Reform in mathematics instruction at the college level has been slow to arrive (Dossey, Halvorson, & McCrone, 2008), and many institutions of higher learning still follow the calculus model, while fewer and fewer students need calculus for their chosen areas of study (Ganter & Barker, 2003). Instead, mathematics that is applicable and transferable to other disciplines is more useful to many of today's college students. The Introduction to the Mathematical Sciences course that was the subject of this research study is a standards-based laboratory class that integrates algebra, statistics, and computer science. It was designed for students at both the high school and college levels who have struggled in mathematics. The intent of the course is to provide students with mathematics that they will find useful in their future careers, or future classes. The course is intended to reflect the ideals of reform mathematics at the college level. The purpose of the study was to examine the implementation of this curriculum, and its impact on student thinking and learning of algebra.
In exploring the research questions, the researcher found that the Introduction to the Mathematical Sciences course provided a reform-instruction setting where students were able to demonstrate their understanding of algebra, statistics and computer science. The students showed skill at moving between a number of representations of algebra concepts, indicating they were developing deeper understanding of those concepts. One of the key components of this course that reflected reform ideals was the extensive discussion that took place in the course. This instance of the implementation of the Introduction to the Mathematical Sciences course provides an example of how reform instruction in line with the recommendations of NCTM, MAA and AMATYC (Baxter Hastings, et al., 2006) can be successful in helping students at the introductory college level gain understanding of mathematics. This research study describes a course that successfully plays out using reform instructional methods that are in sharp contrast to other college courses taught using traditional lecture style methods. High DWF rates among students who take college algebra (Lutzer, et al., 2005) indicate that the current model of instruction at the college level is not working. For students who lack confidence in their mathematical abilities and have seen little success in mathematics, this type of course may be a tool that can provide students the mathematical skills necessary to move forward in their studies and their careers.
University of Minnesota Ph.D. dissertation. July 2010. Major: Education, Curriculum and Instruction. Advisors: Dr. Kathleen Cramer, Dr. Tamara Moore. 1 computer file (PDF); x, 225 pages, appendices A-D.
Hansen, Heidi Britte.
Examining the implementation of an innovative mathematics curriculum..
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