Document Type

Dissertation

Department

Computer Science

First Advisor's Name

Ana Pasztor

First Advisor's Committee Title

Committee Chair

Second Advisor's Name

Cengiz Alacaci

Second Advisor's Committee Title

Committee Member

Third Advisor's Name

Malek Adjouadi

Third Advisor's Committee Title

Committee Member

Fourth Advisor's Name

Peter Clarke

Fourth Advisor's Committee Title

Committee Member

Fifth Advisor's Name

Vagelis Hristidis

Fifth Advisor's Committee Title

Committee Member

Keywords

instructional software, computer science education, induction, proofs by induciton, undergraduate computer science curriculum, educational software

Date of Defense

5-23-2008

Abstract

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.

Identifier

FI08121912

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