College Mathematics Courses Research Articles

A Study of Placement and Grade Prediction in First College Mathematics Courses

A college mathematics placement test with 25 basic algebra items and 15 calculus readiness items was administered to 1572 high school seniors, and first college mathematics course grades were obtained for 319 of these students. Test results indicated that more than two thirds of the high school graduates were not college ready, and the test results were reasonably consistent with the ACT Math benchmark score of 22 for college readiness. Analysis of ACT Math scores, basic algebra scores, calculus readiness scores, and course grades indicated that basic algebra scores are reasonable predictors of grades in College Algebra, whether traditional or modeling-based.

From the Editorial Panel: Let's Work Together

In recent years, schools and teachers have been placed under the microscope and even under attack. Evidence such as the great need for college mathematics courses reviewing preparatory content makes it clear that mathematics learning in North America is far from perfect. The question is, How should we proceed?

Can Technology Help in Mathematical Assessments? A Review of Computer Aided Assessment of Mathematics

Computer Aided Assessment of Mathematics focuses on assessment in college mathematics courses with a special focus on computer-based assessment as a means of providing partial credit and immediate feedback on student work. Written by Chris Sangwin, a senior lecturer in mathematics at the University of Birmingham in the United Kingdom, the book is an important resource for mathematicians or software developers interested in understanding the promise and the pitfalls of using computers to assess student work in college courses. Each chapter of the book addresses a different issue so readers have the option of reading most of them out of order or selecting the chapters that are most valuable to them. Thus, in addition to describing Sangwin's perspectives on teaching and assessing mathematics, this review is designed to help readers decide which chapters in the book will be useful to them.

Using teacher judgment for placement in college mathematics courses: An ethnographic case study at one Midwestern institution

The purpose of this ethnographic case study was to understand the process of making student placements into the mathematics curriculum at one Midwestern university. Historically, the department chair has used an expert teacher's intuitive-based judgment process to assess multiple academic documentations, rather than a more structured method for evaluating multi-faceted evidence of student ability. These measures include, but are not limited to, the ACT Mathematics sub-score (ACT-M), mathematics background, high school transcript, and high school grade point average (HSGPA). Though somewhat archaic, the process was highly individualized, flexible, and highly accurate for this particular institution. As many institutions collect similar information, the impact of using a flexible hierarchy of multiple measures may be applicable to other university's mathematics programs.

Understanding the Peer Assisted Learning Model: Student Study Groups in Challenging College Courses

The Peer Assisted Learning (PAL) program at the University of Minnesota is a primary academic support program for historically difficult, introductory college courses that serve as gatekeepers to academic degree programs. Based upon operating principles of other academic support programs and educational theories, PAL is integrated into the courses it serves. The PAL groups review essential course content, model cognitive learning strategies to deepen understanding, and promote metacognitive awareness so students are autonomous learners in courses without academic support services. The PAL approach operates at the confluence of collaborative learning, cooperative learning groups, and learning communities. This article provides a detailed overview of the PAL model, educational theories upon which it is based, and how variations of it are implemented at the institution. Quantitative and qualitative studies reveal academic and personal benefits for participating students and those serving as PAL facilitators. The studies validate the role of PAL with closing the achievement gap between students of different ethnicities and levels of academic preparedness for rigorous college courses in mathematics and science.

Design and Effectiveness of Modeling‐Based Mathematics in a Summer Bridge Program

AbstractBackgroundSince students' success in their first‐semester college mathematics course is a key factor in their success in engineering, many summer bridge programs for underrepresented students focus on their preparation in mathematics. However, research on the design and efficacy of such programs is limited. We examine the design and effectiveness of a modeling‐based approach to mathematics for entering freshmen engineering students.PurposeThe study addresses two questions: Does a modeling‐based mathematics course in a bridge program positively affect students' performance in their first‐semester college mathematics course? To what extent does a sequence of modeling tasks support the development of students' concepts of average rates of change?Design/MethodThis quasi‐experimental study compared two cohorts of bridge program students over six years to examine the effectiveness of a modeling‐based mathematics course on first‐semester mathematics course grades. Pre‐ and post–tests measured changes in students' concepts of average rates of change.ResultsThe modeling‐based mathematics course closed the previous letter grade gap between bridge program participants and non‐participants in the first mathematics course. We also found significant course grade gains for students who took the modeling‐based mathematics course compared with a previous cohort who took a traditional summer mathematics course.ConclusionsThese results suggest that the modeling‐based mathematics course, with its focus on the development of engineering students' abilities to model changing phenomena, was effective in improving students' concepts of average rate of change and their first‐semester mathematics course grade.

Using the Construct of the Didactic Contract to Understand Student Transition into University Mathematics Education

In this article the concept of the Didactic Contract is used to investigate student ‘transition’ from upper secondary into university mathematics education. The findings are anchored in data from the TransMaths project, more particularly the case of an ethnic minority student's journey from his school to a university mathematics course taught at a large inner-city university in England. Results show that there is a transformation (or rupture) of the Didactic Contract from school to university mathematics, and that this is likely to have serious consequences for students' success, or failure, at this crossroads of students' mathematical development, in particular if students are left to ‘bridge the gap’ from one contract to the other. Further, the author argues that in order to help to smooth the passage, a refinement of the Didactic Contract is helpful, a re-conceptualisation in terms of Normative Didactic Contract and Personal Didactic Contract, and each needs to be considered at each level of development. This is likely to raise awareness about the necessary conditions for success at both sides of the transition junction, and providing appropriate support for students at both levels is likely to provide access for more students to successfully stay in higher education mathematics.

A Case Study on Peer-Teaching

This paper reports on the feedback of a case study on peer-teaching activity in a third year university mathematics course. The objective of the peer-teaching activity was to motivate learning and raise student commitment. From the questionnaires conducted, students welcomed the peer- teaching activity and their learning motivation was also improved.

A Multi-Institutional Study of High School Mathematics Curricula and College Mathematics Achievement and Course Taking

This study examined the relationship between high school mathematics curricula and student achievement and course-taking patterns over 4 years of college. Three types of curricula were studied: National Science Foundation (NSF)-funded curricula, the University of Chicago School Mathematics Project curriculum, and commercially developed curricula. The major result was that high school mathematics curricula were unrelated to college mathematics achievement or students' course-taking patterns for students who began college with precalculus (college algebra) or a more difficult course. However, students of the NSF-funded curricula were statistically more likely to begin their college mathematics at the developmental level.

Student Success in First-Year University Physics and Mathematics Courses: Does the high-school attended make a difference?

This paper considers school factors that contribute to a successful transition from high school to first-year university Physics courses at the University of British Columbia by employing a two-level hierarchical model. It is assumed that there is a relationship between student performance and the high school they graduated from. It is shown that school location and type affect student performance: students from public schools in the Metro Vancouver area perform better in first year compared to students from independent schools and schools in distant communities. The study also considers rankings of schools based on student performance in first-year university Physics and Calculus courses. These university-based rankings differ significantly (essentially in reverse order) from the well-known Fraser Institute rankings based on measures internal to high schools.

Doceamus: Reconsidering the Mathematics Preparation of Pre-service Secondary Mathematics Teachers

mathematics teachers. Hodgson [5] noted that, within such programs, pre-service secondary mathematics teachers “have no explicit occasion for making connections with the mathematical topics for which they will be responsible in school, nor of looking at those topics from an advanced point of view” (p. 509). He endorsed the inclusion of undergraduate coursework that would help preservice teachers develop “deep conceptual understanding of the school mathematics content” (p. 512). In 2001 the Conference Board of the Mathematical Sciences (CBMS) [3] recommended that pre-service secondary mathematics teachers complete “a 6-hour capstone course connecting their college mathematics courses with high school mathematics” (p. 8). Recently, the CBMS has released an updated version of these recommendations [4] and, rather than suggesting a specific capstone course, now proposes that pre-service secondary mathematics teachers complete the equivalent of a mathematics major “that includes three courses with a primary focus on high school mathematics from an advanced viewpoint” (p. 18). The call for pre-service secondary mathematics Secondary mathematics teacher preparation programs typically require pre-service teachers to complete an undergraduate degree in mathematics, or the equivalent [1, 3], along with education coursework and some type of field experience. There has been substantial discussion in the mathematics education community about the mathematics coursework required of pre-service secondary mathematics teachers. Many have questioned the value of traditional undergraduate mathematics programs for future high school Reconsidering the Mathematics Preparation of Pre-service Secondary Mathematics Teachers

A Study on the Curriculum Development and the Management of Basic College Mathematics Courses

A Study on the Curriculum Development and the Management of Basic College Mathematics Courses

Preservice-Teacher Interviews: A Tool for Motivating Mathematics Learning

Helping prospective elementary school teachers (PSTs) recognize that they have something useful to learn from university mathematics courses remains a constant challenge. We found that an initial content interview with PSTs often led to the PSTs' changing their beliefs about mathematics and about their understanding of mathematics, leading to the recognition that (a) there is something to learn beyond procedures, (b) their own knowledge is limited and they need to know more to be able to teach, and (c) engaging in the mathematical activities in their content courses will lead them to learning important content. Thus, such an interview can set PSTs on a trajectory characterized by greater motivation to learn in their content courses.

The Effect of a New Placement Process on Student Success in First Semester Calculus

In this work we describe the placement testing and student intake process at a large, land-grant university and show that long-standing general assessment exams administered during secondary schooling are not accurate predictors of success in university level mathematics courses. We then present results indicating that a placement exam administered during arrival as a first-year student provides a strong indicator of potential for student success in first-semester calculus.

Impacting prospective teachers’ beliefs about mathematics

This study investigated: (1) the changes in the beliefs about mathematics held by 25 prospective elementary teachers as they went through a university mathematics course that aimed, among other things, to promote a problem-solving view about mathematics; and (2) the possible factors that accounted for the observed changes. The course incorporated specific features that prior research suggested reflect successful mechanisms for belief change (e.g., cognitive conflict). The data included students’ reflections, and responses to prompts and interview questions. Analysis of the data revealed the following major trends: (1) a movement towards a problem-solving view from the more traditional Platonist and instrumentalist views; and (2) no change in students’ initial views. Activities creating cognitive conflict, as well as the implementation of instruction valuing group collaboration and explanations, appear to have played important roles in the process of belief change. The findings have implications for research on teacher beliefs and teacher education.

Preservice Agricultural Education Teachers’ Mathematics Ability

The purpose of this study was to examine the mathematics ability of the nation’s preservice agricultural education teachers. Based on the results of this study, preservice teachers were not proficient in solving agricultural mathematics problems, and agricultural teacher education programs require basic and intermediate mathematics as their minimum mathematics coursework requirements. Furthermore, preservice teachers that completed an advanced mathematics course in high school and/or college obtained higher mathematics ability scores. However, a small percentage completed an advanced mathematics course. In addition, preservice teachers that received an A in their highest completed college mathematics course also obtained higher mathematics ability scores. Moreover, 39% of the variance in mathematics ability was explained by completion of an advanced mathematics course in college, a grade of an A in highest level of mathematics completed in college, and being a preservice teacher at University 7, 8, and 9. Based on the data collected in this study, the nation’s teacher education programs may need to further evaluate their mathematics coursework requirements.

Using a Brier Score Analysis to Assess the Effectiveness of a Mathematics Placement Policy

This article describes how a Brier score analysis can be used as an evaluative tool to estimate the predictive accuracy of a course placement policy that was established based on professional or subjective judgment. The policy being evaluated uses the score received on the mathematics portion of the SAT examination as the primary mechanism to place incoming freshmen into the appropriate college mathematics courses best matched to their ability. This placement policy was established based on the idea that the mathematics portion of the SAT examination and a commercially available computerized mathematics placement examination may be placing the majority of students at a similar level in the hierarchy of mathematics courses. The findings of this study indicate that the mathematics portion of the SAT examination can be an effective mechanism for initially placing students in their first mathematics course which is appropriate for their academic ability, and thus can increase their chance of succeeding in their first college mathematics course. Furthermore, a Brier score analysis allowed for comparing and contrasting different scenarios when the placement policy is effective versus when it is not. Implementing this policy allowed for a simpler placement process as well as a substantial financial savings for the institution.

Using Technology-Assisted Instruction and Assessment to Reduce the Effect of Class Size on Student Outcomes in Undergraduate Mathematics Courses

The implementation of online texts, videos, homework, and tests has changed the process of instruction in introductory college mathematics courses. With this change, more of the students’ learning takes place outside of the traditional college classroom and in places such as tutoring centers and dorm rooms. A combination of chi-square tests—for independence with unordered categorical data—and Mann-Whitney two-sample rank-sum tests—for continuous data and ordered categorical data—were used to analyze student outcomes generated from College Algebra and Applied Calculus courses with class sizes ranging from 37 to 129, with common syllabi, homework, quizzes, and tests. These tests showed that medium classes (30–55 students) had little to no benefit over large classes (110–130 students) in student learning and student achievement, with large classes having small to medium positive-effect sizes over medium classes in the area of student satisfaction. The only area in which the small classes had a small positive effect was in the area of student engagement.

Creating and Analyzing the Effectiveness of a Mathematics Placement Policy for New Freshmen

In the mid-1990s, Mercer University's undergraduate schools placed incoming freshmen in their first mathematics course, using only their scores on the mathematics portion of the SAT (SATM). This placement policy was strongly supported by the admissions office because it did not require additional testing of the freshmen in their on-campus summer orientation. Realizing that other academic measures such as a student's academic high school GPA (HSGPA) had a major impact on his or her success in college mathematics courses, a new placement measure called the Mathematics Index (MIDX), which is a function of a student's score on the SATM and his or her HSGPA, was developed by the Department of Mathematics in consultation with the Office of Institutional Research in 2002. The MIDX measure was created by considering success rates in calculus and precalculus as functions of HSGPA and SATM, and finding the level curves corresponding to a 60% success rate in precalculus and a 70% success rate in calculus. After this new placement measure had been used for several years, a study was conducted to determine the success of the new policy. This article reports the method used to create the MIDX measure and the results of our study.

Preparation of Students Completing a Core-Plus or Commercially Developed High School Mathematics Curriculum for Intense College Mathematics Coursework

The purpose of this study was to examine the college mathematics achievement and course-taking of students at a large public research university who completed a commercially developed or standards-based (Core-Plus) high school mathematics curriculum, and who subsequently completed at least 2 college mathematics courses of difficulty level at or beyond precalculus mathematics. Mathematics course-taking and achievement data across 8 college semesters were analyzed for a sample of 1,588 students. Findings indicated that students (including science, technology, engineering, and mathematics majors) were equally prepared for intense college mathematics coursework regardless of which high school mathematics curriculum they completed. These findings inform high school mathematics curriculum adoption decisions for college-bound students, and college policies and practices for advising students enrolling in mathematics courses.