Mathematical Practices of Eighth Graders about 3D Shapes in an Argumentation, Technology, and Design-Based Classroom Env
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Mathematical Practices of Eighth Graders about 3D Shapes in an Argumentation, Technology, and Design-Based Classroom Environment Sule Sahin Dogruer 1
& Didem
Akyuz 1 & A 1
Received: 16 July 2018 / Accepted: 10 October 2019/ # Ministry of Science and Technology, Taiwan 2020
Abstract This design research investigated the mathematical practices that eight graders (14-year-old students) developed when learning about prisms, cylinders, and their surface areas. An inquiry-based learning environment was created for students to engage in argumentation. The instruction was enriched by use of a dynamic geometry software, namely GeoGebra, to assist students in visualizing and reasoning about 3D shapes. Rasmussen and Stephan’s three-phase method (2008) was used to organize the collected data, which in turn were analyzed using Krummheuer’s model of argumentation (2015). The results indicated the emergence of three mathematical practices and several taken-as-shared ideas: (1) defining prisms, (2) computing the surface area of a prism, and (3) computing the surface area of a cylinder. The study’s results revealed that students’ understanding improved when learning concepts simultaneously with argumentation and dynamic geometry software. Keywords Argumentation . Design-based research . Dynamic geometry software .
Mathematical practices . Three-dimensional shapes
Introduction It is a commonly accepted notion that when students learn mathematics through thinking and reasoning, they develop conceptual understanding. Furthermore, it is commonly * Sule Sahin Dogruer [email protected] Didem Akyuz [email protected]
1
Department of Mathematics and Science Education, Middle East Technical University, Universiteler Mah. Dumlupinar Blvd, No: 1, 06800 Ankara, Turkey
Ş. Ş. Doğruer et al.
assumed that there is a strong relationship between social interaction, children’s thinking, and construction of knowledge (Wood, Williams, & McNeal, 2006). Research has found that learning mathematics includes both personal work and collaborative (i.e. social) work, the latter of which involves discussions within the classroom so that students explain and justify their work to others (Yackel & Cobb, 1996). Relatedly, argumentation (Brown, 2017) is essential in mathematics classes, and technology-enhanced environments help to facilitate argumentation (Erkek & Bostan, 2019). As a sub-domain of mathematics, geometry is a subject that can benefit from a classroom environment that supports argumentation, where students can understand geometric structures and theorems, and their relationships, by exchanging ideas. Moreover, by designing instructional sequences enriched with argumentation opportunities, teachers can give students a chance to communicate their ideas with others. Argumentation conducted within a specific learning context allows students to transfer and foster taken-as-shared ideas, which are ideas that help construct mathematical practices (Cobb, Yackel, & McClain, 2012). This study examines classroom mathematical practices that were
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