Problem solving plays a crucial role in the learning of mathematics. Typically the process of problem solving combines knowledge and heuristics with specific strategies for collecting, organizing and treating information, making use of different representations, mathematical models and conversions from one language to another and establishing relationships between the learned contents. Previous research papers reveal several aspects of problem solving present in different teaching-learning strategies which are of a general nature and focus on the study of the logical-economic forms of thinking, without attempting to express the specificities of the processes in their relationship with a certain content. The research carried out on the use of specific content-dependent strategies as an approach to problem solving is yet in its beginning.

Each disciplinary field has its own characteristics, the uniqueness of which means that their treatment requires particular demonstrative procedures, ways of thinking and problem solving processes that involve the specific contents of each particular field. To deal with a specific problem it is therefore often necessary to break down the barrier of general strategies and turn to particular strategies.

We could mention the studies carried out by P. Ruesga and J. M. Sigarreta which present a clear preference for specific strategies for problem solving according to specific contents. Many of the determining factors of problem solving skills are related to cognitive processes. It is obvious that to be successful in the solving of mathematical problems a student must be able to understand and interpret the mathematical relationships involved; but, an effective resolution of the problem is also dependent upon the student's knowledge of specific situations, ie of its contents and the way the student organizes his/her knowledge for that particular situation and the specific strategies corresponding to those contents. Authors such as Hinsley, Hayes and Simon have provided evidence to show that those who are competent in the solving of mathematical problems have a wide knowledge of problems type and the specific strategies required to solve them. The choice of a specific strategy for solving problems according to its specific contents is not incompatible with the general strategies. On the contrary, specific strategies arise naturally within any general strategy.

This paper identifies a specific contents-based strategy for problem solving based on analytical geometry procedures. Here, an appropriate methodology for putting the strategy into practice, will be exposed.