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 and performance of 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.

Improving novice analyst performance in modeling the sequence diagram in systems analysis: A cognitive complexity approach

The Unified Modeling Language (UML) has quickly become the industry standard for object-oriented software development. It is being widely used in organizations and institutions around the world. However, UML is often found to be too complex for novice systems analysts. Although prior research has identified difficulties novice analysts encounter in learning UML, no viable solution has been proposed to address these difficulties. Sequence-diagram modeling, in particular, has largely been overlooked. The sequence diagram models the behavioral aspects of an object-oriented software system in terms of interactions among its building blocks, i.e. objects and classes. It is one of the most commonly-used UML diagrams in practice. However, there has been little research on sequence-diagram modeling. The current literature scarcely provides effective guidelines for developing a sequence diagram. Such guidelines will be greatly beneficial to novice analysts who, unlike experienced systems analysts, do not possess relevant prior experience to easily learn how to develop a sequence diagram. There is the need for an effective sequence-diagram modeling technique for novices. This dissertation reports a research study that identified novice difficulties in modeling a sequence diagram and proposed a technique called CHOP (CHunking, Ordering, Patterning), which was designed to reduce the cognitive load by addressing the cognitive complexity of sequence-diagram modeling. The CHOP technique was evaluated in a controlled experiment against a technique recommended in a well-known textbook, which was found to be representative of approaches provided in many textbooks as well as practitioner literatures. The results indicated that novice analysts were able to perform better using the CHOP technique. This outcome seems have been enabled by pattern-based heuristics provided by the technique. Meanwhile, novice analysts rated the CHOP technique more useful although not significantly easier to use than the control technique. The study established that the CHOP technique is an effective sequence-diagram modeling technique for novice analysts.

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.