Looking back at the beginning: Critical thinking in solving unrealistic problems

We believe that problem-solving skills engage critical thinking at every phase of problem solution. In this research a special attention is given to the fist phase - "understanding the problem". We consider this phase as a continuation of all the previous mathematical experience, in which understanding of new problems requires "looking back" at those solved in the past. Evaluation of the givens in the problem sometimes allows immediate solution whereas in other cases it shows that solution does not exist. We found that it is not easy for mathematics teachers to discover that a problem includes contradictory (i.e. unrealistic) conditions. We suggest that such problems should be included into teachers' professional development programs to develop teachers' awareness of the importance of mathematical accuracy and connectedness.