This study involved 38 primary school students in a detective game about cyber-ethics dilemmas and explored students' skills at making a reasoned decision and presenting a convincing argument. This game continued for five weeks and was supported by a computer system. It started with a given speculation/hypothesis. Then each student collected at least a piece of supporting evidence and wrote it up on the computer system for each week. During the evidence collection period, the researchers, playing a witness of the opposing side, actively provided refuting evidence each week. For the last week, the students were required to draw respective conclusions/decisions based on their collected evidence and given refuting evidence. All the students' constructed arguments for describing evidences and conclusions were analyzed. It was found that most of the students (about 92%) developed arguments consisting of either claims only or claims and data. They would not be able to construct complicated arguments with backings, warrants and rebuttals.