10.3 Shaping (Successive Approximations) and Chaining Procedures

Conceptual Foundations and Operant Mechanics of Shaping

Shaping is the operant process of systematically and differentially reinforcing successive approximations toward a terminal target behavior while placing previously mastered approximations on extinction (Skinner, 1953; Cooper et al., 2020). Through shaping, behavior analysts build novel, complex behavioral repertoires that do not currently exist in the individual's repertoire.

The dynamic engine of shaping is the combination of differential reinforcement and extinction-induced variability:

1. Differential Reinforcement: The clinician reinforces responses that meet a specific approximation criterion, increasing their probability and stability.
2. Extinction: Once an approximation is established, the clinician withholds reinforcement for that specific approximation (operant extinction). Extinction often produces an extinction burst and increased response variability. The learner emits variations in topography, force, or timing; the clinician immediately identifies and reinforces an approximation that is closer to the terminal behavioral objective.
3. Successive Approximations: A sequence of behavioral steps, each progressively closer in form or dimension to the final terminal behavior than the preceding step.

Unlike prompting—which injects external, artificial antecedent stimuli to evoke a response that the learner can already perform—shaping develops entirely novel topographies from within the organism's existing behavioral repertoire.

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Dimensions of Behavior Subject to Shaping

Shaping can be applied across five distinct quantitative and qualitative dimensions of operant behavior:

1. Topography: The physical form, shape, or motor movement of the response. Examples include shaping hand orientation for writing, shaping vocal phonemes into articulate words (e.g., "/m/" $\to$ "/ma/" $\to$ "mom"), or shaping complex gymnastics or athletic forms.
2. Frequency / Rate: The number of responses emitted within a specified temporal interval. Examples include shaping the rate of correct math problem solving from 5 problems per minute to 30 problems per minute, or shaping words read per minute.
3. Latency: The elapsed time between the onset of an antecedent discriminative stimulus ($S^D$) and the initiation of the response. Examples include shaping compliance latency, reducing the delay between a teacher's instruction and the student opening their textbook from 20 seconds to 2 seconds.
4. Duration: The total continuous time that a behavior is sustained. Examples include shaping on-task independent studying from 2 minutes to 25 minutes, or shaping aerobic exercise on a treadmill.
5. Amplitude / Magnitude / Force: The physical force, loudness, or intensity of a response. Examples include shaping vocal volume from an inaudible whisper to a conversational volume, or shaping the force of a pitch or golf swing during athletic conditioning.

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Shaping Across vs. Within Response Topographies

Behavior analysts distinguish between two primary structural applications of shaping:

Shaping Across Response Topographies

In shaping across response topographies, successive approximations involve distinctly different motor or vocal forms. As the learner advances to each new approximation, earlier topographies are placed on extinction and abandoned:

• Clinical Example (Vocal Manding):
  • Initial Repertoire: Guttural grunting.
  • Approximation 1: Reinforce open vowel sound ("/ah/") while grunts are extinguished.
  • Approximation 2: Reinforce bilabial consonant-vowel blend ("/ba/") while "/ah/" is extinguished.
  • Approximation 3: Reinforce word approximation ("/bah-l/") while "/ba/" is extinguished.
  • Terminal Behavior: Clear vocal production ("ball").
• Each stage represents a qualitative transformation in physical motor-vocal execution.

Shaping Within Response Topographies

In shaping within response topographies, the fundamental physical form or motor topography remains constant, but an underlying quantitative dimension (duration, latency, amplitude, rate) is systematically altered:

• Clinical Example (Endurance / Duration):
  • Terminal Goal: A student with ADHD remains seated and engaged in academic work for 30 consecutive minutes.
  • Topography: Sitting in chair, eyes on instructional materials, holding a pencil. The topography never changes.
  • Shaping Process: Reinforcement is initially delivered for 2 minutes of continuous sitting. Once established, the criterion is raised to 5 minutes, 10 minutes, 15 minutes, 20 minutes, and finally 30 minutes.

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Methodological Rules for Systematic Shaping Execution

To implement shaping with high treatment fidelity and avoid behavioral breakdown, clinicians adhere to seven core clinical guidelines:

1. Operationally Define the Terminal Target Behavior: Specify the precise topography, mastery criteria, and dimensional parameters required.
2. Identify the Initial Starting Behavior: Select a response already in the learner's repertoire that shares at least one topographical feature or function with the terminal goal.
3. Outline a Tentative Approximation Hierarchy: Develop a flexible sequence of intermediate approximations (a roadmap), recognizing that the learner may skip steps or emit unexpected variations.
4. Select Immediate, High-Potency Reinforcers: Utilize reinforcers that can be delivered instantly without interrupting responding (e.g., brief tokens, points, small edible bites, or quick vocal praise).
5. Differentially Reinforce with Precision: Deliver dense reinforcement when the current approximation is emitted; withhold reinforcement for lower, previously mastered approximations.
6. Pace Shaping Progress Carefully:
   • Advancing Too Quickly: If the clinician raises the criterion before the current approximation is firmly established, responding will extinguish completely, resulting in behavioral disintegration.
   • Advancing Too Slowly: If the clinician reinforces a single approximation for too many trials, the behavior becomes rigidly entrenched and highly resistant to extinction, preventing the emergence of novel variations.
7. Remediate When Behavior Deteriorates: If responding extinguishes or deteriorates, the clinician must immediately drop back to the previously mastered approximation, re-establish dense reinforcement, and advance with smaller approximation increments.

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Behavior Chains and Task Analysis

The Nature of Behavior Chains

A behavior chain is a specific sequence of discrete operant responses, each associated with a particular stimulus condition. When all components are linked together, the completion of the sequence produces a terminal reinforcer (Cooper et al., 2020).

The Dual Function of Intermediate Stimuli

The fundamental theoretical glue of any behavior chain is the Dual Function of Stimuli. In an operant chain, each intermediate response ($R$) produces an environmental stimulus change ($S$). This resulting stimulus change simultaneously serves two distinct operant functions:

1. It serves as a conditioned reinforcer ($S^R+$) for the response that just occurred.
2. It serves as a discriminative stimulus ($S^D$) for the immediately subsequent response.

Consider the handwashing chain:

$\text{Dry Hands} (S^D_1) \longrightarrow \text{Turn Handle} (R_1) \longrightarrow \text{Flowing Water} (S^R+_1 / S^D_2) \longrightarrow \text{Place Hands Under Water} (R_2)$

The stimulus change—flowing warm water—reinforces turning the faucet handle (looking backward) and simultaneously evokes putting hands under the water (looking forward). The ultimate terminal reinforcer (clean, dry hands + social praise or snack) maintains the stimulus control of the entire chain.

Task Analysis

A task analysis is the systematic process of breaking a complex, multi-step behavioral sequence into smaller, discrete, observable, teachable component responses. Methods for constructing a task analysis include:

1. Performing the Task Oneself: The behavior analyst executes the task, recording each discrete motor action.
2. Observing Competent Performers: Watching a skilled individual or peer complete the sequence in the natural environment.
3. Consulting Subject-Matter Experts: Collaborating with occupational therapists, mechanics, or vocational specialists.

Task analyses must be individualized according to the learner's age, physical stature, motor dexterity, and prerequisite skill repertoires.

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Comparative Chaining Procedures

Behavior analysts teach behavior chains utilizing four primary chaining methodologies:

1. Forward Chaining

In forward chaining, behaviors are taught in their natural chronological order, beginning with Step 1 of the task analysis:

• Instructional Sequence: The learner is trained to complete Step 1 independently. Once Step 1 is emitted, the instructor prompts or completes all subsequent steps of the chain. When Step 1 meets mastery criteria, instruction expands to include Step 2. The learner must now perform Step 1 and Step 2 to contact reinforcement, while the instructor completes the remainder. Training advances forward until all steps are chained.
• Strengths: Preserves the natural, logical chronological sequence of the task; highly intuitive for educators and technicians.
• Limitation: The learner does not experience the terminal, natural reinforcer of the completed chain during early training trials (reinforcement is artificial, delivered after trained steps).

2. Backward Chaining

In backward chaining, all behaviors specified in the task analysis are initially completed by the instructor, with the exception of the final step:

• Instructional Sequence: The instructor completes Steps 1 through 5 of a 6-step chain (e.g., shoe tying). The learner is prompted to perform Step 6 (pulling the loops tight). Upon completing Step 6, the learner immediately contacts the terminal natural reinforcer (tied shoes + access to playground). Once Step 6 is mastered, training moves backward to Step 5 (learner performs Steps 5 and 6 to receive terminal reinforcement). Instruction progresses in reverse until the entire chain is performed independently from Step 1.
• Strengths: The learner contacts the ultimate terminal reinforcer on trial 1 of every single session! This immediate contact with the primary outcome generates exceptionally high reinforcement density, making backward chaining especially powerful for learners with severe developmental delays, limited attention spans, or low persistence.
• Limitation: Requires instructor to complete the majority of steps on every early trial.

3. Total-Task Presentation (Concurrent Chaining)

In total-task presentation, the learner is required to perform every step of the task analysis during every single training trial:

• Instructional Sequence: The learner attempts Step 1; if an error or hesitation occurs, the instructor immediately provides assistance (via graduated guidance or prompt fading) and moves directly to Step 2. Training continues through the entire chain from beginning to end in every session.
• Strengths: Fosters continuous practice of all steps; maintains natural fluid timing and momentum; highly efficient when the learner already possesses many component steps in their repertoire or when the task is relatively short.
• Limitation: Can overwhelm learners with severe cognitive deficits or low stamina if the task analysis contains dozens of steps.

4. Backward Chaining with Leap Aheads

Backward chaining with leap aheads follows the exact structure of backward chaining, with one key modification: steps that the learner already demonstrates during baseline probe trials are skipped ("leaped ahead") during instruction:

• The clinician assesses baseline performance. If a learner cannot perform Steps 1, 2, or 6, but independently performs Steps 3, 4, and 5, the clinician does not train Steps 3, 4, and 5. The clinician trains Step 6, leaps ahead over 5, 4, and 3, and trains Step 2. This drastically reduces instructional time while maintaining backward reinforcement contact.

Behavior Chain Interruption Strategy (BCIS)

The Behavior Chain Interruption Strategy (BCIS) involves intentionally interrupting an established behavior chain at a predetermined juncture (e.g., withholding a spoon during a pudding-eating chain, or locking the supply cabinet during a vocational chain). The interruption blocks access to the next $S^D$, establishing an immediate motivating operation (EO) that evokes functional communication (manding for the missing item) or problem-solving behavior.

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Comparative Analysis: Chaining Procedures

The following table contrasts the training sequence, point of reinforcement, clinical indications, and limitations across chaining methodologies:

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Clinical Troubleshooting and Common Exam Pitfalls

• Pitfall 1: Confusing Shaping with Chaining: This is one of the most frequently tested distinctions on the BACB exam. Shaping replaces prior approximations (earlier topographies are extinguished and disappear, so only the terminal behavior remains). Chaining links distinct, separate discrete responses together into a permanent sequence (ALL steps remain in the final repertoire).
• Pitfall 2: Flawed Task Analysis Granularity: If a task analysis step is too broad (e.g., "Wash hands"), the learner cannot master it. If a step is too microscopic (e.g., "Extend index finger 2 cm toward knob"), instruction becomes cumbersome. Steps must match the learner's developmental and motor repertoire.
• Pitfall 3: Extinction of Behavior Chains: If the terminal reinforcer is abruptly thinned or eliminated, the stimulus changes within the chain lose their conditioned reinforcing value and the whole chain weakens.