Learning to respond to a computer program that is not working as intended is often characterized as finding a singular bug causing a singular problem. This framing underemphasizes the wide range of ways that students and teachers could notice discrepancies from their intention, propose causes of those discrepancies, and implement interventions.…

We address the telling/not-telling dilemma in mathematics education. Telling is instructionally important, but has been downplayed because of (a) perceived inconsistencies between telling and constructivism, (b) increased awareness of the negative consequences of relying too heavily on telling, and (c) a focus on "non-telling" actions as…