What is an example of forward chaining?

IV. Summary

Forward chaining is one of three procedures used to teach a chain of behaviors. A chain of behaviors involves individual stimulus and response components that occur together in a sequence. Forward chaining is a procedure that is typically used with individuals with disabilities or extremely limited abilities. The first step in forward chaining is to conduct a task analysis that identifies each SD and response in the chain of behaviors. To conduct forward chaining you use prompting and fading to teach the first component behavior in the chain. Once the learner engages in the first response without prompts, you teach the second response in conjunction with the first using prompting and fading. Once the learner engages in the first two responses in the chain without assistance, you use prompting and fading to teach the third response in conjunction with the first two. This process continues until the learner can engage in the entire chain of behaviors without assistance. Praise or other reinforcers are delivered on a continuous reinforcement schedule for every correct response during training. Once the learner competently engages in the chain of behaviors without assistance, an intermittent schedule of reinforcement can be used to maintain the behavior.

2.3.1.1 Forward Chaining

Forward chaining involves teaching the learner to initially complete only the first step of the task analysis and requiring independence of only that one step in order to earn a reinforcer. Then, once the learner is able to complete the first step independently, the second step of the task analysis is required so that the learner now has to complete both steps one and two before earning a reinforcer. This process continues in a forward fashion so that each time the learner is able to perform the required steps, another step is added on, until eventually, the learner is able to complete the entire chain (all the steps of the task analysis).

E Forward Chaining

In forward chaining, one begins with the givens and works directly toward the goal. Use of this strategy appears to depend on having a sufficiently deep understanding of a problem to be able to construct a correct concrete representation of it from the problem statement (D. P. Simon & Simon, 1978). This being so, experts are more likely to use this strategy than novices, who are more likely to use such strategies as means–end analysis and working backward (Larkin et al., 1980a, 1980b). It is the experts' ability to classify problems in terms of basic principles and their knowledge of approaches that work for specific problem types that make this possible. Sweller, Mawer, and Ward (1983) found that, when given extended practice with problems of a specific type, subjects tended to switch spontaneously from a means–end strategy that they employed to a forward-chaining strategy.

Backward Chaining

Backward chaining uses the same basic approach as forward chaining but in reverse order. That is, you start with the last step in the chain rather than the first. The therapist can either prompt the learner through the entire sequence, without opportunities for independent responding, until he gets to the final step (and then teach that step), or the therapist can initiate the teaching interaction by going straight to the last step. Either way, when the last step occurs, the therapist uses prompting to help the learner perform the step correctly, reinforces correct responding with a powerful reinforcer, and then fades prompts across subsequent trials. When the last step is mastered, then each teaching interaction begins with the second-to-last step, and so on, until the first step in the chain is mastered, at which point the whole task analysis is mastered.

III.A. Forward Chaining

The first procedure for establishing new behaviors by chaining is forward chaining. In this procedure, the first response of the sequence is taught to an individual. When he or she has mastered that first response, the first and second responses of the chain are linked together, and are then taught until the link has been mastered. Next, the first three responses of the chain are linked together, and are then taught until that link has been mastered, and so forth, until the individual eventually masters the entire chain. Thus, forward chaining is used to teach chains by constructing longer and longer links and adding one response at a time, starting at the beginning of the chain and working forward. The individual's success determines when each next response is added to the most recently taught link. An advantage of forward chaining is that it is conducted according to the natural order in which the individual responses comprising skills or tasks occur in everyday situations.

4.1 Rewriting in theorem proving

From the operational point of view, term rewriting provides a forward chaining method in automated deduction. In other words, its main inference mechanism deduces new lemmas from known theorems, rather than reduces the intended problem into sub-problems and tries to solve them separately. Forward chaining methods are usually not efficient due to the large number of theorems produced which makes the search space unmanageable. As a tradeoff, forward chaining methods usually do not require backtracking, which is necessary in most backchaining methods. In fact, term rewriting is one of the very few successful forward chaining methods. The problem of space explosion is handled in term rewriting through two techniques: a notion of critical pairs, which tries to find only “useful” lemmas, and more importantly, a notion of simplification. Basically, simplification replaces current terms or formulas by others which are logically equivalent but “smaller” according to some well-founded ordering. Since the ordering is well-founded, simplification cannot go on indefinitely.

It has been demonstrated through various implementations and experiments that simplification is indeed an effective way of controlling the search space. In addition to finding complete sets of rewrite rules, other notable problems have been solved using term rewriting including the one-axiom group theory [Lescanne, 1983], the commutativity problem of rings [Stickel, 1984], Boolean algebra problems [Hsiang, 1985; Fribourg, 1985b], SAM’s lemma in lattice theory [Zhang and Kapur, 1988], Moufang identities of alternative rings [Anantharaman and Hsiang, 1990]. In [Hsiang et al., 1992], a survey of the use of term rewriting in automated theorem proving for various systems available in the 1990’s is given. Rewriting techniques also contribute to one of the main successes of automated theorem proving, namely the fully automated solution, obtained by McCune and his system Otter in 1996, of the Robbins problem that had challenged mathematicians for over sixty years [McCune, 1997].

In a different community, interactive proof systems such as PVS [Owre et al., 1992], Isabelle [Nipkow et al., 2002], or Coq [Delahaye, 2000] have also extensively used rewriting techniques through tactics to handle the automated part of reductions. indexordered (or unfailing) completion

6.2.4 Troubleshooting

If the learner feels overwhelmed or unable to attend to solving a problem from start to finish, try using a forward chaining procedure (see Chapter 2, Principles Behind the Lessons, for more information on chaining procedures). It might also help to choose problems that are not likely to evoke frustration or challenging behavior. For example, avoid choosing problems that might result in the learner having a tantrum. Once the learner gets the hang of solving such problems, you can then start to introduce problems that are more likely to evoke frustration. Another general tip is to start teaching problem solving with problems that have a strong reinforcer as the natural consequence for solving the problem. For example, you could secretly take the batteries out of a favorite toy to teach the skill of solving the problem of the toy not working. The natural consequence of solving this problem is being able to play with a favorite toy.

Once you start working on problems that are more serious in nature for the learner, if you notice that the learner becomes emotionally charged, see the Emotional Self-Regulation lesson in Chapter 8, Emotional Self-Regulation and Flexibility, for teaching the learner strategies for coping with difficult emotions.

III.D. Comparing Backward, Forward, and Whole-Task Chaining

Comparative research on the effectiveness of the different chaining methods has produced mixed results. Several studies involving individuals with developmental disabilities have revealed that forward and backward chaining were more effective methods for teaching new skills compared to a whole-task approach. For example, in 1981 Richard T. Walls and colleagues compared all three chaining methods and found that forward and backward chaining resulted in fewer errors when teaching adults with moderate retardation to assemble objects, compared to the whole-task chaining method. In this study, there were no significant differences between forward and backward methods.

On the other hand, in 1983, Fred Spooner and colleagues compared only backward to whole-task chaining when teaching adults with profound retardation to assemble objects and found that whole-task chaining required fewer trials to reach criterion than backward chaining.

Research comparing the effectiveness of chaining methods remains equivocal. However, as Gregory J. Smith suggested in 1999, the mixed results regarding the effectiveness of different chaining methods may be due to the fact that different populations were used in various studies, and different types of behaviors were taught. Therefore, no direct comparisons among chaining methods can be made without first taking these variables into account.

Similarly, as a review of the research suggests, there does not seem to be one method that is more effective than the others across all situations, rather, it is more probable that the effectiveness of the chaining method used is dependent on several factors, including variables associated with the learner (such as level of cognitive functioning) and the type of behavior being taught. Therefore, when deciding which chaining methods to use, clinicians should consider their client's level of intelligence and the type of behavior being taught.

5.05.5.1.4 Chaining

Many behaviors that are of interest to clinicians are complex behaviors consisting of a number of smaller behaviors linked together to form a behavior chain. Each link of the chain can be conceptualized within the usual antecedent-behavior-consequence sequence, and is taught using the procedures described thus far. Additionally, however, the completion of one link is viewed as the antecedent stimulus occasioning the performance of the next link, which in turn becomes the stimulus for the occurrence of the next. The process of developing the final chain can be of three types, forward chaining, backward chaining, and total task training.

When using forward chaining, the initial link of the chain is the first taught, then the second, the third, and so on until the complete chain has been learned. Prompting, shaping, and reinforcing could all be used in the teaching of each separate link. While learning each link the learner is usually helped through all of the remaining links so that task completion can be reinforced. Teaching a child to put on a pair of trousers might be a typical skill taught by using forward chaining.

When using backward chaining (sometimes called reverse chaining) it is the final link in the chain that is taught first, then the others are proceeded with working in reverse order. The initial link thus becomes the last taught. This approach is considered desirable when the complex behavior leads to some naturally occurring reinforcer being available, for example a child learning to use a spoon might start with the final link of placing the food in his mouth. This contiguity of naturally occurring reinforcement and task completion is considered to provide better motivation to learn the earlier links in the chain.

Whereas forward and backward chaining are typically used when a learner has mastered few if any of the separate behavioral links, total task training is more efficient for situations in which the individual has mastered most or all of the links. A child who has mastered simple addition, subtraction, multiplication, and division would typically be taught the behavioral chain involved in completing a long division by using a total task method.

Chaining

A behavioral chain is a complex unit of behavior that consists of several individual responses that are emitted in a specific sequence (Miltenberger, 2015). The first response in a behavioral chain is initiated in the presence of a discriminative stimulus. The completion of each response produces a subsequent discriminative stimulus that serves as a discriminative stimulus for the next response in the chain. Further, the completion of each response also functions as a conditioned reinforcer for the previous step of the chain. Thus, each response in a behavior chain serves two functions (Leslie & O'Reilly, 1999). For example, dirty silverware may be a discriminative stimulus that sets the occasion to clean a fork. The first response in the chain is to put soap on the fork. The presence of soap on the fork would then serve as a conditioned reinforcer for having put soap on the fork, and it would also function as a discriminative stimulus for turning on the water. In this way, a chain of dishwashing responses is emitted, and the terminal response is reinforced by the presence of a clean fork.

Implementation of a chaining procedure first requires a task analysis. A task analysis consists of analyzing a complex behavioral unit into several smaller stimulus-response units, which are referred to as links. In the preceding example, the four links may be: putting soap on the fork (R1), turning on the water (R2), rinsing the fork (R3), and turning off the water (R4). The discriminative stimulus for each response, respectively, would be the dirty fork (for R1), soap on the fork (for R2), running water (for R3), and a clean fork (for R4). A task analysis can be performed by observing a competent person performing the task.

Chaining may be used to teach complex behavior using three main methods: backward chaining, forward chaining, and total task presentation (Miltenberger, 2015). In backward chaining, the last response is taught first, and reinforcement is provided after successful attempts. After the learner masters the last response in the chain, the second-to-last response is taught. In this way, each response is successively added onto the chain, and the learner completes the chain on every single trial. For example, applying backward chaining to washing a fork would require that the learner be first taught, via prompts, the final step of turning off the water. Next, the learner would be taught the penultimate step of rinsing off the soap. At this step, the instructor would provide prompts to rinse off the soap, and the learner would then need to independently complete the last response in the chain to obtain reinforcement.

In forward chaining, the first rather than the last response in the chain is taught first. In this procedure, the initial discriminative stimulus (in our example, the dirty fork) is presented, and reinforcement is provided for the successful completion of the first response (putting soap on the fork). After the first response is mastered, training is conducted for the second response (turning on the water). This consists of presenting the discriminative stimulus for the first response (the dirty fork), allowing the first response (putting soap on the fork) to occur independently, and teaching and reinforcing approximations of the second response (turning on the water). The process would continue, adding one response at a time and only after the learner has mastered the prior steps in sequence, until the learner can complete the entire chain independently.

In contrast to forward and backward chaining, total task presentation consists of teaching the entire complex behavior in one trial (Miltenberger, 2015). With this procedure, the learner is prompted through the entire chain, and reinforcement is provided only when the learner completes the chain. The learner in our example would therefore be prompted at the outset to perform the full sequence of putting soap on the dirty fork, turning on the water, washing the fork, and turning off the water in a single trial. Reinforcement would be provided when the learner completes the entire sequence of the chain, resulting in a clean fork and no water left running.

In comparing the three methods, backward chaining has the advantage of allowing the learner to earn the natural reinforcer at the end of the chain (Miltenberger, 2015). This procedure is especially useful when teaching learners who have difficulty learning complex behavior. In contrast, forward chaining has the advantage of providing extra practice for the responses that occur in the beginning of the chain (Leslie & O'Reilly, 1999). However, a disadvantage is that forward chaining requires the use of arbitrary reinforcers to teach the earlier responses in the chain (Miltenberger, 2015). Moreover, the nature of forward chaining means that earlier responding is placed on extinction as chaining progresses; merely placing soap on the fork is no longer reinforced. Finally, total task presentation has the advantage of practicing all of the responses each time the complex behavior is initiated. The disadvantage of this technique, however, is that reinforcement is delayed until the entire sequence is practiced, which makes teaching the response chain more difficult. The relative merits of the different forms of chaining are not always clear. Thus, a one-size-fits-all recommendation cannot be made; rather, the practitioner will need to assess each situation to determine which approach best suits the client's needs and preferences and the goals of the intervention. One option is to expose clients to different chaining procedures and then determine their preferences for one teaching method over another (Slocum & Tiger, 2013).