Norman W. Bray, Ph.D.
Department of Psychology and
Civitan International Research Center
University of Alabama at Birmingham

Kevin D. Reilly, Ph.D.
Department of Computer and Information Science
University of Alabama at Birmingham

Kathryn L. Fletcher, Ph.D.
Department of Psychology
University of Miami

Lisa F. Huffman, Ph.D. and Lisa A. Grupe, M.A.
Department of Psychology and
Civitan International Research Center
University of Alabama at Birmingham

Mark F. Villa, Ph.D.
Civitan International Research Center
University of Alabama at Birmingham

Vivek Anumolu, Ph.D.
Milwaukee, Wisconsin

We would like to thank Shannon Collins, Larry Hawk, Tracy Hawk, Kelly Van Matre, Julia Ward, and Daphne Wood for their assistance. This research was supported by research grant HD19426 from the National Institute of Child Health and Human Development.

S. Soraci & W. McIlvane (Eds.), Perspectives on Fundamental Processes in Intellectual Functioning. Norwood, NJ: Ablex Publishing, 1998.

Mailing address: Department of Psychology and Civitan International Research Center, SC 313, University of Alabama at Birmingham, Birmingham, AL 35294. Phone: (205) 934-9768, FAX: (205) 975-6330. Send Internet email to: bray@cis.uab.edu

The study of memory has been a vital aspect of cognitive research in mental retardation. Beginning with the stimulus-trace hypothesis of Ellis (1963), the goal has been to understand the functioning of memory processes and strategies in individuals with mental retardation and how these are different from those of individuals without mental retardation. In fact, most of the cognitive theories of mental retardation have either focused directly on the nature of memory deficiencies in individuals with mental retardation or have made memory a central component. In this chapter we focus on the nature of memory deficits in individuals with mental retardation with the hope of contributing to the development of a more general cognitive theory of mental retardation.

Many memory deficiency and memory-related deficiency positions have been advanced to explain memory functioning in individuals with mental retardation. For instance, Zeaman and House (1963) developed an attention-deficit theory of mental retardation that localized the learning problem in attention, a position that was later revised in a memory/attention theory (Zeaman & House, 1979). Ellis (1970) and Belmont and Butterfield (1971) attributed the locus of memory deficits to inadequate use of rehearsal strategies. Subsequently, Ellis developed the "cognitive inertia" hypothesis in which memory deficits were attributed to difficulties in shifting from one dimension of a task to another (Ellis & Dulaney, 1991; Ellis, Woodley-Zanthos, Dulaney, & Palmer 1989). Other deficit theories include the memory organization deficit theory of Spitz (1973, 1979) and a structural deficit theory (Spitz, 1988); the production-deficiency hypothesis applied to mental retardation by Brown (1974), the metamemory deficit theories of Campione and Brown (1977), and several versions of metamemory deficit models by Borkowski (e.g., Borkowski, Carr, & Pressley, 1987; Borkowski & Kurtz, 1987); the componential theory of Sternberg and Spear (1985) which localized the deficit among the metacomponents of the cognitive system; and the working memory limitation position of Ferretti and Cavalier (1991).

Bray, Fletcher, and Turner (in press) and Bray and Turner (1986, 1987) noted that these and other memory deficit approaches have focused on verbally-based laboratory tasks adapted largely from studies of adult verbal learning and memory. These tasks encompass a relatively limited range of strategic behaviors (e.g., the use of rehearsal, categorization in free recall). Within this narrow range of tasks, however, memory deficits have not always been observed (e.g., Belmont, Ferretti, & Mitchell, 1982; Borys & Spitz, 1976; Ellis, 1970; Spitz & Webreck, 1972; see Bray & Turner, 1986 for a review). Although such results have received relatively little comment, such findings are extremely important because they indicate that individuals with mental retardation have memory competencies as well as deficiencies (Bray, Fletcher, & Turner, in press; Bray & Turner, 1986) Further, when tasks are used that allow a variety of strategies (e.g., verbally-based strategies and external orientation strategies) individuals with mental retardation have been observed to use a number of different strategies (Bray, Huffman, Hawk, & Ward, 1994; Bray, Saarnio, Borges, & Hawk, 1994; Fletcher & Bray, 1995). It is possible, even likely, that there has been an overgeneralization of memory deficits and that this may have led to a neglect of evidence for strategy competencies and to a misleading conceptualization of the nature of mental retardation.

The picture of how "deficiencies" and "competencies" are related in individuals with mental retardation has yet to be adequately discussed. In this chapter, we elaborate the notion introduced by Bray, Fletcher, and Turner (in press) that individuals with mental retardation have a number of important cognitive competencies. We begin with an overview of the general evidence for cognitive competencies in individuals with mental retardation and discuss the competency positions beginning to emerge in developmental psychology. We then describe our conceptual framework for understanding strategy competencies and deficiencies. This is followed by a brief review of recent research on external memory strategies in our laboratory and how it relates to our conceptual framework. The final section deals with connectionist¹ models we are currently developing to understand mechanisms of cognitive change that may be responsible for the development of memory strategies and for the differences in strategy use between individuals with and without mental retardation.

Evidence for Cognitive Competence in Individuals with Mental Retardation
Raising the issue of the nature and extent of the cognitive competencies of individuals with mental retardation requires a close examination of what is meant by cognitive abilities. It seems clear that "abilities" has obtained a trait-like status in psychological research in mental retardation. In fact, the strong influence of differential psychology (with its emphasis on measures that are stable over time) has led to a view of relatively static "abilities" that can characterize an individual for a long period of time (if not an entire lifetime). Further, in the area of memory abilities of individuals with mental retardation, the possibility of developmental changes in strategy abilities has received very little attention. Sternberg (1990) has noted that this static view of abilities neglects the considerable body of literature that demonstrates that specific abilities develop and change across the life-span.

Brown (1974) noted that not all aspects of information processing are deficient in individuals with mental retardation. She observed that nonstrategic processes such as visual recognition were equivalent in groups with and without mental retardation whereas deficiencies were consistently observed in tasks requiring the use of strategies. Even though it became generally accepted that individuals with mental retardation "had" memory strategy deficiencies, very little attention was subsequently devoted to describing the nature and extent of the presumed deficiencies. Rather, research on information processing began to focus on "metamemory" (the presumed locus of strategy deficiencies) and on strategy training in the hope that strategy deficiencies could be reduced or eliminated.

Whereas Brown (1974) relied heavily on recognition memory studies to develop her hypothesis, recent studies showing no difference between individuals with and without mental retardation in automatic processing, spread of activation, short-term retention rate, use of stimulus organization, organization of semantic memory, and long-term retention have greatly extended the basis for this hypothesis (e.g., Ellis, Katz, & Williams, 1987; Ellis, Palmer, & Reeves, 1988; Ellis, 1978; Ellis, Meador, & Bodfish, 1985; McCartney, 1987; Sperber, Ragain, & McCauley, 1976; Spitz & Webreck, 1972; Turnure, 1991; Winters, 1982, 1985). Collectively, these studies make a strong case for the position that many structural features of memory in individuals with mental retardation are equivalent to those found in individuals without mental retardation (see Bray, Fletcher, & Turner, in press, for a review).

Given the structural similarities, one interesting theoretical question then is, why do individuals with mental retardation have difficulties in adopting strategies without direct instruction whereas individuals without mental retardation do not (Bray, 1987; Bray & Turner, 1987)? The typical answer to this question involves hypothesizing another level of deficiency: a deficiency in metamemory (e.g., Borkowski et al., 1987). The evidence for a relationship between metamemory and strategy deficiencies, however, is weak and, as noted by Belmont and Mitchell (1987), most explanations of strategy deficiencies relying on metamemory are arguments by fiat with a very post hoc flavor.

Although the metamemory approach is an important one, considerable progress may be made in understanding strategy deficiencies and competencies outside of the metamemory framework. There is increasing evidence, for example, that cognitive abilities are dependent on intricate interactions of person and situational variables and that the theoretical framework for such interactions may ultimately provide a clearer understanding of cognitive competencies. Neo-Piagetian research, for instance, has indicated important situational influences on the assessment of cognitive abilities. As noted by Mandler (1983), Piaget tried to specify the conditions under which "competency" was defined, and his research indicated that infants, toddlers, and preschoolers had many cognitive deficiencies as compared to older children. As situational variables were explored in more detail, Neo-Piagetian investigators found increasing evidence of cognitive competency in infants, toddler, and preschoolers on Piagetian tasks (e.g., Baillargeon, 1994; Baillargeon, DeVos, & Graber, 1989; Bryant & Trabasso, 1971; Gelman, 1969).

Consistent with the discovery of increased cognitive abilities in infants and young children, a number of investigators of everyday cognition have shown that the use of intellectual abilities such as skills in mathematics depends on task context. For instance, Newman, Griffen, and Cole (1984) found that school-aged children were more likely to use quantitative classification skills in a task requiring the formation of all possible pairs of words with pictures of movie stars than in an isomorphic task requiring them to record all possible combinations of household chemicals. Even though the children had shown that a systematic strategy was available for use on the word/picture pairing task, they were not likely to use it because they conceptualized the chemical pairing task as discovering the results of individual chemical combinations. Other context-dependent, cognitive abilities have been demonstrated in a variety of studies of everyday cognition (e.g., Frederiksen, 1986; Lave, Murtaug, & de la Rocha, 1984; Rogoff, 1990).

Cross-cultural studies of cognition have also resulted in a "situational" approach to cognitive abilities in which it is thought that "differences in cognition reside more in the situations to which particular cognitive processes are applied than in the existence of a process in one cultural group and its absence in another" (Cole, Gay, Glick, & Sharp, 1971, p. 233). As noted by Rogoff (1981), "the emphasis on the importance of context leads to a view of cognition as an activity that is not encapsulated within the head of the thinker. Rather, thinking is managed by the person who uses resources and constraints of the social and physical environment" (p. 154).

Conceptual Framework
These situational approaches to cognition, our recent empirical research on external memory strategies, and our connectionist (artificial neural network) modeling have combined to shape our approach to strategy competencies in individuals with mental retardation. Our conceptual framework for strategy competencies and deficiencies draws on these situational approaches to cognition and is an extension of the position developed by Bray and Turner (1986, 1987) and Bray, Fletcher, and Turner (in press) and from the architectural features and strategy mechanisms in our connectionist models (e.g., Anumolu, Bray, & Reilly, submitted; Bray, Reilly, Villa, Grupe, & Sadeh, 1995; Reilly, Villa, Bray & Anumolu, 1993). In this section we will explain the importance of situational influences, our view of the nature of strategy competencies, and the importance of the hierarchical organization of strategies for understanding strategy competencies and deficiencies in individuals with and without mental retardation.

Situational Influences
Our situational approach to the use of cognitive strategies begins with the deceptively simple observation that strategies are devised to cope with the information processing demands of a situation (Bray & Turner, 1987). A "situation", however, is a complex concept. In analyzing situations in which memory strategies are used, there are two dimensions that are particularly relevant. The first is the person's understanding of the present situation in relation to those that the person has experienced in the past. The second is the specific constraints present in the current situation. This is related to the idea that strategies conform to the specific elements of the situation (Siegler, 1991).

We make inferences concerning a person's cognitive capabilities based on performance in specific situations. Although neither of these situational dimensions has received a great deal of attention in accounts of strategy deficiencies in individuals with mental retardation, it is our contention that understanding competencies and deficiencies in strategy use requires an in-depth understanding of the relations between these two situational dimensions and the person's underlying strategy competencies as reflected in the nature and frequency of strategy use. First, consider the role of a child's understanding of the relationship of the present situation to previously experienced ones using performance on a memory task as an illustration. In a laboratory situation the experimenter may say "I am going to show you some pictures; remember these pictures so you can say them back to me in order." If the child views the experimenter as a "teacher", there would be a set of expectations that would be based on the child's previous interactions with teachers. One expectation might be that the child will be given specific instructions as to what to do and, in the absence of such instruction, the child should wait to be told. In this case, if the child does not actively devise a strategy to try to remember the sequence of pictures, it may be due to his/her general conceptualization of the student role in interactions with teachers. The child's lack of active strategy use may not reflect his/her strategy capabilities, rather it may reflect the way the child conceptualizes the roles of teacher and student. We have some evidence that young school-aged children conceptualize an experimenter administering a memory task to a child at school as a teacher rather than a researcher (Bray & Puleo, 1986). It is possible that some degree of "passivity" observed in children with mental retardation is due to their expectation that the "teacher" giving them the memory task will tell them if they need to do something they are not doing (such as not using a memory strategy).

Now consider the role of specific situational constraints. Situational constraints include whether the task is self- or experimenter-paced, and whether or not situational support such as manipulatives or task-relevant models is provided. Other situational constraints include situational variables that are inherent in the task such as whether the person is allowed to study the material an unlimited number of times or just once. For example, Turner and Bray (1985) found that individuals with mental retardation were likely to use a repetition strategy if allowed to study a sequence of pictures an unlimited number of times, whereas numerous other studies have found little rehearsal when individuals with mental retardation are allowed to study a sequence only once. One other important situational constraint is the number of different types of strategies that might be appropriate in a situation. Most laboratory tasks are designed to assess one type of strategy; this is the tradition inherited from laboratory studies of verbal learning and memory. If the situation allows a variety of strategies, it is more likely that the person will select one or more of these to cope with the problem. Thus our inferences concerning a person's strategy competencies will be influenced by the nature of specific task constraints. There is, then, a range of situational influences that are more or less supportive of strategy use. These situational differences are important in the consideration of strategy deficiencies and competencies.

Nature of Strategy Competencies
In addition to a consideration of the relation of the current situation to previously experienced ones and to specific task constraints, understanding strategy competencies requires an analysis of the nature of competence. One basic premise of our approach to strategy competencies is that the difference between individuals with and without mental retardation is not in their tendency to be strategic per se, but in the interaction of their strategy capabilities and degree of situational support. That is, individuals with mental retardation are capable of using memory strategies, but the strategic competence underlying strategy use is more "fragile" than in individuals without mental retardation. Individuals with mental retardation, therefore, require more situational support before the underlying cognitive potentials can be activated to influence their strategic behavior. Broadly speaking, we view the cognitive system underlying strategy development as a system of "cognitive potentials" and "mechanisms" that are activated by the situation to varying degrees. This view seems consistent with the broad outline sketched by the empirical studies of situational variation, contextual support, and cross-cultural differences in strategy use mentioned previously.

As a working premise, we assume that the organization of cognitive potentials in individuals with and without mental retardation is similar. This assumption seems reasonable because there are now numerous studies showing that young children with mental retardation, when given direct instruction, are able to use the same types of strategies as children without mental retardation of the same chronological age (e.g., Brown, Bransford, Ferrara, & Campione, 1983). Further, in our own research, we have shown that, with appropriate physical and verbal prompts (but no direct instruction), children with mental retardation devise sophisticated problem-solving strategies in an external memory task as frequently as children without mental retardation of the same chronological age (Bray, Fletcher, Huffman, Hawk, & Ward, 1994).

Another working premise is that the actual range of cognitive potentials activated in many situations is more restricted for individuals with mental retardation than for individuals without mental retardation. This assumption is based on our prior research showing that strategy adoption by individuals with mental retardation requires more support. For example, individuals with mental retardation are capable of using strategies (without instruction) but seem to require more situational support than individuals without mental retardation. As noted by Bray and Turner (1986):

(Strategy use) seems to be a more fragile phenomenon in retarded groups than in comparable nonretarded groups. Both younger retarded and nonretarded individuals are less likely to use a repetition strategy when the task constrains the number of times the items may be viewed before recall, but the effect of this type of limitation is more severe for retarded individuals than for nonretarded adolescent (Turner & Bray, 1985). Similarly, under some conditions study-time patterns similar to those used by nonretarded groups may be found for retarded groups, but only after exquisitely clear task instructions have been given (Belmont et., 1982). Retarded individuals may show evidence of primacy effects, but in some cases a large number of trials on one task must be given (Turnbull, 1974), whereas primacy is evident in nonretarded groups with relatively few trials (Belmont & Butterfield, 1971). When accuracy on sequences presented at different rates is compared for retarded groups, rate has an effect when relatively slower rates are included (Haynes, 1970), whereas differences due to presentation rate are evident for nonretarded groups even when the rates are relatively fast (Ellis, 1970, Experiment 1). Retarded groups may maintain information during an unfilled retention interval, but their maintenance may not be as effective as in nonretarded groups (Anders, 1971), and it is apparently restricted by a small rehearsal set size (Borys, & Spitz, 1976) (p. 66).

The idea that a "restricted range" of cognitive potentials is activated in many situations in individuals with mental retardation is also related to Estes' (1970) stimulus sampling theory in which learning requires that the features of a task be sampled; younger children and children with mental retardation sample fewer elements at a time. It is also related to the "breadth of attention" mechanism of Fisher and Zeaman's (1973) theory of discrimination learning. Individuals with mental retardation are thought to have a more narrow focus of attention and therefore do not "pick up" on the critical features of a task as readily as individuals without mental retardation. This view is also consistent with more recent theoretical treatments of perceptual features and attention in learning (Soraci & Carlin, 1992).

The Hierarchical Organization of Memory Strategies
Another important aspect of our conceptual framework is that differences in strategy use between individuals with and without mental retardation require a clear understanding of the structure of memory strategies and how memory strategies are "discovered" and how they change ("evolve") with use once they are discovered or learned. Our approach is derived from the architectural features and strategy mechanisms in our connectionist models (Anumolu, Bray, & Reilly, submitted; Reilly, Villa, Bray & Anumolu, 1993). In our conceptual framework, strategies have a hierarchical structure that maps, to various degrees, onto the response requirements of the task. Based on our analysis of strategy discovery and evolution in our external memory task, we believe that, initially, strategies are learned in the context of a task by noticing that components of a strategy can be executed in anticipation of the required response. That is, in the external memory task used by Bray, Saarnio, Borges, and Hawk (1994), children listened to sequences of sentences specifying how movable objects were to be placed relative to fixed targets (see Figure 1). In making the response to the sentence "Put the eraser on the table", the child may notice that the object must be picked up, and begin to pick the object up in anticipation of actually executing the required response of placing the object relative to a target. Picking the object up and holding it while listening to the sentence is called an object encoding strategy. With additional practice, the child may notice that the response requirements also involve moving the object, and the child may begin moving the object toward the target and placing it near the designated target while listening to a sentence. This is called an object-target encoding strategy. Finally, the child may notice that the required response involves placing the object relative to the target and devise a means of representing this relation (e.g, by placing the object on a small ridge in front of the target when the relation is "on" and in front of the ridge when the relation is "in front of"). This is called an object-target-relation encoding strategy.

As in our external memory task, there is also a close correspondence between the response requirements of a sequential memory task and the structure of the strategy adopted in anticipation of making the required response. In a sequential memory task the child is presented with a sequence of items and is asked to recall them in their order of presentation. As sessions progress, or with the increasing age of the child, the child first labels the items to be remembered, says the same label repeatedly, then repeats the labels cumulatively as the items are presented.

Flavell ( 1970) suggested that the response requirements of a sequential memory task may influence the use of the component skills involved in verbal rehearsal strategies. His suggestion was made based on the contrasting results obtained by Moely, Olson, Halwes, and Flavell (1969), who required children to recall to-be-remembered items aurally, and those of Corsini, Pick, and Flavell (1968) and Flavell, Beach, and Chinsky (1966) who required pointing rather than verbal recall. Young children in the Moely et al. (1969) experiment used verbal rehearsal whereas children the same age in the studies by Flavell et al. (1966) and Corsini et al. (1968) did not. Flavell (1970) noted that the difference in the recall requirements of these memory tasks "may have played a causal role, i.e., with naming during recall "priming" naming during stimulus presentation (p. 204).

In this sense, there seems to be some degree of isomorphism between the response requirements of some tasks and the strategies that are discovered to be effective in those tasks. Children "parse" the requirements of these tasks into "tactics" (such as grasping an object, moving it, and placing it in relation to a target) and then assemble these tactics into a sequence (grasp object; move it toward the target; place it to represent the relation). The execution of the tactics in sequence comprises the use of a strategy.

We maintain that it is useful to conceptualize two categories of strategies, each appropriate for different types of tasks and each differing in how the child must parse tactics into sequences and, finally, into strategies. These categories were developed in the course of our connectionist modeling (Anumolu, Bray & Reilly, 1993; submitted; Reilly, Villa, Bray, Anumolu, 1993). What we have discussed to this point are what we call additive strategies which are used in tasks in which the child is asked to make a response that reproduces the to-be-remembered material (e.g., placing objects in specified relations to targets as in the external memory task of Bray, Saarnio, Borges, & Hawk, 1994; recall of sequences of words, digits, or other materials in sequence as in Ellis, 1970; recall of trigrams in a Brown-Peterson short-term memory task and in Peterson & Peterson, 1959, or other tasks that have been used to study "episodic" memory). In these tasks, the child builds a more sophisticated strategy by adding tactics to some initial action (as illustrated here for an external memory strategy and a rehearsal strategy). Most of the extant literature on strategies in children with mental retardation has focused on additive strategies, usually allowing the child a very limited amount of time to practice the task in a situation designed to focus on only one type of strategy (e.g, the "cumulative rehearsal/fast-finish" strategy in the circular recall task, Belmont & Mitchell, 1987).

Next, we discuss what we call reductive strategies in which a person devises more sophisticated strategies by eliminating tactics of a previously learned strategy, thereby economizing the execution of the strategy. For example, in learning addition of two single-digit numbers such as "3 + 5", young children with and without mental retardation use a "sum" strategy in which they hold up 3 fingers of one hand and 5 fingers of the other. They then verify that they have held up 3 fingers by counting them on their first hand ("1, 2, 3") and then verify that they have held up 5 by counting them on their second hand (1, 2, 3, 4, 5). Next, they begin counting the sum of the fingers held up on both hands beginning with the first ("1, 2, 3, 4, 5, 6, 7, 8") (e.g., Bray, Huffman, Ward, & Hawk, 1994; Siegler & Jenkins, 1989). This type of strategy is frequently taught to children learning simple addition and, with practice, this rather cumbersome but effective strategy is simplified by children without direct instruction (Bray, Huffman, Ward, & Hawk, 1994). For example, a "short-cut sum" strategy is the same as the sum strategy except that the verification component is omitted. Similarly, a "finger recognition" strategy is a modified short-cut-sum strategy in which the child holds up the appropriate number of fingers on each hand, but does no overt counting. Finally, a "retrieval" strategy involves no holding up of fingers or overt counting; the sum is given without the aid of an overt or covert counting strategy (Siegler & Jenkins, 1989). This progression from a sum to a retrieval strategy involves "streamlining" of the initial counting strategy, a "reduction" in the number of tactics used in the original strategy. This type of strategy does not require parsing of the required response, it requires parsing the tactics of the original, more cumbersome but effective strategy. This view would imply that "parsing" is a general mechanism that may be applied to "forward chaining" tasks (requiring additive strategies) or "backward chaining" tasks (requiring reductive strategies).

The difficulty in "discovering" an additive strategy is determined by several factors, and understanding them may give us a clearer picture of why young children and children with mental retardation require more situational support to activate the strategy potentials underlying strategy use. One factor contributing to the difficulty of discovering an additive strategy would be the amount of mental effort necessary for parsing the tactics in the response requirements of a task. Parsing the response requirements would demand that a representation of the response requirements be held in memory while simultaneously trying to process the to-be-remembered information. Guttentag (1984) maintains that strategy execution taxes the resources of young children who have more limited working memory and who have not yet automatized the elements of a strategy. We extend this view to parsing of response requirements, which would seem to require the child to hold the elements of the response chain in working memory. In our previous research on memory strategies, we have shown that children with mental retardation need more explanation of the task demands before they are able to discover a strategy (Bray, Justice, & Simon, 1982). Thus, our view is that individuals with mental retardation, who are known to have limitations in working memory (Spitz, 1979), and who also have difficulty comprehending task demands (Bray, et al., 1982), are not as likely to discover additive strategies without appropriate situational support.

Another factor determining the difficulty of discovering an additive strategy is the distinctiveness of the tactics involved in the response requirements. The more "distinct" the tactics are in the response requirement, the more likely that the child will be able to parse the necessary tactics and assemble an additive strategy. For example, the response requirements in the external memory task of Bray, Saarnio, Borges, and Hawk (1994) (grasping, moving, arranging) seem more distinct than the tactics comprising a cumulative rehearsal strategy (e.g., labeling, repeating a label, sequencing labels). This may explain why children with mental retardation are more likely to discover additive strategies sooner in our external memory task than in sequential memory tasks.

At this point we have less to say about the difficulty of discovering a reductive strategy because the conceptualization of strategies into additive and reductive types is a new dimension of strategy use that we introduce herein. Most of what can be said at this point can be found in the work of Siegler and his colleagues and in a recently completed study by Bray, Huffman, Ward, and Hawk (1994). Siegler and Jenkins (1989) conducted a microgenetic study of addition strategies with preschool children utilizing frequent measurements over three to four months during which the children were learning new cognitive skills. Although they do not discuss their research in these terms, we view their study as concerned with the evolution of reductive strategies. They assume that several different strategies are available and that the children select among these depending on the difficulty of the individual problem, the previous accuracy with a particular strategy (accuracy-feedback mechanism), how quickly the strategy can be executed (speed of execution mechanism) and how novel a strategy is (novelty bias mechanism, which accounts for why children try new strategies when old ones were working well). These mechanisms seem to relate to strategy discovery, but they do not account for why the children seem to progress from more complicated, cumbersome strategies such as a sum strategy to a less cumbersome short-cut sum strategy.

Bray, Huffman, Ward, and Hawk (1994) found the same progression in a microgenetic study of addition strategies with children with mental retardation. In our conceptual framework, this progression is due to parsing the tactics involved in the sum strategy, and recognizing that the sum of the addends could be computed without verifying the representation of each addend. This seems to require that the counting skills of the child would have progressed to the point of giving the child confidence that he/she can accurately represent the addend on each hand without the need for explicit verification. Thus, evolution of this type of reductive strategy would depend on parsing the tactics involved in a strategy and the development of appropriate counting skills that may be derived from experience with counting either inside or outside of the context of addition per se. This is an important area of research since mastery of many academic skills such as addition, subtraction, and multiplication, seems to require the use of reductive strategies.

Descriptions of Empirical Studies of External Memory Strategies
Our program of empirical research and connectionist modeling focuses on the ability of individuals with and without mental retardation to devise external memory strategies in situations with varying degrees of situational support, and on the development of a conceptual framework for understanding developmental changes in strategy use in individuals with and without mental retardation. It is generally assumed that developmental changes in memory performance are due, in part, to increases in strategy use and to growth of the knowledge base (Brown, Bransford, Ferrara, Campione, 1983; Siegler, 1991). There is increasing agreement, however, that the precursors of strategy development may be found in early attempts to remember where objects are placed. Very young children use external orientation (touching, pointing, etc.) in tasks requiring memory for the location of objects in the environment. For instance, during a hide­and­seek game, children 18 to 24 months of age will look at the hiding place, point to it, hover near it, and even peek at it during a delay interval (DeLoache, Cassidy, & Brown, 1985). Three-year-old children will look at a target, point to it, or touch it as a means of remembering the location of a hidden object (Wellman, Ritter, & Flavell, 1975). Preschool children will also manipulate to­be­remembered objects, and this manipulation may increase recall accuracy (Baker­Ward, Ornstein, & Holden, 1984; Fletcher & Bray, submitted).

Older children and adults also use external memory strategies. For example, many adults strategically place their briefcase and other items in a special place (next to the door) in order to remember to take them to work (Intons­Peterson & Fournier, 1986). In aging adults, the use of external aids for remembering has been shown to be widespread, and there are many commercially produced items to assist older adults with memory difficulties (e.g., pill organizers and timers; Petro, Herrmann, Burrows, & Moore, 1991). These examples illustrate that across the life span, people use external strategies. Each type of external memory strategy or physical aid, by eliminating the need to covertly encode an object or event, reduces the processing demands on the cognitive system and facilitates adaptation to the environment.

In our first study in this area, we developed an instruction-following task to investigate external memory strategies (e.g., moving and arranging objects in an attempt to remember, Bray, Saarnio, Borges, & Hawk, 1994). The participants were 7- and 11-year-old children without mental retardation and 11-year-old children with mental retardation. In a baseline session, children were shown common objects and given instructions to remember such as "Put the eraser on the chair" and "Put the pencil in front of the table" (see Figure 1). Participants attempted to place objects at specified spatial locations after hearing sequences of tape-recorded instructions. In this situation, children could point to or hold the object (object-encoding strategy), or arrange the objects to represent their correct spatial location (an object arrangement strategy). In an experimental session, participants were randomly assigned to either a prompted or an instructed condition. In the prompted condition, they were told that movement of the objects was allowed and that such movement could aid performance. The purpose was to provide prompts without suggesting specific strategies or tactics. In contrast, participants in the instructed condition were trained to use an object arrangement strategy designed to facilitate recall. All the relevant tactics were specified by providing appropriate spatial coding and retrieval tactics.

During baseline, 7-year-old children with and without mental retardation pointed and held the objects more frequently than 11-year-olds. After prompting, all three groups used more sophisticated object arrangement strategies that represented the correct spatial locations, and all used the same tactics. Virtually all children in the instructed condition adopted an object-arrangement strategy. This study indicated areas of overlap in strategy capabilities among the groups, indicating that children with mental retardation may have more strategy capabilities than indicated by prior studies requiring the use of verbally-based strategies rather than external orientation strategies.

Fletcher and Bray (1995) investigated external memory strategies used by 7-, 9-, 11- and 17-year-old children without mental retardation and 11- and 17-year-old children with mild mental retardation. In order to eliminate any reference to moving the objects, general strategy instruction was used (i.e., "You can do anything that you think will help you remember"). The memory task was embedded in a tape recorded story in which the participant was guided through a "haunted house" by a "friendly ghost". On each trial the participant heard from one to seven sentences such as "The broom is above the ghost" and "The lamp is on the blue side of the broom." At the end of the sequence the participant placed the miniature objects on a computer screen (see Figure 2). For the 7- and 9-year old children, object-oriented external strategies (holding, pointing) were used more frequently than arrangement strategies that encode object/target/relation. For the 11- and 17-year-old children without mental retardation, object-oriented strategies occurred less frequently than arrangement strategies; the frequency of the latter increased with task difficulty. Many children, including children with mental retardation, used an arrangement strategy in which they "imagined" that the ghost on the screen was situated on the board in front of them (see Figure 2) and then arranged the objects around the imaginary ghost as they listened to the sequence of sentences. This is consistent with a "mental model" representation (Johnson-Laird, 1983), in which the elements of the situation are mapped directly into the representation.

In this experiment, across groups, there was a positive relationship between the frequency of arrangement strategy use and recall accuracy. The 11-year-old children with mental retardation used more object-oriented strategies than the 17-year-old children with mental retardation, but the latter used more arrangement strategies, demonstrating a developmental increase in strategy competency in children with mental retardation. The use of the arrangement strategy was a better predictor of accuracy than IQ or age.

In addition to observation of the frequency and type of external memory strategy used, Bray and Fletcher (submitted) investigated children's abilities to provide immediate and delayed self-report of covert and overt memory strategies in the external memory task used by Fletcher and Bray (1995). The participants were 7-, 9-, 11- and 17-year-old children without mental retardation and 11- and 17-year-old children with mild mental retardation. Participants placed objects in specified spatial locations after hearing sequences of tape-recorded sentences. After each trial, half of the children immediately reported the strategy used, and all participants gave delayed reports. There were substantial correlations between immediate report and observed strategy use, and delayed reports were consistent with immediate reports. Children were unlikely to report strategies not related to recall.

Although external memory tasks may offer more support than verbally-based tasks by allowing the use of multiple nonverbal strategies, additional supportive components 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) investigated the use of external strategies in conditions which varied in the degree of situational support for strategy use.

The participants were 7-, 9- 11-, and 17-year-old typical children, and 11- and 17-year-old children with mental retardation. The participants were given the "haunted house" task of Fletcher and Bray (1995). There were four between-subjects conditions. In the model/prompt condition, a model of the computer screen was available during sentence presentation (see Figure 3). During the first day the participants were given a verbal prompt of "You can do anything that you think will help yourself remember." During the second day, the participants were given the verbal prompt of "I want you to move the objects in a way that will help you to remember where the objects are." In the no-model/no-prompt condition the participants were tested without the model and were given no verbal prompt. The other two conditions were no model/prompt and model/no-prompt.

For the 7-year-old children, the physical cues but not the verbal cues facilitated use of external arrangement strategies. For the 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 the 17-year-old group. For the 11-year-old children with mental retardation, neither the verbal nor the physical cues were sufficient to increase the use of arrangement strategies, but for the 17-year-old children with mental retardation, the combination of physical and verbal cues resulted in a level of strategy use equivalent to that of their chronological age peers.

These results demonstrate that the strategy potentials of individuals with mental retardation may be activated to the same level of individuals without mental retardation without direct instruction. This is the first demonstration of this principle in the area of mental retardation. It provides considerable support for our conceptualization of the differences in strategy competency as an interaction of cognitive potentials and situational support. It appears that the range of cognitive potentials is the same in individuals with and without mental retardation, but the cognitive potentials of individuals with mental retardation require more situational support before strategies are adopted (but direct strategy training is not necessary). Additionally, the results demonstrate that individuals with mental retardation are capable of parsing the response requirements in a task requiring an additive strategy, but they require more support in order for appropriate parsing to occur.

In a microgenetic study of addition, using a short-term longitudinal design with trial-by-trial observation of strategies, Siegler and Jenkins (1989) found that young children without mental retardation are able to devise external strategies (e.g., counting on their fingers). Bray, Saarnio, Borges, and Hawk (1994) and Fletcher and Bray (1995) have shown that children with mild mental retardation use external strategies in a memory task (e.g., pointing, holding, and arranging objects in order to remember their placement). These results suggest that children with mental retardation would use external strategies while learning simple addition.

Bray, Huffman, Ward, and Hawk (1994) investigated the used of external counting strategies in children with and without mental retardation still learning simple addition. The children were enrolled in public schools, 10 children with mild mental retardation in third through fifth grade classrooms (M_age= 8.9 years), and 14 children without mental retardation in kindergarten classrooms (M_age = 6.4 years). At the beginning of the study, the groups were roughly equivalent on a screening for accuracy of addition with single-digit addends. All children were tested individually and were given no strategy instruction. There were two sessions per week for 12 weeks with 12 addition problems per session. Problems appeared on a computer screen and the experimenter read the problem aloud ("What is 3 + 5?"). Children were given a colorful sticker after each correct response. Following a response, the child described his/her strategy. Based on videotapes of each session, ten different categories of strategy use were scored with reliability greater than .90.

There were from 2 to 6 different strategies used at least once by the children without mental retardation, and from 1 to 6 used by the children with mental retardation. Seven children without mental retardation showed an increase of 10% or more in the use of a retrieval strategy (the most advanced strategy) during the second 12 sessions as compared to the first 12 sessions; this was true for 3 children with mental retardation. Of the remaining children, 2 without mental retardation and 3 with mental retardation showed a 10% or greater increase in the use of a strategy more sophisticated than used during the first 12 sessions. Increases in the use of more sophisticated strategies were accompanied by decreases in the use of a less sophisticated strategy. Across strategies, accuracy and latency patterns were similar in both intelligence groups, with retrieval as the fastest and most accurate strategy, the more elaborate counting strategies as slow but accurate, and guessing as fast but inaccurate. Reported and observed strategies were positively correlated for both intelligence groups.

In learning simple addition, children with mental retardation use a variety of external counting strategies. Increases in problem difficulty were accompanied by increases in use of external strategies, a result which parallels the results from our external memory tasks (e.g., Bray, Saarnio, Borges & Hawk, 1994; Fletcher & Bray, 1995). Under the conditions of this study, children with mental retardation and with appropriate knowledge of math facts, demonstrate strategy evolution equivalent to individuals without mental retardation by streamlining an initially cumbersome external strategy. The reductive strategies used by children with mental retardation evolved toward more sophisticated levels over a relatively brief period of time.

The results from the external memory studies and from studies of early addition skills in children with and without mental retardation have important implications not only for understanding external representation, but for the apparently limited view of strategy use that has emerged from research with individuals with mental retardation. Our studies indicate that children with mental retardation have more strategy competency than would be expected based on the extant literature on strategy deficiencies. We now discuss how computer models may be used to represent these competencies more explicitly.

The Utility of Computer Models for Understanding Strategies
One important goal of our research is to develop a theoretical framework for developmental differences in strategy competence. This goal includes the description of developmental differences in external strategy use that goes beyond the descriptive level in attempting to make a contribution to understanding possible cognitive mechanisms that may be responsible for developmental differences in strategy use. We believe that discovery of these mechanisms will require a level of theoretical explicitness not characteristic of extant empirical studies. For this reason, we are committed to the development of computer models as an important methodological tool that will aid us in the development of a theoretical framework for addressing the mechanisms responsible for developmental change in children with and without mental retardation.

The development of computer models requires detailed specification of the components and mechanisms of the theory relevant to the behavior to be simulated. Investigators in Artificial Intelligence (AI) frequently claim that the only way to test a theory of cognition is to express it in the form of a computer program and to demonstrate that the simulated behavior is similar to actual behavior (e.g., Newell, Young, and Polk, 1993). If we are to understand the mechanisms of strategy use, it seems particularly important to develop more explicit theory in the area of strategy development, and the use of computer simulations is one methodological tool that will take the area in this direction.

Perhaps the most compelling reason for using connectionist models (which use a neural network metaphor) in the study of situational and contextual effects on strategy use is that these models, like the human brain, respond to multiple simultaneous constraints (Rumelhart & McClelland, 1988). The neurons of the brain respond almost continuously to a variety of environmental and internal patterns of stimulation; this is also a fundamental property of connectionist models. Similarly, strategies are devised in nearly endless varieties in response to changes in context. As noted by Rogoff (1990), an emerging view of cognition is that it involves the use of multiple constraints and the resources provided by a context.

A second related point is that connectionist models deal with systems of components and mechanisms rather than simple (isolated) cause and effect relations usually investigated in empirical experiments. One of the problems that approaches to strategy development such as "metamemory" have had [besides the fact that the empirical relationship between metamemory measures and strategy use has not been very strong (Chi, 1988)] is that the system of components and processes necessary and sufficient for strategy adoption has not been clearly specified.

We believe that part of the problem is that the "metas" all operate on rule-based representations. Connectionist models with distributed representations offer a possible solution to these difficulties because the behavior of the network represents a solution to multiple simultaneous constraints, not manipulation of rule-based knowledge. This view provides a way of looking at the development of rule-like behavior without assuming that the "rules" are in the child's head and are either used or not used because of some "meta" knowledge. 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. Explicit representation of rules, which has been the focus of much effort in developmental psychology and in the area of mental retardation, may simply not be necessary to understand differences between individuals with and without mental retardation in strategy development. This viewpoint is consistent with the approach of Soraci and Carlin (1992) whose research demonstrates that relational responding of individuals with mental retardation can be greatly improved by manipulating "stimulus array structures that make salient the critical dimensions of (the) differences" among stimuli and that these improvements "do not necessitate mediational or symbolically based rule induction" (p. 48).

Elements of a Connectionist Model
Connectionist models are computer programs consisting of a system of interconnected artificial neurons (nodes) constrained, in part, by the metaphor of how the brain operates. As in the brain, each node receives an input from one or more nodes in the system. For example, in Figure 4 (after Wasserman, 1989), the ellipses at the left represent input nodes, and the values IN_m represent inputs from the external environment. Each connection from an input node to an internal node ("artificial neuron") has a weight, W_mn , as shown in Figure 4. In the course of a simulation run, these weights are adjusted to reflect the relative importance of different patterns of external input or events. In effect, the weights represent differential experience and the effects of learning. Usually these weights are updated after each learning cycle. The activation value of each input node is multiplied by the weight of each connection, and the activation value of the artificial neuron is the sum of these products (E NET in Figure 4). If the activation value exceeds a firing threshold, the "squashing function", F, regulates the output of the node, keeping it within mathematically defined limits, and modifies the activation value by means of a sigmoid function; this transformation is the output of the node. (The output of the node will be zero if the activation value does not exceed the threshold.) After some flexible number of cycles, the system generates output that simulates some aspect of intelligent behavior such as pattern recognition, categorization, or, in the case of our models of external memory strategies, strategy use and accuracy of recall.

Other Research Programs Using Connectionist Models
Connectionist models have been used in the study of a wide range of cognitive processes. While an exhaustive treatment of this issue would exceed the space available here (for overviews see Anderson & Rosenfeld, 1988; Anderson, Pellionisz & Rosenfeld, 1990; Bechtel & Abrahamsen, 1991; Carpenter & Grossberg, 1991; Churchland & Sejnowski, 1991; Levine, 1989, 1991; Seidenberg, 1993; Sejnowski, Koch, & Churchland, 1990; Wasserman, 1991), large numbers of investigators have used connectionist models to more clearly understand typical and atypical development and other aspects of cognition (McClelland, 1989). In fact, some of the early psychological issues to which connectionist models were applied involved developmental issues such as how children without mental retardation might learn past tenses of English verbs (Plunkett & Marchman, 1991; Rumelhart & McClelland, 1986, 1987). These models led to the development and empirical tests of other connectionist models of language development in typical children, such as vocabulary (Plunkett & Sinha, 1991), learning to pronounce English words (Sejnowski & Rosenberg, 1987) and the transition from beginning to skilled reading (Seidenberg & McClelland,1989). Connectionist models have also been successfully applied to other aspects of cognitive development such as developmental changes in the judgment of balance using the balance beam task (McClelland & Jenkins, 1991), the development of the concept of same (Smith, 1993), and the learning of simple addition (Anderson, Spoehr, & Bennett, in press; Campbell & Oliphant, 1992; McCloskey & Lindemann, 1992).

Connectionist models have also proven to be useful tools in studies of atypical development as illustrated by the application of these models to the differential diagnosis of autism and mental retardation (Cohen, in press; Cohen, Sudhalter, Landon-Jimenez, & Keogh, 1993), and in the computer simulation of dyslexia (Hinton & Shallice, 1991; Patterson, Seidenberg & McClelland, 1989). Connectionist models have also been used as tools in research on neurological disorders including prosopagnosia in which patients cannot overtly recognize faces but can demonstrate some level of recognition when tested with indirect measures (Farah, O'Reilly,& Vecera, 1993), certain frontal lobe dysfunctions (Levine & Prueitt, 1989), and impairments of semantic memory due to brain lesions (Farah & McClelland, 1991). Connectionist models have provided a new approach to basic aspects of learning and cognitive function as illustrated by the work on classical conditioning (Grossberg & Levine, 1987; Sejnowski & Tesauro, 1990), category learning (Kruschke, 1992; Shanks, 1991), associative memory (Sejnowski, 1989), information processing in the visual cortex (Pouget, Fisher, & Sejnowski, 1993), learning event sequences (Cleeremans & McClelland), visual pattern recognition (Baldi & Hornik, 1989; Carpenter, 1991; Grossberg, 1991), and motor learning (Lisberger & Sejnowski, 1992),

The research programs mentioned here (which represent only a fraction of the application of connectionist models to aspects of cognition) have used these computer models to specifically implement a variety of psychologically and biologically motivated mechanisms and architectures. The results from atypical development, in particular, bode well for the present approach. For example, Cohen (in press), in modelling the learning abilities of children with autism, has used 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, and 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 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) who imposed artificial lesions ("removal" of connections by fixing their weights at zero) in connectionist models trained to decode letter strings. The "damaged" networks exhibited error patterns that were similar to those obtained in individuals with dyslexia. Virtually the same results were obtained regardless of where the "damage" was sustained.

In addition, several investigators have noted the potential usefulness of connectionist models for understanding important aspects of mental retardation. Fox and Oross (1992), in their research on "preattentive" stages of visual information processes, have hypothesized that mildly mentally retarded individuals may have previously undetected neural deficits. Although they did not develop connectionist models of these deficits, they concluded that the neural network metaphor provides a conceptual organization for their empirical research on the nature of the (hypothesized) neural deficits in individuals with mild mental retardation. Also, Soraci and Carlin (1992) note that connectionist models provide a conceptual framework consistent with their empirical research on nonmediational relational learning. Although they did not develop connectionist models for their empirical research, Soraci and Carlin (1992) noted: ". . . one important area for future research will be the simulation of individual difference in relational learning using connectionist models" (p. 48-49).

This brief overview indicates that connectionist models have been successfully applied to a variety of problems in cognition, including problems of atypical development, and that many investigators believe that connectionist models have considerable potential in their application to understanding mental retardation. Although there have been no previous applications of connectionist modeling to the issue of understanding the nature of strategy deficiencies and competencies in children with mental retardation, the models we have developed, which are described next, provide a direct demonstration of how connectionist modeling can be applied successfully to this issue (e.g., Anumolu, Bray, & Reilly, 1993; submitted; Reilly, Bray, Villa, & Anumolu, 1993)

Connectionist Models of External Memory Strategies
Connectionist models fall into two broad families (Rumelhart & McClelland, 1988). In local representation models, each node stands for a complex concept. In such models the representation of the sentence "Put the eraser on the table" would consist of the activation of the nodes for "eraser", "on" and "table" (with the other elements implicit). In these models, it is understood that each node represents a complex system of nodes not yet explicitly developed. Nevertheless, there may be a great deal to be gained by understanding the systemic properties of these networks before developing the details of how each of these sub-networks might be configured. These models have the drawback, however, of being less biologically plausible. We know, for example, that (with the exception of some cells for aspects of facial recognition) complex concepts are not localized in the human brain.

In distributed representation models, each node represents a feature of a stimulus which may or may not be readily identified. For example, a distributed representation of "eraser" might involve activation of the first and second node but not the third node of a system (e.g., 1,1,0). In this system there is no one node representing "eraser"; rather the representation is distributed across the first three nodes. If the first seven nodes of the system were used to represent sentences of a particular type, the sentence "Put the eraser on the table" might then be represented by the activation of a particular pattern of nodes (e.g. 1,1,0,1,0,0,1). In this sense, the representation of the sentence is distributed across seven different "on-off" nodes.

Distributed representation models are more biologically plausible in the sense that representations of complex concepts are distributed. No claim is made, however, that the distribution of activation in the brain is the same as the distribution in connectionist models. Nonetheless, distributed representation models allow the exploration of the implications of increasingly brain-like representation and processing. The disadvantage of this type of model is that the particular pattern of activations cannot always be readily identified with concepts unless the features represented by each node can be specified a priori (which in most cases, especially in large monolithic connectionist models, is not possible).

In our connectionist modeling, we have developed local representation models, distributed representation models, and models with both local representation and distributed representations. In general, each type of model represents a different level of theoretical explanation, local being more symbolic (systemic), and distributed being more "subsymbolic" (Smolensky, 1988). At this point, there are no clear guidelines for which level of model development will be the most informative for understanding the mechanisms of strategy development.

In this section, we provide a brief description of each of the models that we have developed. The family of models using local representation of concepts, listed in order of increasing complexity, includes the Sequencer, Sequencer/Associator, Novelty Bias, Components, and Components/Attention Bias models. The construction of these models has been modular in the sense that the models consist of distinct, interrelated components (Hrycej, 1992), 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.

Sequencer model.. The Sequencer Model (Anumolu, Reilly, & Bray, 1992a) is a connectionist model designed to represent knowledge of a sequence of events (see Sequencer Module, Figure 5, Top). All of our empirical research on external memory involves the presentation of a sequence of sentences such as "Put the eraser on the table; Put the pencil in front of the chair" (Bray, Saarnio, Borges, & Hawk, 1994), with 1 to 4 sentences presented per trial. One of the first steps in our program of developing connectionist models was to devise a network that would represent a sequence.

Sequencer/Associator model. This model (Anumolu, Reilly, & Bray, 1992b) begins with the sequencer module and adds an associative memory module (Figure 5, Top). The result is a modular connectionist network that learns and recalls representations of sentences like those used in our empirical work. Although the Sequencer and Sequencer/Associator models were important for representing sequences and associating these with representations of the object, targets, and relations used in the empirical research, these models do not include representations of external strategies. All of our subsequent models do include strategy representations and mechanisms related to changes in strategy use across simulated trials.

Novelty Bias model. This connectionist network (Anumolu, Bray, & Reilly, 1993) begins with the sequence representation and associative memory modules of the Sequencer/Associator model (Figure 5 , Top) and adds four additional modules representing (a) external strategies, (b) novelty bias, (c) accuracy feedback, and (d) trial initiation (Figure 5).

The external strategy module consists of three nodes, each with selective connections to the entities in the object, target, and relation pools of the associative memory module. This selective connectivity 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 encode objects, targets, and relations. All these connections are excitatory. This architecture means that when a strategy is activated, it raises the activation of the corresponding nodes. Thus when an object encoding strategy is activated, the activation value of the nodes of the object pool is raised, etc.

Novelty bias is a mechanism which represents the empirical observation that adults and children will try new strategies even though the strategies they have used previously are successful (e.g., Siegler & Jenkins, 1989). When a novelty bias unit is activated (Figure 5), the corresponding external memory strategy node receives an increase in its activation that is a random proportion of the weight of the connection between the novelty bias node and the external strategy node. Over simulated trials (epochs), however, there is a steady decay in the connection weights, meaning that the "bias" toward this once "novel" strategy is decreasing, making it more likely that the other strategies will successfully compete for execution.

The accuracy-feedback module is motivated by the computer simulation of Siegler and Shipley (in press) for early addition strategies. Each node has one connection to an "external teacher" which keeps track of whether recall was correct (this external teacher will be replaced in subsequent models by another connectionist module).

The model implements a "winner take all" mechanism in which the strategy with the highest activation value is retained, and the other activation values drop to zero, simulating the use of only one strategy per trial (which has been observed in our empirical research). This aspect of the simulation models the process of "mutual inhibition" similar to the "competitive learning" connectionist networks of Grossberg (1976) and Rumelhart and Zipser (1985) and is an important aspect of some types of neural processing in the brain.

The novelty bias model generates several simulated behaviors that are similar to those observed in our empirical studies of external memory strategies and in Siegler's studies of early addition strategies (Siegler & Jenkins, 1989). First, once a strategy "emerges", it is likely that it will not be used exclusively on subsequent trials, and the simulated child will use less sophisticated strategies such as object encoding after using an object-target encoding strategy as we observed in our empirical work and as Siegler observed in his research on addition strategies. Second, accuracy of recall for our simulated children increased with the sophistication of the strategy, and there were primacy and recency effects in recall as obtained in our empirical research.

Components model. The Components model (Anumolu, Bray, & Reilly, submitted) consists of the same modules as the Novelty Bias model (see Figure 6) with the deletion of the novelty bias module and the addition of a module representing tactics and a dimensional encoding mechanism. 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 motivated by theories which maintain that as children mature, they encode an increasing number of dimensions of tasks and events (e.g., Halford, 1993). In these theories, children begin by encoding information about only one dimension and move to encoding two and then three dimensions.

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 the external memory task used by Bray, Saarnio, Borges, and Hawk (1994), 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 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 signalling 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 and place the object on the yellow divider to represent the relation "on" or in front of the divider to represent "in front of "and thus devise an object-target-relation strategy.

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 tasks and attends to an increasing number of elements of the response chain necessary for making a response. This is quite different than 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 direct the child's attention to the relevant aspects of the task. This view is similar to the view of relational learning described by Soraci and Carlin (1992).

The dimensional encoding mechanism in the Components model consists of a trial initiation signal which triggers excitatory input from the simulation program to the accuracy nodes (called accuracy-attention nodes in the Components model) to start the strategy selection phase. The object, target, and relation accuracy-attention nodes receive an increasing amount of input depending on the trial number (epoch), corresponding to the child attending to the tactics involved in execution of the response. The magnitude of excitatory input depends on curvilinear monotonic functions herein called "T-curves" (to denote change across time). The T-curve controlling input to the object accuracy-attention nodes rises to asymptote faster than the other functions, meaning that in the early trials, there is more excitatory input to the object accuracy-attention units. The T-curve for controlling input to the accuracy-attention nodes for the targets rises to asymptote second, and that for relation rises to asymptote last. The T-curves thus represent increased attention by the simulated child to the tactics involved in making the required response as outlined in our conceptual framework.

Like the Novelty Bias model, the Components model generates several simulated behaviors that are similar to those observed in our empirical studies of external memory strategies and in Siegler's studies of early addition strategies (Siegler & Jenkins, 1989). First, in most simulation runs, the object, object-target, and object-target-relation strategies emerge in that order, as observed in our empirical research. Second, as in the Novelty Bias model, once a strategy "emerges", it is likely that it will not be used exclusively, and the simulated child will occasionally use less sophisticated strategies such as object encoding after using an object-target encoding strategy. Third, accuracy of recall for our simulated children increases with the sophistication of the strategy, and there are primacy and recency effects in recall.

Components/Attention Bias model. Connectionist models seem well suited for modeling systemic changes that occur gradually as in the shift from object encoding to object-target-relation encoding in the Components model. However, in most connectionist models of aspects of cognitive development (i.e., monolithic, multilayered backpropagation networks), it is difficult to model sudden, discrete changes such as instructions or verbal cues given by the experimenter (Schneider & Oliver, 1991). The Components/Attention Bias model overcomes this limitation with the inclusion of "attention bias units." The attention bias module consists of three attention bias nodes placed in the same location as the novelty bias nodes in the Novelty Bias model (Figure 5). The weights for the connections from the attention bias nodes to the strategy nodes represent the degree of attention placed on a particular strategy. All other aspects of the Components/Attention Bias model are the same as the Components model, making this model capable of sensitivity to slowly evolving strategies (as handled by the Components model) and also sensitive to sudden contextual changes such as the experimenter's instructions.

Strategy Abstractor model The architecture of the Strategy Abstractor model (Reilly, Bray, Villa, & Anumolu, 1993) is shown in Figure 7. The input module is a local representation of the sentence presented and has excitatory input to each node of the sequencer module, which is similar to the sequencer modules of the other models. New instance nodes are added, motivated in part by the construction of the Interactive Activation and Competition (IAC) model of McClelland and Rumelhart (1988). These nodes introduce a somewhat more distributed representation of the to-be-remembered sentences. Each instance node is connected to a unique combination of sequencer nodes and to nodes corresponding to the objects, targets, and relations. Thus, the instance nodes are distributed "multidimensional memory traces."

The tactics module (Figure 7, left side) is similar to the tactics module of the Components and Component/Attention Bias models including its selective connectivity to the nodes of the object, target, and relation pools. A major difference is that more tactics are represented (allowing a more detailed representation of our empirical data), and the pool of order nodes has been added to represent coding of order of presentation not tied directly to the sequencer; this has proven important in simulation of recall of sentences in the wrong order.

The Actions module (Figure 7, right side) represents the effector, translating the activation of the object, target, and relation information into a strategy and producing movements of simulated objects on a video monitor. There is no local representation of the strategies; the representation is distributed in the sense that the simulated action (e.g., picking up an object, moving it and arranging it in front of the target) is a result of a particular pattern of activation of the tactics nodes.

This model includes the accuracy feedback mechanism of the Novelty Bias, Components, and Components/Attention Bias models with excitatory connections to the nodes of the tactics module. However, the model was motivated, in large part, to incorporate additional mechanisms of strategy development not yet represented in the other connectionist models. Therefore, the model includes a "speed of execution" mechanism (see Table 1), similar to one in Siegler and Shipley's (in press) model of addition strategies. The longer it takes to execute a strategy, the less likely that the strategy will be used. Another mechanism, "subjective difficulty" (see Table 1), is represented by direct excitatory connections to the tactics module. This mechanism was motivated by Belmont and Mitchell's (1987) theory of strategy use which maintains that there is an "optimum" level of subjective task difficulty that must "challenge" the child. Tasks that are subjectively too "easy" or too "difficult" will result in little or no strategy use.

Simulation of Empirical Data. Bray, Reilly, Villa, Grupe, and Sadeh (1995) conducted a series of evaluation studies to determine whether simulated strategy frequencies generated by the Components/Attention Bias model correspond to the empirical observation of external memory strategies reported by Bray, Saarnio, Borges, and Hawk (1994). The participants in that empirical study were 7- and 11-year-old children without mental retardation and 11-year-old children with mild mental retardation. The simulations required decisions concerning the initial weights for the models and the initial values of the mechanisms of strategy development. Using the parameter values of our prior simulations as a point of departure, a "criterion run" fit the simulated mean frequency for each of the three strategies to the empirical mean frequency for the most developmentally advanced participants. In the empirical study, the most developmentally advanced group was that of the 11-year-old children without mental retardation. Thus, in the "criterion run", the simulated means for the three strategy types were fit to the empirical data from the 11-year-old children without mental retardation. In the empirical study there were 8 trials with 4 sentences each for a total of 32 sentences per child. In the simulation, each run generated 32 epochs on which one of the three strategies was or was not used. The mean proportion of epochs in which each strategy was used (across 12 runs, each run simulating the empirical data of one child) and the empirical mean number of sentences in which each strategy was used by the 11-year-old children without mental retardation are shown in Table 2. There was an excellent fit of the simulated data to the empirical data [P² (3)=.93, p> .92].

Table 2. Mean frequency of empirical and simulated strategy use in the control (prompt) condition for 11-year-old children without mental retardation ("Criterion Run")

	Empirical Data	Simulated Data
No observed strategy	2.25	0.75
Object strategy	0.83	1.08
Object-target strategy	15.25	17.25
Object-target-relation strategy	13.67	12.92

In the next step of the model evaluation, the criterion run constrained the weights used to represent differences among the other age groups. That is, in the course of the best-fit simulations of the oldest group of children without mental retardation, the weights changed as the frequency of the three types of strategies changed. We examined the simulation protocols to find epochs in the simulation that provided the best fit to the empirical results in the standard (control) condition of each experiment for each of the two other groups. For example, we found that epoch 11 of the criterion run provided the best fit to the empirical data for the 7-year-old children without mental retardation and epoch 14 provided the best fit for the 11-year-old children with mental retardation [P² (3) = 7.23, p> .12 for the 7-year-old children without mental retardation andP² (3) = 3.22, p> .52, for the 11-year-old children with mental retardation]. The simulated and empirical mean frequency of strategy use for each group are shown in Table 3. In effect, at an earlier phase of the criterion run, the model, which initially provided an excellent fit for the 11-year-old children without mental retardation, also simulated the empirical data from the less developmentally advanced groups but at earlier points (epochs) of the simulation.

Table 3. Mean frequency of empirical and simulated strategy use in the control (prompt) condition for 7-year-old children without mental retardation and 11-year-old children with mental retardation

	7-year-old children without mental retardation			11-year old children with mental retardation
	Empirical Data	Simulated Data		Empirical Data	Simulated Data
No observed strategy	0.36	3.73		1.00	2.55
Object strategy	3.45	3.27		0.18	1.73
Object-target strategy	28.18	21.45		27.55	22.00
Object-target-relation strategy	0.00	3.55		3.27	5.73

In the next phase of the simulations, the experimental (instruction) condition was simulated and fit to the empirical data. The weights of the model for the best-fit epoch represent the differences and similarities among the three groups. Thus, for the most developmentally advanced children, the weights of the model in the last epoch of the "criterion run" served as a representation of their strategy competence in the standard (control) condition. The weights at epoch 11 represented the developmental and intellectual competence of the younger children without mental retardation and the weights at epoch 14 repesented the competence of the children with mental retardation under the simulated standard (control) condition.

To begin the simulation of the experimental (instruction) condition, the initial weights used in the simulation of differences due to the experimental conditions were those obtained for the standard (control) condition for each age group. The simulation included the incremental manipulation of one mechanism expected to influence the strategy use (i.e., the attention bias mechanism in the Components/Attention Bias model). This was implemented by manipulating the T-curve for the "relation" so that it was given a steeper slope and a higher asymptote than in the "criterion run." This parameter manipulation represents the experimenter's training with the object-target-relation strategy with the assumption that the training resulted in increased attention to coding the relation. The simulated and empirical means are shown in Table 4. In this empirical study, the direct instruction with the object-target-relation coding strategy resulted in no differences among the groups. In our simulation, one theoretically rationalized parameter was manipulated to simulate the empirical results for the experimental (instruction) condition [P² (3)=.00, p= 1.00 for the 7-year-old children without mental retardation and,P² (3)=0.003, p> .99 for the 11-year-old children without mental retardation, andP² (3)=0.23, p> .99 for the 11-year-old children with mental retardation].

Table 4. Mean frequency of empirical and simulated strategy use for the experimental (instruction) condition

	7-year-old children without mental retardation		11-year old children without mental retardation		11-year old children with mental retardation
	Empirical Data	Simulated Data	Empirical Data	Simulated Data	Empirical Data	Simulated Data
No observed strategy	0.00	0.00	0.00	0.00	0.09	0.00
Object strategy	0.00	0.00	0.00	0.00	0.09	0.00
Object-target strategy	0.00	0.00	1.33	1.25	0.55	0.82
Object-target-relation strategy	32.00	32.00	30.67	30.75	31.27	31.18

These simulation results are important for several reasons. First, they demonstrate 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 our approach is able to model differences in experimental conditions with a minimum of parameter manipulation. That is, the simulations of the experimental conditions were constrained by the parameters obtained during the simulations of the control conditions, which were, in turn, constrained by the empirical data from only one of the three groups (the most developmentally advanced children). This type of feasibility demonstration is encouraging, and the use of this protocol will be explored in further research.

Mechanisms of Strategy Development. Across our four connectionist models (Novelty Bias, Components, Components/Attention Bias, and Strategy Abstractor models) we have implemented six different mechanisms of strategy development that may provide a clearer understanding of the nature of strategy development in individuals with and without mental retardation (see Table 1). We are currently designing simulation studies to explore further the relative contribution of these mechanisms to strategy evolution. For example, using the parameters obtained by Bray, Reilly, Villa, Grupe, and Sadeh (1995) in the simulations of the empirical data of Bray, Saarnio, Borges and Hawk (1994), we will be able to manipulate each of these mechanisms across a wide range of values and observe their effects on strategy use and accuracy of recall.

For example, all four models include the accuracy feedback mechanism. Each model allows feedback from an external teacher (which may be considered a simulation of input from another connectionist module). We assume that strategy evolution is dependent, in part, on this mechanism and therefore the accuracy of this feedback would be important for simulated strategy use. One of the simulations will investigate this assumption by varying the level of noise introduced into the feedback; the percentage of error in the feedback would be varied from 0.0 (as in the simulations to date) to 1.0 (feedback that correct responses are wrong and incorrect responses are right) in increments of 0.1. We expect that this mechanism will have a powerful effect on simulated strategy use and will lead to future empirical research on this issue. A similar simulation/empirical research strategy will be used for the other five mechanisms in our models.

Conclusions
Our conceptual framework leads us to believe that a more balanced treatment of strategy deficiencies and competencies will lead to 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 from parsing the response requirements into tactics (or parsing the tactics of a previously used strategy) and assembling the tactics into a strategy results in a deeper level of processing than that provided by direct instruction. The exciting implication of this is that if 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 with generalization of strategies when trained directly. However, Bray, Fletcher, Huffman, Hawk, and Ward (1994) found that children with mental retardation devised 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 view is that the future of research on strategy use in individuals with mental retardation will begin to focus more on strategy competencies rather than exclusively on strategy deficiencies. This will be a welcome change since the deficiency approach has not led to the development of a theoretical framework for understanding the differences between individuals with and without mental retardation. Additionally, the connectionist modeling approach described here can be expected to 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. Whereas 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 educational training programs that are tailored to the strengths of individuals with mental retardation and which aid in the remediation of their deficiencies.

References

Anderson, J. A., Pellionisz, A., & Rosenfeld, E. (1990). Neurocomputing 2. Cambridge, MA: MIT Press.

Anderson, J. A., & Rosenfeld, E. (1988). Neurocomputing: Foundations of Research. Cambridge, MA: MIT Press.

Anderson, J. A., Spoehr, K. T., & Bennett, D. J. (in press) A study in numerical perversity: Teaching arithmetic to a neural network. In D. D. Levine (Ed.), Neural networks for knowledge representation and inference. Hillsdale, NJ: Lawrence Erlbaum.

Anumolu, V., Bray, N. W., & Reilly, K. D. (submitted). Neural network models of strategy development in children. Neural Networks.

Anumolu, V., Bray, N. W., & Reilly, K. D. (1993). A neural network model of strategy selection and evolution. In World Congress on Neural Networks - '93, pp. 1528-1535.

Anumolu, V., Reilly, K. D., & Bray, N. W. (May, 1992a). Neural networks for learning, recognition, and control. Poster presented at A Research Conference at the Wang Institute of Boston University, Boston, MA.

Anumolu, V., Reilly, K. D., & Bray, N. W. (1992b). A hybrid neural network system with serial learning and associative components. In Proceedings of Workshop on Neural Networks and International Simulation Technology Conference, Society for Computer Simulation, San Diego, CA, pp. 455-462.

Baillargeon, R. (1994). How do infants learn about the physical world? Current Directions in Psychological Science, 3, 133-140.

Baillargeon, R., DeVos, J., & Graber, M. (1989). Location memory in 8-month-old infants in a non-search AB task. Cognitive Development, 4, 345-368.

Baker-Ward, L., Ornstein, P.A. & Holden, D.J. (1984). The expression of memorization in early childhood. Journal of Experimental Child Psychology, 37, 555-575.

Baldi, P, & Hornik, K. (1989). Neural networks and principal component analysis: Learning from examples without local minima. Neural Networks, 2, 53-58.

Bechtel, W., & Abrahamsen, A. (1991). Connectionism and the mind. Cambridge, MA: Blackwell.

Belmont, J. M., & Butterfield, E. C. (1971). Learning strategies as determinants of memory deficiencies. Cognitive Psychology, 2, 411­420.

Belmont, J. M., Ferretti, R. P., & Mitchell, D. W. (1982). Memorizing: A test of untrained retarded children's problem solving. American Journal of Mental Deficiency, 87, 197-210.

Belmont, J. M., & Mitchell, D. W. (1987). The general strategies hypothesis as applied to cognitive theory in mental retardation. Intelligence, 11, 91-105.

Borkowski, J. G., Carr, M., & Pressley, M. (1987). "Spontaneous" strategy use: Perspectives from metacognitive theory. Intelligence, 11, 61-75.

Borkowski, J. G., & Kurtz, E. B. (1987). Metacognition and executive control. In J. G. Borkowski and J. D. Day (Eds.), Cognition in special children: Comparative approached to retardation, learning disabilities, and giftedness. Norwood, NJ: Ablex Publishing.

Borys, S. V., & Spitz, H. H. (1976). Short­term retention in retarded adolescents as a function of load, delay, and interpolated activity. Journal of Psychology, 94, 207­216.

Bray, N. W. (1987). A symposium: Why are the mentally retarded strategically deficient? Intelligence, 11, 45-48. Bray, N. W., Fletcher, K. L. (submitted). Developmental and intellectual differences in the relation of verbal self-report and strategy use. Developmental Psychology.

Bray, N. W., Fletcher, K. L., Huffman, L. F., Hawk. T. M., & Ward, J. L. (April, 1994). Developmental differences in the use of models and verbal prompts in support of external strategies. Paper presented at the Conference on Human Development, Pittsburgh, PA.

Bray, N. W., Fletcher, K. L., & Turner, L. A. (in press). Cognitive competencies and strategy use in individuals with mild retardation. In W. E. MacLean Jr. (ed.) Handbook of Mental Deficiency, Psychological Theory and Research (3rd ed.). Hillsdale, NJ: Lawrence Erlbaum.

Bray, N. W., Justice, E. M., & Simon, D. L. (1982). The sufficient conditions for directed forgetting in normal and educable mentally retarded adolescents. Intelligence, 2, 153-167.

Bray, N. W., Huffman, L. F., Ward, J. L., & Hawk, T, M. (March, 1994). A microgenetic study of addition strategies in young children with and without mental retardation. Paper presented at Gatlinburg Conference on Research and Theory in Mental Retardation and Developmental Disabilities, Gatlinburg, TN.

Bray, N. W, & Puleo, S. G. (1986). Memory performance and children's conceptualizations of an experiment. Unpublished manuscript, University of Alabama at Birmingham.

., Bray, N. W., Reilly, K. D., Villa, M. A., Grupe, L. A., & Sadeh, B. (April, 1995). Hybrid neural network models of strategy development. Paper presented at Society for Research in Child Development, Indianapolis, IN.

Bray, N, W., Saarnio, D, Borges, J. M., & Hawk, L. W. (1994). Intellectual and developmental differences in external memory strategies. American Journal on Mental Retardation, 99, 19-31

Bray, N. W., & Turner, L. A. (1986). The rehearsal deficit hypothesis. In N. R. Ellis & N. W. Bray (Eds.), International review of research in mental retardation (Vol. 14, pp. 47-71). New York: Academic Press.

Bray, N. W., & Turner, L. A. (1987). Production anomalies (not strategic deficiencies) in mentally retarded individuals. Intelligence, 11, 49-60.

Brown, A. L. (1974). The role of strategic behavior in retardate memory. In N. R. Ellis (Ed.), International review of research in mental retardation (Vol. 7). New York: Academic Press.

Brown, A. L., Bransford, J. D., Ferrara, R. A., & Campione, J. C. (1983). Learning, remembering and understanding. In J. H. Flavell, & E. M. Markman (Eds.), Handbook of child psychology (4th ed., pp. 77­166). New York: Wiley. Bryant, P. E., & Trabasso, T. R. (1971). Transitive inferences and memory in young children. Nature, 232, 456-458.

Campbell, J. I. D., & Oliphant, M. (1992). Representation and retrieval of arithmetic facts: A network-interface model and simulation. In J. I. D. Campbell, (Ed.), The nature of and origins of mathematical skill (pp. 331-361). Amsterdam, Netherlands: North-Holland.

Campione, J. C., & Brown, A. L. (1977). Memory and metamemory development in educable retarded children. In R. V. Kail, Jr., & J. W. Hagen (Eds.), Perspectives on the development of memory and cognition (pp. 367-406). Hillsdale, NJ: Lawrence Erlbaum.

Carpenter, G. A. (1991). Neural network models for pattern recognition and associative memory. In G. A. Carpenter & S. Grossberg, S. (Eds.), Pattern recognition by self-organizing neural networks (pp. 2-33). Cambridge, MA: MIT Press. Carpenter, G. A., & Grossberg, S. (1991). Pattern recognition by self-organizing neural networks. Cambridge, MA: MIT Press.

Chi , M. T. H. (1988). Children's lack of access and knowledge reorganization: An example from the concept of animism. In F. E. Weinert & M. Perlmutter (Eds.), Memory Development: Universal changes and individual differences. Hillsdale, NJ: Lawrence Erlbaum.

Churchland, P. S., & Sejnowski, T. J. (1992). The computational brain. Cambridge, MA: MIT Press Cleeremans, A., & McClelland, J. L. (1991). Learning the structure of event sequences. Journal of Experimental Psychology: General, 120, 235-253.

Cohen, I. R. (In press). An artificial neural network analogue of learning in Autism. Biological Psychiatry Cohen, I. R., Sudhalter, V., Landon-Jimenez, D., & Keogh, M. (1993). A neural network approach to the classification of autism. Journal of Autism and Developmental Disorders, 23, 443-466.

Cole, M., Gay, J., Glick, J., & Sharp, D. (1971). The cultural context of learning and thinking. New York: Basic. Corsini, D. A., Pick, A. D., & Flavell, J. H. (1968). Production of nonverbal mediators in young children. Child Development, 39, 53-58.

DeLoache, J.S., Cassidy, D.J., & Brown, A.L. (1985). Precursors of mnemonic strategies in very young children's memory. Child Development, 56, 125-137.

Ellis, N. R. (1963). The stimulus trace and behavioral inadequacy. In N. R. Ellis (Ed.), Handbook of mental deficiency (pp. 134-158). New York: McGraw-Hill.

Ellis, N. R. (1970). Memory processes in retardates and normals. In N. R. Ellis (Ed.), International review of research in mental retardation (Vol. 4, pp. 1-32). New York: Academic Press.

Ellis, N. R. & Dulaney, C. L. (1991). Further evidence for cognitive inertia of persons with mental retardation. American Journal on Mental Retardation, 95, 613-621.

Ellis, N. R., Katz, E., & Williams, J. E. (1987). Developmental aspects of memory for spatial location. Journal of Experimental Child Psychology, 44, 401­412.

Ellis, N. R., Meador, D. M., & Bodfish, J. W. (1985). Differences in intelligence and automatic memory processes. Intelligence, 9, 265­273.

Ellis, N. R., Palmer, R. L., & Reeves, C. L. (1988). Developmental and intellectual differences in frequency processing. Developmental Psychology, 24, 38­45.

Ellis, N. R., Woodley-Zanthos, P., Dulaney, C. L., & Palmer, R. L. (1989). Automatic-effortful processing and cognitive inertia in persons with mental retardation. American Journal on Mental Retardation, 93, 412-423.

Farah, M. J., O'Reilly, R. C., & Vecera, S. P. (1993). Dissociated overt and covert recognition as an emergent property of a lesioned neural network. Psychological Review, 100, 571-588.

Farah, M. J., & McClelland. (1991). A computational model of semantic memory impairment: Modality specificity and emergent category specificity. Journal of Experimental Psychology: General, 120, 339-357.

Ferretti, R. P., & Cavalier, A. R. (1991). Constraints on the problem solving of persons with mental retardation. In N. W. Bray (Ed.), International review of research in mental retardation (Vol. 17, pp. 153­192). San Diego, CA: Academic Press. Fisher, M. A. & Zeaman, D. (1973). An attention-retention theory of retardate discrimination learning. International review of research in mental retardation (Vol. 6, pp. 171-251). New York: Academic Press.

Flavell, J. H. (1970). Developmental studies of mediated memory. Advances in child development and behavior (Vol. 5, pp. 181-211). New York: Academic Press.

Flavell, J. H., Beach, D. H., & Chinsky, J. M. (1966). Spontaneous verbal rehearsal in a memory task as a function of age. Child Development, 37, 283-299.

Fletcher, K. L. & Bray, N. W. (submitted). External memory strategy use in preschool children. Merrill-Palmer Quarterly. Fletcher, K. L. & Bray, N. W. (1995). External and verbal strategies in children with and without mild mental retardation. American Journal on Mental Retardation, 99, 363-375. Fox, R., & Oross, S, III. (1992). Perceptual deficits in mildly mentally retarded adults. In N. W. Bray (Ed.), International review of research in mental retardation (Vol. 18, pp. 1-25). New York: Academic Press.

Frederickson, N. (1986). Toward a broader conception of human intelligence. In R. J. Sternberg & R. K. Wagner (Eds.), Practical intelligence: Nature and origins of competence in the everyday world (pp. 84-118). New York: Cambridge University Press.

Gelman, R. (1969). Conservation acquisition: A problem of learning to attend to relevant attributes. Journal of Experimental Child Psychology, 7, 167-187.

Grossberg, S. (1976). Adaptive pattern classification and universal recording: Part I. Parallel development and coding of neural feature detectors. Biological Cybernetics, 23, 121-134.

Grossberg, S. (1991). Neural pattern discrimination. In G. A. Carpenter & S. Grossberg, S. (Eds.), Pattern recognition by self-organizing neural networks (pp. 113-156). Cambridge, MA: MIT Press.

Guttentag, R. E. (1985). The mental effort requirements of cumulative rehearsal: A developmental study. Journal of Experimental Child Psychology, 37, 92-106.

Halford, G. S. (1993). Children's understanding: The development of mental models. Hillsdale, NJ: Lawrence Erlbaum. Hinton, G. E., & Shallice, T. (1991). Lesioning an attractor network: Investigations of acquired Dyslexia. Psychological Review, 98, 74-95.

Hrycej, T. (1992). Modular learning in neural networks: a modularized approach to neural network classification. New York: Wiley.

Intons-Peterson, M. J., & Fournier, J. (1986). External and internal memory aids: When and how often do we use them? Journal of Experimental Psychology: General, 115, 267-280.

Johnson-Laird, P. N. (1983). Mental Models. Cambridge, MA: Harvard University Press.

Kruschke, J. K. (1992). ALCOVE: An exemplar-based connectionist model of category learning. Psychological Review, 99, 22-44.

Lave, J., Murtaugh, M., & de la Rocha, O. (1984). The dialectic of arithmetic in grocery shopping. In B. Rogoff & J. Lave (Eds.), Everyday cognition (pp. 67-94). Cambridge, MA: Harvard University Press.

Levine, D. S. (1989). Neural network principles for theoretical psychology. Behavior Research Methods, Instruments, & Computers, 21, 213-224.

Levine, D. S. (1991). Introduction to neural & cognitive modeling. Hillsdale: Lawrence Erlbaum.

Levine, D. S., & Prueitt, P. S. (1989). Modeling some effects of frontal lobe damage - novelty and perseveration. Neural Networks, 2, 103-116.

Lisberger, S. G., & Sejnowski, T. J. (1992). Motor learning in a recurrent network model based on the vestibulo-ocular reflex. Nature, 360, 159-161.

Mandler, J. M. (1983). Representation. In J. H. Flavell & E. M. Markman (Eds.), Handbook of child psychology, Vol. 3: Cognitive development (pp. 420-494). New York: Wiley.

McCartney, J. R. (1987). Mentally retarded and nonretarded subjects' long­term recognition memory. American Journal of Mental Retardation, 92, 312­317.

McClelland, J. L. (1989). Parallel distributed processing: Implications for cognition and development. In R. G. M. Morris (Ed.), Parallel distributed processing: Implications for psychology and neurobiology (pp. 8-45). New York: Oxford University Press. McClelland, J. L., & Jenkins, E. (1991). Nature, nurture, and connections: Implications of connectionist models for cognitive development. In K. VanLehn (Ed.), Architectures for Intelligence (pp. 41-73). Hillsdale, NJ: Lawrence Erlbaum. McClelland & Rumelhart (1988). Exploration in parallel distributed processing: A handbook of models, programs, and exercises. Cambridge, MA: MIT Press.

McCloskey, M., & Lindemann, M. A. (1992). MATHNET: Preliminary results from a distributed model of arithmetic fact retrieval. In J. I. D. Campbell, (Ed.), The nature of and origins of mathematical skill (pp. 365-409). Amsterdam, Netherlands: North-Holland. Newell, A., Young, R., & Polk, T. (1993). The approach through symbols. In D. Broadbent (Ed.), The simulation of human intelligence. Cambridge, MA: Blackwell.

Newman, D., Griffen, P., & Cole, M. (1984). Social constraints in laboratory and classroom tasks. In B. Rogoff & J. Lave (Eds.), Everyday cognition (pp. 170-193). Cambridge, MA: Harvard University Press.

Ornstein, P. A., Medlin, R. G., Stone, B. P., & Naus, M. J. (1985). Retrieving for rehearsal: An analysis of active rehearsal in children's memory. Developmental Psychology, 21, 633-641.

Patterson, K., Seidenberg, M. S., & McClelland, J. L. (1989). Connections and disconnections: Acquired dyslexia in a computational model of reading processes. In G. M. Morris (Ed.), Parallel distributed processing: Implications for psychology and neurobiology (pp. 131-181). Oxford: Oxford University Press.

Peterson, L. R., & Peterson, M. J. (1959) Short-term relation of individual verbal items. Journal of Experimental psychology, 58, 193-198.

Petro, S. J., Herrmann, D., Burrows, D., Moore, C. M. (1991). Usefulness of commercial memory aids as a function of age. International Journal of Human Development, 33, 295-209.

Plunkett, K., & Marchman, V. (1991). U-shaped learning and frequency effects in a multi-layered perceptron: Implications for child language acquisition. Cognition, 38, 1-60.

Plunkett, K., & Sinha, C. (1992). Connectionism and developmental theory. British Journal of Developmental Psychology, 10, 209-254.

Pouget, A., Fisher, S. A., & Sejnowski, T. J. (1993). Egocentric spatial representation in early vision. Journal of Cognitive Neuroscience, 5, 150-161.

Reilly, K. D., Bray, N. W., Villa, M. F., & Anumolu, V. (1993). Neural network and hybrid modeling of external memory strategy acquisition in humans and intelligent robots. In SIMTEC 1993 Proceedings.

Rogoff, B. (1981). Integrating context and cognitive development. In M. E. Lamb & A. L. Brown (Eds.), Advances in developmental psychology (Vol. 2, pp. 125-170). Hillsdale, NJ: Lawrence Erlbaum.

Rogoff, B. (1990). Apprenticeship in Thinking: Cognitive Development in Social Contexts. Oxford: Oxford University Press. Rumelhart, D. E., & McClelland, J L., Eds. (1986). On learning the past tenses of English verbs. In J. L. McClelland & D. E. Rumelhart & the PDP research group, (Eds.), Parallel distributed processing: Explorations in the microstructure of condition. Volume 2. Cambridge, MA: MIT Press.

Rumelhart, D. E., & McClelland, J L., Eds. (1987). Learning the past tenses of English verbs: Implicit rules or parallel distributed processing. In B. McWhinney (Ed.), Mechanisms of language acquisition (pp. 195-248). Hillsdale, NJ: Lawrence Erlbaum. Rumelhart, D. E., & McClelland, J. L. (1988). Parallel distributed processing: Explorations in the Microstructure of Cognition. Volume 1: Foundations. Cambridge, MA: MIT Press.

Rumelhart, D. E., & Zipser, D. (1985). Feature discovery by competitive learning. Cognitive Science, 9, 75-112. Schneider, W. & Oliver, W. L. (1991). An instructable connectionist/control architecture: Using rule-based instructions to accomplish connectionist learning in a human time scale. In K. VanLehn (Ed.), Architectures for intelligence: The 22nd Carnegie Mellon symposium on cognition (pp. 113-146). Hillsdale, NJ: Lawrence Erlbaum.

Seidenberg, M. S. (1993). Connectionist models and cognitive theory. Psychological Science, 4, 228-235. Seidenberg, M. S., & McClelland, J. L. (1989). A distributed, developmental model of word recognition and naming. Psychological Review, 96, 523-568.

Sejnowski, T. J. (1989). Skeleton filters in the brain. In G. E. Hinton & J. A. Anderson (Eds.), Parallel Models of Associative Memory (pp. 223-246). Hillsdale, NJ: Lawrence Erlbaum.

Sejnowski, T. J., Koch, C., & Churchland, P. S. (1990). Computational Neuroscience. In S. J. Hanson & C. R. Olsen (Eds.), Connectionist modeling and brain functioning: The developing interface. Neural Network Modeling and Connectionism (pp. 5-35). Cambridge, MA: MIT Press.

Sejnowski, T. J., & Rosenberg, C. R. (1988). Learning and representation in connectionist models. In M. S. Gazzaniga (Ed.), Perspectives in Memory Research (pp. 135-178). Cambridge, MA: MIT Press.

Sejnowski, T. J., & Tesauro, G. (1990). Building network learning algorithms for Hebbian synapses. In J. L. McGaugh, Weinberger, N. W. & G. Lynch (Eds.), Brain Organization and memory: Cells, systems, and circuits (pp. 338-355). New York: Oxford University Press.

Shanks, D. R. (1991). Categorization by a connectionist network. Journal of Experimental Psychology: Learning, Memory, and Cognition, 17, 433-443.

Siegler, R. S. (1991). Children's thinking. Englewood Cliffs, NJ: Prentice Hall.

Siegler, R. S., & Crowley, K. (1994). Constraints on learning in non-privileged domains. Cognitive Psychology, 27, 194-226.

Siegler, R. S., & Jenkins, E. (1989). How children discover new strategies. Hillsdale, NJ: Lawrence Erlbaum. Siegler, R. S. & Shipley, C. (in press). Variation, selection, and cognitive change. In G. Halford and T. Simon (Eds.), Developing cognitive competence: New approaches to process modeling. Hillsdale, NJ: Lawrence Erlbaum.

Smith, L. B. (1993). The concept of same. Advances in Child Development and Behavior (Vol. 24, pp. 216-251). New York: Academic Press.

Smolensky, P. (1988). On proper treatment of connectionism. Behavioral and Brain Sciences, 11, 1-74. Soraci, D. A., & Carlin, M. T. (1992). Stimulus organization and relational learning. In N. W. Bray (Ed.), International review of research in mental retardation (Vol. 18, pp. 29-53). New York: Academic Press.

Sperber, R. D., Ragain, R. D., & McCauley, C. (1976). Reassessment of category knowledge in retarded individuals. American Journal of Mental Deficiency, 81, 227­234.

Spitz, H. H. (1973). The role of input organization in the learning and memory of mental retardates. In N. R. Ellis (Ed.), International review of research in mental retardation (Vol. 6, pp. 149-168). New York: Academic Press. Spitz, H. H. (1979). Beyond field theory in the study of mental deficiency. In N. R. Ellis (Ed.), Handbook of mental deficiency, psychological theory and research (2nd ed., pp. 121-141). Hillsdale, NJ: Lawrence Erlbaum.

Spitz, H. H. (1988). Mental retardation as a thinking disorder: The rationalist alternative to empiricism. In N. W. Bray (Ed.), International review of research in mental retardation (Vol. 15, pp. 1-32). New York: Academic Press. Spitz, H. H., & Webreck, C. A. (1972). Effects of spontaneous vs. externally-cued learning on the permanent storage of a schema by retardates. American Journal of Mental Deficiency, 77, 163-168.

Sternberg, R. J. (1990). Metaphors of mind: Conceptions of the nature of intelligence. New York: Cambridge University Press. Sternberg, R. J., & Spear, L. C. (1985). A triachic theory of mental retardation. In N. R. Ellis & N. W. Bray (Eds.), International review of research in mental retardation (Vol. 13, pp. 301-326). New York: Academic Press. Turner, L. A., & Bray, N. W. (1985). Spontaneous rehearsal in mildly retarded children and adolescents. American Journal of Mental Deficiency, 90, 57-63.

Turnure, J. E. (1991). Long­term memory and mental retardation. In N. W. Bray (Ed.), International review of research in mental retardation (Vol. 17, pp. 193­217). San Diego: Academic Press.

Wasserman, P. D. (1989). Neural computing theory and practice. New York: Van Nostrand Reinhold. Wellman, H.M., Ritter, K., & Flavell, J.H. (1975). Deliberate memory behavior in the delayed reactions of very young children. Developmental Psychology, 11, 780-787.

Winters, J. J., Jr. (1982). Proactive inhibition in retarded persons: Factors influencing accumulation and release. In K. D. Gadow, & I. Bialer (Eds.), Advances in learning and behavioral disabilities: An annual compilation of theory and research (Vol. 1, pp. 151­190). Greenwich, CT: JAI Press.

Winters, J. J., Jr. (1985). Proactive inhibition in retarded persons: Some clues to short-term memory processing. In N. R. Ellis & N. W. Bray (Eds.), International review of research in mental retardation (Vol. 13, pp. 279-300). New York: Academic Press. Zeaman, D., & House, B. J. (1963). The role of attention in retardate discrimination learning. In N. R. Ellis (Ed.), Handbook of mental deficiency (pp. 159-223). New York: McGraw-Hill.

Zeaman, D., & House, B. J. (1979). A review of attention theory. In N. R. Ellis (Ed.), Handbook of mental deficiency (2nd ed., pp. 63-120). Hillsdale, NJ: Lawrence Erlbaum.

Footnote

¹According to Bechtel and Abrahamsen (1991) "connectionist networks are dynamical systems that are described by mathematical equations" (p. xiii), and which have "simple units which dynamically adapt to their environments" (p. 21). Connectionist models use a neural network metaphor without claiming that the architecture or the processes simulated are isomorphic with the structure and function of the brain (Rumelhart & McClelland, 1986). In this chapter we refer to our networks as connectionist networks, but this type of cognitive model is also frequently referred to as neural network models, and elsewhere we have used this latter term ourselves (e.g., Anumolu, Bray, & Reilly, 1993; Bray, Reilly, Villa, Grupe, & Sadeh, 1995). The term, connectionist, however, makes it clear that we are not modeling specific aspects of neural architecture whereas the term "neural network" may have that unintended connotation.