This study was designed to compare the success rates in College Algebra between two groups of students attending a Mississippi community college. Eighty students enrolled in a College Algebra course were taught using traditional instructional techniques, and 70 students received technology-enhanced instruction. This study considered the effects of grade scores on a mathematics-achievement pretest and posttest, student attitudes toward mathematics, time-on-task while using technology during mathematics study, mathematics subscores on the American College Test, and withdrawal rates. Data collected for this study were derived from the official transcripts of students enrolled in spring 2007 College Algebra classes of a Mississippi community college serving as the study site. A total of 150 students participated in the study. Statistical analysis included t tests, chi-square tests, Pearson product-moment correlations, and analysis of covariance to examine relationships between the two groups of students. The results indicate that the students who received College Algebra instruction via technology-based methods learned equally as well as the students who received the same instruction via traditional methods. The findings also indicate that the students who participated in the traditional College Algebra course had improved attitudes toward mathematics upon completion of the semester. With regard to those who participated in the technology-based College Algebra course, the amount of time devoted to technology use during mathematics study did not correlate to their final grades (i.e., grades were not higher as this expenditure of time increased).

Recent scientific evidence shows the incredible potential of the brain to grow and change. Students with a growth mindset view errors and obstacles as opportunities for growth. These students welcome challenges and the opportunity to learn from their mistakes. Although some university instructors are incorporating growth mindset into their lectures, attitudes, and exams in small classes, the traditional exam method used in large lecture undergraduate mathematics classrooms follows a fixed mindset model. The growth mindset structured assessments developed for this study incorporate a testing center portion (matching, short answer, fill in the blank and free response) with structured rework opportunities, a written portion with peer reviews, and a group portion. The purpose of this study was to understand the relationship between (1) large lecture college algebra undergraduate growth mindset structured assessments and (2) students’ achievement, drop/fail/withdraw rates, mindsets, and anxiety. This relationship is determined using the final exam scores, the withdraw and fail rates, and the responses from a Likert scale survey and a Qualtrics free response survey. No statistically significant difference in mean final exam scores was found, however, withdrawal and fail rates were lower for the class participating in the growth mindset structured assessments than the control classes. Lower levels of math test anxiety and higher levels of growth mindset were demonstrated in the class participating in the growth mindset structured assessments.

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As Mathematics Educators, we want to help our students not only develop a deep, conceptual understanding of mathematical concepts and processes, but also a positive disposition towards mathematics. Despite the importance of helping students develop a positive mathematical disposition, little research has been conducted examining how students' dispositions develop as they progress through their mathematical studies. In particular, the effects of college algebra on students' mathematical dispositions is not well understood. To examine the influence of college algebra on students' dispositions, students using two different college algebra curriculums were studied at Brigham Young University. Using a mathematical disposition survey, student interviews, and open response surveys, data were gathered about changes in students' dispositions as they progressed through the course. Results suggest that college algebra, on average, does not improve students' mathematical dispositions, and can actually be harmful to students' beliefs about mathematics being sensible and useful, students' beliefs about the importance of hard work and perseverance, and students' self-efficacy beliefs. However, the Pathways college algebra course, which was context-based and conceptual in nature, was less harmful than a more traditional college algebra course. These results corroborate other college educators and researchers' perceptions that the content of college algebra needs to be reexamined and changed, in addition to how it is taught.

Master of Science / Mathematics / Andrew G. Bennett / This study utilizes eye-tracking technology as a tool to measure college algebra students’ mathematical noticing as defined by Lobato and colleagues (2012). Research in many disciplines has used eye-tracking technology to investigate the differences in visual attention under the assumption that eye movements reflect a person’s moment-to-moment cognitive processes. Motivated by the work done by Madsen and colleagues (2012) who found visual differences between those who correctly and incorrectly solve introductory college physics problems, we used eye-tracking to observe the visual attention difference between correct and incorrect solvers of college algebra problems. More specifically, we consider students’ visual attention when presented tabular representations of linear functions. We found that in several of the problems analyzed, those who answered the problem correctly spend more time looking at relevant table values of the problem while those who answered the problem incorrectly spend more time looking at irrelevant table labels x, y, y = f(x) of the problem in comparison to the correct solvers. More significantly, we found a noteworthy group of students, who did not move beyond table labels, using these labels solely to solve the problem. Future analyses need to be done to expand on the differences between eye patterns rather than just focusing on dwell time in the relevant and irrelevant areas of a table.

This study compared the effectiveness, in terms of mathematical achievement and mathematics self-efficacy, of online homework to textbook homework over an entire semester for 145 students enrolled in multiple sections of college algebra at a large community college. A quasi-experimental, posttest design was used to analyze the effect on mathematical achievement, as measured by a final exam. A pretest-posttest design was used to analyze the effect on mathematics self-efficacy, as measured by the Mathematics Self-efficacy Scale. The control group completed their homework using the textbook and the treatment group completed similar homework using an online homework system developed by the textbook publisher. All class sections followed a common syllabus, schedule, and homework list and completed a common, departmental final exam. Classroom observations were also used as a way to establish the similarity between groups. The results of the study found that while the treatment group generally scored higher on the final exam, no significant difference existed between the mathematical achievement of the control and treatment groups. Both the control and treatment group did experience significant improvements in their mathematics self-efficacy, but neither group demonstrated more improvement than the other. When students were divided based on incoming math skill level, analysis showed that low-skilled students who used online homework exhibited significantly higher mathematical achievement than low-skilled students who used textbook homework. Exploratory analysis also showed that more students with low incoming skill levels and more repeating students received a passing grade when using online homework than did their higher-skilled, first-time counterparts, although the differences were not significant. Based on this study it appears as if online homework is just as effective as textbook homework in helping students learn college algebra and in improving students' mathematics self-efficacy. Online homework may be even more effective for helping the large population of college algebra students who enroll in the course with inadequate prerequisite math skills. Instructors and researchers should consider the possibility that online homework can successfully help certain populations of students develop understanding better than traditional approaches. This study has implications for mathematics instructors and for online homework system developers.

The purpose of this study was to study the effects of goal setting on students in a developmental algebra course. This study examined the effects on test scores for students that were prescribed a test score goal, students that created their own test score goal, and then compared to a control group. Three classes of developmental algebra were chosen with a total of 25 participants with reported results. Results showed that students with a goal on a test did not score significantly better than students without a goal, but did score significantly better on a test after the goal than tests before the goal.

ABSTRACT STANDARDS-BASED INSTRUCTION: A CASE STUDY OF A COLLEGE ALGEBRA TEACHER by Anthonia Ekwuocha The lecture method has dominated undergraduate mathematics education (Bergsten, 2007). The lecture method promotes passive learning instead of active learning among students, thus contributing to attrition in undergraduate mathematics. Standards-based instruction has been found to be effective in reducing students’ attrition in undergraduate mathematics (Ellington, 2005). College algebra is gatekeeper for higher undergraduate mathematics courses (Thiel, Peterman & Brown, 2008). Research indicates that if college algebra is taught with standards-based teaching strategies, it will help reduce students’ attrition and encourage more students to take higher level mathematics courses (Burmeister, Kenney, & Nice, 1996). Standards-based instructional strategies include but are not limited to real life applications, cooperative learning, proper use of technology, implementation of writing, multiple approaches, connection with other experiences, and experiential teaching (American Mathematical Association of Two-Year Colleges (AMATYC), 2006). Despite all effort to improve undergraduate mathematics instruction, there are still limited empirical studies on standards-based instruction in college algebra. Research in undergraduate mathematics education is a new field of study (Brown & Murphy, 2000). Research reported that overall students’ attrition in college algebra could be as high as 41% in a community college (Owens, 2003). This high attrition rate in college algebra may impact students’ continuation in higher mathematics courses and their interest in the field of mathematics. As a result more research efforts must be focused on ways to improve college algebra instruction. Thus, the purpose of this study was to explore the teaching practices of a college algebra teacher who adopts standards-based techniques in his classroom. The research questions that guided the study were: What teaching practices are used in the mathematics classroom of a college algebra teacher? How are the teaching practices of the teacher aligned with the characteristics of standards-based instruction? The participant of the study was a college algebra teacher who was identified as a standards-based teacher. The teaching practices of the teacher were analyzed and presented using a qualitative single case study method. Data were collected from interviews with the teacher, classroom observations, and artifacts. The research project was drawn from the frameworks of culturally relevant pedagogy theory, symbolic interaction theory, experiential teaching theory, and standards-based instruction. Analysis of the data showed that the teaching practices of the participant were mathematical communication, proper use of technology in instruction and assessment, building mathematical connections, multiple representations, motivating students to learn mathematics, and repetition of key terms. The teaching practices aligned with the characteristics of standards-based instruction. Findings from the study suggest that standards-based instruction strategies should be used in undergraduate mathematics education, especially in teaching college algebra to alleviate some of the problems. Moreover, university administrators at college level should organize workshops and professional development about standards-based instruction strategies for their teachers.

The purpose of this study was to advance knowledge about the relationship between graphing calculator use and classroom norm development. An interpretive case study design incorporating qualitative and quantitative research methods was used to explore the question: What happens when an exemplary teacher uses graphing calculators in a college algebra class? The purposively selected participants were the teacher and eleven students of a Texas community college algebra course. All 29 classes of the 14-week spring 2006 semester were observed in their entirety by the researcher. The theoretical frameworks guiding the study were the affective representation system and the Multiple Representations Model of Learning and Teaching with the use of the Mathematics and Science Classroom Observation System for data collection, analysis, and profiling of classroom lessons. Originally developed for grades K-12, the use of the instrument was extended to college algebra. Triangulation of data sources using constant comparative and content analysis methods were used to support the three major findings: (1) The instructor's proactive orchestration of specialized instruction, support materials, and designed activities contributed to the establishment of graphing calculator use as an essential part of classroom norms and promoted students' independent use of the tool; (2) The dynamic and interactive features of the TI-84 Plus graphing calculator facilitated the delivery of instruction at high cognitive levels during student interactive activities providing access to, exploration of, and use of multiple representations for some mathematical concepts and solutions not easily attainable using traditional methods; and (3) Although the majority of students had never used a graphing calculator before the course, all students used the tool at appropriate times during instructional activities, self-reporting that their use of the calculator was generally beneficial for enhancing their understanding of lessons and supporting class interactions. Additionally, all students independently chose to use the calculator during major assessments and reported knowledgeable use of the tool to facilitate improved test performance. Replication of the study is limited because the norms developed in this case are unique to the teacher and students who negotiated their establishment. Suggestions are given regarding educational policies, reform practices, and research extensions.

Four out of five Americans will require some postsecondary education. Therefore, a majority of population will return to a community college for retraining and personal growth (McCabe, 2003). Since the turn of this century, many studies have been conducted to examine the success and challenges of the relatively new community college system. One of the most significant challenges is the large percentage of the U.S. population requiring remedial coursework. Fifty-five percent of students entering Florida's postsecondary system require remediation. Of this large remedial population, only 51% will complete their preparatory classes. Students who do complete classes take an average of two years to finish preparatory classes and move on to college-level work. It is hypothesized that learning styles information will empower students with knowledge about their study habits and positively effect academic achievement. This research first examined the quantitative effect that learning styles information had on student achievement. The second qualitative phase of the study examined students' perceptions of learning styles information. Three Introductory Algebra (MAT 0024) courses at a large suburban community college were intensively studied during one spring semester. Due to the size of the study (N=69), results obtained in the quantitative portion were not significant enough to accept the hypotheses. Responses in focus groups showed that students generally felt that learning styles information was useful and half the class used the information to modify how they studied. Half of the students in the control group modified their study habits in response to knowing more about their learning style. Although the qualitative data was supportive of the usefulness of learning styles information in the classroom the quantitative data did not support the hypotheses that learning styles information improves achievement.