Students’ struggles with temporal order in the limit definition: uncovering resources using knowledge in pieces

A few case studies have suggested students’ struggles with the temporal order of epsilon and delta in the formal limit definition. This study problematizes this hypothesis by exploring students’ claims in different contexts and uncovering productive resources from students to make sense of the critical relationship between epsilon and delta. A three-step analysis supports these aims. The analysis starts by investigating the generalizability and specificity of the struggle with the temporal order. Then, analysing students’ justifications reveals dominant ideas supporting students’ claims. Finally, attending to the foci of the justifications reveals the potential resources to make sense of the temporal order. This study illustrates the productivity of the principles context sensitivity, cueing priority, and reliability priority from Knowledge in Pieces in understanding students’ struggles. The study offers the three-step analysis as a method to approach students’ understanding from an anti-deficit perspective.