Formalization of tasks generation for complex of interactive web-tests on math

Abstract

The approach to the formalization of the generation of problem situations applicable to the development of tutoring programs consisting of many tasks is considered. The main errors arising during the software-based generation of parameters are specified. Mathematical modeling of parametrical generation algorithms examined by examples of tasks that make up complex tests on mathematics for secondary schools. The parametric generation method proposed in the article allows getting the large quantitative variations in task problem situations. Thereby, every learner will get a personal unique set of tasks. The structure and functionality of web-tests complex consisting of tasks generated via the proposed method are described. The subject of research in the article is the process of computer training in mathematics. The goal is to develop a method for task generation for mathematical disciplines. Tasks. Research and analysis of the set of mathematical problems. Parameterization of each task and development method and algorithms for automated generation parameters with the determination of incorrect combinations of parameters or problem situations that have no solution. Estimation of borders of admissible for approximate answers. Evaluation of the user solution of a single task and a sequence of tasks. The general objective of the work is to make the software product consisting of a sequence of mathematics tasks. The software should have an extended user interface for the graphical presentation of various problem situations in various mathematical topics. The program must be accessible via the Internet. The following results were obtained: developed methods and algorithms of task generation, which provide correct problem situations and unique parameter sets for each user; described the program complex structure and developed the software system of mathematical web-tests provides two levels of difficulty. Conclusion. The scientific novelty lies in the development of the method of task generation for interactive web tests on the mathematics and its computer implementation with the possibility of graphical representation of tasks and checking of tasks correctness.