Expert Recurrence of Linear Problem Posing

Abstract

According to Pelczer & Gamboa (2009) the Mathematical problem posing process of the skilled problem posers (teachers, mathematically gifted students) is usually cyclic whilst the novices usually pose problems in a linear way. (Cyclic model means that the skilled problem poser is able to switch between the phases of problem posing, to learn from his/her mistakes, to transform the idea which is not suitable. Linear model is just a simple straight way.)In my study I set expert category. (Expert = professional in problem posing, preparing problems for Mathematical competitions such as Mathematical Olympiad.) With respect to previous statements the hypothesis would be that the experts will show nearly no signs of linear problem posing process. But this is not true – there is some recurrence of linear problem posing in the expert group. The signs of the problem posing process are seemingly the same as in the novices’ case. But the background is different. The expertness lies in the fact that the expert is so experienced that he/she is able to come with an idea that needs no transformations. During the problem posing trajectory the experts usually perform the Final assessment stage. The experts also do not perform multiple Setup stages. (They may return to the Setup stage in order to do Transformations but they usually do not restart their work by the use of totally new Setup.)