Flipping College Algebra: Effects on Student Engagement and Achievement.
This study compared student engagement and achievement levels between students enrolled in a traditional college algebra lecture course and students enrolled in a "flipped" course. Results showed that students in the flipped class had consistently higher levels of achievement throughout the course than did students in the traditional course, despite no differences in demographics. Moreover, students in the flipped course reported greater gains in affective variables related to mathematics than did students in traditional courses. In addition, this study found evidence that the flipped course experience was especially impactful for Hispanic women. Introduction Colleges and universities have increasingly been concerned with "bottleneck" or "gateway" courses: that is, entry level courses with high level enrollment but low success. Failure of these courses to effectively serve students can have a severely detrimental effect on both the student and the institution. At the forefront of identified bottleneck courses is college algebra, a one semester mathematics course that can either be taken for general education credit or as a prerequisite for further mathematics courses. Each year more than 1,000,000 students take college algebra or a related course (Lutzer et. al, 2007) Moreover, studies have placed the non success/withdrawal rate for these courses nationally in the 40 50% range (Herriot, 2006) In April 2013, California State University Chancellor Timothy P. White's budget proposal included funding to reduce the negative 116 TLAR, Volume 21, Number 1 impact of bottleneck courses through the use of innovative online technologies. One such type of course redesign is the initiative to "flip" the classroom. In a flipped class, students watch online video lectures before coming to class, complete a pre assessment assignment, and then engage in a classroom discussion of the material facilitated by the instructor. This is in contrast to the traditional lecture model, where students independently take lecture notes and then attempt to complete homework problems on their own. In this paper, we present the results of flipping a college algebra class using online technologies. Our conceptual model addresses the following two research questions: 1. How does the academic achievement of students in a flipped college algebra class compare with that of students in a traditional lecture model college algebra class? 2. What variables may serve as predictors for student achievement in a flipped college algebra class? This paper presents a current literature review and theoretical model; the methodology used in the study with regard to questionnaire design and data collection; the data analysis; and the results and implications of this research. Literature Review and Theoretical Model Review of Recent Studies The struggle that students face to pass college algebra is well documented. In 2010, a national U.S. Department of Education study found that 80 percent of high school dropouts cited their inability to pass Algebra I as the primary reason for leaving school (Schachter, 2013) Problems common to algebra students include the student's previous knowledge of the subject, the effectiveness of the instruction, and their motivation to work hard enough to succeed (Thiel, Peterman, Brown, 2008) Many college students, not just those in college algebra, have misconceptions about their "math ability" and have since given up on the notion that they could ever truly succeed in math (Boaler, 2013) These types of perceptions, coupled with the difficulty of the material and its reliance on prerequisite math skills from K 12 math classes, lead to many students failing college algebra, often multiple times. Flipping College Algebra| 117 Intervention strategies have been implemented to try and increase student pass rates in college algebra with varying degrees of success. Examples leveraging the use of modern technology include Carla Thompson and Patricia McCann's study to redesign college algebra to improve student retention (2010) Sherry Herron's study on the use of computer algebra systems in the classroom to improve pass rates (2012) and Neil Hatem's study on the use of graphing calculators (2010) Other types of technology used in college algebra have included online homework, online tutoring services, and multimedia technology (Kersaint, Dogbey, Barber, Kephart, 2011) Approaches such as tutoring and supplemental instruction have also been found to be helpful for increasing both academic performance and improving attitudes towards math (Corey Legge, 2010; Ugo, 2010) While college alebra professors share one major goal, to increase pass rates, it is also important to consider the affective component of student success. The term "affect" in mathematics, while not strictly well defined, generally relates to a student's beliefs and attitudes towards studying math (Di Martino Zan, 2010) Studies have shown that a college student's positive attitude towards mathematics tends to be correlated to higher achievement in a math courses (Hemmings Kay, 2010; Hodges Kim, 2013) Although studies have been conducted on improving both achievement and affect in traditional college algebra settings, few explore flipped class college algebra courses. Several recent studies on general flipped class strategies have been conducted, including Kathleen Fulton's study (2012) of flipping high school classrooms (2012) Maloy's study of flipping a college community engagement course (2014) and Demski's "expert tips" article (2013) However, few studies focus on a college mathematics courses in general, let alone for college algebra specifically (Wilson, 2013; Sparks, 2011) With this study, we hope to address a gap in the literature to examine the effects on student achievement of flipping college algebra in a university setting. The learning process can be analyzed with Anderson and Krathwohl's revision of Bloom's Taxonomy in Figure 1(Krathwohl Anderson, 2010) 118 TLAR, Volume 21, Number 1 Figure 1. Revised Bloom's Taxonomy In the traditional classroom model, the first two levels, "remember and understand," are presented during classroom time. The student is responsible for the higher levels of comprehension on her or his own. By comparison, the flipped class is structured to allow in class time for higher levels of comprehension. Since students watch pre recorded lecture videos on the material before coming to class, class time can incorporate a problem solving workshop format where students can work independently or in groups to solve more difficult problems. This allows the first two levels of Bloom's taxonomy to take place before class, and allows the instructor and students to build the upper levels of comprehension together during class time. Flipped Class Structure The flipped class used in this study is based on a three step process. The student is expected to watch a 7 12 minute online module for each section of the text prior to coming to class. These modules include explanation of main ideas, examples, and embedded comprehension questions that the student answers as he or she watches and completes a pre assessment "Ticket in the Door" prior to coming to class. He or she then brings the completed Ticket in the Door to class the next day; this serves as the basis for the class discussion and work. Students present their solutions to Ticket in the Door problems and then spend the rest of the class period engaged in problem solving of more difficult problems that would traditionally be assigned as homework (Figure 2) Flipping College Algebra| 119 Figure 2. Three Part Flipped Class Model Theoretical Model This study aims to measure differences in achievement between students in a flipped college algebra class and students in a traditional lecture class. In addition to the standard marker variables of ethnicity and gender, we consider how being in a flipped class as well as previous attempts at college algebra may predict a student's affective response to college algebra. We use this set of variables, along with the student's affective responses, to predict academic achievement in college algebra (Figure 3) Figure 3. Theoretical Prediction Model Method This study was based on students at California State University Fullerton (CSUF) who completed Math 115: College Algebra, during the spring 2014 semester. CSUF is a large, urban, 4 year public university in Southern California, with approximately 38,000 students. The 669 students who completed the Math 115 course in Spring 2014 120 TLAR, Volume 21, Number 1 were included in this study. Information regarding ethnicity, gender, number of college algebra attempts, and grades was reported via university records for all participants. For the population of 669 students, 40.1% of the students self identified as male and 59.9% of the students as female. Approximately 18.1% of students self identified as Asian/ Asian American; 19.1% as White/Caucasian; 49.9% as Hispanic/Latino/a; 3.0% as Black/African American; 6.3% as multiracial; 0.6% as "other" and 3% as unknown/decline to state. Since this was a spring semester, we considered the number of times the student had attempted college algebra. First time students accounted for 49.9% of the population; students who had taken the class once previously accounted for 46.9% of the population, and students who had taken the class two or more times accounted for 3.1% Thus, half of the students had either previously failed or withdrawn from college algebra at CSUF. Because the flipped program was a pilot, the flipped group was smaller than the traditional lecture group. There were 19 sections of college algebra, with 3 flipped sections and 16 traditional lecture sections. Of the three instructors who taught flipped classes, two of them also taught traditional lecture classes. The flipped classes accounted for 19.9% (133) of the students, while 80.1%