Author(s):

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

Mathematics is useful for solving today’s real world problems (NCTM, 2000). Because the redesigned College Algebra had an increased focus on real world applications, history was used to strengthen this connection by focusing on the real world problems that spawned the need to explore today’s College Algebra concepts. Modules were included that detailed how the Egyptians (in surveying the floods each year) developed methods to measure the area of quadrilaterals, how logarithms were developed as a means to save time multiplying and dividing large numbers, and how probability was secretly applied to the ancient games of gambling in order to make the most profitable choices. In the historical class discussions, real world applications for which the concept was originally developed were tied to today’s real world applications of the concept.

Using the historical development of complex numbers and Boolean algebra, students learned the idea that sometimes in the history of mathematics, concepts that were explored on a strictly pure, abstract level come to be extremely useful for real world applications long after they were originally developed. The usage of both complex numbers and Boolean algebra in electronics and computers occurred more than a century after their initial development. Students were posed these questions: “What would the world look like today if neither concept was developed?” and “Could both electronics and computers be at the stages they are today if early developers had not understood that complex numbers or Boolean algebra were the solutions they were looking for?”

D. Goodwin (Black Hills State University) and G. W. Hagerty (Black Hills State University) and S. Smith (Black Hills State University), "The Unique Effects of Including History in College Algebra - Mathematics for Today's Real World Problems," *Convergence* (June 2010), DOI:10.4169/loci002530