Quantifying the Zone of Proximal Development in Digital Educational Systems

The concept of the zone of proximal development (ZPD) is a fundamental notion in the field of pedagogy. It is this concept of L. Vygotsky that is the scientific and methodological basis of adaptive learning. To enhance the efficiency of the educational process, it is essential to conduct it within the ZPD, which varies for each learner. Proficient educators possess the capability to ascertain the ZPD through direct interaction with their students. This opportunity is absent when utilizing e-learning platforms. At present, there is a scarcity of instances where the zone of proximal development has been quantitatively operationalized for the automatic generation of individual ZPDs in e-learning systems. This article introduces a mathematical model for the zone of proximal development, utilizing an exponential relationship, designed for the implementation of pedagogical measurement techniques under the umbrella of Item Response Theory. The structure of the framework was determined on the basis of logical and mathematical analysis of the ZPD concept, and its parameters have been established through statistical processing of the results of the pedagogical experiment conducted at universities in Russia and Ecuador. This model enables the individualization of assessment, evaluation, and instructional materials for learners in digital educational platforms, by computing their unique zone of proximal development based on their current academic ability level.