Abstraction is the process of developing a conceptual veneer that hides the complexity of internals. It is central to computational thinking, in general, and high quality software development, in particular. Use of mathematical modeling makes the abstraction precise. The need for undergraduate CS students to create and understand such abstractions is clear, yet these skills are rarely taught in a systematic manner, if they are taught at all. This paper presents a systematic approach to teaching abstraction using rigorous mathematical models. The paper contains a series of representative examples with varying levels of sophistication to make it possible to teach the ideas in a variety of courses, such as introductory programming, data structures, and software engineering.This paper presents results from our experimentation with the ideas over a 3-year period at our instiution in a required course that introduces object-based software development, following CS2. The data analysis focuses on students who fall in the bottom half of the performance curve to avoid the bias introduced by top performers, who tend to do well regardless of the teaching approach.

Undergraduate computer science students need to learn analytical reasoning skills to develop high-quality software and to understand why the software they develop works as specified. To accomplish this central educational objective, this article describes a systematic process of introducing reasoning skills into the curriculum and assessing how well students have learned those skills. To facilitate assessment, a comprehensive inventory of principles for reasoning about correctness that captures the finer details of basic skills that students need to learn has been defined and used. The principles can be taught at various levels of depth across the curriculum in a variety of courses. The use of a particular instructional process is illustrated to inculcate reasoning principles across several iterations of a sophomore-level development foundations course and a junior-level software engineering course. The article summarizes how learning outcomes motivated by the inventory of reasoning principles lead to questions that in turn form the basis for a careful analysis of student understanding and for fine-tuning teaching interventions that together facilitate continuous improvements to instruction.