This paper explores the challenges of using the Toulmin model to analyze students' dialogical argumentation. The paper presents a theoretical exposition of what is involved in an empirical study of real dialogic argumentation. Dialogic argumentation embodies dialectical features--i.e. the features that are operative when students collaboratively manage disagreement by providing arguments and engaging critically with the arguments provided by others. The paper argues that while dialectical features cannot readily be understood from a Toulminian perspective, it appears that an investigation of them is a prerequisite for conducting Toulminian analysis. This claim is substantiated by a detailed review of five of the ten most significant papers on students' argumentation in science education. This leads to the surprising notion that empirical studies in the argumentation strand--even those studies that have employed non-dialectical frameworks such as the Toulmin model--have "implicitly" struggled to come to terms with the dialectical features of students' discourse. The paper finally explores how some scholars have worked to attend directly to these dialectical features; and it presents five key issues that need to be addressed in a continued scholarly discussion.