本研究旨在探究盲生於遊戲式數學活動中的困難，以及教學者如何在遊戲式數學活動中進行有效的介入。研究者參照Dienes的數學學習歷程六階段，界定盲生在遊戲中的學習任務。並透過主題分析法，歸納出盲生在遊戲式數學活動前二階段中遇到的困難，以及資深經驗教學者的介入策略。本研究之研究參與者包括國小五年級到國中二年級的八位全盲學童，以及兩位資深數學教師。研究者發現，盲生在遊戲式數學活動中的困難，可歸納為「不熟悉遊戲脈絡」、「不熟悉規則」、「動機受情緒影響」三大類。同時，本研究亦歸納出帶領盲生進行遊戲式數學活動的教學方法，教學者可以將遊戲的資訊切割，逐步增加遊戲的複雜度。在正式遊戲開始前，可教導盲生利用觸覺與透過口語互動助其掌握遊戲局勢的策略與習慣，以降低盲生在遊戲時的認知負荷。另對於遊戲掌握度較佳的學生可提供遊戲多變性，對遊戲掌握度較低的學生，則以同理與鼓勵之方式，以舒緩其焦慮。本研究為盲生遊戲式數學活動教法之前導研究，經由教師介入後，盲生能突破數學學習歷程前二階段的大部分困難。未來研究可繼續探究針對盲生遊戲式數學活動之教學如何進行有系統提問及促進盲生間之討論，以幫助他們從中習得數學概念。

Introduction In recent decades, studies have reported that students with blindness can efficiently learn mathematics. However, practitioners have found that students with blindness find the process of learning mathematics more difficult than their sighted peers. As a result, students with blindness are more likely to feel frustrated and lose motivation for learning math than sighted students. However, some studies have indicated that students with blindness would be as motivated and engaged as their sighted counterparts if teachers add game-based elements in their class. This study hopes that the game-based teaching approach can be used for mathematics learning by students with blindness in Taiwan to help alleviate their frustration and overcome their difficulties in learning mathematics. Research Purpose The purpose of this qualitative study was to investigate the difficulties faced by students with blindness in game-based mathematics activities and how teachers can effectively intervene to increase the motivation of students with blindness and alleviate their frustration. The study adopted a qualitative case study approach for data collection. Data Collection For data collection, the researchers used a videotaping technique to record two game-based activities instructed by two teachers at two locations. Additionally, the researchers and the teaching assistants took field notes to accurately report the participants’ facial expressions and body language. Moreover, three scales were used to collect descriptive statistics as supporting data. The participants in this study comprised eight students with blindness (Grades 5 to Grades 8) and two senior mathematics teachers. The student participants had no additional disabilities other than visual impairment. Consent forms were acquired from the parents, and assent forms were obtained from the other participants. Data Analysis A thematic analysis was adopted to determine the difficulties encountered by students with blindness in the first two stages of mathematics activities. The intervention strategies of the two experienced teachers were also coded and summarized. Results In this study, in the “free play” stage, the information obtained by the participants through tactile sense is fragmentary and partial; thus, they tend to ignore key information in the game. Therefore, teachers should help students with blindness integrate all partial information to form a whole picture. Next, when students with blindness entered the “game” stage, they encountered more challenges, including those related to the identification of the location and characteristics of game objects, which changed during the game process. Thus, students with blindness might be unable to find the location of game objects or lose considerable time, thus reducing their chances of winning. Accordingly, teachers must provide more prompts or lead them to review the game protocol and help them capture the dynamic situations. Moreover, teachers can increase the frequency of verbal cues to promote the students’ use of hearing to receive information. The researchers found that in the “game” stage, students with blindness tended to ignore and violate the rules. In addition, the participants may infer the rules incorrectly in specific situations. They also may be unfamiliar with mathematical definitions and may, thus, ignore rules meant for specific purposes. Accordingly, teachers can remind them directly or teach them the game rules step-by-step with a demonstration of the operation before the game starts. In contrast to GBL for sighted students, GBL for students with blindness requires teachers to provide multiple sensory information pieces to help the students enhance their use of the senses of touch and hearing. Additionally, teachers can provide more step-by-step instructions and more direct guidance. During the “game” stage, high-level students got bored easily and wished to speed up the game, whereas low-level students got frustrated because they tend to think and act slowly, which thereby reduced their engagement. To avoid this, teachers can lead students to try out the rules and manipulate the game objects smoothly or design games with different degrees of complexity to increase students’ curiosity in the game and, thus, their engagement and motivation levels. Furthermore, teachers can encourage students with a low performance level. When students with blindness engage in game-based activities, they are often a part of groups comprising heterogeneous members of various ages. A small proportion of students with blindness is present in Taiwan. Therefore, adding collaborative elements to the game can balance the uneven abilities of heterogeneous members and increase their intrinsic motivation. Discussion and Conclusions The challenges of students with blindness in game-based mathematics activities can be divided into three major categories, namely “unfamiliarity with the game context,” “unfamiliarity with the rules,” and “motivation affected by emotion.” Moreover, the teaching strategies for leading the students with blindness in game-based mathematics activities are summarized. To overcome the “unfamiliarity with game contexts” aspect, instructors should remind students to use their sense of touch more often during game-based mathematics activities and tell them specifically where and what they can touch at that particular moment. They can also design introductory activities to help students use their sense of touch to become familiar with manipulating game objects. For mastery in the dynamic context, in addition to the use of tactile inspection, the instructor can gradually help students with blindness to perceive the game situations through retrospective questions. To overcome the difficulty due to “unfamiliarity with the rules,” instructors should remind students to pay attention to the rules during the core game stage and to understand the reasons for the violation of the rules. By understanding the reasons for the violation of the rules or by specifically analyzing and explaining the reasons, students can overcome the learning challenges. To overcome the third type of difficulty, “motivation affected by emotion,” instructors can divide the game into several stages, from easy to difficult, and gradually add new elements to each stage. Moreover, to motivate students who are anxious about being unable to keep up, instructors can provide scaffolding support including empathy and encouragement. This strategy can help students with low mastery of the game to relieve their anxiety and enhance their motivation and engagement. Suggestions for Future Research In the future, to help students advance to the third stage of Dienes’ “searching for communalities,” teachers must add more activities in the GBL and increase the opportunities for student–teacher discussions and student–student discussions, so that students can explore the meaning behind the GBL modules through teachers’ or peers’ scaffolding. This study explored the effectiveness of teaching students with blindness through game-based mathematics activities. After the activities, students with blindness were able to overcome most of the difficulties they encountered in the first two stages of the mathematics learning process. Future scholars should continue to explore how teachers can systematically ask questions to facilitate discussions among students with blindness and help them learn mathematics concepts. Furthermore, this study recommends that future studies should check whether the three major aforementioned difficulties occur in other mathematics topics (such as in geometry) in game-based activities to explore the feasibility of additional instructional strategies.