In the study reported on here, we investigated the effects of the use of dynamic geometry software (DGS) (i.e., GeoGebra) on learners’ learning and a teacher’s beliefs. The learners and teacher involved in the study were from a high-poverty, rural high school in South Africa. We compared grade 11 learners (N = 56) who used GeoGebra in the context of learning circle geometry with learners who experienced geometry through traditional lecture-based instruction. Participating learners were from classes in a public school located in the rural Umkhanyakude district of KwaZulu-Natal, Republic of South Africa. Results showed that learners using GeoGebra were more successful at solving problems and justifying their statements, while the other learners provided a limited justification for their answers. In a parallel and complementary investigation the teacher’s attitudes toward using GeoGebra as an instructional tool were considered qualitatively. Results showed that even in high-poverty, rural settings where the availability of technological resources are limited, the use of GeoGebra affected learners’ learning and had positive effects on the teacher’s beliefs regarding teaching and learning. Keywords: Euclidean geometry; GeoGebra; performance; theorems and proofs

中文翻译：

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GeoGebra 学与教：平行调查

在这里报告的研究中，我们调查了使用动态几何软件 (DGS)（即 GeoGebra）对学习者学习和教师信念的影响。参与研究的学习者和教师来自南非一所贫困的农村高中。我们将在学习圆形几何的背景下使用 GeoGebra 的 11 年级学习者（N = 56）与通过传统讲座式教学体验几何的学习者进行了比较。参与的学习者来自位于南非共和国夸祖鲁-纳塔尔省 Umkhanyakude 农村地区的一所公立学校的班级。结果表明，使用 GeoGebra 的学习者在解决问题和证明他们的陈述方面更成功，而其他学习者为他们的答案提供了有限的证明。在一项平行和互补的调查中，教师对使用 GeoGebra 作为教学工具的态度被定性地考虑。结果表明，即使在技术资源有限的高贫困农村地区，使用 GeoGebra 也会影响学习者的学习，并对教师的教学信念产生积极影响。关键词：欧几里得几何；GeoGebra; 表现; 定理和证明 表现; 定理和证明 表现; 定理和证明