What are We Developing? A Case Study of a College Mathematics Program

Abstract

Over one‐third of all college mathematics enrollments are in courses considered to be developmental. While such courses have been the subject of a large body of research, one question that seems not to have been studied empirically is the alignment of the content of developmental and college level mathematics courses. This paper gives the results of such a study, conducted at a medium sized public liberal arts university. While the content of the developmental mathematics courses was used subsequently in the Precalculus course, most of the content of the Intermediate Algebra course was not used in other college level mathematics courses. It is hoped that the results of this paper will serve as a catalyst for other institutions to examine carefully and define the mission of both their developmental and college level mathematics courses.

Investigating Predictors of Academic Success in a Foundational Business Mathematics Course

“…Mathematics educator Catherine Fosnot (1996) emphasized that "teachers who base their practice on [student-centered learning] reject the notion that meaning can be passed on to learners via symbols or transmission, that learners can incorporate exact copies of teachers' understanding for their own use or... out of context" (p. ix). College mathematics professors often use a behaviorist teaching approach, which requires students to learn mathematics out of context and in disjointed pieces (Frankenstein, 1997;Johnson, 2007;Mesa, 2012). But "knowledge is not created and recreated in the fragmented forms in which most… subjects are presented.…”

“…A number of studies have examined the perceptions that college mathematics professors have about their incoming students (Blanchard, 2008;Corbishley & Truxaw, 2010;Johnson, 2007;McDuffie & Graeber, 2003;Mesa, 2012;Zelkowski, 2011). Their findings are described in the next section.…”

“…Over the past two decades, some qualitative research has been devoted to student attitudes towards mathematics and their mathematical anxiety, as these factors seem to be linked to student achievement (Hall & Ponton, 2005;Kesici & Erdogan, 2009;Parker, 2005;Tobias, 1987;Thiel et al, 2008). Most literature focuses on the problems with the current conditions of mathematics in higher education (Ballard & Johnson, 2004;Blanchard, 2008;Corbishley & Truxaw, 2010;Davis & Shih, 2007;Hall & Ponton, 2005;Johnson, 2007;Reisel et al, 2012). A key weakness in the literature is the general lack of proposed solutions to these problems.…”

“…Mathematics professor Pete Johnson (2007) performed a longitudinal, qualitative study analyzing developmental mathematics courses. He discovered that over one third of all college students in the United States were enrolled in what have been designated as "remedial" or "developmental" mathematics courses, indicating that the material presented in the courses was supposed to have been covered in a typical high school curriculum.…”

“…He discovered that over one third of all college students in the United States were enrolled in what have been designated as "remedial" or "developmental" mathematics courses, indicating that the material presented in the courses was supposed to have been covered in a typical high school curriculum. Because the material presented in these courses is not considered to be "college-level," students often do not receive college credit for taking these courses (DeBerard, Julka, & Spielsman, 2004;Hall & Ponton, 2005;Johnson, 2007;Mesa 2012;Zelkowski, 2011). Students become frustrated when they enroll in and pay for courses covering material they were exposed to previously in high school, but often still struggle to successfully complete these courses (Johnson, 2007).…”