"Select Net" is a very simple "adaptive
store" designed especially to perform two functions for the Adaptive
Arithmetic Tutor and the Guidance/Assessment module:
Select Net "infers" what the student knows by adaptively adjusting an "activation value" that describes the student's recent response accuracy and speed.
Each "node" of Select Net corresponds to a single arithmetic fact. Thus each node responds to the student's performance with respect to one particular, corresponding fact.
Here is the "activation function" of Select Net:
The "activation" is a function of the "weighted input". For small inputs, the activation is uniformly low; for moderate inputs, the activation increases linearly as the input increases; for large inputs, the activation is constant and large.
The weighted input consists of a sum of terms that are set from the student's responses. The individual terms that comprise the weighted input represent recent averages of the student's response time, the error rate, and the cumulative time since the fact was last presented.
The poorer the student's knowledge of a given fact, the greater the corresponding S-Net node's activation.
Now, when the adaptive tutor asks Select Net to choose a fact for presentation, S-Net uses the activation of the nodes to perform a Roulette style selection. That is, the activations of all active neurons are placed in a line that is like the circumference of a Roulette wheel. Each "slot" represents a given arithmetic fact:
A random number "selector" is chosen (thrown, like the Roulette ball) that selects (lands in) one of the segments and the corresponding fact is added to the presentation list.
The less well a fact is known, the more frequently it will be selected for presentation.
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