In the course of a research project now in progress, two pairs of externally similar but essentially different problems were presented to 7th‐12th grade students. In each pair, one problem related to infinity and the second to the paniculate nature of matter. The first pair pertained to a process of successive division (of a line segment and a copper wire respectively). Students were asked to judge whether each process will come to an end. For the second pair students were asked to compare the number of points/atoms in two differently sized line segments/copper wires. Our data show most students unable to differentiate between the two theoretical frameworks (mathematics vs. science). A substantial number of students hold a generalized finite viewpoint and solve all problems from this perspective. With age and/or instruction students lose this finite perspective and respond to the problems according to their external features. Successive division in both mathematics and science triggered ‘infinite’ responses whereas both comparison problems yielded finite responses.