Algebra, Calculus, and the ACT
thesisposted on 29.04.2017, 00:00 authored by Alex S. Krysl
It is a common saying that "the hardest part of calculus is the algebra". Unfortunately, I found that many students lack the necessary, prerequisite algebra skills and knowledge in order to utilize completely the novel calculus concepts learned. For calculus to be effective, algebraic manipulation presents itself as an essential precondition. As an example, students apply exponent rules throughout the whole differentiation and integration process—like the power rule. For students who lacked a solid background or basis in algebraic concepts like exponent rules, factoring, rewriting equations, and graphing functions, I observed their learning taking place in the calculus classroom as laborious and arduous. There is another catch here: in high school, many of the students taking this first-year calculus course are juniors preparing to take the ACT. However, the ACT omits calculus from its tests. Teachers are required to prepare their students for the mathematics portion of the ACT, all the while progressing and teaching calculus. So, the question becomes: How do teachers prepare students to take the ACT while continuing to propel them forward in their knowledge and application of calculus? Through my student teaching experience, I found that through applying a method called "Just-In-Time Review", combined with specific ACT preparation, students improved their algebraic knowledge while enhancing their learning of calculus and preparing for the ACT. I will propose some methods or ideas that will help teachers be successful in regards to both the ACT and their calculus—mathematics—course.