Abstract:
One of the methods to stimulate middle school students' cognitive activity is their teacher's intellectual challenge at the lesson. The results of American teachers' analysis have shown that the majority of them avoid challenge during lessons [1]. Avoidance of challenge is pedagogically contagious, meaning that a teacher avoiding challenge transmits this disposition to his students. Teacher's ability
to pose a challenge while teaching mathematics is related to two factors: on the one hand, they are able to solve difficult problems during lessons and, on the other hand, they are capable of classifying tasks according to their level of difficulty. Two approaches have been used to reveal the term "difficult
tasks" these are the tasks requiring high cognitive demand and the tasks requiring high cognitive activity during their solution. Both approaches lead to similar classification of tasks: Tasks at Different Levels of Cognitive Demand [2] and Tasks at Different Levels of Achievement.
