Mathematical problems designed with the use of functional equations as theoretical tools for examining subject matter knowledge of functions

Assessing the mathematics teachers' Subject Matter Knowledge (SMK) is currently important problem of research. Mathematics teachers should have profound and thorough SMK, understood as skills and knowledge of mathematics, its methods and history, which are indispensable for teaching. There is a need to find appropriate tools for continuous assessment of that competence of mathematics teachers. However, literature review reveals that functional equations have not been used yet as diagnostic tools. I claim that specially designed tasks related to functional equations can very effectively reveal teachers' SMK of function. As such, this dissertation is a new contribution to the research on possibilities of using the mathematical discipline of Functional Equations (39BXX AMS Subject Classification) in the field of Didactics of Mathematics.The paper is a modified version of the author's lecture presented 2nd July 2008 at the Pedagogical University of Krakow during the doctoral defense. Prof. Maciej Klakla (Pedagogical University of Krakow, Poland) was a supervisor of the PhD thesis; reviewed by: Prof. Anna Sierpinska (Concordia University, Montreal, Canada); Prof. Stanisaaw Midura (University of Rzeszow, Poland) and Prof. Bogdan Jan Nowecki (Pedagogical University of Krakow, Poland).