Pre-service teachers' algebraic reasoning and thinking barriers in solving algebraic problem

Algebraic reasoning is a process in which student generalize mathematical ideas from a set of particular instances, establish those generalizations through the discourse of argumentation, and express them in increasingly formal and age-appropriate ways. This is descriptive qualitative research. The primary interest was to explore pre-service teacher' thinking that might be foundational to algebraic reasoning and to describe their thinking barriers in solving an algebraic problem. There are twelve pre-service teachers who have participated in this study. The task was designed and given to all participants. Documents were the subjects' test results and unstructured interview transcripts. The results showed that the subjects had difficulties in generalizing and connecting mathematical patterns. Based on the subject's difficulties, we concluded that the subjects have barriers that include confirmation bias, mental set, functional fixedness, and unnecessary constraints. The intensity of each barrier will be discussed further in this article.