This paper presents a new model of strategy development in young children. Traditional approaches to strategy development have (a) relied on top-down mechanisms, (b) have not incorporated situational influences, and (c) have not been biologically motivated. A neural network model is described which addresses the limitations of these traditional approaches. The development of the model was influenced by (a) a modular approach to neural networks, (b) the general theoretical framework of Siegler, and (c) empirical research on external representation and memory. Empirically, in situations requiring memory for the arrangement of objects, younger children frequently use simple external memory strategies (e.g. pointing at objects) where older children tend toward more advanced strategies (e.g., inter-object orienting) to aid remembering. Computer simulations with the model show that accuracy history can account for selection and evolution of strategies from simple to advanced and demonstrate behavioral evolution using selective encoding mechanisms. The models suggest alternatives to the traditional approaches to strategy development and suggest that the strategy evolution mechanisms involved may apply to a variety of situations.

The purpose of this paper is to describe a new modular neural network model of memory strategies with an emphasis on how the use of strategies evolves during childhood. The ability to devise a strategy for remembering, i.e., "a goal-directed, non-obligatory procedure that is easy to execute and helps overcome the limitations of working memory" (Siegler & Jenkins, 1989), involves executing some procedure to increase the probability of remembering later. An example of an internally executed strategy is verbal rehearsal to memorize a list of digits. Examples of externally executed strategies include writing a reminder note or adding two numbers by counting on one's fingers.

Traditional theoretical approaches to memory strategies in the area of cognitive development have used "top-down" explanations in which changes in strategy use during development are attributed to changes in a relatively global process or structure. These approaches do not specify the mechanisms that underlie the development of strategies. For example, Sternberg (1985) explained developmental changes in strategies in terms of changes in "metacognitive knowledge" which includes knowledge about a given task, knowledge of environmental variables, and knowledge about existing strategies. According to Sternberg's theory, gradual changes in metacognition during childhood are responsible for developmental changes in the construction of strategies.

There are three important limitations to traditional approaches to strategy development in children. The first is that theoretical a construct such as metacognition, although rich in descriptive content, does not provide a precise theory of the processes that underlie the development of strategies, making it difficult to implement these theories in computer simulations. The second limitation is that the picture of strategy development provided by theories of metacognition is likely incomplete because such theories rely nearly exclusively on top-down processing. Bray, Fletcher, and Turner (in press) have argued that many aspects of strategy development can be understood in terms of "bottom-up" processing which include the influence of the physical characteristics of the particular situation and the degree of situational support provided for the child. The third limitation of traditional approaches is that they are not biologically motivated. The extant theories are relatively abstract psychological approaches that are not constrained in any way by what is known about the neurobiological underpinnings of cognition.

This paper is the initial report of a program of research to develop a theoretical framework that is more explicit than traditional theories of strategy development, one that can be implemented in computer simulations, and constrained, in part, by neurobiological structures and processes related to cognition. We build on Siegler and Jenkins' (1989) theory of strategy development and extend it to account for strategy development in children with mental retardation but depart from his simulations by developing neural net models rather than simulations relying on statistical regression models. In the connectionist vein, we believe that the representation and processing of knowledge in neural networks putatively comes closer to that in the brain than schemes such as statistical regression models used in Siegler's theory. Moreover, neural networks exhibit characteristics such as adaptability and generalization that are evident in the strategy evolution among humans and may be based on learning mechanisms that are biologically plausible (e.g., Hebbian learning rules).

The instruction-following task used by Bray, Saarnio, Borges, and Hawk (1994) serves as one of the bases of our program of research. This task was designed to be an analog of a situation in which a child must listen to sentences and carry them out (as in the assembly of an object or functioning as a student in a classroom). We focused on external strategies because of their importance in cognitive development and because they can be readily observed.

While listening to the sentences, children use a variety of strategies including pointing at or holding an object (object encoding), moving an object with orientation toward a target (object-target encoding) and placing an object in front of or on top of a wooden separator directly across from a target (object-target-relation encoding). The latter two external strategies may reduce the load on working memory and increase accuracy.

Bray et al. (1994) found that older children use object-target encoding and/or object-target-relation encoding strategies more frequently than younger children and mentally retarded children of the same age. The latter groups tend to use object encoding strategies most frequently and, to a lesser degree, object-target encoding strategies. In the broader context of our goals, we are interested primarily in identifying the cognitive mechanisms that may mediate intellectual and developmental differences in strategy use.

Our approach to neural network modeling is consistent with the modular approach of Hrycej (1992). He maintains that modeling problems in cognition may be more easily solved by modular neural networks than by monolithic neural networks. It seems, however, that, with few exceptions, Grossberg's work being perhaps the most notable, neural network models of cognitive development have been monolithic, with most of them relying on back propagation (e.g., Plunkett & Sinha, 1992). Our modeling is an exception to this trend, relying exclusively on the use of the Hebbian rule to associate elements within each module and to interface each module rather than a back-propagation algorithm for a single monolithic network.

The sequencer module (Figure 2, top) is designed to represent knowledge of a sequence of events. All of our empirical research on external memory with the instruction following task 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, et al., 1994), with 1 to 4 sentences presented per trial. One of the first steps in our program of developing neural network models was to devise a module that would represent a sequence.

The associative memory module (Figure 2, top) consists of a modular neural network that learns and recalls representations of sentences like those used in our empirical work.

The strategy module consists of three or more nodes, depending on the nature of the strategies simulated, 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.

The attention bias module consists of three or more attention bias nodes, depending on the nature of the situation to be simulated, which provide additional activation for each of the three strategy nodes (see Figure 2). The weights for the connections from the attention bias nodes to the strategy nodes represent the degree of attention placed on a particular strategy. Neural network models seem well suited for modeling systemic changes that occur gradually as in the shift from object encoding to object-target-relation encoding. However, in most neural network 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. The Generalized Components/Attention Bias Model overcomes this limitation with the inclusion of "attention bias units." This model is therefore capable of sensitivity to slowly evolving strategies and also sensitivity to sudden contextual changes such as the experimenter's instructions which may be implemented by activation of the attention bias units.

The tactics module represents our theoretical construction 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, the child begins by encoding information about only one dimension and moves to encoding two and then three dimensions.

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. 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.

The accuracy-attention module was motivated by the computer simulation of Siegler and Jenkins (1989) 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 eventually be replaced by another neural network module). Each node also receives input for the dimensional encoding mechanism.

The dimensional encoding mechanism in the components model consists of a trial initiation module which triggers excitatory input from the simulation program to the accuracy nodes 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 Generalized Components/Attention 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, 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.

Additionally, we conducted a series of evaluation studies to determine whether simulated strategy frequencies generated by the model correspond to the empirical observation of external memory strategies in the instruction following task reported by Bray, et al. (1994). The simulations required decisions concerning the initial weights for the models and the initial values of the mechanisms of strategy development. One of the contributions of this paper is the illustration of a simulation protocol for attacking this issue.

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 consisted 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 per session with 4 sentences each for a total of 32 sentences per child. In the simulation, each run generated 32 epochs in 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 1. There was an excellent fit of the simulated data to the empirical data [X² (3)=.93, p> .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 [² (3) = 7.23, p> .12], and epoch 14 provided the best fit for the 11-year-old children with mental retardation [² (3) = 3.22, p> .52]. 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. This suggest that the younger children, with and without mental retardation, are on the same developmental trajectory, only at an early, less developmentally advanced point, as compared to the older children without mental retardation. This is consistent with developmental theories of mental retardation that maintain that mentally retarded children proceed through the same sequence of cognitive development as children without mental retardation, but at a slower rate.

Traditional theoretical approaches to strategy development in children (a) have not been implemented in computer simulation models, (b) have relied on "top-down" explanations without including "bottom-up" mechanisms, and (c) have not been constrained by the neurological underpinning of cognition. In light of the original goal of going beyond these limitations of the traditional approaches by developing neural network models of strategy development, it is first important to note that the neural network model provided quite extensive simulations of the strategy behavior of children without relying on the statistical regression models used in the computer simulations of Siegler and Jenkins (1989).

Second, the successful simulation of strategy behavior was accomplished by relying on "bottom-up" mechanisms of strategy development (e.g., accuracy feedback and selective encoding) without relying on "top-down" mechanisms such as "metacognitive knowledge." Cognitive mechanisms of strategy development such as metacognitive knowledge , which, to our knowledge, have not yet been implemented in computer simulations, are relatively vague, especially when compared to the mechanisms and more explicit "bottom-up" architecture of our neural net models.

Third, the model presented here is more biologically motivated than traditional theories of strategy development. The architecture was inspired by the parallel distributed processes of the brain and the activation functions depend heavily on the Hebbian rule, as well as other aspects of neurobiological function. We recognize that like other connectionist models, ours can be refined and brought even closer to "wet mind" (Kosslyn & Koenig, 1995), but the initial results are encouraging of further development of this approach to the higher cognitive processes involved in strategy use in children.

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