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You Have the Big Idea, Concept, and Some Examples ... Now What?

Abstract

Conducting a concept or content analysis is essential in planning efficient effective instruction. Sequencing instruction when teaching a concept is equally essential. Through instructional sequencing, the upfront analysis of identifying critical and variable attributes comes to life and makes for a successful teaching arrangement. Learning concepts can be made easier or more difficult based on the order in which instructional stimuli are introduced and described. In this article we will describe Direct Instruction’s emphasis on clear instruction (faultless communication) and its method for sequencing and arranging positive and negative examples (juxtaposition). We will demonstrate how Direct Instruction’s five principles of juxtaposition inform examples should be presented to maximize student learning.

Cecil sits across the table from me making eye contact and sitting perfectly still. Clearly he's ready for instruction. Today I'm going to teach him “big” and “small.” In the seconds before he starts fidgeting in his seat, I reach into my bin of stimuli and quickly grab a big Lego (actually, I think it's called a Duplo™), a small toy car, and a nickel that just happened to make its way from my pocket. “Good waiting,” I say brightly as I place the three items in an array on the table. Using my teacher voice I give the first instruction, “Point to big.” He points to the car. “That’s not big. It’s a car.” I point to Duplo, “This is big. See, it’s large.” I put the nickel next to the Duplo. “See, this smaller.” I point to the Duplo again and say, “Point to big.” Having experienced hundreds of instructional corrections, Cecil dutifully imitates my pointing. I rearrange the items on the table and try a new one. “Point to small.” And so it goes.

No doubt the instruction described in this scenario is not perfect, however, it is also likely not uncommon. There are vast variations in instructional delivery when teaching stimulus discriminations (as speaker or listener behavior). Behavior analysts may argue for improvements in certain aspects of the interaction—the handling of the correction, the switch to a new instruction before gaining independent responding on the previous instruction, or the lack of data collection, and presumably much more. Although those are important features of instruction, they do not address the practice of appropriately selecting the stimuli for instruction and the presentation sequence needed for those stimuli to establish control over learner behavior. That is the focus of this article. We’ve designed this article as an interactive reading experience, with the hope that our instruction will translate into your practice.

Our goal is to highlight one targeted aspect of concept teaching: example selection and sequencing. We follow, in a logical sequence, the analyses presented on content (Slocum & Rolf and concept analysis (Johnson & Bulla) in this issue. These three articles offer a strong introduction on what should be done before working with learners to make it more likely the instruction is effective. They are crucial components of teaching, and it is important to consider them as part of a process that also includes subsequent practice and application.

There are a number of facts and rules about communicating through examples that are not often part of typical behavior analytic training, yet that often have an impact on the effectiveness of behavior analytic programming. Attention to the selection and sequencing of instructional stimuli reduces learner error and confusion, and improves instructional efficiency (Granzin & Carnine, 1977). We will describe evidence-based best practices for arranging the presentation of examples. Our recommendations are based on Engelmann and Carnine’s (1982, 1991) Theory of Instruction: Principles and Applications (ToI),Footnote 1 and both informed by a logical analysis of concepts (Klausmeier & Feldman, 1975; Markle, 1975; Tennyson & Park, 1980) and supported in the behavior analysis literature (see Kinder & Carnine, 1991; Twyman, 2021a). In ToI, Engelmann and Carnine describe, with exacting detail and thoroughness, the underlying theory that guides the design and development of Direct Instruction (DI) curricula.

Where Does Instruction Start?

There is so much to learn. This is true for all students and even more true for students who are behind, have disabilities, or other learning needs. Therefore, our teaching must be effective and efficient, and saturated with enough reinforcement that the behaviors involved in learning are increased, or at least maintained. Because there is so much to learn, we must analyze and organize subject matter in ways that make it as easy as possible for students to learn. “Big ideas” offers one such way. Big ideas are concepts most crucial within a content area; they enable teachers to produce more learning out of less instruction (Dixon et al., 1996; Slocum, 2004; Slocum & Rolf, 2021). For example, a big idea in beginning reading is phonemic awareness (Simmons et al., 2011), which is the understanding that words are made of separate sounds, or phonemes, and the ability to manipulate these separate sound units. Phonemic awareness is a big idea because it is essential in linking speech to print, and in learning to read in an alphabetic writing system. Another example, from a DI history curriculum, concerns the theme of change through history and offers the big idea of “problem-solution-effect” to generate understanding of numerous historical movements (Carnine et al., 1994). Big ideas have generality; once learned it is easier to learn related facts or concepts. In DI, big ideas provide the framework for analyzing and organizing subject matter and determining what concepts to teach.

The Analysis of Instruction: Concept Teaching

Concept teaching is a large part of behavior analytic practice. Layng (2018) provides a succinct analysis of concepts: “A concept is defined by a set of common attributes found in each example of the concept” (p. 346). For example, a triangle has a common set of attributes that define it as a closed, two-dimensional shape with three straight sides. Each and every example of the concept of triangle must have these characteristics. This is true of a triangle regardless of its size, location, orientation, color, weight, origin, construction material, durability, or any other characteristic that may change. When we teach a “concept” we are the teaching learner to respond to “information about an item or a class of items” by which the learner can “discriminate the item or the class of items from other items” (Klausmeier, 1990, p. 94). In concept teaching, learners respond to a set of characteristics that define that concept. When effective, learners can identify new (untaught) examples of the concept and discriminate between examples that do or do not exemplify the concept.

From the functional perspective described in Skinner’s Verbal Behavior (1957), word meanings or their referents are established within the circumstances in which the words are “used” by speakers and “understood” by listeners (see also Skinner, 1974). Meaning “is not a property of behavior as such but of the conditions under which behavior occurs” (Skinner, 1957, pp. 13–14).

Tact is the term that Skinner (1957) used to describe a verbal operant in which a response is evoked (or at least strengthened) by a particular object or event or property of an object or event. Given that a subset of stimuli control the response, concepts may be considered generic extensions or abstraction of tacts (Fraley, 2004). However, it is important acknowledge that the procedures that we outline below are not restricted to teaching tacts. These principles apply to all discriminated behavior.

A note about terms is also in order. In the concept analysis and design literature, a number of different words are used to refer to the same thing. To identify properties of an object or event. Engelmann and Carnine (1991) use the term “quality” (and sometimes “property” or “characteristic”) to specify any irreducible feature of the example (p. 4). Stimuli that exhibit that quality are “positive examples,” those that do not are “negative examples.” “Attribute” is a term similar to quality that is more common in the behavior analytic design literature, particularly with Tiemann and Markle’s (1990) introduction of the terms “critical attributes” to describe essential features, and “variable attributes” to describe properties that may vary and have no relevance to the essential features of the concept (see also Markle, 1975). Referring back to our example of triangle, critical attributes are a closed, two-dimensional shape with three straight sides. Variable attributes are its size, location, color, construction material, or other changeable characteristics, which Engelmann and Carnine (1991) refer to as irrelevant features. Although we will try to stay true to the terminology used in ToI, depending on the context and underlying research, we will use the terms quality, feature, and attribute interchangeably.

The range of what might constitute a concept is vast, from something as seemingly simple as an apple, as complex as photosynthesis, or as vague as delicious. Staying within Engelmann and Carnine’s (1991) specification of “basic forms” of concepts, such as nouns, noncomparative sequences, and single-dimension comparisons, primarily will be used as examples in this article. That is not to say more complex concepts cannot be taught via DI, in fact, a cadre of programs exist that have been extremely effective in teaching just that (such as the DI program “Understanding U.S. History,” Carnine et al., 1994, mentioned previously). Whether teaching basic nouns (e.g., triangle, apple, or car), noncomparative concepts (e.g., big, happy, or steep), or single-dimension comparisons (e.g., bigger, happier, or steeper), we are teaching discriminations.

When teaching, visual, auditory, tactile, kinetic, or other stimuli are used to represent what is being taught. We use the plural term, stimuli, because regardless of what it is we are teaching, “one example is never enough.” Any example presented has an indefinitely large number or range of qualities. Any of those qualities could serve as the basis for a discrimination. For any given concept we are teaching, we need to ask, “Which are the qualities that matter?” If we present a line drawing of a bicycle to teach the concept of bicycle, what properties of that stimulus are relevant? The image shape, size, background, predominant color, even the act of holding it up, all have the potential to control responding. Hence, a single example by itself, cannot teach anything.

Teaching any concept requires a carefully selected set of examples. As exemplified in general case programming (Horner & Albin, 1988; O'Neill, 1990; Scott & Dubuque, this issue), an extension of DI, instruction and generalization are improved with carefully selected examples and nonexamples and by arranging them so that similarities and differences are readily apparent.

The Design of Instruction: Example Sequencing

In this article we make several assumptions about our readers. We assume you will take full advantage of the array of excellent articles about DI presented in this special section, such that many of the points from those articles do not need to be repeated here. We assume that although research and theory are essential, you are primarily interested in incorporating that knowledge into your practice, hence we will focus on implementation. However, the preceding articles in this issue covering big ideas in teaching (Slocum & Rolf, 2021) and concept analysis (Johnson & Bulla, this issue), as well as the discussion of “faultless communication” in Perspectives on Behavioral Science (Twyman, 2021b) are recommended additional reading.

DI programs (1) are designed from a systematic, thorough content analysis that primes generalization (while teaching the big ideas of instruction); (2) instruct with clear, faultless communications (which specify the instructional wording, sequence, and presentation of examples); (3) have specific instructional formats (including student grouping, teacher interactions, and error corrections); and (4) follow a hierarchical sequence (such that prerequisites are taught before using a strategy, simpler skills are taught before more difficult ones, and instances consistent with the rule being taught are presented before exceptions) (Kinder & Carnine, 1991; Watkins & Slocum, 2004).

Instruction can be arranged so that differences between stimuli are more salient. This improves instructional efficiencies and reduces ambiguity for learners. As noted by Watkins and Slocum (2004), “Irrelevant aspects of the teaching must be held constant to minimize confusion, and relevant aspects must be carefully manipulated to demonstrate important differences” (p. 78). To reduce misinterpretation, we need to sequentially provide an array of examples that either rule out some generalizations or confirm others. We can do this first through the careful selection of stimuli and then through the presentation order of our stimuli. In this article, we pick up with the assumption that a concept or content analysis has been conducted, with examples containing both critical and variable attributes selected. We turn our discussion to instructional sequencing.

Juxtaposition

An effective teaching sequence contrasts examples. To indicate sameness, we present examples that are different yet treat each example in the same way (the variety of forks used to eat is an example). To indicate difference, we present examples that much the same but treat those examples differently (such as a fork and spoon from the same set of silverware). Engelmann and Carnine’s (1991) principles of juxtaposition teach us how to do that effectively.

Juxtaposition occurs when two (or more) stimuli are placed close together (or presented one immediately after the other) to emphasize their differences. Juxtaposition primes the learner to notice the differences. A well-known English proverb provides an example: “Better late than never” puts being late, which is often perceived as negative, next to never, which is even worse (Literary Devices, n.d.). A simple visual example is seen in Fig. 1, which shows a seagull sitting on a post, next to a prohibition sign which bans exactly that behavior, emphasizing the contrast between the two (and the unlikelihood that the gull can read the sign). Regardless of form (e.g., spoken, signed, written), the critical effect of juxtaposition is that the comparison highlights a contrast between the items. That contrast does not have to be opposite, just different. Juxtaposition is aided when the items also share some similarities, which may serve to occasion the comparison.

Fig. 1
figure1

An example of juxtaposition. Note: This image of a seagull sitting on a post, next to a sign that appears to bans exactly that behavior is an example of juxtaposition, emphasizing the contrast between the two (and the unlikelihood that the gull can read the sign). Image source: Shutterstock Standard License

Because it primes the discrimination of the differences between stimuli, juxtaposition is frequently used in literature, art, and advertising. The juxtaposition of a set of examples influences what is salient about those examples, such as how they are the same or how they are different. Five principles of juxtaposition from ToI, Chapter 4, “Facts and Rules about Communicating through Examples” are “how to” guidelines for effectively sequencing and presenting positive and negative examples of the quality being taught (Engelmann & Carnine, 1991). Those principles are: (1) the wording principle; (2) the setup principle; (3) the difference principle; (4) the sameness principle; and (5) the testing principle (see Table 1).

Table 1 Engelmann and Carnine’s (1991) five juxtaposition principles

Each principle starts with a description from Engelmann and Carnine (1991), which is supported by further explanation and made concrete by examples across subject matter and level. For each of the five juxtaposition principles we provide practice exercises presenting examples and nonexamples of that principle.

Principle 1: The Wording Principle

The Wording Principle states: “To make the sequence of examples as clear as possible, use the same wording on juxtaposed examples (or wording that is as similar as possible)” (p. 63). For instance, when the Wording Principle to teach the basic noun concept of “dog,” similar wording across examples (dog) and nonexamples (not dog) is used. The teacher presents a picture of a dog, and says dog, which the learner vocal-verbally imitates. The teacher then removes that picture and presents a picture of a cat, and says not dog; the learner imitates by saying not dog. The teacher does not say cat, This is a cat, or even This is not a dog. The wording is simply, dog or not dog.

In the opening scenario with Cecil, the variation that occurs when randomly using the words “large” and “big,” could inadvertently signal a difference in our positive examples. The communication is further complicated with the addition of “small” as a new positive example, and its potential variations (e.g., little, tiny), setting up multiple terms that must be discriminated. Two points arise regarding terms and teaching concepts: (1) for many learners it might be more efficient to teach a single concept in initial instruction; and (2) when introducing a new concept, if the learner is not already fluent with the terms used for the negative examples, use not “blank” rather than a second unfamiliar term.Footnote 2 Therefore, rather than presenting potentially four or more terms, a teacher could reduce or eliminate any confusion by saying big and not big.

Of course, “blank” and “not blank” are not the only means to clearly communicate differences between examples. The pair This is a car; What is this? (learner: a car) is another example, as are the sentences: This is[a vehicle]; This is not [a vehicle]; What is this? (learner: a vehicle); and Is this a vehicle? (learner: yes or no).

The Wording Principle is also relevant when teaching complex discriminations. For example, when teaching learners to discrimination multiplication word problems from other word problems (e.g., addition), the teacher can state the rule: If a problem deals with the same number again and again, it is a multiplication problem; if it does not deal with the same number again and again, it is not a multiplication problem. Then the teacher may model a positive example: Every time the man went to the store, he bought five apples. This is a multiplication problem. Each subsequent positive or negative example or would follow the same format, but with the question, Is this a multiplication problem? Consistency in wording can (and should) occur over time, as illustrated in the example of a scripted sequence teaching carrying in addition shown in Fig. 2.

Fig. 2
figure2

An example of the WordingPrinciple teaching carrying in addition https://www.nifdi.org/resources/free-downloads/programs/ell-eld-1/direct-instruction-spoken-english-dise-2/lesson-scripts/891-lesson-5-script/file.html

Engelmann and Carnine’s (1991) premise is that “[b]y using the same wording with all examples, we assure that the learner focuses on the details of the example and is not misled by variations in the wording” (p. 38). In addition, we want to keep our communication clear and succinct, as unnecessary information may lead to faulty stimulus control (Green, 2001; Tarbox et al., 2009).

We have now reached the first practice exercise, on the Wording Principle (Table 2). Cover the shaded cells at the right of each row and answer what the teacher’s questions on your own. Begin with the first row and analyze the Positive (+) Example, Presented Stimuli, and what the Teacher Says to determine whether or not the criteria of the Wording Principle is met. Check your response against the correct answer in the shaded cell at the end of the row, then cover up the shaded cells again and proceed to the next row.

Table 2 Wording principle practice exercise

Principle 2: The Setup Principle

The Setup Principle states: “To minimize the number of examples needed to demonstrate a concept, juxtapose examples that share the greatest possible number of features” (Engelmann & Carnine, 1991, p. 39). The positive examples and negative examples should have as many variable attributes in common as possible. Although perhaps counterintuitive, selecting examples that share features often leads to the shortest, most efficient instructional sequence. It allows a concept to be demonstrated with fewer examples while emphasizing—because they do not change across examples—the features that are critical to the concept. When positive and negative examples share many features, they ways in which they differ become more important. As noted by Engelmann and Carnine (1991), “If examples share the maximum number of features, they differ in the minimum number of ways. These are the ways that are relevant to the concept. The probability is therefore great that the learner will attend to the features and changes that are relevant to the concept” (p. 65).

In our scenario with Cecil, we violated the Setup Principle first by randomly selecting positive and negative examples which shared few if any features (they differed greatly on both critical and variable attributes). There was no preplanning to ensure that all the examples (positive and negative) shared the maximum number of features. To get closer to the Setup Principle we could have presented several Duplo™ pieces as positive examples (with the wording This is big), and juxtaposed them with similar colored Lego™ pieces as negative examples (This is not big).

We provide another example of the Setup Principle from early reading. When teaching initial sounds, one could prepare a list of consonant-vowel-consonant (CVC) onset-rime words ("onset" is the initial phonological unit of any word; "rime" refers to the letters that follow, often a vowel and final consonant), such as pat, cat, rat, hat, mat, and so on. These similar examples are in keeping with the Setup principle (all end in “at”) and with consistent teacher dialogue (e.g., This word is “pat.” What’s the first sound? /p/) illustrate the Wording Principle.

Violations of the Setup Principle are common. If teaching a learner to discriminate a dog from other animals (or things), a positive example of a teaching set might contain a photograph of a big, long-haired dog running outside, several other photographs of dogs engaged in different activities, a few clip-art dog images, and perhaps a stuffed toy dog (all selected in an effort to “promote generalization”). Perhaps the negative examples set includes a variety of cats or other animals also engaged in a variety of behaviors. These examples violate the Setup Principle and would make identifying the differences between “dog” and “not dog” almost overwhelming. Is an example “dog” because it is outside, or because it is a photograph? Perhaps “dog” means running versus sleeping, or long-haired versus hairless. The random, myriad differences makes identification of the qualities of “dog” difficult to discern (and yet it is exactly what we did with Cecil when we used a Duplo™, toy car, and nickel to teach the concepts of “big” and “small”). Better examples that support the Setup Principle might be set of stimuli that are line drawings of dogs and things that are not dogs.

Let’s practice identifying the Setup Principle using Table 3. Readers should cover the shaded column at the right, then start with the first row and analyze the content in the nonshaded cells. An example pair is presented in each row. An example may be positive (indicated by +) or negative (indicated by -). Given the concept being taught, are the related examples pairs instances of the Setup Principle? Readers may check their response against the correct answer in the shaded cell at the end of the row.

Table 3 Setup principle practice exercise

The activity presents only two examples for each row; however, readers should note that the Setup Principle applies to ALL the positive and negative examples within a teaching set (and testing set, as we will see later).

Principle 3: The Difference Principle

The Difference Principle states: “To show differences between examples, juxtapose examples that are minimally different and treat the examples differently” (Engelmann & Carnine, 1991, p. 39). Positive and negative examples provide the most information to the learner when (1) they are only slightly different from each other, and (2) the examples are juxtaposed (one presentation immediately following the other or position the examples next to each other) to emphasize those differences. This sequencing helps the learner note the difference because fewer things have changed.

The Setup Principle occasions the selection of stimuli that have a common context. The Difference Principle focuses on the minimal differences in stimuli within that common context. Given a common context, if two things are treated differently, they must be different based some quality or feature. For example, if we juxtapose two examples that are identical in all details except one, and label one “blue” (an unused jumbo blue crayon) and the other “not blue” (an unused jumbo red crayon) that single feature (color) is the only logical basis for calling one of them “blue.” Presenting other identical objects, whose only variation is the color (unused jumbo crayons in orange, white, and yellow), further highlights the critical quality—the color hue blue.

In Fig. 3, we use a matrix to illustrate adherence to or violation of the Difference Principle using the concept “vehicle.” In initial teaching trials the wording might so something like this: Teacher: This is a car. What is this? (learner: A car). Teacher: A car is a vehicle. What is a car? (learner: A vehicle).

Fig. 3
figure3

Adherence to and violation of the difference principle. Note: Presenting highly similar positive and negative examples supports the Setup Principle (cells 1 and 2). Presenting negative examples that are minimally different from positive examples supports the Difference Principle (cell 2). Presenting a variety of line drawings, photographs, or toys violates the (minimal) Difference Principle for examples (cell 3), as does presenting negative examples are maximally different from the concept “vehicle” (cell 4). Images are a limited sample of possible examples. Images source: Freepik by Flaticon

Let’s practice identifying the Difference Principle using Table 4. Readers should cover the shaded column at the right, then start with the first row and analyze the content in the nonshaded cells. An example pair is presented in each row. An example may be positive (indicated by +) or negative (indicated by -). Given the concept being taught (and in some cases an initial example), are the following examples pairs instances of the Difference Principle? Readers may check their response against the correct answer in the shaded cell at the end of the row.

Table 4 Difference principle practice exercise

When thinking about your own teaching, remember to keep the essential features (critical attributes) constant across examples. Look at your negative examples, and consider what irrelevant features (variable attributes) could be similar or identical to your examples. Do your positive and negative examples share features that are NOT the critical to the concept? Are the differences between your positive and negative examples minimal, except for those critical features? Revise your stimuli until positive and negative examples are only slightly different from each other, then name, tact, or otherwise treat the negative examples differently than the positive examples.

Principle 4: The Sameness Principle

The Sameness Principle states: “To show samenesses across examples, juxtapose examples that are greatly different and indicate that the examples have the same label” (Engelmann & Carnine, 1991, p. 39). As noted by Engelmann and Carnine, “[a]ny sameness shared by all examples that are treated in the same way describes a generalization" (p. 9). When positive examples that hold the critical features constant (and vary the irrelevant, noncritical features) are treated the same, they both: (1) reinforce the concept being taught; and (2) show that those changing features are irrelevant to the concept. When forming a new concept, the positive examples must show the range of acceptable variation. The negative examples must show the limits of the concept.

Returning to the concept of “dog,” an instance of the Sameness Principle would be the juxtaposition of two black and white photos, one of a chihuahua and the other of a Newfoundland and referring to each as a dog. Another might be reading the temperature across many types of thermometers (e.g., mercury thermometers, digital thermometers).

In Fig. 4 we use the concept of horse and a new matrix to depict the Sameness Principle. Although all are drawings (in keeping with the Setup Principle) each positive example of horse is different: in posture, position, mane, or other features. The goal is to “stretch” the concept to its boundaries, while treating each example as the same (i.e., as an instance of “horse”). As designers and arrangers of instruction, we must constantly think: “What is the greatest variation we can include, yet still consider the example to be a member of the concept class?” This idea of extending and pushing boundaries applies to negative examples as well.

Fig. 4
figure4

Demonstrating of the sameness principle. Note. Presenting black-filled drawings for both positive and negative examples supports the Setup Principle (cells 1 and 2). Presenting a range of positive examples that are greatly different from each other (cell 1) supports the Sameness Principle and indicates which features irrelevant to the concept. Presenting a limited range positive horse examples (cell 3) limits generalization. The negative examples must show the limits of the concept but in accordance with the Sameness Principle, need to vary as well (cell 4). Images are a limited sample of possible examples. Images source: Freepik by Flaticon

When employing the Sameness Principle it is important to simultaneously follow the aforementioned principles: using the same wording across all examples/nonexamples (the Wording Principle), reusing objects that appeared in juxtaposed examples (the Setup Principle), and selecting examples with the greatest number of differences (the Sameness Principle). It is clear that Engelmann and Carnine’s (1991) principles of juxtaposition build and expand upon each other. Let’s practice using Table 5. Are the following rows examples or nonexamples of the Sameness Principle?

Table 5 Sameness principle practice exercise

Principle 5: The Testing Principle

The Testing Principle states: “To test the learner, juxtapose examples that bear no predictable relationship to each other” (Engelmann & Carnine, 1991, p. 40). In behavior analytic terms this is the test for generalization (and is used to test our instruction). This involves the presentation of carefully selected, novel positive and negative examples and is often considered a true test of the effectiveness of teaching a particular concept. Just like in earlier Principles, the Setup and Wording Principles apply and positive examples must show the range of acceptable variation, whereas the negative examples show the limits of the concept. Using the concept of dog, Figure 5 presents a sample teaching set then illustrates the Testing Principle with a ranges of positive and negative examples not yet seen by the learner. The Testing Principle upholds the tenets of the other principles and allows the teacher to determine if the concept has been learned.

Fig. 5
figure5

The testing principle. Note: The Testing Principle is illustrated with a ranges of positive and negative examples of dog used in teaching as well as those not before seen by the learner. The first column presents the set of examples used in teaching, the top row contains positive examples that highlighting a range of possible variation of irrelevant features (e.g., size, color, position). The bottom row contains a range of negative examples that share some features with positive examples but not the relevant ones, thus indicating the limits of the concept. The second columns presents the Testing Set with novel examples selected using the same criteria, used to determine whether or not the concept has been learned and generalized

Not only does the Testing Principle determine the effectiveness of the teaching sequence, errors that occur when testing point to where or how the communication (teaching) around the concept might have failed. For example, errors can inform an instructional designer of where the range of positive examples might have been over extended. In our example of teaching “dog,” a potential error could be responding dog only when the stimulus shows a dog sitting, and thus should occasion the analysis of a potential faulty rule (e.g., “all dogs are sitting”).

It is important to ensure the testing set includes the full range of examples made possible by the teaching sets. For instance, when teaching the color blue, we presented numerous hues of blue ranging from light blue to medium blue, but never examples of blue from the darker end of the spectrum (e.g., navy blue), we could not test using navy or dark blue. Those positive examples were outside our teaching set and not an accurate test of the learner’s concept of “blue.” They may, however, be a test of our learner’s extension of the concept of “blue” as we will discuss next. Let’s use the Testing Principle to identifying whether, based on the examples within the teaching set, the testing set presents full range of examples. In Table 6, we use arbitrary symbols to quickly convey a range of examples. Is the example an instance of the Testing Principle?

Table 6 Testing principle practice exercise

Using Juxtaposition

Although positive and negative examples may exemplify the qualities of the concept being taught, it is the juxtaposition of the examples that highlights or contrasts the differences between them (Tennyson et al., 1972) . Juxtaposing positive examples highlights differences and indicates the boundaries of range of acceptable variation. Juxtapositioning positive and negative examples enhance the saliency of the relevant quality being taught and could be seen as a means to establish stimulus control by restricting response alternatives. In teaching, juxtaposition can be used to test performance by presenting the greatest contrast in varying attributes or to teach the concept with a minimal range of varying attributes. Both the Sameness and Difference Principles rely on juxtaposition to determine whether to treat an example as positive (based on sameness) or negative (based on differences), and always paired, simultaneously or sequentially, with another example.

Extension

Engelmann and Carnine’s (1991) five principles of juxtaposition form a very effective protocol for teaching a wide range of discriminations. When maintaining the Setup Principle across the four other principles, the contextual features of instruction (and testing) are held constant. As such, it is essential that these contextual features, such as instructional language, response modality, supplemental information are presented and varied in subsequent activities. Because the principles of juxtaposition are designed to promote learning new discriminations, they are essential for initial instruction. Initial introduction is fundamental, and as such it is only the beginning of the scope of discrimination teaching.Footnote 3

Returning to Skinner’s functional analysis of communication in Verbal Behavior (1957), learners may “extend” the tact, most commonly as a generic extension. This is an example of stimulus generalization (Cooper et al., 2020), because the untaught (novel) stimulus contains all of the relevant, critical features of the original set of stimuli and is demonstrated within the Testing Principle. However, once the Testing Principle has been demonstrated, it is important to build a learner’s repertoire beyond stimulus generalization. To promote further extension and stimulus or response generalization, one should test (and further teach) with varied instructions, feedback, response topographies, and rate of responding requirements (see Johnson & Layng, 1992). Continuing the example of teaching a learner to discriminate “dog,” Fig. 6 illustrates a few of the many ways (such as alternative antecedent instructions, changes in response topography, and the addition of supplemental information in the consequence) that discriminations and concept learning could be extended.

Fig. 6
figure6

Extension. Note. The language in the speech bubbles and the additional novel positive and negative examples illustrate some of the many ways that discriminations and concept learning could be extended. Images source: Freepik by Flaticon

Conclusion

Concept teaching is a large part of behavior analytic practice. Most instruction, whether teaching the meaning of “wet” to a learner with autism (Knight et al., 2012) or inferential statistics to college students (Fienup & Critchfield, 2010), involves the teaching of big ideas and concepts. We reiterate that effectively teaching any concept requires thoughtful selection of positive and negative example stimuli (examples and nonexamples) based on an analysis of the concept’s relevant and irrelevant features (critical and variable attributes). Equally indispensable to effective concept teaching is how, when, and what we say when presenting those stimuli to learners.

To provide clear communications to the learner about what is being taught, we must design a sequence that considers how examples are juxtaposed (compared and contrasted). In ToI, Engelmann and Carnine (1991) provide five juxtaposition principles for effectively presenting examples and nonexamples (Table 1). An instructional sequence must show relevant samenesses and relevant differences in the examples, and the wording associated with either examples or nonexamples must be precise. Because we have chosen our examples analytically, the Setup Principle guides us towards using few examples. After instruction we provide an immediate test that requires the learner to respond to novel examples, which ensures the concept has been learned. Beyond demonstrating mastery, we can extend a learner’s repertoire to antecedent conditions, different response topographies, supplemental information, all while doing so fluently.

In this article, we attempted to show the utility and importance of using Engelmann and Carnine’s (1991) principles of juxtaposition when teaching a new discrimination or a set of related stimuli (i.e., concept formation). This content may have been previously unknown to some of the BAP readership; it is hoped that this article opens the door to a literature that, due to its detailed analysis, could greatly increase and extend the power of behavior analysts’ programming efforts. As noted, the instructional principles described in this article are not limited to teaching tacting. These principles apply to all discriminated behavior, from the most basic self-help skills to the most advanced language or academic content. They are appropriate for the entire universe of learners at any age or ability, from learners who need the most support, to learners who are considered “gifted.”

What we have presented (and encouraged readers to practice) is just the beginning of what it takes to consider logical and research-demonstrated strategies as part of one’s efforts to improve student learning. There is so much more within the rich treasure trove of Theory of Instruction that interested readers are encouraged to explore and understand. To that end, we end with a few related applications and research topics that warrant further attention:

  • Consider and test guidelines for the very specific order of example presentation. ToI Section IV: Programs (Engelmann & Carnine, 1991), or through Gilbert’s (1962, 1969) protocols of mathetics.

  • Study components and composites of a behavior or repertoire (Merbitz et al., 2004), in order to get to higher-order applications as part of “broadening” a concept or members of a set via interpolation, extrapolation, or stipulation (Engelmann & Carnine, 1991) or through generative teaching strategies (Johnson et al., 2021).

  • Learn about concept teaching through the analyses described by Johnson and Bulla (this issue), Layng (2018), Markle and Tiemann (1970, 1971), Markle (1975), and others in the tradition of behavior analytic instructional design

Notes

  1. 1.

    Interested readers may note that the National Institute for Direct Instruction has made ToI into an ebook, available at https://www.nifdi.org/.

  2. 2.

    We thank Reviewer 1 for this point.

  3. 3.

    Again we would like to thank Reviewer 1 for this important point.

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Correspondence to Janet S. Twyman.

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The first author (Twyman) also served as a co-guest editor for the journal’s special section on Direct Instruction, in which the manuscript will be published. The second author (Hockman) has no nonfinancial conflicts of interest.

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Twyman, J.S., Hockman, A. You Have the Big Idea, Concept, and Some Examples ... Now What?. Behav Analysis Practice 14, 802–815 (2021). https://doi.org/10.1007/s40617-021-00638-9

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Keywords

  • Direct Instruction
  • Juxtaposition
  • Sequencing
  • Concept teaching
  • Instructional design