Papers and Presentations

Return to Home Page | Return to Resources Menu

Cybernetic Instruction: How Frequency and Celeration Data Show What Works and What Does Not Work

John W. Eshleman, Ed.D.

ELS, Inc.

October 15, 1999, May 24, 2000

Abstract

This paper describes how a cybernetic system of instruction uses frequency and celeration data to improve teaching. Improvement refers to a change in efficiency, effectiveness, or productivity. A cybernetic system has one or more feedback loops between its deployment and its redesign; where the behavior of the instructor comes under effective stimulus control of the changes to student behavior brought about by the arranged instructional contingencies. Frequency refers to rate of response, and celeration to a change in rate. The data presented in this paper indicate both (a) what works, and (b) what problems arise and how to solve them. System features that work, remain, those that do not are changed or removed; hence, the system "evolves." Frequency data reveal that the use of paired associate teaching techniques (SAFMEDS and CBT) both hold high reinforcing value. Further data reveal that stimulus control forms a necessary and defining condition of "fluency." Further data illustrate the relationship between response amplitude and frequency, and suggest changes to the basic SAFMEDS paired-associate learning model. The reliability of the present data are assured by two means: (a) machine transduction in the case of CBT data, and (b) the demonstrated repeatability of the results (e.g., see Sidman (1960) and Johnston & Pennypacker (1980) for a discussion of repeatability as a scientific criterion for reliability.)

An instructional system represents an organized, planned, and arranged means for teaching effectively. As a system it meets R. Buckminster Fuller's basic definition of 'system.' Fuller defined a system as a closed configuration of vectors that divides all Universe into six parts: (1) all events that occur outside the system, (2) all events that occur inside the system, (3) all events that occur nonsimultaneously, remotely, and unrelatedly prior to the system events, (4) the events that occur nonsimultaneously, remotely, and unrelatedly subsequent to the system events, (5) the arrayed set of events comprising the system itself, and (6) all events that occur synchronously and/or coincidentally to and with the system's events (Fuller, Synergetics, 1975, p. 95). Moreover, any set of methods that works will qualify as an instructional system.

An instructional system has organization, and involves planning, deployment, operation, and evaluation. We can view an instructional system, therefore, as one organized into various subsystems. These subsystems include (1) design of the system, (2) development of the system, (3) deployment of the system, (4) evaluation of the system, and (5) re-design of the system (see the Table below). Note that not all instructional systems include the last subsystem, redesign. Redesign makes an instructional system "cybernetic." That is, such a system becomes self-corrective and evolves over time.

Cybernetic Instructional Systems

The type of system described on this site has been named, by E.A. Vargas, as "cybernetic." The word "cybernetic" has Greek origins, and means "to steer." Steering, in this case, further means that the system "changes course." Think of a helmsman steering a vessel. The destination appears in the form of a better system, one that increases in efficiency, effectiveness, and productivity. Any instructional system can be made cybernetic. Few examples of cybernetic systems exist.

A cybernetic system contains multiple feedback loops. The principal feedback loop concerns the efficiency, effectiveness, and productivity of the system back into the system (see Figure 1). Accordingly, a cybernetic system contains two important steps beyond implementation, delivery, and deployment of the system. These two steps include (1) evaluation of the data generated by the system, and (2) redesign of the system based on the evaluation. This results in a somewhat revised system. The steps then proceed around again, through the same steps in the same loop. Once a system has been redesigned, it then gets redeveloped, redeployed, and reevaluated. The cycle can continue indefinitely.

Because a cybernetic system is both iterative and cyclical, one can illustrate it with a circular loop:

Figure 1. A cybernetic loop.

Another way of looking at feedback in a cybernetic system of instruction goes like this: The system gets designed so that the verbal behavior of the designer comes under effective stimulus control of the changes to learner behavior effected by the system. In such a system, the behavior of the teacher becomes just as important as the behavior of the learner. The teachers verbal behavior changes as a function of effective, efficient, and productive change to the learners behavior. Change to the behavior of both becomes an overall objective of the system.

A cybernetic system of instruction differs from what I refer to as "one-shot," or linear systems. A "one-shot" system typically has only the first three phases -- design, development, and deployment. Such a system lacks an explicit feedback loop. Any improvement to such a system will thus run haphazardly, and may not happen at all. A "one-shot" system can remain unchanged. And even if change does get made to a "one-shot" system, the basis for change may include factors other than the system's efficiency, effectiveness, and productivity. In fact, those data may not serve as a basis for change at all. Change, if it occurs, probably does so if the content of the instruction changes, the target population changes, or for other purposes such as new agreements with an end client or profits that allow an expansion of a curriculum.

"One-shot" systems also differ with respect to the three steps shared with a cybernetic system. A "one-shot" system may display less concern with precision in pinpointing behavior, and in writing objectives. The resulting "blueprint" may thus appear sparse and less exact. Additionally, in a "one-shot" system there may be less attention on changing behavior, because any data on behavior change would have no feedback and revision purpose. Thus, the resulting instructional activities may be fewer in number, involve far less active student responding, involve little or no measurement of student responding, and center mainly on presenting content to learners. In a "one-shot" system, therefore, deployment becomes largely a matter of delivery. If you think of delivery in the same terms as the Post Office delivering a letter, or a radio station delivering a broadcast, you will have a fairly good picture of what delivery means in a "one-shot" system.

In a "one-shot" instructional system, "teaching" usually gets accomplished with the delivery. In such instances, teaching does not explicitly mean changing behavior. Nor does it mean explicitly arranging conditions so that student behavior will change. If student behavior does change, it typically does so in large part outside of the instructional system.

A "one-shot" instructional system can become fairly good, however, if effective instructional principles are followed during the design, development, and deployment phases. To the extent that this happens, a "one-shot" system works and achieves some measure of real education. So, the difference between a "one-shot" system and a cybernetic system does not reduce to a false dichotomy based on one being ineffective and the other effective. Rather, a cybernetic system can make an already effective system even more effective (and more efficient and productive as well).

A "one-shot" system tends to be linear and static. A cybernetic system is spiral-orbital, looping around, and is predicated on variation and selection. A cybernetic system "evolves." Those elements that work, which produce effectiveness, efficiency, and productivity with respect to student behavior will remain. Those elements that do not work, are removed over time. A cybernetic system, therefore, represents an application of the selectionist model (see Figure 2):

Figure 2. Variation and Selection Mark a Cybernetic System. The colored boxes represent different elements featured in an instructional system. The event change comes with the evaluation and redesign of the system. Elements that work remain part of the system; those that do not work do not remain. In this case, the features denoted by the reddish boxes are selected out and do not "survive" as part of the next iteration of the system.

Frequency and Celeration as Measurable Dimensions of Behavior

To produce an effective cybernetic system of instruction requires that one use the best available measures of behavior and of behavior change. To reiterate, the mission of a cybernetic system is to bring the verbal behavior of the teacher or instructional designer under effective stimulus control of the changes produced to the behavior of the learner. Thus, we want good, clear, precise, and reliable measures of learner behavior, as well as similarly good measures of the change to behavior.

H.S. Pennypacker (1976) stated that scientific units of measurement are absolute, standard and universal. What do these three defining properties mean? A scientific unit becomes absolute when its existence as a unit is independent of the number and frequency of its use. A standard unit remains invariant over time, and so its definition does not vary. Finally, a unit becomes universal when the physical objects or events being measured do not dictate the choice of the scientific unit. A science of behavior should seek, use, and promote such units. Fortunately, two absolute, standard, and universal measures are available for a science of behavior. These are rate of response, or frequency, and the change to rate, or celeration. Without the former, the science based on the scientific work developed by B.F. Skinner simply would not be possible.

Definition of Frequency:

Frequency refers to "the number of cycles or completed alternations per unit of time." In general, frequency means some count per unit of time. In behavior analysis the most common measure of frequency has been responses per minute. In behavior analysis, frequency often gets renamed as "rate" or as "rate of response."

Definition of Celeration:

Celeration forms the root word of acceleration and deceleration. Celeration refers to number per unit of time per unit of time. In behavior analysis (Precision Teaching) the most common measure of celeration has been number per minute per week.

The respective properties and features of frequency and celeration are listed and compared in Table 1:

Frequency Defining Attributes:

Simply put, frequency denotes how often something happens. We use the word in that manner in our everyday language. The word "frequently" likewise connotes something that happens repeatedly. So, to use a word that Dr. Ogden R. Lindsley once used to describe frequency, it denotes "oftenness."

Frequency has two dimensions: count, and time. The definition of frequency always denotes some count per unit of time. The counts themselves can run in a regular, evenly spaced manner, as with sine waves whose curve shapes do not change. Or the counts can run in an irregular manner within the specified unit of time. When the latter happens, the frequency would vary if one broke the time period down into smaller units of time.

Frequency has a scientific unit name, designated Hertz. This unit is named after Heinrich Rudolph Hertz (1857-1894), a German physicist. The scientific abbreviation for Hertz is Hz. The naming and abbreviations for frequency follow the metric system. Hence, 1000 Hz equals 1 kilohertz, or 1 kHz for short. Likewise, 1,000,000 Hz equals 1 megahertz, or 1 MHz for short.

One Hertz equals one cycle per second, or a count of one event per second. In physics 1 Hz often means one wave per second. In that usage, a frequency means the number of waves that pass a given point per unit of time. A frequency of 1 Hz means that one wave, or wave crest, passes a point in a second's worth of time. A frequency of 10 Hz means that 10 waves pass the same point in one second of time. For 1 megahertz, one million waves pass a point in a given second.

For the study of human behavior, however, the Hertz unit proves somewhat inconvenient. A frequency of 1 Hz, or 1 cycle per second, equals 60 per minute. In human behavioral terms, 60 per minute already means a behavior repeating very quickly. Moreover, 60 per minute exceeds the bulk of daily behavior. In addition, B.F. Skinner and other behavior scientists selected number per minute as their frequency measure of choice. So, casting behavioral frequencies in terms of number per minute may prove more convenient than using the Hertz scale directly. Note that one can always convert from a count per minute to a count per second and vice versa.

As noted, behavioral scientists such as B.F. Skinner, Ivan P. Pavlov, and Ogden R. Lindsley measured behavior frequencies as counts per minute. Skinner and Lindsley studied responses per minute, Pavlov cc's per minute. Such count per minute frequencies, however, have no unit name. Therefore, I propose either the "Skinner," or the "Lindsley" as the unit name for frequency as defined in terms of count per minute.

Frequency has played a critical and vital role in the development of a science and technology of behavior. To put it bluntly, without frequency we could not have had the science of human behavior that B.F. Skinner and his associates and successors built. Frequency formed the absolutely necessary measure of behavior, and dimension of behavior, used in B.F. Skinner's two primary research books, The Behavior of Organisms, and Schedules of Reinforcement (the latter written with C.B. Ferster, who is listed as first author). Skinner represented frequency with cumulative records in both of these books. Take out the cumulative records, and you remove virtually all of the data. Take away all of the inductions and conclusions based on the frequencies shown on the cumulative records, and both books would almost completely vanish. Remove all scientific publications that are based on the findings and implications in these two books, and almost all of the science that ensued from B.F. Skinner's work would disappear. Note, however, that neither applied behavior analysis nor behavior analysis in general would disappear, since both of these fields have origins in the works of individuals other than Skinner.

The best graphical depictions for frequency, for a science of human behavior, are (1) the cumulative record, and (2) the Standard Celeration Chart. B.F. Skinner devised the cumulative record, where the slope of a line equals frequency (see Figure 3). O.R. Lindsley devised the Standard Celeration Chart, where a point equals frequency, and the slope of a line equals celeration. Lindsley has proposed the name "Standard Frequency Chart" in place of "cumulative record" for Skinner's charts. On both, the slopes form the standards.

Figure 3. Sample frequency finder grid based on Ferster & Skinner (1957). The different slopes equal different frequencies, or rates of response.

Under construction

Return to Home Page

Direct URL: http://standardcelerationcharttopics.pbwiki.com/Cybernetic Instruction

E-mail: standardcharter@aol.com

Webmaster: John W. Eshleman, Ed.D.

Copyright 2000 by John W. Eshleman, Ed.D. (Just the form the information is presented in on this page)

Revised -- May 20, 2000.

widget.hideFooter();