Embedded in a Systemic Functional understanding of education as an initiation into knowledge structures and specific activities, both of which are fundamentally mediated by language, this paper addresses one of the critical concerns around CLIL: a possible mismatch between students' cognitive level and their L2 proficiency. The focus is on acts of classifying, comparing and contrasting facts, objects, phenomena, abstract ideas and concepts. Such cognitive and verbal actions are key in the construction of specialist knowledge, having been bundled in an umbrella cognitive discourse function (CDF) categorize. To operationalize this CDF, we develop a conceptual map through an exploratory, data-driven analysis of an oral learner corpus in L2 English and L1 Spanish on science and history topics collected in primary bilingual schools in Madrid. We also use SFL tools to examine lexico-grammatical choices which students employ to realize categorize across the two subjects and languages. The analysis shows that students encounter a range of difficulties, both conceptual and linguistic, when forming complete and appropriate categorizations in both languages. The results obtained across subjects reveal clear subject-specific tendencies in how categorizing is carried out: comparing seems to be a defining figure of thought in history while classifications were predominant in science.