Acquiring conceptual understanding of functions is far from being trivial for most students, especially language learners. The article reports on a design research project with students in Grades 8-11 (n = 94) that fostered academic language learners’ development of conceptual understanding in the interplay of different semiotic representations. Theoretical and qualitative analyses of students’ learning pathways and obstacles allowed the specification of school academic language demands based on concept demands for dealing with functional relationships. The strong interplay between concept and language demands can be described by the correspondence of conceptual compaction of conceptual facets and the language-related condensation of their verbalizations.
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