The performance model

In chapter 7, cognitive maps were introduced as representations of data. A cognitive map is a graph structure constructed from an individual s oral or written response. The map represents the main details of the response as nodes that are linked in a network, and it preserves the relationships among ideas - revealed in the responses - as links between nodes. An important feature of the cognitive map is the way in which linkages are determined Two nodes are connected by a link only if the verbal details represented by those nodes occur together in the verbal response. 

As demonstrated previously, cognitive maps are useful as a basis for the examination of group responses. Thus, as I described earlier, we can study similarities and differences among different groups by aggregating general characteristics of students maps. For example, cognitive maps can yield information about broad 

Part of this chapter is a revised description of the research first reported in Marshall 1993b and reproduced here with permission of Kluwer Academic Publishers. 

The purpose of this chapter is to describe in detail a simulation of the performance of the students who participated in the initial 

In a feedforward model, signals that will determine the eventual output are passed only in a forward direction from one layer of nodes to the next. Model activity initiates at the input level, and each input unit sends its signal forward to the layer immediately above it. Because activation can spread only forward and not laterally, two layers of units are needed to represent student knowledge. The first layer receives the activation signals from the input units. The second layer permits the student knowledge nodes to spread activation to each other. By having two layers of nodes, we circumvent the problem of mixing forward and lateral connections and preserve the feedforward nature of the model. 

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Determine the criterion for optimization and specify the objective function in terms of the above variables together with coefficients. This step provides the performance model (sometimes called the economic model when appropriate). 

Berube and Nair (1998) reached similar conclusions. They also found that the response model analysis was much more efficient than the performance model analysis. In addition, their work highlighted the importance of choosing noise factors that account for a substantial fraction of overall process variation. 

For parallel computers the performance model is a function of the parallel computer model. A general observation that is always useful to have in mind, is... 

With respect to the first question, we can look to a model that makes its selections randomly, with each of the five response options having equal probability of selection. We would expect such a model to match the students responses 20% of the time, simply by chance. The issue is whether the performance model does better than this random model in accounting for the students responses. We can see from Table 13.2 that the performance model exactly matched the students responses on 71% of the... 

Thus, we conclude that we would not arrive at similar results by chance. The performance model predicts student responses much better than either random model. Moreover, it can also be successfully extended beyond the original data from which its parameters were derived. Using the connection weights from the first experiment, the model gave satisfactory predictions for the second experiment as well. The structure of the model holds for additional students responding to additional test items. 

The performance model is extraordinarily simple. It qualifies as a connectionist model because it depends critically on the ways in which activation is passed from the input units through the knowledge nodes and on to the output units. No learning occurs in this model its function is to mimic the performance of students. It corresponds to the final form of a connectionist model that has stabilized its learning and is no longer modifying its connections. The... 

The inputs to the model are a set of 100 binary vectors nearly identical to the ones described in chapter 13 for the performance model. Each vector represents one arithmetic story problem, and the problem is coded according to the presence or absence of the general characteristics presented in Table 13.1. The difference between the input vectors of the learning model and those of the performance model is the inclusion here of coded information about the form of the question stated in the problem. In the performance model and in the empirical studies simulated by it, the items were complete stories and contained no questions. Both the learning model and the hybrid model of chapter 15 require problem statements as well as story information if we are to model the full problem-solving process. The two additional characteristics reflect whether the question focuses on what or how much. ... 

The performance model supplied guidelines for the learning model.1 The input units for the learning model are essentially the same ones required by the performance model, as are the output... 

In a single trial the layer of input units comprises one input vector. Each element of the input vector takes a value of 1 if the characteristic it represents is present in the current story problem or 0 if it is absent. The input vector to the learning model contains the original 25 elements used in the performance model plus an additional 2 elements, as noted earlier, to code the question, resulting in a 27-element vector. 

The first conclusion to be drawn is that the model learns to make the classifications. It takes many trials, but it does successfully classify the situations. A second conclusion is that it achieves a form that is very similar to that of the performance model. Recall that the performance model does not account for learning. Rather, it begins with a stable state for each student and carries out a set of decisions given that state. The learning model provides a plausible, but by no means unique, explanation of how the stable state of the performance model could be achieved. 

In conclusion, I want to repeat that this is not an optimal model with optimal parameters. Its function was to verify that the classification was possible and that learning could result in something that resembles the performance model. I am not arguing that individuals reach the performance model point via this route. They almost certainly do not. We do not present individuals with thousands of problems and expect them to learn the important features. Most individuals learn primarily about such things from direct instruction. However, they also learn by repeated observation, just as the model does, and the learning model is a first step in examining knowledge acquired in this way. 

Task 6 Validate and optimize the performance model so that the performance characteristics of most any chemical hydride or carbon storage media can be viewed independently of scale. 

The performance model reflects and is limited by the current state-of-the-art in algae growth. Several important, basic relationships have yet to be quantitied. As a result, several parameters must be introduced as input data. For example, the level of wastewater treatment is only partially predictable by the process options selected. Nutrient removal efficiencies must be input for each different level of treatment. Similarly, the solar conversion efficiency cannot be predicted by the model and must be input. Finally, algae digestion is essentially a "black box" operation at this point. This fact prevents a quantitative assessment of nitrogen and phosphorus mass balances in the system. Within these limitations, equations were developed to predict (1) the flows and (2) the required equipment sizes for the various process operations. 

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