以擴增實境表徵學習數學分數概念對學生學習理解之影響

Abstract

表徵（Representations）常見於STEM教學當中，教師在教學中常以圖示、操作物等表徵，將學生難以理解的抽象概念予以具體化。然而，應用表徵進行學習，學生並非能自然而然習得其對應的抽象概念，甚至應用至真實情境當中。此外，大多數低先備知識學生，因無法掌握所學數學概念與生活間之關聯，導致缺乏學習數學的動機，甚至也傾向只注意表徵表層資訊，而無法更深入注意到關鍵資訊。本研究提出以擴增實境技術所創造的表徵 (AR Representations)，將數學概念以不同於常見具體或抽象的方式呈現，導引學生從真實情境中出發注意關鍵表徵資訊，來解決以上之問題。為檢測此教具之教學效果，本研究採用準實驗法，並有來自北台灣共101位國小三年級學生參與本次實驗。學生的前後測試卷分數為學生理解之量化數據，高低先備知識則以前測分數進行區別，同時亦採集質性的訪談資料。研究結果顯示，實驗組學生在使用擴增實境表徵學習後，高低先備知識學生之後測成績並不顯著。總結而言，藉由擴增實境表徵學習，低先備知識學生之理解與高先備知識學生之間的差異呈現彌平的趨勢。此外，透過質化訪談討論，更發現這一群學生比起其他組別能將所學應用至更多元的例子中。本研究亦根據結論，提出教育意涵及未來研究建議。

Representations are widely used in science, technology, engineering, mathematics (STEM) fields. Teachers often make use of representations, such as pictures, manipulatives, to demonstrate abstract concepts, which students find hard to understand, in more concrete and tangible ways. However, it is not automatically that students can pick up the target abstract concepts with those representations. Moreover, learning with pictures in textbooks, students have difficulty in translating from pictures to real-life situations. Nevertheless, most low prior knowledge students are lack of learning motivation in face with the mathematics concepts because they are not able to relate what they learned with their own real-life situations, and vice versa; also tend to pay attention to the task-irrelevant information. With the technique of augmented reality, the present study proposed “AR Representations” instructions, which are different from the well-used concrete or abstract concepts. By redirecting students’ attention to the most relevant information, the instructions aimed to solve the above problems. Thus, quasi-experiments were performed to verify the effectiveness of AR Representations instructions. 101 3rd-grade elementary students in northern Taiwan have participated. Pretest and posttest scores were collected as quantitative data of understanding. Levels of prior knowledge were also derived from pretest scores. Results of this study showed there was no significant difference on students’ understanding between high and low level of prior knowledge after learning with AR Representations. In conclusion, With the aid of AR representations, (1) low prior knowledge students’ understanding would equate with the higher ones’, and (2) low prior knowledge students could identify more novel examples other than textbooks provide. Pedagogical implications and future research are also discussed.