The Cartesian coordinate system is a fundamental concept for mathematics and science and poses a teaching challenge at primary school level. Learning the Cartesian coordinate system has the potential to promote numerical cognition through number-space associations, as well as core geometric concepts, including isometric transformations, symmetry, and shape perception. Immersive virtual reality (VR) facilitates embodied forms of teaching and learning mathematics through whole-body sensorimotor interaction and offers benefits as a platform to learn the Cartesian coordinate system compared with "real world" classroom activities. Our goal was to validate the Cartesian-Garden, a serious game designed to provide an educationally robust but engaging vehicle to teach these concepts in primary-level mathematics in a multisensory VR environment. In the game, the child explores a Cartesian-Garden, that is, a field of flowers in which each flower corresponds to x and y coordinates. Specifically, we tested whether exploring numbers spatially represented improved spatial and numerical skills independently from the use of VR. Children (n = 49; age 7-11 years old) were divided into experimental and age-matched control groups. The experimental group explored the Cartesian-Garden and picked flowers corresponding to target coordinates; the control group played a VR game unrelated to Cartesian coordinates. To quantify potential improvements, children were tested before and after training with perceptual tests investigating number line and spatial thinking. The results point toward differential age-related improvements depending on the tested concept, especially for the number line. This study provides the guidelines for the successful use of the Cartesian-Garden game, beneficial for specific age groups.

中文翻译：

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小学生对沉浸式虚拟现实中笛卡尔平面坐标多感官严肃游戏的反应。

笛卡尔坐标系是数学和科学的基本概念，对小学教学提出了挑战。学习笛卡尔坐标系有可能通过数字空间关联以及核心几何概念（包括等距变换、对称性和形状感知）来促进数字认知。沉浸式虚拟现实 (VR) 通过全身感觉运动交互促进数学教学和学习的具体形式，并且与“现实世界”课堂活动相比，作为学习笛卡尔坐标系的平台具有优势。我们的目标是验证笛卡尔花园，这是一款严肃的游戏，旨在提供一种具有强大教育意义且引人入胜的工具，用于在多感官 VR 环境中教授初级数学中的这些概念。在游戏中，孩子探索笛卡尔花园，即一片花田，其中每朵花都对应于 x 和 y 坐标。具体来说，我们测试了在空间上探索数字是否代表了独立于 VR 使用的空间和数字技能的提高。儿童（n = 49；年龄 7-11 岁）被分为实验组和年龄匹配的对照组。实验组探索笛卡尔花园，采摘目标坐标对应的花朵；对照组则玩与笛卡尔坐标系无关的 VR 游戏。为了量化潜在的改进，在训练前后对孩子们进行了测试，通过感知测试调查数轴和空间思维。结果表明，根据测试的概念，尤其是数轴，与年龄相关的改善有所不同。这项研究为成功使用笛卡尔花园游戏提供了指导方针，对特定年龄段的人有益。