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

Abstract

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. student" 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 participated 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.

Teaching with digital technology

“…More recently, dynamism is being interpreted in multimodal environments (Noble, Nemirovsky, Wright & Tierney, 2001 ) to incorporate more embodied approaches. It is also evolving towards a learning perspective, supporting students in experiencing inquiry (Soldano, Luz, Arzarello & Yerushalmy, 2019 ), and towards a teaching perspective, supporting teachers to design authentic resources as scenarios for classroom situations (Cusi, Swidan, Faggiano & Prodromou, 2020 ).…”

Chinese students’ access, use and perceptions of ICTs in learning mathematics: findings from an investigation of Shanghai secondary schools

“…Research has revealed that, in mathematics education, ICTs make mathematics more authentic by providing opportunities to access real-world data (e.g., Clark-Wilson et al, 2011 ), make mathematical representations more visual and dynamic (e.g., Vahey et al, 2020 ), and make mathematical communication and collaboration more convenient (e.g., Geiger et al, 2010 ). ICTs support students in developing conceptual understanding (e.g., Bos, 2007 ), improving problem-solving skills (e.g., Granberg & Olsson, 2015 ), strengthening inquiry-based learning (e.g., Soldano et al, 2019 ), and promoting students’ interest in mathematics (e.g., Deng et al, 2020 ). Meanwhile, there also exist concerns about the inappropriate use of ICTs, leading, for example, to the deterioration of students’ competencies in arithmetic skills (e.g., Alhumaid, 2019 ) and to distractions (Ditzler et al, 2016 ).…”

Compendium for Early Career Researchers in Mathematics Education

“…Within game activities we also observed the activation of another type of logic, the "logic of not" (Arzarello and Sabena 2011), which guides students in the indirect validation of a conjecture, by observing empirically the impossibility of refuting it. 13 This logic is triggered by the verifier/falsifier dynamics (Soldano et al 2018). In fact, the falsifier, in order to establish if there is a possibility for her/him to win, 12 Peirce called the two types of proof theoretical and corollarial.…”