Grasping mathematical objects as related to processes is often considered critical for mathematics understanding. Yet, the ontology of mathematical objects remains under debate. In this paper, we theoretically oppose internalist approaches that claim mental entities as the endpoints of process-object transitions and externalist approaches that…

Efficient recognition of geometric shapes is an important aspect of proficiency in geometry. Building theoretically on the cultural-historical approach enriched by the physiology of activity, we investigate theoretical perception in geometry--the ability to recognize conceptual geometric aspects of visual figures. Aiming to understand the…

Many students persistently misinterpret histograms. This calls for closer inspection of students' strategies when interpreting histograms and case-value plots (which look similar but are different). Using students' gaze data, we ask: "How and how well do upper secondary pre-university school students estimate and compare arithmetic means of…