论文标题
在地理格拉（Geogebra）中综合建模，可视化和编程作为教学和学习的有效方法
Synthesis of Modeling, Visualization, and Programming in GeoGebra as an Effective Approach for Teaching and Learning STEM Topics
论文作者
论文摘要
Geogebra是用于教学和学习数学，科学和工程设计的互动几何，代数，统计和微积分应用程序。它的动态接口使用户可以准确，交互式地可视化其工作，模型和结果。 Geogebra采用三个关键特征的综合：建模，可视化和编程（MVP）。许多研究表明，地理学对与科学，技术，工程和数学有关的学习和教学主题的效率和有效性的积极影响。在这项研究中，我们拒绝了地理布拉如何提供学习环境，该环境在学习者和讲师之间非常互动和协作。我们还展示了如何将地理学结合到学习方案中可以帮助提高许多高级数学课程的学校和大学生的技能和知识，例如计算，数学统计，线性代数，线性编程，计算机辅助设计，计算机辅助的几何学设计，分析和投影性的几何元和图形代表。因此，这项研究表明了地理学及其在科学和工程方面的MVP关键特征的效率，尤其是在与数学 - 马修有关的主题中。彻底分析了地理学的每个关键特征，并讨论了地理格拉对不同主题有帮助的进一步分析。
GeoGebra is an interactive geometry, algebra, statistics, and calculus application designed for teaching and learn-ing math, science, and engineering. Its dynamic interface allows its users to accurately and interactively visualize their work, models, and results. GeoGebra employs the synthesis of three key features: modeling, visualization, and programming (MVP). Many studies have shown the positive effects of GeoGebra on the efficiency and effectiveness of learning and teaching topics related to science, technology, engineering, and mathematics. In this study, we dis-cuss how GeoGebra provides an environment for learning that is very interactive and collaborative between the learner and the instructor. We also show how integrating GeoGebra into the learning scheme can help improve the skills and knowledge of school and university students in numerous advanced mathematical courses, such as calcu-lus, mathematical statistics, linear algebra, linear programming, computer-aided design, computer-aided geomet-ric design, analytic and projective geometry, and graphical representation. Therefore, this study shows the effec-tiveness of GeoGebra and its MVP key features in science and engineering, particularly in topics related to mathe-matics. Each key feature of GeoGebra is thoroughly analyzed, and further analyses, along with how GeoGebra can be helpful in different topics, are discussed.
