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The Unique Effects of Including History in College Algebra - The Modules (1)

D. Goodwin (Black Hills State University) and G. W. Hagerty (Black Hills State University) and S. Smith (Black Hills State University)

Each module was designed to improve students’ understanding and desire to continue mathematics, with the goal of increasing enrollment in Calculus. During the discussion phase of elevating the role of history of mathematics, it was decided to move beyond the level of history seen in even the most progressive of textbooks. Each week, a significant essay was written about both the development of mathematics as a tool to improve society, as well as the need for each generation to improve their mathematics skills to ensure the further advancement of society. The modules helped motivate the student on the topic of the week, but also was connected with previous lessons so that each lesson increased understanding of the effort required to be successful in mathematics, and also gave the students a greater appreciation for the need of mathematics in their lives.

The modules tell solid stories at manageable lengths. Students were asked to read two to three pages of mathematics history each week. Every teacher of every section of College Algebra implemented the historical modules beginning in 2005. The first nine history lessons are outlined below.

Introductory Lesson: Introduces the term "algebra" and its Arabic origin. It then briefly gives a timeline of the movement through Europe, including the addition of the Cartesian coordinate system, the introduction of the function nomenclature by Leibniz, and the popularization by Euler of the symbolic notation \(f(x)\) for a function (The Function Concept, 2007). The goal was to introduce both the longevity of the subject and the amount of effort required to invent the subject as it is known today.

Quadratics and Parabolas: Looks at the development of quadratic equations (as an application of finding areas for quadrilaterals) and parabolas. The goal is to further extend the notion of the fluidity of mathematics and the time span required to develop today’s mathematics. Also, this module introduces the need for vocabulary and the process in which vocabulary was developed.