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A precisian professor had the habit of saying: "... quartic polynomial ax^4+bx^3+cx^2+dx+e, where e need not be the base of the natural logarithms."
A Mathematician's Miscellany, Methuen Co. Ltd., 1953.
The Unique Effects of Including History in College Algebra
Most of the student attitude evaluations were informal. In a recent conversation with a student who is taking College Algebra at the request of her job, the student informed us that she greatly appreciated the historical readings. The readings gave her a greater understanding of why mathematics was important and gave her “non-mathematical” explanations (her definition of non-mathematical can be interpreted as not algorithmic) as to what was going on. She felt that the historical backgrounds made it easier for her to understand and learn the mathematical processes. This type of attitude seems to have grown in the students over time and as they realize mathematics is more than just a set of facts and rules to be memorized. In informal discussions with Trigonometry students who had taken College Algebra with the historical modules, students credited the history modules with assisting them to reflect on the mathematics needed for their careers, and the modules gave the students a better understanding for effort required for their success. Furthermore, the history modules combined with other changes appear to have also affected the students’ realization that they needed to understand the concepts as well as just complete the assigned work.
An approximate 10% increase in the College Algebra passing rate since 2005 has come since the addition of the historical modules. Today, over 70% of BHSU’s College Algebra students pass the course with a C or better. The College Algebra faculty have maintained a strong stance against grade inflation and have worked diligently to ensure that the 20% increase in passing rates over the course of the reform was not caused by a reduction in the quality of the course. One outside measurement tool has been the CAAP test (CAAP, 2004). The state mandates that all students take the CAAP test at the end of their sophomore year of college. Analysis of this information gives strong statistical data that grade inflation is not occurring. Furthermore, for students whose only math course while attending BHSU is College Algebra, CAAP scores have improved by a statistically significant 10.9% since 2005 (p < .01).
The faculty at Black Hills State University believe that the historical aspect of College Algebra is vital for the student to realize both the need for additional mathematics courses and the effort required to be successful. The inclusion of history has also had some affects on instructors. College Algebra instructors are seeing their former students returning during office hours to discuss mathematical history. During the first month of the current semester, one instructor has had the opportunity to discuss concepts of Boolean Algebra and the Fibonacci sequence with former students. These discussions help ignite the fires in College Algebra instructors and make them want to reach even more students. The faculty feels that including historical development of mathematics is of key importance and believe that the full benefits of history inclusion have yet to be reached. At this time, the faculty is looking for means to increase the use of history. While much has been done to improve the College Algebra course, it seems as though there may be some effects that can only be accomplished through the effective inclusion of the historical development of mathematical concepts.
Hagerty, G. W., S. Smith and D. Goodwin, "The Unique Effects of Including History in College Algebra," Loci (October 2007), DOI: 10.4169/loci002530
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