Writing in a Reformed Differential Equations Class

In an attempt to promote the development of understanding over rote memorization, writing in mathematics has received increased attention in recent years. In Calculus, the Rule of Three (based on communicating ideas through algebraic, graphical and numerical means) has been replaced by the Rule of Four in which writing plays a central role. Educators agree that the benefits of writing include the promotion of understanding, and the initiation of the posing of questions. Writing also helps generate meaning, and helps in the retentio n of content. In this paper, I evaluate the use of writing for analyzing a problem and its solution. The setting is a reformed differential equations class offered at the Lebanese American University. Unlike a traditional ode course where students are provided with a cookbook of methods for solving differential equations, the emphasis in a reformed ode course is placed on the geometry of the solutions and on an analysis of the outcomes. In many instances, students are asked to solve a differential equation by plotting its solution curves without identifying them analytically, and the sketch is to be supplemented by an argument justifying it. In addition, various real life problems are modeled and essay questions are asked to analyze the graphs describing these models. Results show that students first reject the idea, but later rate writing as essential. Furthermore, an improvement in the style and content of the writing exercises is usually noticeable at the end of each semester.