Efficiently Forming Equivalence Classes: Strategies and ......Run DMC Nirvana Johnny Cash Country...

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Efficiently Forming Equivalence Classes: Strategies and Applications

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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.

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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

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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

ClevelandNashville New York City

NashvilleNew York City Cleveland

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

Johnny Cash

Nirvana

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 FameHip Hop

Hall of Fame

New York City

Country Music

Hall of Fame

Hip Hop

Hall of Fame

Nashville

C-B Pre-Test

New York City

Nashville

Cleveland

A-B Training Step 1

Correct!

Johnny Cash Run DMC Nirvana

Correct!

Run DMCNirvana Johnny Cash

Correct!

A-B Training Step 2

Correct!

A-B Training Step 3

Correct!

A-C Training Step 1

Correct!

Nashville New York City Cleveland

Correct!

New York CityCleveland Nashville

Correct!

A-B Training Step 2

Correct!

A-B Training Step 3

Correct!

Post-Test Intermixed Relations

Rock and Roll

Hall of FameHip Hop

Hall of Fame

Run DMC

Johnny Cash

Rock and Roll

Hall of Fame

Country Music

Hall of Fame

Hip Hop

Hall of Fame

Cleveland

New York City

Country Music

Hall of Fame

Hip Hop

Hall of Fame

Johnny Cash

Nirvana

Rock and Roll

Hall of FameHip Hop

Hall of Fame

New York City

Nashville

Rock and Roll

Hall of Fame

Country Music

Hall of Fame

Hip Hop

Hall of Fame

Nirvana

Run DMC

Country Music

Hall of Fame

Hip Hop

Hall of Fame

Nashville

Cleveland

Reflexivity slide

A-B Training

A-C Training

Symmetry Post-Test

Transitivity Post-Test

Scoring and Reporting on Results

Scoring Pretest Results

Hypothetical Pretest Results

Scoring Posttest Results

Hypothetical Posttest Results

Reflexivity

Trained Relations

Symmetry

Transitivity

Various Visual Displays

Keintz, Miguel, Kao, & Finn (2011)

Visual Analysis

Cowley, Green & Braunling-McMorrow

(1992)

Tests for Delayed Emergence

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

Jaguar

alpaca

cria cygnetchrysalis

alpaca

cria cribcrow

tick track truck

tick tier tint

3. Stimulus Class Size and Number of Classes

• Minimum class size is 3

• Can have larger classes

• Determine number of classes to be demonstrated

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

D - Spelling

Black Line = Established Relations Prior to the StudyRed Line = Taught RelationsDashed Line = Potential Emergent Relations

(Breault, 2015)

"flower" C "flower"

*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

One to Many (Arntzen, 2012)

cranberry

bog Ocean Spray

Many to One (Arntzen, 2012)

cranberry

bog Ocean Spray

Linear Series

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

A-B A-C B-A C-A B-C C-B

Relation

Figure 2. Percent correct during pretesting for one hypothetical participant.

Relation

5. Training and Testing Criteria

• Establish acquisition criteria for training and testing phases

Relation

A-B A-C

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

# 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)

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

Toothpaste

Deodorant

Cheese

Popsicles

Chicken Nuggets

Toothpaste

Deodorant

Cheese

Popsicles

Chicken Nuggets

Toothpaste

Deodorant

Cheese

Exaggeration

GENIUSMEDIOCRE

SKINNER

AMATEUR

Exaggeration

GENIUSMEDIOCRE

SKINNER

AMATEUR

Exaggeration

GENIUSMEDIOCRE

SKINNER

AMATEUR

Superimposition

PENGUIN

Superimposition

PENGUIN

Superimposition

Positional Prompts

Symmetry

Reflexivity

Transitivity

Positional Prompts

Symmetry

Reflexivity

Transitivity

Positional Prompts

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

11. Data Analysis

Relation

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!

cyorlets@rcsconsultingne.com

cking@rcslearning.org

mbreault@rcslearning.org

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

Efficiently Forming Equivalence Classes: Strategies and ......Run DMC Nirvana Johnny Cash Country...

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