Resumen de Illogical use of the converse of a theorem that can cause an incorrect solution

Victor Oxman, Moshe Stupel

• We present action research of a problem posed as part of a multiparticipant national (Israeli) test checking the mathematical knowledge of high school students at the ages of 16–17, where some of those who solved this problem made an error by using the converse to a well-known theorem, where the converse is not true. In order to examine the danger of using a wrong converse, the problem was posed as field research to a group of pre-service teachers and training teachers in the ‘methods (of teaching mathematics)’ course, where similar failures were discovered. The conclusion is that a large part of the students was not aware that the converse is not always true, and its correctness is to be tested before it can be used. The investigation of the problem was accompanied by a dynamic geometry environment software that allowed us to examine the problem in the general case and so to make conclusions for particular cases.