The effect of different college algebra courses on students' understanding of linear and exponential function concepts

Over the last five to ten years, many of the changes that have strengthened mainstream collegiate calculus have been implemented in the college algebra course. Refocusing the college algebra course has resulted in an effort to realign the rationale and course goals with the needs of its current students. Refocusing college algebra has brought about a change in the content taught in the course as well as the implementation of different pedagogical methods.;This study uses an evaluative case study design, using quantitative and qualitative methods, to explore differences between student cohorts based on the type of college algebra instruction they receive. The participants of the study are 170 students enrolled at a four-year university in the Midwest enrolled in a college algebra course. Students in the experimental cohort (n = 95) are taught from a contemporary perspective which focuses on modeling mathematical situations, working in a discovery-based environment, and solving problems within-context. Students in the control group (n = 75) are taught from a traditional perspective which primarily uses lecture methods to teach students to master a list of algebraic rules that will enable them to solve equations of many different forms.;The effect of the two different courses on students' understanding of linear and exponential functions is assessed using ten common exam questions given to each cohort. The exam questions cover both topics over five different objectives: procedural, conceptual, multiple solution methods, representation translation, and within-context. Results support a belief that students from the contemporary cohort may have a more connected and flexible understanding of the content.;Qualitative data is collected from twelve B level students. Students are asked questions about two different situations which can be modeled by a linear or exponential function. Students are evaluated based on their ability to navigate through the Lesh Translational Model and work with different representations of the same content. Analysis of the qualitative data shows that students taking college algebra from a contemporary perspective may have more flexibility with their knowledge and understanding of the two function types when asked to present and discuss them in multiple modes.