This research is based on an individual case finding, where the response from individuals in answering the mathematical problems is initiated with perplexity to proceed with the new finding by reflecting on the previous experience. This research aimed at contributing practically on the indicators causing a perplexity on students which described the initial process of reflective thinking through students' argument exploration when responding to a problem. This research is a qualitative research with a case study of two students as research subjects. This finding showed that students stated four sequences of Arguments which described perplexity of the students during the interview. This perplexity showed several indicators that were students' unfamiliarity in imagination and creation on nonregular questions; incompatibility of problem-solving strategy owned by someone with the new problem-solving coming from; misunderstanding of students due to incompatibility in students' experience, or the existence of a forgetfulness factor; and the failure in generating new ideas and strategies.