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 [3].

Intellectual challenge in solving difficult mathematics tasks during lessons is connected with implementation of teacher’s creative and exploratory skills. To prove this thesis, 25 mathematics teachers from Kazan, Russian Federation, took part in the experiment. At the first stage, there was a questionnaire survey for teachers. Teachers’ ability to understand the levels of cognitive demand in solving mathematical tasks was analyzed. Their capacity to model a list of tasks on one theme at different levels was researched. Next, there was the analysis of audio recordings of the lessons and the interviews with teachers. The results of this research have shown that even though the teachers have a high level of content and pedagogical knowledge they are not ready to accept challenge. According to theoretical criteria, only two teachers out of 25 were diagnosed to have posed a challenge to students. Other teachers’ lessons demonstrated that their mode of behaviors, chosen teaching material and atmosphere at the lessons created poor conditions for its implementation. The reasons of this phenomenon are being analyzed. Methodological recommendations are being offered to provide mathematics teachers with psychological and methodological support while they are teaching students to solve mathematical tasks requiring intellectual challenge.

References:
[1] Tchoshanov, M. (2010). Relationship between teacher knowledge of concepts and connections, teaching, practice, and student achievement in middle grades mathematics. Educational Studies in Mathematics. An International Journal. 76, 141–164.
[2] Stein, M.K., Grover, B.W., Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms American Educational Research Journal, 33, pp. 455–488.
[3] Bespalko V.P. (1989). The terms of pedagogical technology. Moscow: Pedagogic, 192 p.

Keywords:

Cognitive demand, intellectual challenge, middle school mathematics teacher, mathematical task.