Many software systems exist to help students learn mathematics. Despite their objectives, such systems are usually unsuccessful as educational tools. The primary reason for their failure can be traced to a lack of similarity between the fundamental symbolic manipulation algorithms they use and the ones that students are expected to learn. Work presented in this dissertation is based on the premise that a symbolic manipulator for educational use must be designed differently from one that is used by professional mathematicians. As a result of this approach, the Algebrator software system for learning elementary algebra was developed. Unlike most existing systems it was implemented in a procedural programming environment, without the benefit of existing symbolic manipulation libraries or algorithms. Algorithms necessary for solution of algebraic problems were designed to mimic the thought process of elementary mathematics teachers, and therefore were primarily based on selective recognition of symbolic patterns. To further enhance the didactical value of the system, an original method was developed to create on-demand context sensitive explanations for each step performed by the symbolic engine. Instead of simply tracing transformations applied during the solution process, Algebrator creates a dynamic data structure containing references to employed rules, reasons for employing them, and, most importantly, current problem subexpressions to which they apply. The ease of interaction between the student and the system is important in any educational software. It is crucial in a system in which the ability to deal with a complex data input process is a necessary prerequisite for reaping any educational benefits. The inherently difficult process of entering mathematical expressions was substantially simplified in Algebrator by providing real-time feedback during problem input. This approach necessitated implementation of two parallel expression representations (string and multiway tree) with transparent conversion, as well as efficient partial parsing and two-dimensional expression redrawing algorithms. Besides providing a didactically sound solution process, Algebrator is able to recognize classes of common student errors, known as mal-rules. While the concept of mal-rules is not new, its implementation within the Algebrator system is, because it allows dynamic expansion of mal-rule patterns by the system supervisor. Complexity that originates from a large number of available features can threaten the basic educational objective of the system. In Algebrator, this potential conflict is resolved by providing a number of programming environments accessible only to the system supervisor. These can be used to adapt the system characteristics to fit the needs of the local student community. Programmability permits modification of explanation text language and contents; presentation of the solution process; creation of interactive tutoring sessions; and, addition of audio-visual enhancements. The resulting software system constitutes a complete, fully adaptable learning environment in the domain of pre-college algebra. It is based on sound theoretical principles of cognitive and computer science, and also provides a unique and practical tool for teaching and learning elementary mathematics.