Sense making is one important goal of learning processes in school mathematics. Empirical studies on genuine sense constructions of mathematics students show the importance of sense construction categories with a subjective and an inner-mathematical orientation at the same time. From a theoretical point of view, we investigate two ways of fostering such sense constructions within school mathematics, by means of aesthetic experiences on the one hand and through reflection of problem solving processes on the other. In both cases, affective aspects play an important role. We also discuss the merits of intertwining aesthetic experiences and problem solving processes regarding sense construction. We finish with some remarks on possible ways of employing our theoretical results practically.