The Behavior Analyst 1995, 18, 93-98 No. 1 (Spring)

Contingency Diagrams as Teaching ToolsMark A. Mattaini

Columbia University School of Social Work

Contingency diagrams are particularly effective teaching tools, because they provide a means forstudents to view the complexities of contingency networks present in natural and laboratory settingswhile displaying the elementary processes that constitute those networks. This paper sketches recentdevelopments in this visualization technology and illustrates approaches for using contingency di-agrams in teaching.Key words: contingency diagrams, graphic visualization, behavior analysis

Not only did Skinner say it first, healso drew it first. Skinner sometimesused diagrams to clarify the terms in-volved in behavioral contingencies(see, e.g., Skinner, 1957, pp. 38-39,84-85). Words are often poor media toportray complex concurrent phenome-na, because by their very nature theygenerally must be presented one ...word ... at ... a ... time. Images, onthe other hand, given their expandedbandwidth, allow many bits of data tobe viewed concurrently as a transac-tional whole (Bertin, 1983; Mundie,1989; Tufte, 1983, 1990). For example,in our current research examining themultiple antecedents and consequencesassociated with acts of violence, we areusing relatively complex contingencydiagrams as a primary analytic medi-um. Several of us work together to re-fine them, integrating what is knownfrom the literature, and later our stud-ies, into meaningful subtypes.As the classes of actions become in-

creasingly complex, graphic tools arelikely to become increasingly importantto behavior analysts, not only for anal-ysis but also for education. One partic-ular advantage of their use in teachingis that diagrams allow students to seethe ways in which behavior analysis cancapture complexity, as well as how thiscomplexity is constructed from relative-

The author thanks Richard W. Malott for help-ful comments on earlier drafts.

Correspondence may be directed to the authorat Columbia University School of Social Work,622 West 113th Street, New York, New York10025 (E-mail: mattaini@columbia.edu).

ly simple elements (as is true in othernatural sciences).The graphic visualization of behav-

ioral contingencies in this article haslargely been sparked by the work ofMalott (Malott, 1992a, 1992b; Malott,Whaley, & Malott, 1993). One of hisdiagrams is reprinted in Figure 1 (Mal-ott, 1993b). Note that the situationshown here is already relatively com-plex, incorporating not only the basicthree-term contingency as well as anestablishing operation, but also repre-senting, in Malott's terms, a rule-gov-erned analogue of reinforcement (to-matoes do not appear immediately af-ter planting). The graphic also showsthe motivating condition resulting fromthe establishing operation; this is insome ways a less central concept, butis an extremely useful notation forteaching purposes. Malott and his col-leagues have also developed and dis-seminated a variety of teaching toolsthat incorporate contingency diagrams(e.g., Malott, 1993b).

I recently described several modifi-cations of the basic notation that I havefound to be valuable (Mattaini, 1993).Many of the arrows in the followingcontingency diagrams are double head-ed, reflecting the transaction nature ofbehaviorally significant events in com-plex, particularly social, situations. Thearrows used dashed lines rather thansolid ones to indicate that operant re-lations are probabilistic rather thanmechanistic (i.e., contingencies affectrate but do not automatically elicit re-sponses). To capture the full situation,

93

94 MARK A. MATTAINI

Occasion(SD)

firstfrost-free

day

Establishing Motivatng Behavior Conse nOperation Condition

P,no home- P,home-a long grow n plant

grownwinter ~ tomatoes selnstomatoes

Figure 1. A simple contingency diagram (from Malott, 1992a).

it is often important to show multipleconcurrent consequences associatedwith a single behavior, as well as mul-tiple antecedents.

Finally, the diagrams that follow in-corporate the class-and-object symbol(a dark rectangle surrounded by a grayone) from object-oriented systemsanalysis in computer science to repre-sent a class of functionally equivalentinstances. This notation increases pre-cision, because behavior analysts areseldom interested in a single instanceof a behavior, a consequence, or evenan establishing operation, but rather inmultiple instances (e.g., stimulus class-es, response classes). Where a singleevent or condition is of primary inter-est, however, the gray rectangle isomitted. Further variations not shownhere may be required to adequatelycapture the interlocking contingenciesof interest for cultural design, particu-larly where sequences are important(Mattaini, in press).

Examples

Contingency diagrams are particu-larly useful for the analysis and pre-sentation of the complex concurrentcontingencies often found in natural

settings. For example, Figure 2 por-trays some important antecedents andconsequences related to the rate of actsof affection provided by a previouslyneglecting father, including those pro-vided as part of an intervention plan.Without the intervention, note that cur-rent supports for affection are relative-ly weak. In the meantime, extinction ofthe desired paternal repertoire willprobably result from terminating theintervention before natural contingen-cies supporting the desired behaviorstabilize. This figure uses everydayterms (some borrowed from Malott) tomake the image accessible to studentswith limited technical verbal reper-toires. Others below incorporate moreprecise technical language.The contingency diagram shown in

Figure 3 moves toward applying thistechnology to cultural practices and cul-tural design. (For the moment, ignorethe gray box on the right.) The graphicdepicts consequences associated withschool attendance for a class of individ-uals-certain young mothers on wel-fare. For simplicity of presentation, an-tecedents have been omitted here. It isnot hard to understand why attendancefor such a student may be poor-there

CONTINGENCY DIAGRAMS 95

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FactorCondition arousal ~~~~~~~~~(response___________ ~~~~~~~~duetoMoel effortrctonImitation &rrstelf

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are few reinforcing consequences andsignificant aversive consequences asso-ciated with this behavior. Note alsowhat is missing: Often these families donot notice or reinforce attendance,much less achievement. Now imaginethat a transparency is laid over this im-age (an effective teaching technique)adding the $60 per month bonus shownin the gray box, as is done in Ohio. Thedata suggest that this helps in about20% of the cases, which is impressiveto some but fails to be a "slam-bang"effect. (Of particular concern is the factthat a corresponding penalty is leviedon the other 80%, resulting in increasedpoverty overall; Opulente & Mattaini,1993.) Why is the effect not greater?The answers are clear in the diagram.Not only is the bonus relatively small

and poorly scheduled, but the othercontingencies involved have notchanged. This is a good teaching ex-ample, showing why functional analysisis often required, and that there are lim-its to simply reinforcing reports of at-tendance. (Given the delay involved,the procedure probably should beviewed as, at best, analogous to rein-forcement. The delay, for a group ofsubjects with relatively weak trackingand pliance repertoires established, mayaccount in part for why the bonus is noteffective in the vast majority of cases.)The use of transparencies simplifiesoverlaying and separating multiple con-tingencies, but note that color (or gray)can also be used, as here, to depict suchlayering (see also Tufte, 1990, chap. 3).

Other questions emerge from the di-

96 MARK A. MATTAINI

Consequence

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Cnsequenceexposed to

/ pool targetedschool work, leadingto failur or boredom

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Ieerspr_Wd

social aversivesI ~Consequence

V..r"reglryatnin gt

(no opporu|nonyfo rei*:nforcement

attending peers)o

Figure 3. Consequences associated with school attendance for some young mothers.

agram. For example, why do familymembers sometimes not reinforce atten-dance, and why do teachers often subtly(or not so subtly) punish it? Here iswhere the diagrams become particularlyimportant, precluding any attempts toblame the victim. The teachers are not

inherently evil or intellectually inade-quate. Rather, the natural contingenciesare "just devastating" (Malott, 1993a,p. 52). The limited support for a pri-mary emphasis on positive reinforce-ment by teachers can be traced in con-tingency diagrams (see Mattaini, 1993,

CONTINGENCY DIAGRAMS 97

Rules SD onsequence

| "Al these * youthkids under- present, I youthstand is..." acting attends7"That Idd * classmom less oftenno good" isolation

_4 t

Establishing ConsequenceOperations

* social rein-* stressful, aversive - r - forcement

working environment from other* aversves from students,

specificyouth - ers

Structural Models for ConsequenceAntecedents Imitation

* no conse-* large cdasseg I peers quencewi limited * modelsfr I from admin-teaching own life Istratorstechnology_!

Figure 4. Contingencies supporting aversive, punitive acts by a teacher toward academically low-functioning youth with attendance (and perhaps behavior) problems.

p. 245), as can those for their currentpunishing repertoire, as in Figure 4.Once the contingencies are clarified,

plans to change them can be developed.Note that this may require changes inthe behavior of other classes of actorsin the behavioral ecosystem, for each ofwhom it may be necessary to developa detailed contingency diagram, until astable, interlocking system is achieved.Developing a series of such diagramsmay itself be a useful student assign-ment. With some planning, it is possibleto layer several diagrams over each oth-er on transparencies so the behavioralsituation can be examined as a wholeand can also be deconstructed.

Construction of complex contingen-cy diagrams need not be difficult or

time consuming. I usually work from aprepared blank template that allows meto simply add words (and edit as nec-essary) either on a transparency inclass or at the computer for more fin-ished work. To prepare these templatesor finished work, all that is required isa program that allows drawing rectan-gles and arrows and the placement oftext. High-end drawing programs (likeCanvas or Framemaker) provide exten-sive options for details like the shapeof arrowheads, but the straightforwarddrawing tools in current standard Win-dows or Macintosh word processors(e.g., Microsoft Word or WordPerfect)are entirely adequate. These programscan produce rounded rectangles in var-ious shades of gray and format text as

98 MARK A. MATTAINI

desired, easily producing professional-looking output. The diagrams can thenbe printed on paper or transparencieswith a basic laser or ink-jet printer.

Teaching Strategies

I have used contingency diagrams ina variety of ways in my classes and inworkshops, and suspect that an instruc-tor could develop many other creativeapproaches. In written handouts, I com-monly diagram sample case situations;I also ask students to diagram their ownexamples on templates (a strategy bor-rowed from Malott, 1993b). Anotherapproach is the use of transparencieswith an overhead projector in class. Theinstructor can begin with a blank dia-gram, insert the behavior of interest,and then use a Socratic process to guidestudents in exploring the complexitiesof the contingency networks withinwhich the behavior is embedded. As anexample, I may put "act of physicalabuse" on the diagram, and ask stu-dents to identify consequences and an-tecedents that could shape and maintainsuch behavior. It can be valuable to di-vide the class into small groups for 5 to10 min and ask each group to drawtheir own diagram; these are then pre-sented and evaluated in the largergroup, and a composite is developed.This process often leads to active dis-cussion and energetic participation,both in the small groups and during thepreparation of the composite.

Another useful strategy is to use thediagrams to present research findings,particularly to coherently integrate theresults of multiple studies. For exam-ple, in looking at youth violence, onecan become overwhelmed with thesheer volume of available information.Contingency diagrams offer a way toput it all together-to see that somerisk factors are actually establishingoperations, and reminding us of the es-sential connections among antecedents,acts of violence, and their conse-quences. It is possible to shape verbalrepertoires in this process, for example,

by calling some condition or event a"contextual factor" and then discrim-inating those that are more preciselyestablishing operations from those thatare structural antecedents. Experiencesuggests that students need not be pri-marily behavior analytic in orientationto be engaged by these methods.

Contingency diagrams can clarifyfor students what otherwise can bevery confusing and complicated situa-tions. They can facilitate learning, be-cause students can learn to constructand unpack them piece by piece, andas they do so, come to see that behav-ior analysis can aid in understandingcomplex patterns of human behavior,including social exchange and culturalpractices.

REFERENCESBertin, J. (1983). Semiology of graphics: Dia-grams networks maps. Madison: University ofWisconsin Press.

Malott, R. W. (1992a). Saving the world withcontingency diagramming. The ABA Newslet-ter, 15(1), 45.

Malott, R. W. (1992b). The three-contingencymodel of performance management. The ABANewsletter, 15(2), 6.

Malott, R. W. (1993a). Behavior analysis as aworldview and lifestyle. Kalamazoo, MI: Be-haviordelia.

Malott, R. W. (1993b). How to analyze behav-ioral contingencies. Kalamazoo, MI: Behav-iordelia.

Malott, R. W., Whaley, D. L., & Malott, M. E.(1993). Elementary principles ofbehavior (2nded.). Englewood Cliffs, NJ: Prentice-Hall.

Mattaini, M. A. (1993). More than a thousandwords: Graphics for clinical practice. Wash-ington, DC: NASW Press.

Mattaini, M. A. (in press). Public issues, humanbehavior and cultural design. In M. A. Mat-taini & B. A. Thyer (Eds.), Science, humanbehavior, and social problems. Washington,DC: APA Books.

Mundie, C. (1989). Interacting with the tiny andthe immense. BYTE, 14(4), 279-288.

Opulente, M., & Mattaini, M. A. (1993). To-ward welfare that works. Behavior and SocialIssues, 3, 17-34.

Skinner, B. F (1957). Verbal behavior. Engle-wood Cliffs, NJ: Prentice-Hall.

Tufte, E. R. (1983). The visual display of quan-titative information. Cheshire, CT: GraphicsPress.

Tufte, E. R. (1990). Envisioning information.Cheshire, CT: Graphics Press.