Components of Didactic Complexity of Mathematical Problem and Their Evaluation

Abstract

The problem of estimating the didactic complexity of a mathematical task, which together with the solution is a multidimensional object characterized by a set of applied methods, is studied. The formation degree of the student's mathematical thinking is also determined by the set of mathematical methods he/she has mastered. Therefore, it is logical to consider the complexity of using certain methods of solution as the didactic complexity components of a particular task. It has been established that: 1) each mathematical problem can be characterized by a one-dimensional matrix, the components of which are proportional to the complexity of applying the corresponding method to solve it; 2) as the main methods for solving a mathematical problem, we can choose: methods of reading text, arithmetic calculations, algebraic transformations, method of the geometric constructions and operations with vectors use, combinatorial method, the trigonometric method, the method of logarithms and exponential functions, the differentiation and integration method, the operator method; 3) the complexity of applying a particular method in solving given task can be determined using a special computer program by counting the number of corresponding marker-terms and taking into account their complexity. The article evaluates the various components of the didactic complexity of 9 mathematical tasks on various topics and determines their general didactic complexity. It has been established that task 9 for calculating the divergence and rotor of a vector field is about 20 times more difficult than task 1 for solving a first-degree equation with one variable.