The Pre-number Period of Teaching Mathematics in Russia: A Psychological Analysis from the CHAT Standpoint

The objective of this chapter is to discuss the principles developed in the mainstream of the Cultural-Historical Activity theory (CHAT) for analyzing the goals of the pre-number period of teaching mathematics in Russia from a psychological point of view. We have shown that the most important issues in mathematics education concern the type of concepts proposed for assimilation in this period; the type of students’ actions by which these concepts can be assimilated and practiced; and kinds of means to carry out these actions which are provided. According to these principles, it was developed an original program for teaching mathematics in the pre-numerical period (15 experimental sessions, 15–20 min for each session, mini-groups of 3–4 children). We started introducing children to mathematical reality by having them master an elementary mathematical concept such as magnitude (length, area, and volume), which can help them understand the dependence of number on measurement. The control group did not attend any special sessions but learned some mathematical concepts and skills as part of regular school preparation classes conducted by their teachers. The total number of participants was 37 (18 in the experimental and 19 in the control group). Before and after the sessions, each participant was tested on their mastery of the mathematical concepts and skills. The results demonstrated that the children who attended the experimental program showed a significantly greater increase in post-test scores than the children from the control group. This occurred in their mastery of the concepts of length and area and the dependence of number on the means of measurement, and their ability to select values and assemble “complex” sets. The results have proved the effectiveness of the program built in accordance with the CHAT principles.