Research Problems in the School Mathematics Curriculum: Classification and Methodological Aspects of Teaching

Abstract

The article discusses the definition of the concept of a task. The understanding of the concept of a mathematical task
at the primary school level is discussed. Various definitions of the concept of a mathematical task by scientists are discussed. Our
position and the definition that we use when using the concept of a task are emphasized. The largest class of tasks considered at
school - text tasks - is discussed. From text tasks, the class of tasks that we attribute to research tasks is distinguished, these are:
non-standard, search, Olympiad, logical, mathematical games and puzzles, mathematical tasks with the content of intersubject
connections, mathematical tasks with the content of other subjects, tasks in which there is excess, missing, or containing
alternative conditions. The main components of the task structure are discussed: C–condition, R–theoretical or practical
justification, S–solution and T–conclusion, i.e. the requirement to find unknown components. Based on the introduced
notations, the tasks are classified according to their level of difficulty: 1) Standard. All components of the text task SRST are
known. This type of tasks is indispensable, as it allows students to learn the necessary concepts and also provides an opportunity
to assess how well they have mastered the studied educational material; 2) Educational. CRSx, CRxT, CxST, xRST, where x is an
unknown component. This type is the most common and has many variations in practice; 3) Research, non-standard, search and
Olympiad. They have two unknown components. Tasks of this type are of a higher level of difficulty and stimulate students'
thinking; 4) Olympiad tasks of very high complexity, in which three components are unknown.