Treasure-Hunting in Baghdad: Al-Khwārizmı̄ on Quadratic Equations

We introduce and present the scripts of three classroom dialogues set in ninth-century Baghdad, designed to bring to life the context and style of al-Khwārizmı̄’s teaching of equation-solving, inferred from records of his writings. Each dialogue aims to display Islamic cultural perceptions of mathematics as well as the technical innovations of al-Khwārizmı̄ and his contemporaries, while illustrating some fundamental aspects of mathematical practice in his time. As dramatic presentations, these plays also aim to be engaging, and so demonstrate the power of theatre (and history of mathematics) to motivate learners in algebra. The original verbal approach of al-Khwārizmı̄, and the associated geometrical demonstrations and probable sand-tray pictures, are represented as authentically as possible, and a transcription is given in modern mathematical notation of the procedures, which we would think of as solving quadratic equations. The plays include introduction and commentary by a narrator and a modern mathematics teacher. Comparisons with modern procedures highlight the great achievement, over the succeeding millennium, including acceptance of negatives, multiple solutions, complex solutions, and logical foundations for the number system. But the comparison also poses the pedagogical question of what might have been lost in the clarity and visual impact of diagrams, and the concern with proof of algorithms.