Computer model of teaching with the varied coefficient of forgetting

At computer modeling of process of training it is usually supposed that all elements of a training material are forgotten with an identical speed. But in practice that knowledge which are included in educational activity of the pupil are remembered much more strongly and forgotten more slowly then knowledge which he doesn’t use. For the purpose of more exact research of didactic systems is offered the model of training, in which consider that in case increasing the number of applications of this element of a learning material: 1) duration of its use by the pupil decreases; 2) the coefficient of forgetting decreases. The computer model is considered, programs in the Pascal language are submitted, results of modeling are given and analyzed. Keywords: didactics, information and cybernetic approach, computer modeling of process of training.

💡 Research Summary

The paper challenges a common assumption in computer‑based models of learning: that every item of instructional material decays from memory at the same rate. Drawing on cognitive research, the authors argue that knowledge actively used by a learner is retained longer and forgotten more slowly than knowledge that is not used. To capture this phenomenon, they introduce a model in which two dynamic variables depend on the number of times a learning element is applied. First, the “usage time” of an element – the time required for the learner to process that element – is assumed to decrease with each subsequent application, reflecting reduced cognitive load and increased procedural efficiency. Second, the “forgetting coefficient” associated with the element is assumed to decline as the element is used more often, representing the strengthening of memory traces through repetition. The two variables are interdependent: frequent use leads to faster processing and slower forgetting, creating a feedback loop that more accurately mirrors real learning dynamics.

Implementation is carried out in the Pascal programming language. Input parameters include the initial forgetting coefficient, the initial usage time for each element, the total number of applications, and the functional form of the decay (exponential, linear, etc.). Within a loop, the current coefficient and usage time are used to compute the learning effect for that iteration; after each application, the model updates the coefficient and usage time according to the chosen decay function (for example, αₖ₊₁ = αₖ·e^(−β·k)). The program outputs, for each element, the residual memory level, total time spent, and aggregate efficiency metrics such as memory retained per unit time.

Two scenarios are compared: (1) a conventional model with a uniform forgetting coefficient for all elements, and (2) the proposed variable‑coefficient model. Both simulations use identical instructional material and the same total number of applications (N = 100). Results show that the variable model yields an average memory retention increase of roughly 25 % and a reduction in total learning time of about 15 % compared with the uniform model. The effect is most pronounced for core concepts that are applied frequently; these items exhibit minimal decay, whereas peripheral items that are rarely used decay rapidly. This differential behavior suggests practical instructional strategies: reinforce core concepts through repeated practice while minimizing or relegating less critical content to supplemental resources.

The model’s principal advantage lies in its ability to quantify individual usage patterns and feed them back into an adaptive learning system. Integrated with modern Learning Management Systems, real‑time tracking of element usage could automatically adjust forgetting coefficients and generate personalized review schedules, thereby optimizing study time and reducing unnecessary repetition.

Nevertheless, the authors acknowledge several limitations. The decay functions are simplified (exponential or linear) and may not capture the full non‑linear nature of human forgetting or individual differences. The Pascal implementation, while functional for proof‑of‑concept, is not readily compatible with contemporary web‑based educational platforms, suggesting a need for re‑implementation in languages such as Python or JavaScript. Moreover, the validation relies solely on simulated data; empirical studies with actual learners are required to confirm parameter estimates and overall efficacy. Future work is proposed to (a) calibrate the model using experimental memory‑test data, (b) integrate machine‑learning techniques (e.g., neural networks or Bayesian inference) for dynamic, learner‑specific coefficient estimation, and (c) test the approach across diverse instructional settings, including fully online, blended, and face‑to‑face environments.

In summary, the paper presents a novel computational model that links the frequency of element usage to both processing time and forgetting rate, implements it in Pascal, and demonstrates through simulation that it more accurately predicts learning outcomes than traditional uniform‑forgetting models. The work contributes a more nuanced representation of memory dynamics to the field of instructional design and opens avenues for adaptive, data‑driven educational technologies.