Technology-based inquiry in geometry: semantic games through the lens of variation

The paper describes two versions of an inquiry-based activity in geometry, designed as a game between two players. The game is inspired by Hintikka’s semantic game, which is a familiar tool in the field of logic to define truth. The activity is designed in a dynamic geometry environment (DGE). The inquiry is initially guided by the game itself and later by a questionnaire that helps students discover the geometry theorem behind the game. The activity is emblematic of describing a geometry-based inquiry that can be implemented with various Euclidean geometry theorems. The analysis of the first "student vs. studen" version associates the example space produced by the students with their dialogue, to identify the different functions of variation. Based on the results of this version, we designed a "student vs. computer" version and created filters for the automatic analysis of the players’ moves. Our findings show that students who articipated in the activity developed forms of strategic reasoning that helped them discover the winning configuration, formulate if-then statements, and validate or refute conjectures. Automation of the analysis creates new research opportunities for analyzing and assessing students’ inquiry processes and makes possible extensive experimentation on inquiry-based knowledge acquisition.