College Algebra Course Research Articles

Anchoring Inverse and Injective Functions with Techtivities

Inverse and injective functions are topics in most college algebra courses. Yet, current materials and course structures may not afford students’ conceptual understanding of these important ideas. We describe how students’ work with digital activities, “techtivities,” linking two different looking graphs that represent relationships between variables in the same dynamic situation, can help to address this problem. To bolster our argument, we provide empirical data from a broader study, drawing on student work and instructor interviews across three institutions. We conclude with illustrations of how techtivities can serve as instructional anchors for injective and inverse functions.

Shortening the Math Sequence Through a Corequisite College Algebra Course with Embedded Personalized Learning

This paper reports on a novel corequisite design and implementation for College Algebra at Florida International University. The corequisite course uses online, just-in-time, prerequisite assignments delivered on an open-educational platform. Students get help from near-peer learning assistants inside a math emporium environment. The course remains three credits after the redesign and now supports all students who would otherwise be taking Intermediate Algebra as a prerequisite course.

How One Instructor Can Teach a Large-Scale, Mastery-Based College Algebra Course Online

ABSTRACT Mastery-based testing is an assessment scheme that encourages students to learn from their mistakes and develop an understanding of material before moving on. For an entry-level course with large enrollment like College Algebra, this could allow some students to move at an appropriate pace for themselves. This paper outlines the changes made to make College Algebra at the University of Florida an asynchronous mastery-based course for the 500+ students who take the course per year and concludes with a series of lessons learned from the endeavor.

Examining the effect of inquiry-based learning versus traditional lecture-based learning on students’ achievement in college algebra

The focus of this study was to examine the effect of teaching based on inquiry-based learning versus traditional learning on mathematics achievement scores of undergraduate students enrolled in a college algebra class in a university classified as a Predominantly Black Institution. A college algebra course was chosen in this study due to the critical role it plays as a gateway for college completion and due to the generally high failure rate in college algebra. This study used a quasi-experimental design, with pre- and post-test to determine the effect of the instructional pedagogy on mathematics academic achievement of students. Analysis of covariance results from 41 students revealed, when controlling for college algebra readiness pre-test scores, students in the inquiry-based learning section showed significantly higher mathematics achievement post-test scores than in the traditional lecture section.

Construct Validation of an Instrument That Assesses Quality of Instruction in Community College Algebra

ABSTRACT The Evaluating the Quality of Instruction in Post-secondary Mathematics (EQIPM) is a 14-item instrument that uses videos of teaching to investigate the quality of instruction in college algebra courses taught at community colleges. We hypothesize that quality of instruction can be characterized along three distinct factors, the interactions between: (a) students and the content, (b) instructors and the content, and (c) students and the instructors. We used confirmatory factor analysis to empirically evaluate this hypothesis. Using coding of over 900 segments of video of instruction from 40 intermediate and college algebra teachers from eight community colleges, we performed a factor analysis to identify the structure of the instrument. Our findings suggest that the EQIPM instrument captures the three hypothesized underlying factors of quality of instruction with adequate fit statistics and factor loadings. The availability of this instrument opens the door for further research on aspects of quality that influence student performance and for promising programs of professional development for community college faculty teaching mathematics.

Using guided notes to support learning in first-year calculus

This research explores the use of guided notes in a post-secondary calculus course and the extent to which use enhanced students’ success in a first year calculus course. Guided notes have been previously shown to be perceived as helpful to learning by students, and one study showed that the use of guided notes improved pass rates in a first year college algebra course. Using an experimental design, our results show that guided notes improved outcomes for students when compared to a control group that did not use guided notes–logistic regression modelling found evidence that guided notes, mathematical aptitude and gender (male) were associated with a higher probability of a student successfully completing the course. No significant interactions between guided notes and gender was observed. Implications for further research and practitioners are included.

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>

Using Worked Examples with Active Learning in a Large lecture College Algebra Course

At a research university near the east coast, a college algebra class has been restructured into two large lectures a week, an active recitation size laboratory once a week, and an extra day devoted to active group work called Supplemental Practice (SP). SP was added as an extra day of class where the SP leader has students work in groups on a worksheet of examples and problems, based on worked example research, that were covered in the previous week’s class material. Two sections of the course were randomly chosen to be the experimental group and the other section was the control group. The experimental group was given the SP worksheets and the control group was given a question-and-answer session. The experimental group significantly outperformed the control on a variety of components in the course, particularly in light of the number of days students attended SP.

Effects of digital learning skill training on the academic performance of undergraduates in science and mathematics.

Many science, engineering, technology, and math (STEM) majors fail to complete their degrees, and those who leave report they lack learning skills required for STEM coursework. In 2 studies, we examined the effects on students’ exam performances when they were assigned to complete a brief digital learning skills training program we embedded into their course site on the university learning management system for their large lecture science and math courses. Study 1 examined whether delivering brief trainings that teach learning skills to students directly within their STEM course site during the first weeks of class would encourage undergraduate science learners to adopt effective learning behaviors and improve their achievement on exams. Additional analyses examined benefits to a group underrepresented in the STEM workforce: first-generation college students. Students who spent time completing training made greater use of resources supporting planning, monitoring, and cognitive strategy use and outperformed students in the control group on initial and final exams. Study 2 examined whether the same, domain-general learning skill training could produce effects when placed in a college algebra course. Random assignment to treatment and control was conducted early in the second course unit. Those in the skill training condition outperformed a control group who solved additional algebra problems on the next 2 unit exams. Across studies, effects of training were similar for first-generation and continuing generation students. However, the effects obtained often improved the exam scores of first-generation students from below to above the minimum score which requires course reenrollment and delays STEM degree completion. (PsycInfo Database Record (c) 2021 APA, all rights reserved)

Exploring Mathematics of the Sociopolitical Through Culturally Relevant Pedagogy in a College Algebra Course at a Historically Black College/University

In collegiate mathematics, college algebra continues to be a barrier to graduation for students (specifically non-science, mathematics, engineering, and science majors). Each year, nearly half of enrolled students struggle to “pass” this course with a grade of C or better (Herriott, 2006). Using innovative constructed lessons geared towards African American students, this research study was designed to investigate the effects of a sequence of such lessons grounded in the principles of culturally relevant pedagogy on students enrolled in an introductory college algebra course at a historically Black college/university. Using critical race theory as a lens, along with culturally relevant pedagogy, this study explored students’ abilities to apply mathematics to address contentious and present-day sociopolitical problems through eight in-depth semi-structure student interviews. Further, findings also suggest the need for collegiate mathematics instruction to have more emphasis on cultural components to build students’ sociopolitical consciousnesses, because this is integral in helping students be able to think critically and use mathematics in their everyday lives. Students in this experimental course were able to discuss difficult issues, such as the pervasiveness of racism in America (DeCuir & Dixson, 2004) and the importance of cultural identity for African American students (Martin, 2009).

Preliminary outcomes from a learning community to increase biology course knowledge

ABSTRACT The purpose of this study was to evaluate the preliminary outcomes of a learning community intervention (LC), which was based on the performance pyramid theoretical model of student supports. The LC integrated college algebra into biology course work. We used a quasi-experimental design to compare LC students to separate General Biology I and College Algebra course control groups on respective measures of biology and algebra course knowledge, and an assessment of perceived performance pyramid supports. Participants included 198 students (LC, n = 22; biology control, n = 52; mathematics control, n = 124) at a Historically Black University in the Southern United States. An analysis of covariance (ANCOVA) indicated that the LC students had significantly greater performance from pre- to post-test on a measure of biology course knowledge (Cohen’s d = 0.76) compared to the biology control group. An ANCOVA indicated that the LC and mathematics control students performed similarly on a measure of algebra course knowledge. Group differences from a multivariate analysis of covariance on perceived performance pyramid supports were mostly statistically non-significant. Overall, the LC increased biology course performance. Implications for improving biology course performance and better assessment of students’ perceptions of support for academic success are discussed.

Incorporating Statistics Into College Algebra

The authors discuss the status of college algebra and related offerings and their relationship to introductory statistics education. They also describe an innovative approach to college algebra that integrates a significant amount of statistical reasoning and concepts and statistical methods as natural applications of basic ideas that are part of a modern college algebra course. This can serve either as an introduction to a subsequent introductory statistics course or as a reminder/reinforcement of key statistical ideas for students who have previously taken an introductory statistics course.

Let Me Say It for the Folx in the Back, GOOD TEACHING ISN'T GOOD ENOUGH : Quantifying Academic Achievement in a College Algebra Course Centered on CRP

The purpose of this pre/post-intervention quantitative experimental study was to investigate the effects of a sequence of lessons grounded in the principles of culturally relevant pedagogy on students enrolled in a college algebra course at an HBCU. In particular, the paper focuses on the interaction between these lessons and academic achievement (students' ability to learn, process, and affinity towards the subject they are learning about) with regards to students' grades and their views about mathematics. Two classes of students, an experimental group and a control group, engaged in mathematics lessons that were grounded in rigorous mathematical teaching practices; but the experimental course received lessons that also incorporated principles of culturally relevant pedagogy. Results indicated that students in the experimental course showed significant quantitative gains on the various measures related to academic achievement and self-efficacy in mathematics.

Active learning strategies with positive effects on students’ achievements in undergraduate mathematics education

The paper describes active learning strategies used in undergraduate college algebra and business calculus courses. There are a variety of active learning strategies described in the literature. We wanted to implement a few that together, satisfy the key characteristics of active learning strategies. The active learning strategies described in this paper are, interactive presentation style, group-work with discussion and feedback, volunteer presentations of solutions by groups, raise students’ learning interest towards specific topics, involve students in mathematical explorations, experiments, and projects, and last but not least, continuous motivation and engagement of students. We analyse the relationship between the average results of 27 college algebra and business calculus sections and the effects of the level of use of these active learning strategies. We demonstrate that the application of these strategies has a positive effect on the average results of the sections and the passing rates of the students.

Implementing Standards-Based Grading in Large Courses Across Multiple Sections

Standards-based grading (SBG) is an assessment/grading system that attaches scores to the mastery level of specific learning objectives. This methodology is gaining momentum in the K-12 environment but has been largely overlooked at the post-secondary level. In this paper, I will discuss the implementation of this practice in a College Algebra course. I will also discuss the motivation in attempting an alternative assessment system, the development and implementation process and describe the resulting system. Comparisons will be made between a College Algebra course utilizing the traditional points-based system and the same course in which SBG was incorporated. These comparisons will include observed student behaviors, student perception, the administrative efforts required of the instructor, and student performance in subsequent courses.

Teaching College Algebra Using Web-Based, Project-Based and Peer-Led-Team Learnings

The University of Arkansas at Pine Bluff (UAPB) is the second oldest historically black land-grant institution in the state of Arkansas and has been producing well-qualified STEM scholars. However, STEM students at UAPB are affected by Mathematics classes, especially College Algebra. The purpose of this article is to share how the Department of Mathematics and Computer Science (MCS) increased the passing rates of College Algebra courses. MCS utilized three evidence-based (EB) instructional methods (WebAssign, Peer-Led-Team-Learning and Julia computer programing) and created a Co-Requisition College Algebra course to improve the passing rates of College Algebra courses. In addition, Math faculty received a 2-day faculty development training on EB instructional methods to properly and efficiently implement EB instructional methods. Through these activities the passing rates of College Algebra courses have improved. In addition, students who are enrolled in EB instructional College Algebra classes showed positive attitudes toward learning College Algebra according their survey results.

Assessing the Emporium Model Through Student Performance and Persistence

The mathematics emporium model (MEM) was implemented to improve student success and retention rates. The college algebra course sequence was redesigned using the emporium model to establish consistency, emphasize active learning, modularize course materials, and provide one-on-one personalized on-demand assistance from faculty and teaching assistants. The emporium model ensured consistent content coverage and learning experiences, improved course coherence, and improved quality control. This study compared the course performance of students enrolled in a college algebra and trigonometry course using the MEM and traditional, lecture method. The results on whether the MEM or traditional students performed better were mixed. Also, the course effectiveness rates, which examines the successful performance of students enrolled in two successive courses that are associated such that the first course provides the foundation for the second, were similar for both the MEM and traditional methods.

Effects of a Flipped Classroom Model in an Introductory College Mathematics Course

Introductory and remedial courses in college mathematics often serve as a gateway to student success. However, these university courses have seen little innovation despite historically low success rates. We sought to address deficits of the traditional lecture model and enhance student learning in an introductory college algebra course through the implementation of a flipped classroom. In this paper, we fully describe the course design, and discuss the interplay between online and in-class activities. We then present data regarding student self-efficacy and success rates in subsequent quantitative courses from our work across five semesters of implementing and researching the course.

Exploring mathematics identity: an intervention of early childhood preservice teachers

ABSTRACTEarly childhood and elementary preservice teachers often fear mathematics, find it irrelevant, have mathematics anxiety, hold negative self-perceptions, and have low mathematics achievement. This study investigates the influence of an identity exploration intervention on preservice teachers’ mathematics identities during a college Algebra course specifically designed for education majors. Results provide insight into the patterns of change in identity and motivation. Data was analyzed following a theoretical framework on role identity that highlights the interaction between self-perceptions, beliefs, goals, and action possibilities. Analysis identified patterns of change in student identities. Themes across cases highlight the differences in change amongst participants, the influence of initial identity, and the impact of perceived relevance on identity exploration.

Active Learning in Computer-based College Algebra

We describe the process of adjusting the balance between computer-based learning and peer interaction in a college algebra course. In our first experimental class, students used the adaptive-learning program ALEKS within an emporium-style format. Comparing student performance in the emporium format class with that in a traditional lecture format class, we found an improvement in procedural skills, but a weakness in the students’ conceptual understanding of mathematical ideas. Consequently, we shifted to a blended format, cutting back on the number of ALEKS (procedural) topics and integrating activities that fostered student discourse about mathematics concepts. In our third iteration using ALEKS, we made use of ALEKS-generated data to design peer-to-peer activities that matched student progress.