B A-C B-A C-A B-C C-B
Perc
ent
Corr
ect
Relation
Figure 2. Percent correct during pretesting for one hypothetical participant.
12. Train specified relations
•Train specified relations using selected prompting procedure
• Continue training until specified criteria is demonstrated
• Can train relations separately or together
13. Post-test all relations
•Post-tests should be same as pre-test trials
14. Data Analysis
• If all relations are not demonstrated to criteria during 1st post-test, post-test again
• After several post-tests, re-visit training -may need to train again
Identity Matching Trained Relations Potential Emergent Relations
B=B C=C A1-B1 A2-B2 A3-B3 A1-C1 A2-C2 A3-C3 B1-C1 C1-B1 B2-C2 C2-B2 B3-C3 C3-B3
Pretest 78 100 16 0 66 0 50 83 0 33 50 66 100 83
Posttest I 100 88 100 83 50 50 100 100 83 83 66 100 83 100
Posttest II ---- ---- 100 100 100 100 100 100 66 100 33 66 100 66
Posttest III ---- ---- ---- ---- ---- ---- ---- ---- 100 100 100 100 100 100
Table 1Pre-Test and Post-Test Results for all Stimulus-Stimulus Relations
“Despite the number of important demonstrations… in some ways the work has
just begun” (O’Donnell & Saunders, 2003, p. 146)
Thank you!
References
Arntzen, E. (2012). Training and testing parameters in formation of stimulus equivalence: Methodological issues. European Journal of Behavior Analysis, 13, 123-135. doi: 10.1080/15021149.2012.11434412
Cowley, B. J., Green, G., Braunling-McMorrow, D. (1992). Using stimulus equivalence procedures to teach name-face matching to adults with brain injuries. Journal of Applied Behavior Analysis, 25, 461-475. doi: 10.1901%2Fjaba.1992.25-461
Green, G. (2001). Behavior analytic instruction for learners with autism. Focus on Autism and Other Developmental Disabilities. 16, 72-85. doi: 10.1177/108835760101600203
Keintz, K. S., Miguel, C. F., Kao, B., Finn, H. E. (2011). Using conditional discrimination training to produce emergent relations between coins and their values in children with autism. Journal of Applied Behavior Analysis, 44, 909-913. doi: 10.1901/jaba.2011.44-909
References
LeBlanc, L. A., Miguel, C. F., Cummings, A. R., Goldsmith, T. R., & Carr, J. E. (2003). The effects of three stimulus-equivalence testing conditions on emergent U.S. geography relations of children diagnosed with autism. Behavioral Interventions, 18, 279-289. doi: 10.1002/bin.144
Lynch, D. C., & Cuvo, A. J. (1995). Stimulus equivalence instruction of fraction-decimal relations. Journal of Applied Behavior Analysis, 28, 115–126.
Mackay, H. A. (1985). Stimulus equivalence in rudimentary reading and spelling. Analysis and Intervention of Developmental Disabilities, 5, 373-387. doi: 10.10.1016/0270-4684(85)90006-0
McDonagh, E. C., McIlvane, W. J., & Stoddard, L. T. (1984). Teaching coin equivalences via matching to sample. Applied Res Mental Retardation, 5(2),177–197.
O’Donnell, J. & Saunders, K. J. (2003). Equivalence relations in individuals with language limitations and mental retardation. Journal of the Experimental Analysis of Behavior, 80, 131-147. doi: 10.1901/jeab.2003.80-131
Persson, Maguire, & Cameron (2009). Multiplication and division relations. In Preparation.
ReferencesSidman, M. (1971). Reading and auditory-visual equivalences. Journal of Speech and
Hearing Research, 14, 5-13. Retrieved from http://jslhr.pubs.asha.org/
Sidman, M., Rauzin, R., Lazar, R., Cunnigham, S., Tailby, W., & Carrigan, P. (1982). A search for symmetry in the conditional discriminations of rhesus monkeys, baboons, and children. Journal of the Experimental Analysis of Behavior, 37, 23-44. doi: 10.1901%2Fjeab.1982.37-23
Sidman, M., Willson-Morris, M., & Kirk, B. (1986). Matching-to-sample procedures and the development of equivalence relations: The role of naming. Analysis & Intervention in Developmental Disabilities, 6, 1-19. doi: 10.1016/0270-4684(86)90003-0
Sidman, M. & Tailby, W. (1982). Conditional discrimination vs. matching to sample: An expansion of the testing paradigm. Journal of the Experimental Analysis of Behavior, 37, 5-22. doi:10.1901/jeab.1982.37-5
Sumner, Maguire, & Cameron (2010). Geometry relations. In Preparation.
Terrace, H.E. (1963). Discrimination learning with and without errors. Journal of the Experimental Analysis of Behavior, 6, 1-27. doi: 10.1901/jeab.1963.6-1
