The aim of this mixed-method study is twofold: The first aim concerns pre-service science teachers' (PSTs) perceptions about what makes an argument persuasive. At the first phase, an in-depth analysis of their views about persuasiveness of different quality level arguments in three socioscientific contexts which were global climate change, base stations, and hydro-electric power plants was conducted. For this purpose, 91 PSTs were enrolled by filling a questionnaire including ill-structured arguments with missing elements such as claim, data, warrant, backing, and rebuttal or irrational connections among these elements. The second aim examines how explicit formal argumentation instruction contributes to the improvement of PSTs' views about persuasiveness of an argument and their provided criteria about persuasive argument. At the second phase, argumentation instruction was conducted with 15 PSTs out of 91; the PSTs were interviewed before and after the instruction to find out the changes in their perceptions about persuasiveness of an argument. The findings from the first phase revealed that the PSTs evaluate persuasiveness of the socioscientific arguments regarding five different characteristics such as 'elements of argument', 'content of argument', 'rhetoric of argument', 'characteristics of arguer', and 'argumentative relationship with SSI'. The findings from the second phase revealed that explicit instruction improved PSTs' awareness about argument elements that should be in a persuasive argument, and that while PSTs were merely able to imply before instruction, yet the PSTs were more able to explain in an explicit way that all elements should be used in a persuasive argument after explicit instruction.