An Innovative Approach to Teaching Structural Induction for Computer Science

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.

A survey of music educator's understanding and use of advanced audio technology in their instructional methods and strategies

This study examines the correlation between how certified music educators understand audio technology and how they incorporate it in their instructional methods. Participants were classroom music teachers selected from fifty middle schools in Miami- Dade Public Schools. The study adopted a non-experimental research design in which a survey was the primary tool of investigation. The findings reveal that a majority of middle school music teachers in Miami-Dade are not familiar with advanced audiorecording software or any other digital device dedicated to the recording and processing of audio signals. Moreover, they report a lack of opportunities to develop this knowledge. Younger music teachers, however, are more open to developing up-to-date instructional methodologies. Most of the participants agreed that music instruction should be a platform for preparing students for a future in the entertainment industry. A basic knowledge of music business should be delivered to students enrolled in middle-school music courses.