Proofs by induction are central to many computer science areas such as data structures, theory of computation, programming languages, program efficiency-time complexity, and program correctness. Proofs by induction can also improve students’ understanding of and performance with computer science concepts such as programming languages, algorithm design, and recursion, as well as serve as a medium for teaching them. Even though students are exposed to proofs by induction in many courses of their curricula, they still have difficulties understanding and performing them. This impacts the whole course of their studies, since proofs by induction are omnipresent in computer science. Specifically, students do not gain conceptual understanding of induction early in the curriculum and as a result, they have difficulties applying it to more advanced areas later on in their studies. The goal of my dissertation is twofold: 1. identifying sources of computer science students’ difficulties with proofs by induction, and 2. developing a new approach to teaching proofs by induction by way of an interactive and multimodal electronic book (e-book). For the first goal, I undertook a study to identify possible sources of computer science students’ difficulties with proofs by induction. Its results suggest that there is a close correlation between students’ understanding of inductive definitions and their understanding and performance of proofs by induction. For designing and developing my e-book, I took into consideration the results of my study, as well as the drawbacks of the current methodologies of teaching proofs by induction for computer science. I designed my e-book to be used as a standalone and complete educational environment. I also conducted a study on the effectiveness of my e-book in the classroom. The results of my study suggest that, unlike the current methodologies of teaching proofs by induction for computer science, my e-book helped students overcome many of their difficulties and gain conceptual understanding of proofs induction.

多媒體教學被認為是一種最適合人類學習認知的教學方法，可預見的未來 ，多媒體技術將大量運用於教學。多媒體教學軟體的開發須整合多種媒體 ，不僅開發費用龐大且設計繁瑣，造成發展與開發成本估算的困難。本研 究乃針對多媒體教學軟體開發過程中所需考量的因素，探討多媒體教學軟 體開發成本估算模式。建立『多媒體教學軟體開發流程工作項目』，說明 多媒體教學軟體開發過程中所需注意的細節與步驟。藉此，專案開發者可 以更加瞭解多媒體教學軟體專案之開發流程與所需注意的細節，改善專案 管理之品質，此外，此一開發流程亦為開發成本估算的基礎。由於成本估 算的單位為細步工作項目，開發者較能掌握所需耗費之資源，增加成本估 算的精確度。而基於協助成本估算自動化的觀點，考量系統使用者多為管 理階層人員遇與其之資訊需求，提出『多媒體教學軟體開發成本估算系統 設計架構』，以為多媒體教學軟體成本估算系統設計之參考與建立多媒體 教學軟體開發成本估算先導系統之基礎。功能架構包括友善之使用者介面 、資料庫管理、統計資料圖表與專案管理等四項功能本研究另一重點乃依 據多媒體教學軟體開發流程與成本估算先導系統設計架構，建立『多媒體 教學軟體開發成本估算先導系統』，實際建立一多媒體教學軟體開發成本 估算先導系統，協助開發成本估算的自動化，並驗證成本估算系統設計架 構的可行性。在使用者介面功能上，先導系統乃以滑鼠與功能式選單為主 ，並提供使用者線上查詢與選取的功能。在資料庫管理功能方面，包括線 上資料庫查詢與定期資料庫更新。此外系統提供專案支出費用明細表、現 金支出圖、階段期間圖與階段現金圖等統計資料報表以協助開發者決策的 進行。