Although geometry is important and strongly related to our surroundings, students still have few chances to learn it through practicing in authentic contexts. Therefore, ubiquitous geometric (UG) APP in mobile devices was developed in this study and allowed students to apply and practice geomety in authentic contexts. This study focused on the influence of measurement behaviors in authentic contexts on learning achievement and estimation ability with UG support. Furthermore, the relationship among measurement behaviors, their learning achievement and estimation ability were also deeply investigated. This 1-month experiment was conducted with three groups, experimental group with UG (EG), control group with rulers (CG-R) and control group using traditional teaching approach (CG-T). The results showed that EG got significantly better performance than CG-T only in learning achievement while EG performed significantly better than CG-T and CG-R in estimation ability. It demonstrated that measurement in authentic contexts can indeed help geometric learning and estimation ability. Regarding students’ perception, most of them perceived that measurements in the real situation can stimulate their motivation, then effectively improve their geometric learning. Besides, students also expressed their high satisfaction toward the proposed system and learning activities in authentic contexts. Thus, we strongly suggested that geometry learning should be applied to authentic contexts with UG support to consolidate geometry concept learning and facilitate geometry problem-solving.

中文翻译：

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探索无处不在的几何的真实上下文，以促进小学生的几何学习

尽管几何很重要，并且与我们的周围环境息息相关，但学生仍然很少有机会通过在真实环境中进行练习来学习几何。因此，本研究开发了移动设备中无处不在的几何（UG）APP，使学生能够在真实的环境中应用和实践几何。这项研究的重点是在真实情况下的测量行为在UG支持下对学习成绩和估计能力的影响。此外，还对测量行为，学习成绩和估计能力之间的关系进行了深入研究。这项为期1个月的实验分为三组，分别是UG（EG）实验组，带尺子的对照组（CG-R）和使用传统教学方法（CG-T）的对照组。结果表明，仅在学习成绩上，EG的性能明显优于CG-T，而在估计能力上，EG的性能明显优于CG-T和CG-R。结果表明，在真实情况下进行测量确实可以帮助几何学习和估计能力。关于学生的感知，他们中的大多数人认为，在实际情况下进行测量可以激发他们的动力，从而有效地提高他们的几何学习能力。此外，学生们也对拟议的系统和真实情况下的学习活动表示高度满意。因此，我们强烈建议在UG支持下将几何学习应用于真实上下文，以巩固几何概念学习并促进几何问题的解决。