College Algebra Students Research Articles

Enhancing the Success of College Algebra Students by Incorporating Adaptive Technologies

College students in the United States often enrol in introductory mathematics courses to acquire skills and knowledge that will enable them to solve related problems in their careers and daily activities. However, previous studies have shown limited levels of improvement that perpetuate a lack of proficiency. As a result, the gap in performance between top students and those at the bottom continues to increase. Using modern technology has been suggested as part of the solution to help students resolve their difficulties in mathematics and achieve better learning outcomes. This study assesses the longitudinal effect of redesigning College Algebra classes at a large public university, switching from a modified emporium model to a lab-based adaptive model. The results show that after redesigning the course, the pass rate increased from 68% to consistently being over 80%, while the withdrawal rate fell from 8% to 3%.

Worked Example Mid-Semester Intervention in College Algebra

The enrollment in lower-level mathematics courses has been on the increase in the last decade. It has been estimated that the DFW rate may rise to the level of 50% in courses that can be classified as college algebra. Numerous interventions have been utilized for college algebra and other mathematics classes to help students, including supplemental instruction, peer-led team learning, group learning, flipped classrooms, and integrating technology. In this study, we offered a half-semester course that implemented worked example worksheets, which were used in a previous full-semester intervention, to help students with the college algebra material. Results showed that the thirty students who participated in the worked example pass/fail mid-semester class significantly outperformed the college algebra students who did not participate in the intervention on total points in the course, quizzes, and tests 3 and 4. In addition, participants earned a significantly higher course GPA, attended significantly more regular class lectures, and earned a higher final exam score. Finally, we analysed the qualitative data to develop five themes about the worked examples and intervention. We conclude that the mid-semester intervention is a good just-in-time mechanism to implement after the semester has started to help students succeed in the class.

The Effectiveness of the Link2Success Program on Freshman Level Math Course Achievement

<p style="text-align:justify">To improve college students’ achievement and success rate in the College Algebra course, a new program called Link2Success (L2S) was implemented in several sections of the course at the study’s university. The program required students to increase their class time to six hours. Three of those hours were spent with certified tutors who helped students with the content preview and homework preparation. The purpose of this study was to investigate the effectiveness of the Link2Success program based on the achievement of College Algebra students. One College Algebra class with embedded L2S and one College Algebra class without L2S were randomly chosen and the grades of several assignments and exams were compared. A survey was given to L2S students to explore their experience and opinion about the program. Another survey was given to non-L2S students to find out if they felt that learning with an L2S program was beneficial to them and would have improved their grades. The results showed that L2S did not have a positive effect on the College Algebra students’ achievement. However, L2S students felt more confident and rated the program highly where as non-L2S students felt they would have benefited from the program if it were implemented in their class.</p>

An Evaluation of College Students’ Perceptions of Statisticians

The widely used Draw a Scientist Test was revised to focus on statistics and 110 Elementary Statistics students were asked to draw a statistician. In addition, to better understand students’ drawings and have some relative comparison, 173 College Algebra students were asked to draw a mathematician. A detailed analysis of students’ images and students’ demographic information was conducted using descriptive statistics, categorical data analysis, logistic regressions, and hierarchical cluster analysis. Results showed that students tend to perceive statisticians and mathematicians as primarily White and male. However, female students were more likely than male students to draw a female statistician and mathematician. Two themed clusters emerged from the hierarchical cluster analysis for both the math and statistics students. We discuss the implications of the results for teaching and future research.

Unboxing mathematics: creating a culture of modeling as critic.

From the socio-critical perspective of mathematical modeling, reflexive discussions about the nature, criteria, and consequences of mathematical models are not a natural consequence of modeling in school. This report is part of a larger study focused on stimulating reflexive discussions in practice employing constructivist grounded theory as a research method. Twenty-seven college algebra students engaged in a 3-week modeling project at a community college in the USA. Audio-recorded group discussions and written reflections were collected to determine how reflexive discussions were taking place. Analysis of students’ actions and reflexive discussions during the modeling project produced four concepts: voicing mathematics, personalizing mathematics, challenging mathematics, and negotiating mathematics. These concepts are integrated into an overall process for stimulating reflexive discussions and are conceptualized as unboxing mathematics. The overarching concept of unboxing mathematics represents one interpretation of how reflexive discussions may be constituted during modeling activities and identifies classroom mathematical practices specific to the socio-critical modeling context of this study.

Identifying Student Responsibilities While Watching Mathematics Instructional Videos

This study investigated the ways in which college algebra students watch mathematics instructional videos about completing the square with the goal of identifying student responsibilities within a particular video and across different videos. Guided by the theory of didactic situations that have defined implicit teacher and student responsibilities within the context of the face-to-face mathematics classroom, participants watched three different videos about completing the square and answered interview questions. Using categories previously identified by the didactic contract for the face-to-face classroom, this study expanded the types of student responsibilities identified specifically for video watching and found that participants, regardless of overall prior knowledge but who had prior knowledge of completing the square, held a responsibility to use the specific set of steps they were taught by their teacher to solve problems. Findings may be useful to both mathematics teachers and video creators.

Promoting Proactive Behavior through Motivation: Required Math Lab Hours Case

Requiring that students enrolled in college algebra to spend hours in a computer lab has been a practice in colleges and universities to improve success and retention. In part, because students come with different backgrounds, skills, and the computer lab environment allows for personalized supplemental instruction and tutoring. However, the way this practice may cause problems among students. Prior to this study, we realized that college algebra students are not pleased with having to wait outside the lab to get in and have to spend three hours per week to a receive a small credit. The wait time is due to the limited lab capacity that cannot house a large number of students when they visit at the last minute or right after a large class meeting. Hence, we attempted to stimulate a proactive behavior of visiting the lab early in the week through offering an incentive. It entails reducing the number of lab hours for the same credit after achieving a certain mastery. The results show that the students responded well to the modification. The final exam mean test shows that the modification was an improvement.

The Effects of Instructional Approach and Social Support on College Algebra Students’ Motivation and Achievement: Classroom Climate Matters

College algebra has been noted as a critical course in post-secondary institutions because it serves as a gateway for major selection and college completion. Combinatorial topics like repeatable permutations are often overlooked in K-12 and undergraduate curricula. Likewise, students’ achievement and motivation are affected by the type of classroom climate created in the undergraduate mathematics classroom. Inquiry-based mathematical education (IBME) is a viable instructional approach because of its focus on community meaning-making of the mathematical content. However, lecture-style approaches still dominate post-secondary mathematics classrooms even though they have been criticized for their focus on procedural knowledge and disinviting environment. Therefore, the purpose of this quasi-experimental study was to test the effects of instructional approach (i.e., lecture-style vs. IBME) and social support (i.e., absence or presence) on undergraduate student motivation and achievement of combinatorial mathematics. Findings indicated that intentional social support-building – regardless of pedagogical method – had the strongest effects on students’ perceived autonomy-support, competence and achievement. Although no differing pedagogical effects were discovered (most likely due to the one-time implementation of the lesson formats), the findings provide evidence for the necessity of community-building efforts -- an aspect of education that is often overlooked in the undergraduate mathematics classroom.

Enhancing the Teaching and Learning of College Algebra with ColAlgMap

Teaching and learning lower level mathematics courses on the college level can be challenging and overwhelming. This paper will demonstrate how to design and develop a maplet package to aid in the teaching and learning of mathematics, to serve as a private tutor with infinite patience for college algebra students, and as a useful pedagogical tool for instructors. By using interactive worksheets and animated graphics in maplets, students will find the opportunity for numerous experiments that will foster their development of mathematical conceptual understanding and of computational skills.

Impact of Implementing Graphing Calculators on College Algebra Students’ Performance, Satisfaction, and Motivation

The purpose of this study was to investigate the impact graphing calculators had on students’ performance, satisfaction, and motivation. A quasi-experiment was performed on an experimental group ( n = 33) and a control group ( n = 42) comprised of college algebra students from Miami Dade College, to compare their final grades. Experimental group participants were also surveyed about their satisfaction and motivation with using graphing calculators. Results of independent samples t tests revealed insignificant difference between the control and experimental groups’ performance (p = .560), but a significant difference was between the two groups’ motivation (p = .003) and satisfaction (p = .018). These results suggest that graphing calculators may play important roles other than simply enhancing student performance, which then opens the door for future investigations into their use in mathematical education. https://doi.org/10.26803/ijlter.18.6.6

A Psychometric Analysis of the Algebra and Precalculus Concept Readiness Assessment for Community Colleges

Understanding students’ readiness for precalculus and calculus at the community college level is critical not only because of the key role community colleges play in higher education but also because calculus remains a gateway course for students in advancing to higher level mathematics. The Algebra and Precalculus Concept Readiness Assessment for Community Colleges (APCR-CC) was designed to investigate community college students’ quantitative reasoning abilities and conceptual understanding in algebra. The present study investigates the psychometric properties of the APCR-CC instrument using item response theory based on a sample of intermediate and college algebra students from six community colleges collected in a pretest ( N = 1,131) and posttest ( N = 772) setting. We examine unidimensionality, item fit, local item independence, measurement invariance, and sensitivity to instruction. Our findings suggest that the APCR-CC instrument is sufficiently characterized by one underlying construct, local dependence does not seem to be an issue, and 80% of the items in the APCR-CC instrument are sensitive to instruction.

Community College Placement Policy Implications Regarding a Discrepancy in the Placement of Students in College Algebra

ABSTRACTCommunity college administrators face a dilemma in the implementation of placement policies regarding college algebra students. Extensive literature devoted to this subject has been generated in the last 100 years without consensus. Furthermore, faculty opinions of the current placement policies contribute to the presence of a discrepancy in the interpretation of placement models used in policy generation. Utilizing a statistically derived and analyzed model in conjunction with faculty and administrator interviews, a new interpretation of the results generated by placement models in terms of the type of prediction generated may assist in the generation of future placement policies. This new interpretation serves to resolve the discrepancy by redefining the capabilities of the statistical model within the context of the faculty and administrator views of current placement policy.

Factor structure of problem-solving efficacy among college Algebra students

This paper discusses the development of the Problem – Solving Efficacy Scale on College Algebra. Through factor analytic research design, the scale underwent five development stages including assessment of factorability of the data, factor extraction, factor rotation and interpretation, rotation confirmation, and internal consistency analysis. In the 80 – item questionnaire administered to 80 randomly selected College Algebra students of Isabela State University, structural validity was attained with 34 scale items grouped into four components; namely, physiological/somatic responses, social persuasions, vicarious experiences, and mastery experiences. The developed instrument can explain 55.36% of the overall variance and has a high reliability coefficient ( .87), confirming that the four factors are integral to problem-solving efficacy in College Algebra. Physiological/Somatic responses and social persuasion explain greater amount of variance than mastery experience and vicarious which suggests that while teachers give importance on improving students’ mastery level and modelling them with successful others in problem-solving activities in College Algebra, they should also encourage students to like the subject and see themselves successful in it, and provide them with sincere and timely encouragements especially problem-solving is a challenging learning tasks. College Algebra teachers should then design attainable learning goals coupled with challenging teaching-learning activities and constructively aligned assessment, and de-emphasize drills, speed tests, and competitions in problem-solving lessons.

Writing to Promote and Assess Conceptual Understanding in College Algebra

Concept-focused quiz questions required College Algebra students to write about their understanding. The questions can be viewed in three broad categories: a focus on sense-making, a focus on describing a mathematical object such as a graph or an equation, and a focus on understanding vocabulary. Student responses from 10 classes were analyzed. Students’ writing provided insight into misunderstandings they had about linear and quadratic equations and systems of linear equations and difficulties using correct mathematical vocabulary. Instructors can use this type of information, which may be undetected with other forms of assessment, to make instructional decisions that meet students’ needs.

Reflecting to learn mathematics: supporting pre-service teachers’ pedagogical content knowledge with reflection on writing prompts in mathematics education

The use of and reflection on writing prompts in mathematics education can allow pre-service teachers to enhance their own mathematical knowledge and broaden their understanding of students’ learning needs. In this paper, we share results from a study with secondary pre-service mathematics teachers who were asked to respond to writing prompts related to various mathematical concepts, reflect on their responses, and then give the same prompts to a group of college algebra students. Our analysis of the data shows that the prompts helped the pre-service teachers to reflect on their role as learners, student thinking and needs and classroom practices. We relate these findings to a framework for looking at pedagogical content knowledge and discuss the usefulness of writing prompts with pre-service mathematics teachers for expanding such knowledge.

Improving college students’ attitudes toward mathematics

This study was conducted to investigate the effectiveness of a treatment designed to improve college algebra students’ attitudes toward mathematics. Keller’s ARCS motivational design model was used as a guiding framework for the development of a motivational video, which was delivered online. The application of motivational design to improve mathematics attitudes in an online environment extends the use of motivational design. A pretest-posttest control group design was used to test the effectiveness of the treatment. The participants in this study were 43 students enrolled in a college algebra course offered at a large state university in the mid-Atlantic region of the United States. Statistically significant results were observed for improved attitudes toward mathematics.

Longitudinal changes in college math students’ implicit theories of intelligence

This study examined changes over time in implicit theories of intelligence and their relationships to help-seeking and academic performance. College algebra students completed questionnaires during the second week of classes and 2 weeks before the end of the semester (ns = 159 and 145, respectively; 61 students completed questionnaires at both waves). The questionnaires assessed entity and incremental implicit theories of general and math intelligence (beginning and end of semester) and help-seeking (end of semester). Results indicated that students had more incremental views of general than math intelligence. Further, their views became less incremental over the course of the semester; however, this decrease was greater for math than for general intelligence. Participants who exhibited a stronger incremental theory of general intelligence at the beginning of the semester subsequently reported greater help-seeking during the semester. Finally, students who had more entitative views of math intelligence earned lower course grades.

Teaching Tip: Are You Changing the Rules? Again?

SummaryStudents often complain that the rules of mathematics are being changed. A short conversation between a professor and a class of college algebra students dramatizes this in the realm of complex numbers and the legal realm of speed limits.

EXAMINING THE RELATIONSHIPS AMONG CLASSROOM CLIMATE, SELF-EFFICACY, AND ACHIEVEMENT IN UNDERGRADUATE MATHEMATICS: A MULTI-LEVEL ANALYSIS

For nearly 50 years, leaders in American industry, military, education, and politics have focused considerable attention on STEM (science, technology, engineering, and mathematics) education. Given the increased societal demand for STEM careers, the relationships among classroom climate, self-efficacy, and achievement in undergraduate mathematics needed to be examined. A purposeful sample of college algebra instructors (n = 15), employed at public 4-year universities in various states (n = 10) across the nation, was administered the Principles of Adult Learning Scale at the beginning of the semester to assess classroom climate. At the end of the course semester, their college algebra students (n = 326) were administered the Mathematics Self-Efficacy Scale-Revised and final college algebra examinations. The results of the multi-level analysis indicated: (a) students having higher mathematics self-efficacy also had higher mathematics achievement, (b) teacher-centered classroom climates had greater mathematics self-efficacy levels, (c) classroom climate was not a significant predictor of mathematics achievement, (c) classroom climate did not moderate the relationship between mathematics self-efficacy and achievement, and (d) although boys reported higher mathematics self-efficacy than girls, gender differences were not found to exist in regard to mathematics achievement.

Activities for Students: Rational Functions: A New Perspective

The study of asymptotes constitutes one of the earliest and most significant encounters a high school mathematics student can have with infinity. The study of horizontal asymptotes, in particular, contributes to a student's later understanding of limits and the notion of “arbitrarily close to.” Typically, students are exposed to horizontal asymptotes in the contexts of exponential and rational functions. Real–life applications of exponential functions abound, but real–life applications of rational functions do not. In this article, we present a hands–on activity that allows students to explore horizontal asymptotes of graphs of rational functions visually and mathematically and that has been used successfully with intermediate algebra, precalculus, college algebra, and mathematics methods students.