This paper presents research activity in the solution of geometric tasks by mathematics teachers and by mathematics teacher trainees at a College of Education as part of an advanced courses. This activity tested the level of knowledge and ability to apply it in the solution of problems that can be solved in a number of ways: by using various tools from the same branch of mathematics, or by integrating tools from several mathematical branches. The participants left the classroom research activity with an understanding of the importance of the knowledge base and the ability to use various tools in solving interesting problems.