The aims of this paper are twofold. First, we present, justify, and characterise an instrument for analysing students' argumentative reasoning developed from Walton's ideas. Then, from the analysis of students' argumentative discussion about a socio-scientific controversy, we identify the advantages and disadvantages of using the instrument. The results show that the analysis of students' argumentative reasoning require nine stages, which have logical and pragmatic criteria that should be used in order to decrease the subjectivity of the analysis. The analysis sheds light on the characterisation of students' argumentative reasoning by supporting the understanding of the move of students' argumentative clusters, since it enables us to understand that: the argumentative quality depends on the relations between arguments and other statements; and an argumentative cluster can be developed according to the frequency of refutations or attacks by means of questions involving its constituents. This is because when arguments, questions, and/or claims are evaluated, the individuals have the possibility of bringing other reasons and/or arguments that support them in the discussion. Therefore, the main contribution of this study is the development of an instrument, based on dialectical principles, that contributes to analyse students' argumentative discuss and to support discussions of their argumentative quality.