College Mathematics Courses Research Articles

Relationship of Mathematics Self-efficacy and Competence with Behaviors and Attitudes of Engineering Students with Poor Mathematics Preparation

This mixed methods research study focuses on two relevant factors in students’ decisions to pursue and complete an engineering major: mathematics preparation and mathematics self-efficacy. This study describes the relationship of mathematics self-efficacy on engineering students’ performance, behavior, and attitudes in their first college mathematics courses. Participants completed a mathematics self-efficacy survey (n=408); 11 were selected to be interviewed. A grounded theory approach was used to examine participants’ behaviors and attitudes in college mathematics courses, their mathematics self-efficacy beliefs, and how these beliefs aligned with their mathematics competence. Interview participants reported relatively high mathematics self-efficacy, but many revealed a mismatch between their mathematics self-efficacy beliefs and mathematics competence levels. Participants who had a balance between these two factors reported being more likely to spend extra time working to overcome their mathematics deficiencies and seeking extra help. However, participants with a mismatch reported being more likely to procrastinate and put little effort into improving their mathematics competence, blaming external factors for their struggles. Despite showing different behaviors and attitudes, all participants reported being likely to continue taking mathematics courses required for their major even after failing their first college mathematics course.

Diagnostic Effects of an Early Mastery Activity in College Algebra and Precalculus

The purpose of this study was to investigate implementation of an early intervention mastery activity during the first two weeks of college algebra and precalculus courses at a large U.S. public university. Statistical modeling of (N = 935) students’ performance in the courses, including a logistic regression model of pass/fail course achievement with students’ high school rank, ACT Mathematics scores, and performance on the intervention as explanatory variables, suggested significant independent differences in course performance across performance levels on the early mastery activity. An evaluation of diagnostic validity for the model yielded a 19% false negative rate (predicted to fail the course, but passed) and a 7% false positive rate (students predicted to pass the course, but failed), suggesting the early mastery activity, when combined with admissions indicators of mathematics readiness, may be useful in better identifying students at risk of failing their first university mathematics course. This strategy, which also yields information for focused intervention efforts, is currently being explored through a campus-wide advising tool at the research site.

Assessing the Effectiveness of Quantway®: A Multilevel Model With Propensity Score Matching

Objective: Quantway is a Carnegie Math Pathways initiative, which redesigns the content, pedagogy, and structure of traditional developmental mathematics courses to simultaneously tackle traditional barriers to student success and support a broad range of developmental students in achieving their mathematics potential. Specifically, Quantway is a quantitative reasoning sequence that is comprised of a single term accelerated developmental mathematics course called Quantway 1 and a college-level mathematics course called Quantway 2. This study assesses the effectiveness of the developmental mathematics course, Quantway 1, during its first six semesters of implementation. Method: We used a hierarchical linear modeling technique to conduct propensity score matching across 37 student characteristics to compare the course performance of Quantway 1 students with matched comparison students from traditional developmental mathematics courses. Results: Quantway 1 students demonstrated significantly higher odds of success in fulfilling developmental mathematics course requirements and enrolling in college mathematics courses in the following year than matched comparison students. In addition, Quantway 1 effects were positive across all sex and race/ethnicity subgroups as well as in nearly all classrooms and colleges. Contributions: This study provides robust evidence that Quantway 1 increases student success in fulfilling developmental mathematics requirements and advances equity in student outcomes. Implications of and future directions for the Pathways are discussed.

Teach the Mathematics of Mathematicians

The secondary-school mathematics curriculum is narrow in scope and technical in character; this is quite different from the nature of the discipline itself. As a result, it offers little inspiration to both students and teachers, and provides students with poor preparation for university mathematics courses and indeed for life. Over the past century, recently more than ever, there have been calls for change, for a curriculum that is true to the subject of mathematics as the creation and study of patterns and structures. While there are hopeful responses to this at the elementary level, there is almost nothing at the secondary level. Ironically, it is felt that in order to prepare students for university calculus, the secondary curriculum simply has to be what it is. This is a special case of a myth that needs to be destroyed.

The Flipped Classroom in a Terminal College Mathematics Course for Liberal Arts Students

The purpose of this study was to assess the effect of flipping the classroom on final exam scores in a terminal general education college mathematics course for a diverse student population. We employed a quasiexperimental design. Seven instructors collectively taught 13 sections of each pedagogy (flipped/traditional). Six hundred thirty-two students participated. Common final exams were graded concurrently. Mixed-model analyses were performed. Students in flipped sections scored 5.1 percentage points higher on average than those in traditional sections (p = .02) when controlling for math SAT and financial aid status, an improvement of 7.8 points among Black students (p < .01) and 1.0 points among Whites (p = .67). The estimated average difference between White and Black students, conditional on covariates, was 5.2 percentage points in traditional sections (p < .01) and –1.6 in flipped sections (p = .39). The 6.8-point difference in achievement gap between pedagogies was statistically significant (p < .01). Flipping the classroom was associated with improved student performance, particularly among Black students.

Impact of Online Summer Mathematics Bridge Program on Placement Scores and Pass Rates

An online four-week summer mathematics bridge program was implemented at a Midwest university with historically low pass rates in College Algebra and Remedial Mathematics. Students who completed the four week program significantly increased their mathematics placement exam scores. These students also had a higher pass rate in their initial college mathematics course compared to the overall student population taking the same courses.

The Effects of a Project-based Course on Students’ Attitudes Toward Mathematics And Students’ Achievement at a Two-year College

IntroductionMathematics anxiety is phenomenon that blocks students from learning mathematics. Mark Ashcraft defines math anxiety as a feeling of tension, apprehension, or fear that interferes with math (Ashcraft, 2002). Extended mathematics anxiety can contribute to the development of negative attitude toward the subject. On the other hand, some researchers used mathematics anxiety as part of their instrument to measure attitudes toward mathematics (Tapia, 1996). Thus, Mathematics anxiety and attitude toward mathematics can be interrelated, both having implications in teaching and learning mathematics. Anxious individuals will avoid subjects, courses, and careers that involve mathematics. Such avoidance can limit students' opportunities and career pathways. For this reason, Hoffer reported that attitudes change rapidly and must be studied more intensely (Hoffer, 1993). Moreover, many professional associations for mathematics have emphasized the need to improve students' attitudes toward mathematics.Howson and Wilson suggested that mathematics courses must offer materials that are personally engaging and useful, or motivating in some ways (Howson & Wilson, 1986). Additionally, implementing real-life applications in class has been proven to be effective to improve students' attitudes toward mathematics (Wade, 2013). At the University of Cincinnati, Foundations of Quantitative Reasoning, project-based course, was designed in 2012 to teach students to better understand the mathematics used in their daily lives and to use mathematics effectively to make better decisions every day. Contents are organized, with engaging coverage in sections like Taking Control of Your Finances and full chapter about Mathematics and the Arts. After taking the course, students are expected to recognize that mathematics is important and relevant to their lives. This new course serves non-STEM majors to fulfill their mathematics requirements. While Foundations of Quantitative Reasoning contains heavy load of applications, it has similar Student Learning Outcomes regarding mathematical concepts that are also covered in College Algebra. Both courses are college level; however, College Algebra falls in slightly higher level because the prerequisite for College Algebra is minimum score of 430 from the Math Placement Test while the prerequisite for Foundations of Quantitative Reasoning is minimum score of 420 from the same test.Related LiteratureStudents' attitudes toward mathematics have been studied for at least the last forty years (Neale, 1969; Aiken, 1976; Ma & Kishor, 1997; Alkhateeb & Mji, 2005; Hemmings & Kay, 2010). Several researchers reported negative correlation between mathematics anxiety and low performance in mathematics, and negative attitudes towards mathematics (Fennema, 1977; Fennema & Shermon, 1977; Richardson & Suinn, 1972; Tobias & Weissbrod, 1980). Belbase discussed that perceptions of mathematics can have possible impacts on learning with the subsequent development of attitudes toward mathematics and associated mathematics anxiety (Belbase, 2013). In addition, negative attitudes toward mathematics often lead to poor engagement causing students to fail the course (Mayes, Chase, & Walker, 2008). There is also correlation between attitudes toward mathematics and withdrawal rates from mathematics courses (Ma & Willms, 1999). There is some evidence showing that students' positive attitudes toward mathematics have positive impacts on students' achievement in college statistics and mathematics courses (House, 1995; Evans, 2007). The effect of the emporium teaching approach on students' attitudes toward mathematics and students' achievement is positive (Bishop, 2010). In particular, there is another study of the effectiveness of implementing real-life applications in class to improve students' attitudes toward mathematics in college mathematics courses (Hodges & Kim, 2013). …

The Math Emporium: Effective for whom, and for what?

This study explores three aspects of a math emporium (ME), a model for offering introductory level college mathematics courses through the use of software and computer laboratories. Previous research shows that math emporia are generally effective in terms of improving final exam scores and passing rates. However, most research on math emporia does not investigate 1) whether the emporium serves certain populations differently than others, 2) the nature of mathematical learning that occurs in the ME, or 3) how the emporium is perceived by the enrolled students. In this paper, we used mixed methods to investigate each of these aspects in the case of a single ME serving nearly 300 intermediate algebra students. We found that the emporium appeared to best serve students with higher math achievement, who enjoyed mathematics, and who spent more time taking their exams. In terms of mathematical learning, the emporium appeared to improve students’ ability to recall and use formulas for familiar problem types, but had limited impact in terms of developing meaning for symbols or flexibility in solving unfamiliar tasks. In addition, students expressed mixed feeling about the autonomy provided by the structure of the emporium.

Lottery Strategy: An activity for new undergraduate students to introduce and reinforce introductory statistical concepts

Most university mathematics courses involve the students studying a statistics module in their first year. However, depending on which modules they took at A-level, they arrive at university with varying degrees of interest and ability in statistics. This article presents a classroom activity that introduces and reinforces introductory probability concepts to help prepare and engage the students for the statistics that they will encounter on their course. In the activity, the students consider and contrast two different strategies for selecting numbers for a lottery, in order to conclude which is best under which circumstances. It comprises a mixture of experimentation using a lottery machine, analysis using probability theory, and simulation using computers.

The Effects of Instructional Strategies, College Division, and Gender on Students’ Performance in College Algebra at a University in South Texas

College Algebra courses have often served as gatekeepers to advancement toward a bachelor’s degree for many undergraduate students in colleges and universities all over the United States. As College Algebra is a core requirement for graduation, it is very important that fail and drop rates for this course be minimized. The ability to pass this class has a direct influence on 4-year/6-year graduation rates as well as retention rates for undergraduate students. Research has been carried out throughout the United States in attempts to tackle this issue. The present study was designed to explore the differences in final grades in College Algebra courses regarding different instructional strategies, college division and gender. Test findings indicated that the performance of college students as measured by final grade in College Algebra courses was significantly different among diverse instructional strategies. In addition, the performance of college students as measured by final grade in College Algebra courses was not significantly different in each college division or gender for different instructional strategies. Findings provided useful information for increasing student retention in college mathematics courses. Students will be more likely to learn and retain mathematical knowledge when diverse approaches for teaching and learning mathematics are applied.

Being a Mathematics Teacher Educator in China: Challenges and Strategic Responses

In this exploratory study, we developed a portrait of the challenges and strategic responses of secondary mathematics teacher educators (MTEs) in Chinese universities. The MTEs reported encountering more challenges when teaching pedagogical courses and supervising student teachers than when teaching college mathematics courses and teaching mathematical problem-solving courses. This finding reflects a key difference between the content, goals, and teaching demands of these 2 elements of mathematics teacher education programs (acting in the role of an MTE versus the role of a mathematics teacher). In this study, we also analyzed the strategies that MTEs use to deal with the challenges that arise in their work and the suggestions they have for the training of future MTEs.

A Longitudinal Study of Students in a Dual-Enrollment Mathematics Program: A Focus on Preparation for Calculus

This is a continuation of a longitudinal study implemented to determine if students enrolled in a dual-credit mathematics program are sufficiently prepared for success in first semester calculus. In the current cycle, thirty high school students enrolled in a year-long sequence of two university mathematics courses were followed through their first-year, on-campus calculus course. Course grades, interviews and surveys were used to determine factors that influence student success. The dual-enrollment courses in this study meet the same level of rigor as the courses taught to traditional students at the partner post-secondary institution. Results indicate that students who complete dual-credit algebra and trigonometry courses through an outreach program are as least as well prepared for Calculus I as those who take those courses on campus. However, over the course of this longitudinal study it has been found that prior experience in calculus is also an important factor to consider in student success.

A critical discourse analysis of practical problems in a foundation mathematics course at a South African university

Mathematical problems that make links to the everyday and to disciplines other than mathematics—variously referred to as practical, realistic, real-world or applied problems in the literature—feature in school and undergraduate mathematics reforms aimed at increasing mathematics participation in contexts of inequity and diversity. In this article, we present a micro- and macro-analysis of a prototypical practical problem in an undergraduate mathematics course at a South African university. This course offers an alternative route to a mathematics major for students considered disadvantaged by enduring educational inequalities in South Africa. Using a socio-political practice perspective on mathematics and critical discourse analysis—drawn from Norman Fairclough’s critical linguists—we describe what mathematics and mathematical identities practical problems make available to students and compare this to what is valued in school mathematics and other university mathematics courses. Our analysis shows that these practical problems draw in complex ways on sometimes contradictory practices in the wider context, requiring the student to work flexibly with the movement of meaning within and across texts. We raise for further consideration the possible consequences of this complexity and offer suggestions for practice that take into account issues of power.

Implementation and outcomes of inquiry-based learning in mathematics content courses for pre-service teachers

This mixed-methods study describes classroom characteristics and student outcomes from university mathematics courses that are based in mathematics departments, targeted to future pre-tertiary teachers, and taught with inquiry-based learning (IBL) approaches. The study focused on three two-term sequences taught at two research universities, separately targeting elementary and secondary pre-service teachers. Classroom observation established that the courses were taught with student-centred methods that were comparable to those used in IBL courses for students in mathematics-intensive fields at the same institutions. To measure pre-service teachers' gains in mathematical knowledge for teaching, we administered the Learning Mathematics for Teaching (LMT) instrument developed by Hill, Ball and Schilling for in-service teacher professional development. Results from the LMT show that pre-service teachers made significant score gains from beginning to end of their course, while data from interviews and from surveys of learning gains show that pre-service teachers viewed their gains as relevant to their future teaching work. Measured changes on pre-/post-surveys of attitudes and beliefs were generally supportive of learning mathematics but modest in magnitude. The study is distinctive in applying the LMT to document pre-service teachers' growth in mathematical knowledge for teaching. The study also suggests IBL is an approach well suited to mathematics departments seeking to strengthen their pre-service teacher preparation offerings in ways consistent with research-based recommendations.

A Study of the Relationship Between the ACT College Mathematics Readiness Standard and College Mathematics Achievement

This study examined the relationship between the American College Testing (ACT) college mathematics readiness standard and college mathematics achievement using a sample of students who met or exceeded the minimum 3 years high school mathematics coursework recommended by ACT. According to ACT, a student who scores 22 or higher on the ACT mathematics test has a relatively high probability of earning a passing grade in his or her first college mathematics course. Data from 11,324 students who attended 1 of 27 four-year postsecondary institutions in the upper Midwest were used to study this relationship. Overall, there was evidence that meeting the mathematics readiness standard was related to college mathematics achievement for students who completed at least 3 years of high school mathematics. The results have important implications for school district staff advising college-intending students on mathematics course-taking, college admissions staff evaluating student readiness for college-level mathematics, and researchers studying college readiness.

Conceptualization, development and implementation of a web-based system for automatic evaluation of mathematical expressions

Assessment and feedback are important parts of the teaching and learning of mathematics; and in general, the process can benefit by the introduction of technology. MathDIP is a web-platform which provides automatic evaluation and feedback of each step of the solution of a math problem. The system incorporates a Computer Algebra System to perform the evaluation and a mathematical expression editor which allows the user to interact with the system using his/her own handwriting. This paper reports on the design, development and evaluation of the system. The usability results of its implementation on an Introductory University Mathematics course show good performance in design and functionality issues. Also, results show that in general, the students participating in the study have a high level of acceptance for the system and perceive that its use motivated and strengthened their learning of the specific math topics covered in the course.

The Status of Proving Among US Secondary Mathematics Teachers

This report examines teachers’ self-espoused attitudes and beliefs on proving in the secondary mathematics classroom. Conclusions were based on a questionnaire of 78 US mathematics teachers who had completed at least 2 years of teaching mathematics at the secondary level. While these teachers placed importance on proving as a general mathematical skill, when they discuss their own classrooms, procedural skill consistently surpasses proof-related activities in importance for a majority of high school teachers. Furthermore, teachers labeling their own past experiences in proving as causing anxiety are predictably more likely to put less value on proving. Interestingly, the quantity of past college mathematics courses is a reverse predictor indicating that further study should consider how students perceptions of proving change as they pass through a mathematics major.

Preservice Teachers of High School Mathematics: Success, Failure, and Persistence in the Face of Mathematical Challenges

The goal of this study was to identify variables related to success and resilience in an undergraduate, high school mathematics teacher education program. Over a five‐year period, we tracked the academic performance and achievement motivation goals of multiple cohorts of students. Students who successfully completed their degrees had higher grade point average (GPAs) upon entering the program, earned higher grades in their first college mathematics course, and failed fewer courses than students who left the program or university. Learning and performance motivational goals did not predict success in the program. Performance goals decreased over time. Nearly half the successful students repeated one or more mathematics courses. Ten students completed their degrees, obtained a teaching license, and are teaching despite the need for multiple repetitions of the same mathematics courses. These persistent students did not differ from their peers in motivational goals. Our results suggest that although students with higher GPAs and initial mathematics grades were more likely to complete the program, students who experienced challenges in mathematics courses were able to succeed. We discuss the implications of these results for recruiting, advising, and retention of students in mathematics education programs.

Making meaning about educational experiences through participatory action research: a project conducted with adults enrolled in a community college mathematics course

This paper discusses the findings of a group of co-researchers involved in a participatory action research (PAR) project conducted with adults in a developmental education program. The co-researchers were mostly individuals of Hispanic descent, who had struggled in the past with schooling. Because the educational experiences of Hispanics often involve marginalizing events, the experiences of the co-researchers are contextualized by explaining how Hispanics and other persons of color experience schooling, and the lasting impact of those experiences on their psyche. The study was based on principles of PAR especially tied to the notion of vivencia (genuine human experiences), and on examples of the use of PAR in educational environments. In order to understand the meaning of the co-researchers’ experiences conveyed during dialogue sessions, the author/researcher used thematic analysis of dialogue and journals that was guided by ‘hermeneutic phenomenological reflection’. Those themes were then critically analyzed by the co-researchers in subsequent sessions. The initial dialogue session gave group members a chance to see commonalities in their educational experiences, contradictions between their experiences in and out of school, and differences in their purpose for being in school. In the second dialogue session, co-researchers discovered through critical dialogue that for people of color, educational experiences involve alienating racism encountered in various forms.

Sage를 활용한 수학 3D 프린팅 웹 도구 개발 - 대학 수학교육을 중심으로 -

본 원고는 대학에서 배우는 수학적 지식이 사회가 필요로 하는 인력이 갖추어야 할 지식 및 능력과 어떤 관계가 있는지를 구체적으로 확인해 주는 대학 수학교육 논문이다. 최근 3D 프린팅의 상용화가 가속화되면서, 각 분야에 적용할 수 있는 3D 프린팅의 고급 기술개발이 중요한 과제로 떠오르고 있다. 이 과정에서, 수학적 지식의 적절한 활용은 필수적이다. 따라서 본 연구는 대학에서 배우는 수학적 지식을 바탕으로, 시간과 장소에 구애받지 않고 누구나 무료로 3D 프린팅 기술을 활용할 수 있도록 하는 클라우드 컴퓨팅 환경을 제공하고, 그를 활용하여 얻은 성과를 공유하는데 그 목적이 있다. 이러한 목적을 달성하기 위하여 한국에 맞게 자체적으로 개선한 오픈소스 소프트웨어 "Sage" 기반의 서버를 이용하여, 3D 프린팅에 필요한 STL 도면 파일을 생성하는 프로그램과 웹(Web) 도구를 개발하였다. 본 논문에서는 새롭고 혁신적인 3D 프린팅 환경을 바탕으로, 수학적 모델링의 기초지식인 미적분학과 선형대수학을 중심으로 우리가 형상화한 다양한 3D 객체(Object)들의 개발 과정을 공유하며, 이 과정을 같이 경험하는 수학전공자들이 대학에서 배운 전문 지식을 활용하여 3D 프린팅의 다양한 관련 분야로 진출하여 그 역량을 발휘 할 수 있는 비전을 제시한다. 특히 수학을 전공한 인력이 3D프린터를 보다 창의적이고 혁신적으로 활용할 수 있는 인력, 그리고 이들을 교육하는 인력으로 성장할 수 있다는 것을 확인한다. Recently, the widespread usage of 3D-Printing has grown rapidly in popularity and development of a high level technology for 3D-Printing has become more necessary. Given these circumstances, effectively using mathematical knowledge is required. So, we have developed free web tools for 3D-Printing with Sage, for mathematical 3D modeling and have utilized them in college education, and everybody may access and utilize online anywhere at any time. In this paper, we introduce the development of our innovative 3D-Printing environment based on Calculus, Linear Algebra, which form the basis for mathematical modeling, and various 3D objects representing mathematical concept. By this process, our tools show the potential of solving real world problems using what students learn in university mathematics courses.