Arithmetic and algebraic problem-solving approaches of prospective teachers and teachers in service

The aim of this study is to determine mathematical problem-solving approaches of elementary school pre-service mathematics teachers and elementary school mathematics teachers. This is a mixed method research and was carried out using exploratory sequential pattern. The sample of the study consists of 128 pre-service teachers (59 sophomores, 41 juniors and 28 seniors) registered to department of elementary mathematics teaching in a state university located in the Eastern Anatolian Region of Turkey and 22 secondary school mathematics teachers working in different cities of Eastern Anatolia Region at the same period. Clinical interviews were conducted with 12 pre-service teacher and 5 teachers. The data were obtained by Problem-solving Test [PST] and Semi-Structured Interview Form [SSIF]. The PST was prepared to examine the problem-solving processes of the teachers and pre-service teachers participating in the research. According to the findings of the research, it was observed that the participants preferred the algebraic approach while solving the problems and could not solve the problem with an arithmetical approach. It is also understood that they tend to use algorithms they know by heart while making algebraic solutions. These results show that the participants have some deficiencies in terms of bringing both arithmetic and algebraic solutions to the problems.