利用 Unity 於數位化數學遊戲之開發與教學應用

Abstract

本研究利用 Unity 遊戲引擎以及相關軟體輔助開發數位化數學遊戲，並以數 學遊戲為主軸設計出一系列工作單與教學活動，使學生能夠接觸數學遊戲相關素 材以及了解基礎知識，並使用更精緻的數位化教材進行學習。論文中提供多種雙人對弈的數學遊戲，「二子棋」—雙方輪流移動棋子直到 其中一方無法移動；「公主與玫瑰」—雙方輪流取玫瑰，並試著將最後一朵玫瑰 取走；「格隆第分豆遊戲」—雙方輪流將綠豆分堆，直到綠豆無法再進行分堆； 「玩弄銅板遊戲」—雙方將銅板輪流移向錢袋，並試著取走最後一枚銅板；「斷 線取幣遊戲」—雙方輪流將銅錢從線上剪下，並試著獲得更多的銅錢；「橫豎擺 放磚頭遊戲」—雙方輪流在棋盤上放置磚塊，直到其中一方無法繼續放置；「大 衛‧蓋爾的搭橋遊戲」—雙方輪流在棋盤中搭橋，並試著連通自己顏色的土地； 「夏農的連通遊戲」—雙方輪流在棋盤空白處塗上自己的顏色，試著塗出一條連 通土地的路徑；「夏農的斷開遊戲」—一方試著連通左右兩點，另一方試著阻止 左右兩點連通；「皮納姆的吃餅精靈」—雙方輪流操控吃餅精靈吃掉棋盤上的餅， 並試著吃到最後一塊餅；以及單人解謎「哈密頓連線遊戲」—在不同的平面與立 體圖形上找出一筆畫連通所有的頂點。本研究中的數學遊戲皆完成軟體開發，適用於電腦、Android 系統手機、平 板等裝置，並同時設計教學工作單輔以教學，數學遊戲軟體與工作單皆提供下 載網址，提供教師教學使用。最後章節將說明所有遊戲程式設計的思路，公開 核心運作腳本的原始碼，希望有興趣嘗試開發的教師有參考作為切入點。This research utilizes the Unity game engine and related software to develop digital math games. The main focus is to design a series of worksheets and teaching activities around math games, enabling students to engage with math-related materials and acquire fundamental knowledge using more sophisticated digital learning materials.The paper presents several two-player mathematical games, including"Two-Coins Game" — where players take turns moving coins until one player cannot make a move; "Princess and Roses" — players take turns picking roses, trying to be the one to pick the last rose; "Grundy Bean Game" — players take turns dividing green beans into piles until no further division is possible; "Coin Flip Game" — players take turns moving coins into a bag, attempting to take the last coin; "Break Lines Take Coins Game" — players take turns cutting coins from a line, trying to collect more coins;"Arrange Bricks Game" — players take turns placing bricks on a board until one player cannot continue; "David Gale's Bridge Building Game" — players take turns building bridges on a board, aiming to connect their own colored territories; "Shannon's Connect Path Game" — players take turns coloring empty spaces on a board with their own color, attempting to create a path of connected territories; "Shannon's Switching Game" — one player tries to connect two points horizontally, while the otherplayer tries to prevent the connection;"Bynum's Eat Cake Elf" — players take turns controlling a eat ake elf to consume cakes on the board, striving to eat the last piece; and a single-player puzzle game called "Hamilton Connection Game" — where players need to find a path that connects all vertices on different planes and solid figures. All the math games in this study have been developed as software applications suitable for computers, Android smartphones, tablets, and other devices. Additionally, teaching worksheets are designed to accompany the games. Both the math game software and the worksheets are available for download through a provided URL, enabling teachers to utilize them in their teaching activities. In the final chapter, the thought process behind the game programming will be explained, and the source code for the core scripts will be made publicly accessible. This is intended to serve as a reference point for teachers who are interested in attempting further development, providing them with a starting point.