The beginning of the nineteenth century witnessed a significant improvement in mathematical literacy in the US. People started to realize that mathematics is not merely numbers and operations, but also a mental discipline that could increase the rationality of the American population (Stanic, George, and Kilpatrick, 2003). It then affects the development of the teaching and pedagogical approaches that tended to vary and depend on students’ needs. In this era were three methods introduced, namely rule (memorizing and practicing rules), inductive (determining rules by first working on problems), and analytic (a detailed explanation of a particular way to think through the solution of the problem) (Stanic, George, and Kilpatrick, 2003). Even though the last two methods were considered more significant in improving students’ mathematical literacy as they involved more logic and reasoning, students found those methods confusing. This motivated schools to reform their curriculum and teachers to improve their teaching approach.

There was a major enhancement in the topic of mathematics taught in economy. The context was getting wider, not only to track earnings and spending but also to supervise government spending and taxation and expand the market economy (Stanic, George, and Kilpatrick, 2003). The context incorporated in the second half of this century was even broader. Students started to learn about banking, insurance, and taxation along with some practices in business, credit transactions, and good shipping (Stanic, George, and Kilpatrick, 2003).

In this era, textbooks started to contain applications even though most of the problems were still very abstract and contained pure number exercises. For example, a textbook written by Ray and Tappan (1868) demonstrated the use of quadrilaterals in construction and ornament but did not provide real world examples in Trigonometry.