In this study, the purpose is to develop and illustrate a method that facilitates investigations of students' learning processes in classroom discussions about socioscientific issues. The method, called transactional argumentation analysis, combines a transactional perspective on meaning making based on John Dewey's pragmatic philosophy and an argument analysis based on Toulmin's argument pattern. This analytical method consists of three steps. In the first step, we analyze the direction of the students' meaning making, that is, the relations construed in and by action. In the second step, we use a functional interpretation of Toulmin's argument pattern to clarify the meanings in terms of argumentative elements. Finally, we investigate the students' learning progress, both in terms of the way the arguments are constructed and the knowledge content used, by comparing each student's arguments over time. The empirical material consists of a video-recorded lesson in a Swedish upper secondary school. Two examples of learning processes identified during the classroom discussion are described: "learning to specify the conditions for one's claim" and "learning to find new solutions." These examples show that the suggested method can be used to identify the different kinds of learning progressions that take place during students' argumentative discussions. (Contains 8 tables and 6 footnotes.)