One important problem in cognitive science is to understand the development of cognitive processes in children and to devise computer models to explore the mechanisms that underlie these changes. Our research addresses these general goals. In particular, we are concerned with developmental changes in cognitive strategies in typical children and in children with mild mental retardation.

Before the late 1950s, psychological theories of mental retardation were very global, simply stating that individuals with mental retardation failed to learn because they had low intelligence. Philip Vernon, in the mid 1970's, pointed out that this view resulted in a circular explanation: to say that individuals with mental retardation have difficulty learning because they have low intelligence adds nothing to the understanding of the nature of mental retardation.

To break the circularity of this global approach, more specific theories of mental retardation began to evolve. Most either focused directly on the nature of memory deficiencies in individuals with mental retardation or made memory a central component. In the early 1960's, David Zeaman and Betty House developed an attention-deficit theory of mental retardation that localized the learning problem in attention. Norman Ellis identified the deficit in learning as a faulty short-term memory trace. Later, John Belmont and Earl Butterfield attributed the locus of the learning deficit to inadequate use of rehearsal strategies.

Though these more specific approaches attempted to break the circularity of the low-intelligence explanation of learning deficits in individuals with mental retardation, they created a deficit approach which has resulted in a rather unbalanced focus on limitations of individuals with mental retardation. A more comprehensive view of the cognition of children with mental retardation can be achieved by looking not only at ways they differ from but also at ways they are similar to children without mental retardation.

Our program of cognitive research started with the assumption that we would find deficiencies in the information processing of individuals with mental retardation. We did find some deficiencies, but the capabilities of the children in our studies were particularly salient because of the zeitgeist which led us to expect only deficiencies. So, in devising a model of cognitive processes we have taken a more balanced approach. Our first goal was to discover which processes in children with mental retardation might differ or be deficient and which might be similar or identical to those in children without mental retardation. We now provide a brief overview of what we found to be the main cognitive deficiencies and competencies of children with mental retardation.

Research during the last 25 years has established deficiencies in three aspects of information processing in individuals with mental retardation. At the very early stages of information processing, individuals with mental retardation do not process some basic aspects of visual stimuli in the same way as individuals with average intelligence do. Robert Fox and Stephen Oross, at Vanderbilt University, conducted a series of experiments in the late 1980s showing that individuals with mild mental retardation, do not process depth cues or movement cues with the same degree of accuracy as control individuals without mental retardation. In some of their studies, they used random dot stereograms, with one matrix of random dots presented to the right eye and the other to the left (dioptic presentation). Under some conditions, controls see a form (e.g., square) immediately, whereas individuals with mental retardation do not form such percepts. The findings of Fox and Oross, raise the possibility that some aspect of neural functioning involved in preattentive processing are deficient.

The second aspect of information processing that is deficient in individuals with mental retardation is encoding, which refers to the initial aspects of making information meaningful. For example, the letters of the word "horn" are nothing more than a set of black lines placed on a page, but once encoded, these lines become recognized as a word corresponding to a musical instrument, a safety feature of an automobile, or a hard piece of cartilage extending from the snout of a rhinoceros, depending on the context. Deciding that a word is "horn" and not another similar word such as "born" takes some time (on the order of .4 sec), and this decision may be made with varying degrees of accuracy.

There are many studies which suggest that individuals with mental retardation take longer to encode information and are less accurate in encoding information. For example, from 1970 to 1985 at the University of Alabama in Tuscaloosa, Norman Ellis conducted a number of studies of short-term memory. In one prototypical study, participants were shown a single word and asked to recall it either immediately or during several retention intervals with delays of up to 30 seconds. Individuals with mental retardation demonstrated consistently poorer recall than control subjects, even on the immediate recall test. Further, the magnitude of the difference at each retention interval was the same as the difference observed on the immediate test. These findings led to the conclusion that information is forgotten at the same rate in both groups, but that less information is encoded by the individuals with mental retardation (an encoding deficit).

The most firmly established finding in the study of individuals with mental retardation is that they have deficiencies in the use of cognitive strategies. A strategy is a method consciously devised by an individual to reach some goal. For example at the University of Kansas in the 1970s, John Belmont and Earl Butterfield conducted a program of research on memory strategies used to remember a sequence of letters, words, and picture names. The participants were asked to recall the items in their order of presentation. The sequence of the items was controlled by the experimenter, but the exposure time was controlled by the participant. In this type of task, individuals without mental retardation increased their study time as they progressed through the list, an indication that they were using a cumulative rehearsal strategy in which they reviewed the earlier items as the later items were exposed. The study time patterns for the individuals with mental retardation, however, were flat; they used the same exposure time for each item in the sequence. The failure to use a rehearsal strategy to keep track of the order of the items resulted in poor recall. Similar types of strategy deficiencies have been observed in a variety of memory tasks and specific deficits have be found in memory-related processes such as in the inhibition of irrelevant information (Merrill & Taube, 1996) and in speed of processing (Kail, 1993).

It is clear, then, that there are deficits in some aspects of information processing in individuals with mental retardation. However, in the 1970s, Ann Brown at the University of Illinois noted that not all aspects of information processing are deficient. She observed that nonstrategic processes, such as visual recognition memory, were equivalent in subjects with and without mental retardation whereas deficiencies were consistently observed in tasks requiring the use of strategies. Although Brown relied heavily on recognition memory studies to develop her hypothesis, more recent work has greatly extended it. Studies on a variety of structural features, such as automatic processing, spread of activation, short-term retention rate, stimulus organization, organization of semantic memory, and long-term retention show no difference between individuals with and without mental retardation. Virtually all these areas of competency, however, were investigated in the context of the deficit approach. That is, the investigators did not discuss the implications of their findings for a more balanced view of both deficits and competencies; results were instead discussed as indicating a "lack of a deficit", not as evidence for competence.

These results, however, make a strong case that many structural features of memory in individuals with mental retardation are equivalent to those found in individuals without mental retardation suggesting that the same information processing architecture exists for children with and without mental retardation. The significance of these findings for a computational model is that these potential differences, having been ruled out, no longer serve as candidates to explain observed differences between the cognitive performance of individuals who differ in native intelligence.

Strategy competencies. There are several investigators who have found evidence for strategy competencies in children with mental retardation. Tuner, Hale and Borkowski (1996), in a longitudinal study of strategy development, found that the rate of increase in strategy use was the same for children with and without mental retardation. This finding suggests that the mechanisms of strategy change across childhood are similar regardless of level of intelligence. Also, Baroody (1996) found that children with mental retardation are capable of "inventing" their own counting and addition strategies when learning the simple addition facts, a result that suggests strategy competencies beyond what would be expected by a deficit position.

Although others have obtained results showing strategy competencies, our research team is the only one which had as its goal the investigation of strategy competencies in children with mental retardation. In our studies, the importance of deficits in perception and encoding discussed previously have been minimized by using tasks in which the stimuli are easily perceived and in which the rate of presentation allows ample time for encoding. Our research is deliberately set up so that of the three deficits discussed previously, only a strategy deficit might be observed.

In one of our studies of strategy competency, Bray, Saarnio, Borges, and Hawk (1994) investigated external memory strategies in a task which allowed the use of both internal (e.g., verbal) and external (e.g., pointing at, orienting toward, and manipulating objects) memory strategies. The participants were shown movable objects and fixed targets and asked to follow sequences of instructions, such as "Put the eraser on the chair; put the pencil on the table."

In a baseline condition, the children with mental retardation were more likely to use an object-oriented strategy (pointing to or holding the movable objects) than the controls. Although these strategies are not as efficient as target-oriented strategies (moving objects toward the targets), it is clear that children with mental retardation were actively attempting to remember the instructions. The groups differed in the likelihood that they would use an object-oriented strategy, but there were similarities in the choice of tactics, suggesting commonalities in the cognitive abilities that underlie these choices. Further when children with mental retardation were given very minimal prompts, they devised more efficient and beneficial strategies that incorporate the same tactics as children without mental retardation. In contrast to a substantial literature showing deficiencies in the use of verbally-based strategies, this study showed areas of overlap in strategy competency in children with and without mental retardation.

Similar results were obtained by Fletcher and Bray (1995) in a more complex task that allowed both verbal and external strategies. The memory task was embedded in a tape-recorded story in which the participant was guided through a "haunted house" by a "friendly ghost." As the participant entered each imaginary room, (s)he heard from one to seven instructions such as "The broom is above the ghost" and "The lamp is on the blue side of the broom." The "blue side" referred to the right-hand side of the room, and the "pink side" was the left-hand side. At the end of the sequence, the experimenter opened a plexiglass door which blocked access to a computer screen (devised to represent the imaginary room) which displayed a spatial arrangement of velcro dots with a small, plastic ghost at the center. The participant then placed the miniature objects (e.g., broom, lamp) on the velcro dots.

All groups of children with and without mental retardation used a variety of external memory strategies including pointing to the objects and holding and/or moving them on the table in front of them. In addition, many participants arranged the objects either in their hands or on the table. The arrangement strategies were the most interesting and most effective. Using these strategies, the participants arranged the objects relative to a central point (ostensibly representing the ghost at the center of the screen) either in their hand or on the table (e.g., for "The broom is above the ghost; the lamp is on the blue side of the broom," the broom was placed above the central point and the lamp to the right of the broom).

In the external memory task, there was considerable similarity in the pattern of performance on the arrangement strategy and virtual overlap in performance on the pointing and holding strategies between the two intelligence groups. However, there was no overlap on a task that allowed no external strategies. In this task, the participants were given similar verbal instructions but were asked to recall the instructions verbatim. This pattern of results suggested that individuals with mental retardation have strategy capabilities underestimated by verbally-based tasks. In tasks that allow external representation, children and adolescents with mental retardation show considerably more strategy competency than they do on verbally-based tasks.

When the frequency of all observed external strategies and verbal strategies was combined on trials with three or fewer sentences to remember, there were no differences between the children with and without mental retardation. This suggests that the children with mental retardation were as likely to use a memory strategy as were children without mental retardation of the same chronological age.

Although external memory tasks may offer more support than verbal memory tasks, additional supports such as verbal or physical cues may also increase external strategy use in children with and without mental retardation. A study by Bray, Fletcher, Huffman, Hawk, and Ward (1994) described the use of external strategies in conditions that varied in the degree of situational support for strategy use.

For 7-year-old children, the physical cues (a model of the computer screen) but not the verbal cues (to use any strategy they might choose to use) facilitated the use of external arrangement strategies which, in turn, aided recall. For 9- and 11-year olds, both the verbal cues and physical cues facilitated the use of arrangement strategies, whereas only the verbal cues did in 17-year-olds. For 11-year-old children with mental retardation, neither the verbal nor the physical cues were sufficient to increase the use of arrangement strategies. For 17-year-old children with mental retardation, however, the combination of physical and verbal cues resulted in a level of strategy use equivalent to that of their chronological age peers.

These results show that the strategy competency can be "activated" to the same level in children with and without mental retardation without direct instruction. Strategy competency in children with and without mental retardation is similar, but the cognitive potential of children with mental retardation requires more situational support before strategies are adopted.

If our team of cognitive scientists endeavored to write a computer program to simulate the performance of children with and without mental retardation, the deficit position would postulate that the strategy routines for children with mental retardation should contain deficits. A literal interpretation of the deficit position would be that the strategy routines, whatever their nature, should be nonoperational in the children with mental retardation. Our empirical research, however, does not support this type of model. It has shown that children with mental retardation are strategic. The models would have to include some degree of situational support, not a lack of strategy capabilities.

Our team has approached the development of a cognitive model of strategy use in children with and without mental retardation with the basic assumption that the structural features (architecture) are the same for children with and without mental retardation, but the underlying competencies of the children with mental retardation require more situational support before they become evident in the children's performance on cognitive tasks.

The Utility of Connectionists Models for Understanding Strategies. Detailed descriptions of the elements of connectionists models may be found in the chapter by Jeffrey Elman in this volume. Perhaps the most compelling reason for using connectionist models (which use a neural network metaphor) is that these models, like the human brain, respond to multiple simultaneous constraints. Similarly, strategies are devised in nearly endless varieties in response to changes in context. Connectionist models also provide a way of looking at the development of rule-like behavior without assuming that the "rules" are in the child's head. Rather, rule-like behavior is generated in response to learning under multiple constraints and to being tested under conditions with the same or similar constraints.

Other Research Programs Using Connectionist Models. Connectionist models have been successfully applied to a variety of problems in cognition, including problems of atypical development. For example, Ira Cohen in the early 1990s modeled the learning abilities of children with autism using connectionist models to investigate the possible consequences of having too many or too few neuronal connections. His results indicate that models with too few connections led to problems in discrimination learning and poor generalization. Models with too many connections led to good discrimination but poor generalization, the latter being the pattern typically observed in children with autism. His simulations may lead to additional work on the hypothesis of the presence of an abnormally large number of neurons in the brains of children with autism.

A second encouraging example of the application of connectionist models to an aspect of atypical development is that of Hinton and Shallice (1991). They imposed artificial lesions ("removal" of connections by fixing their weights at zero) in connectionist models trained to decode letter strings. The "damaged" networks exhibited a mixture of visual and semantic error patterns that were similar to those obtained in individuals with dyslexia. Virtually the same types of mixed error patterns were obtained no matter where in the connection pool the "damage" was sustained. It is known that along with other aspect of the syndrome, the visual and semantic error patterns observed with dyslexics varies widely. The qualitative correspondence between the simulations and mixed error patterns obtained in dyslexia suggests that the lesions involved may not be specific to one site.

In the remainder of this essay we demonstrate how connectionist modeling can be applied successfully to the issue of understanding the nature of strategy deficiencies and competencies in children with mental retardation.

The Generalized Components model (Anumolu, Bray, & Reilly, 1996; Bray, Reilly, Villa, & Grupe, in press) is modular in the sense that it consists of distinct, interrelated components, each designed to represent one aspect of strategy behavior. The development of each module was constrained by the tasks used in our empirical research to study external memory, prior empirical and theoretical concepts drawn from developmental psychology, prior connectionist research, and basic aspects of neurobiology.

This model consists of seven modules, as shown in Figure 1. The first is the sequence module (to represent the sequence of sentences presented in our empirical research) and the second is the associative memory module (which learns and recalls representations of sentences like those used in our empirical work). Other modules, requiring more description, include (a) strategies, (b) attention bias, (c) tactics, (d) accuracy feedback, and (e) trial initiation.

Figure 1. Generalized Components Model

The strategy module consists of three nodes, each with selective connections to the entities in the object (e.g., eraser), target (e.g., table), and relation (e.g., on) pools of the associative memory module. This selective connectivity shown in Figure 1 is crucial for understanding how the model generates different levels of recall depending on the strategy used. Node 1, representing an object encoding strategy, is only connected to nodes in the object pool because only objects are involved in an object encoding strategy observed in our empirical research. Node 2 is connected to the nodes of the object and target pools because both objects and targets are encoded with this strategy. Node 3 is connected to the nodes of all three pools because object-target-relation strategies involve encoding objects, targets, and relations. In this architecture, when a strategy is activated, it raises the activation of the corresponding nodes. Therefore, when an object encoding strategy is activated, the activation value of the nodes of the object pool is raised, etc.

The attention bias module represents different levels of attention to the components of the strategy used. For instance, child might be biased to attend to the objects and give less attention to the target and to the relations (where the objects are to be placed). In this case, the simulated child would likely use an object-oriented strategy rather than a more sophisticated strategy based on attention, where the object is to be place in relation to the target.

The tactics module represents our theoretical construct that the tactics involved in strategies in general, and external strategies in particular, have a hierarchical structure. The dimensional encoding mechanism was derived from theories that maintain that as children mature, they encode an increasing number of dimensions of tasks and events. In these theories, children begin by encoding information about only one dimension and move to encoding two and then three dimensions. In the accuracy-feedback module, each node has one connection to an "external teacher" which keeps track of whether recall was correct.

In our conceptual framework, the significance of the hierarchical nature of the tactics is that as children perform the external memory task, they perform actions very similar to those necessary to construct strategies. That is, in our external memory task, when responding to the sentence "Put the eraser on the chair", the child picks up the eraser (grasping tactic), moves it toward the chair (moving tactic), and places it on the chair (arrangement tactic). With experience, children parse the component of the response chain and, during the presentation of the sequence of sentences to be remembered, begin executing parts of the response chain in anticipation of the actual response. Young children begin executing the first component of this chain while listening to sentences by picking up a to-be-remembered object and holding it until the "bell" rings signaling the end of a sequence of sentences. Older children also execute the first and second tactics, moving the objects toward the target while listening to the sentences. With practice, older children and adolescents may execute all three tactics.

Our view is that the mechanism that underlies the "discovery" of these types of strategies is one in which the child parses the response chain required by the task. In doing so, s/he attends to an increasing number of elements of the response chain necessary for making a response. This is quite different from thinking of strategies as being "in the child's head"; rather, strategies evolve because the child attends to the appropriate aspects of the context provided by the task. In our view, strategy evolution is in response to the multiple constraints and resources provided by the context that directs the child's attention to the relevant aspects of the task.

The simulations, like the actual external memory task, involve two phases, a study phase and a recall phase. During the study phase, representations of the sentences are presented to the model and a strategy is selected. The sentences are represented by the sequential activation of the appropriate nodes in the sequencer module and the corresponding entities in the entity pools. For instance, in simulating the presentation of the sentence "Put the eraser on the table", the first node of the sequencer module would be activated simultaneously with the "eraser", "on", and "table" nodes in the associative memory module. Using a Hebbian learning rule, the connections between the first sequencer node and the corresponding associative memory nodes would be increased. This procedure would continue for each sentence in a sequence.

During the recall phase, the model recalls the sentences presented in the last study phase. The recall interval begins with the activation of the recall initiation node, which, in turn, activates the nodes of the sequencer module. As each node is activated, the nodes of the associative memory module are activated in proportion to the previous learning during the study phase. In this way, it is likely that the weights connecting the first node of the sequencer and the items "eraser", "on", and "table" will be activated, resulting in the recall of the first sentence "Put the eraser on the table", although errors are made because of the relative strength of weights for the connections to other entities in the associative memory module.

The Components Model generates several simulated behaviors that are similar to those observed in our empirical studies of external memory strategies and Robert Siegler's studies of early addition strategies. In most simulation runs, the object, object-target, and object-target-relation strategies emerge in that order, as observed in our empirical research. Once a strategy "emerges," it is likely that it will not be used exclusively, and the simulated child will occasionally use fewer less sophisticated strategies such as object encoding after using an object-target encoding strategy. Accuracy of recall for our simulated children increases with the sophistication of the strategy, and there are primacy and recency effects in recall. Also, we are able to simulate the difference between children with and without mental retardation in terms of learning history, rather than specific process deficits. In both groups, we have been able to simulate different levels of situational support (e.g., verbal cues) by the manipulation of only one parameter.

These simulation results are important for several reasons. First, they show that individual differences can be modeled within the same architecture -- consistent with the assumption that strategy potentials are the same in children with and without mental retardation. Second, these simulations illustrate that the model can simulate differences in experimental conditions with a minimum of parameter manipulation.

Our conceptual framework leads us to believe that a more balanced treatment of strategy deficiencies and competencies can provoke new research within the area of mental retardation. For example, future research on the parsing mechanism and strategy use will focus on transfer of an uninstructed strategy. Devising a strategy by parsing the response requirements into tactics and assembling the tactics into a strategy results in a deeper level of processing than that provided by direct instruction. The exciting implication is that situations can be engineered so that children with mental retardation "discover" new strategies without direct instruction. The self-organized knowledge so derived is more likely to be transferred to similar situations requiring similar strategies. It is well known that children with mental retardation have particular difficulty generalizing strategies when trained directly. However, our research shows that children with mental retardation may devise effective external memory strategies with the same frequency as their chronological age peers when given the appropriate physical and verbal prompts. This finding raises the possibility that these strategies devised without direct instruction will transfer to other tasks more readily than the same strategies taught directly to children with mental retardation.

Our team's view is that the future of research on strategy use in individuals with mental retardation will begin to focus more on strategy competencies than exclusively on strategy deficiencies. This will be a welcome change since the deficiency approach has not led to the development of a framework for understanding the differences between individuals with and without mental retardation. Additionally, the connectionist modeling approach described herein may lead to a clearer understanding of the nature of strategy competencies and deficiencies in individuals with mental retardation and mechanisms that may be responsible for the pattern of observed differences. Extant intervention techniques for the remediation of strategy deficiencies have met with limited success. It is our hope that the deeper understanding of the nature of mental retardation afforded by our approach will eventually lead to more effective educational training programs. These will be tailored to the strengths of individuals with mental retardation and aid in the remediation of their deficiencies.

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