幾何形狀在我們的生活隨處可見，但過去的研究很少讓學習者有機會將幾何學習運用在真實情境中。除此之外，很少研究深入探討那種單一形狀與幾何學習有關係，並缺乏探討其對幾何學習成效與幾何估算能力的影響。 因此，本研究針對國小幾何數學開發一套Ubiquitous Geometry (UG)系統，探討學習者在真實情境中使用UG來量測真實物體並進行解題，對其幾何學習成效與幾何估算能力的影響，在更進一步的探討學習行為與其幾何學習成效與幾何估算能力之相關。研究對象為國小五年級學生共77位，分成實驗組（UG）、控制組-尺量測組與傳統教學組三組，實驗時間為一個月。 研究結果發現，在幾何學習成效，實驗組顯著優於傳統教學組。在幾何估算能力，實驗組皆顯著優於兩組控制組。在學習行為的單一周長中，學習者使用「菱形」與幾何學習成效呈現顯著正相關；使用「平行四邊形」與幾何估算能力呈現顯著正相關。在單一面積中，學習者使用「菱形」與「平行四邊形」與幾何學習成效呈現顯著正相關；使用「菱形」與「梯形」與幾何估算能力呈現顯著正相關。在複合式面積中，使用「三角形」與「長方形」與幾何學習成效呈現顯著正相關。最後，多數的學習者皆認為透過在真實情境下的量測是能夠有效提升其幾何數學。 ;Geometry is everywhere in our lives, but past research has rarely given learners the opportunity to apply geometric learning to real situations. In addition, few studies have delved into the relationship between single shape and geometric learning, and lack of discussion on its impact on geometric learning effectiveness and geometric estimation. Therefore, this study developed a Ubiquitous Geometry (UG) for the geometric mathematics of elementary school students, so that learners can apply geometric mathematics to life. The main purpose is to explore the use of UG by learners in real situations. To measure real objects, and to carry out geometric measurement to solve problems, and to explore its influence on geometric learning effectiveness and geometric estimation ability, to further explore the relationship between learner′s geometric measurement behavior and its geometric learning effectiveness and geometric estimation ability. This study consisted of 77 students in fifth grade, divided into experimental group which is using UG system (EG), control group-ruler measurement group (CG-R) and control group-traditional teaching group (CG-T), which lasted about one month. The results of the study found that in the post-test geometry learning results, EG was significantly better than the CG-T. Among the geometric estimation ability, the EG was significantly better than CG-R and CG-T. In the geometric measurement learning behavior, the learner uses the "diamond" measurement learning and the post-measurement geometry learning performance to show a significant positive correlation; the "parallelogram" measurement learning and geometric estimation ability is significant. Positive correlation. In a single area, learners use the "diamond" and "parallelogram" measurement learning and post-measure geometry learning performance to show a significant positive correlation; the use of "diamond" and "trapezoid" measurement learning and geometric estimation ability showed a significant positive correlation. In the compound area, there is a significant positive correlation between the use of "triangle" and "rectangle" measurement learning and post-measurement geometry learning. Finally, the learners of the questionnaire survey group found that most of the learners believe that the measurement in the real situation can effectively improve their geometric learning scores.
