Scaffolds for seeing, using, and articulating logical structures in proofs: Design research study with high school students.

Logical structures count as critical learning content for learning to prove. They are often not sufficiently explicated, and students struggle to use and articulate them in their proofs. In this design research study, we adopt a scaffolding approach to engage high school students in using and articulating logical structures. The qualitative analysis of the design experiments reveals the potentials and limitations of graphical scaffolds, showing how graphical scaffolds must and can be complemented by linguistic scaffolds to enable students to select and combine arguments in a deductive chain and write a proof text. Implications for language-responsive proof teaching and learning are discussed. • Logical structures count as critical learning content for learning to prove. • A scaffolding approach to engage high school students is adopted. • Qualitative analysis reveals the potentials and limitations of graphical scaffolds. • Empirical findings show the requirement of linguistic scaffolds. • Discussion of implications for language-responsive proof teaching and learning. [ABSTRACT FROM AUTHOR]