Yolanda Rosas-Rivera

Background. The process of teaching mathematics represents a challenge for primary education, due to the different perspectives and disciplines involved. In addition, as an active and flexible process, it requires feedback on what the students actually achieved. An analysis of the different learning and development outcomes allows the teacher to understand the mathematical content and the method of teaching it in the classroom, with the objective of promoting the students’ conceptual development.

Objective. The objective of our study was to analyze the general skills for problem solving which students developed, by applying dynamic evaluation. 

Design. A verification method was used to identify the students’ abilities and difficulties. A protocol for evaluating the process of solving mathematical problems was organized. The assessment included four simple problems and four complex ones. The participants were 15 students in the third grade of primary school attending a private school located in Mexico City.

Results. The results showed that the students identified the types of mathematical operations (addition, subtraction, multiplication, and division) required to solve the problems as their objective. Therefore, their preparation of a solution plan, its execution, and its verification were based only on empirical thinking and quantitative information. 

Conclusions. We concluded that problem-solving is an intellectual activity that requires conceptual development to carry out a solution plan, execute it, and verify it, in addition to the  main objective of answering the question posed by the problem. We propose that these characteristics be included in the organization of mathematics teaching in order to develop mathematical thinking.

The goal of the present study was to describe the organization of a guided activity for problem solution in primary school. The method, which was applied to mathematical problems, allowed us to propose a specific orientation for the proper solution of arithmetic problems by pupils. The study was based on the activity-theory approach applied to the process of teaching and learning. It was carried out with pupils in the second grade of a private school in the city of Puebla (Mexico). The method was used in the classroom during 30 school sessions of 1 hour per day. The methodology of formative experiment was used in the study. Qualitative analysis of the pedagogical process of teaching and learning was conducted. The results show that, after participation in the formative process, the schoolchildren became able to identify essential elements, data, and all relationships among them in order to solve mathematical problems. At the end of the program the verbal external level was raised for the process of orientation and the solution of problems together with the ability to use logarithms independently. We conclude that orientation, as a guided form of activity in primary school, is essential for the development of the ability to analyze problems.