Giovanna Valori

Finding teaching methods that foster students' development of geometric thinking and visualization skills is still a current challenge. This study analyses the effects of the combined use of paper folding and dynamic geometry on high school students’ geometric thinking and visualization skills. A quasi-experimental study pre-test/post-test design was conducted in distance learning in Italy. The instruments employed were van Hiele Geometry Test (VHGT) and the Visual Test (VT) before and after the treatment. The data were analysed using statistical tests according their nature. The results revealed that both groups have improved in the post-tests compared to their respective pre-tests. However, the students in the experimental group achieved better geometric thinking scores and performed better in three out of four sections of the visual test compared to the students in the control group. Thus, the proposed combination of instruments may be suggested in high school to make geometry teaching more effective, even with distance learning.

The combined use of origami and dynamic geometry software has recently appeared in mathematics education to enrich students’ geometric thinking. The objective of this research is to study the roles played by the interaction of two artifacts, paper folding and GeoGebra, in a construction-proving problem as well as its generalization in the Euclidean geometry context. For this, we designed and implemented two mathematical tasks with 52 secondary education students (15–16 years old, 10th grade) during the COVID-19 emergency lockdown period in Italy. The tasks involved four phases: constructing, exploring, conjecturing, and proving. This article presents an epistemic analysis of the tasks and a cognitive analysis of the answers given by one of the students. The theoretical tools of the onto-semiotic approach supported these analyses. Cognitive analysis allows us to confront the intended meanings of the task and the meanings actually employed by a student, thus drawing specific conclusions about the roles of such artifacts in written arguments and give an interpretation of their combined use in mathematics education.