Showing papers in "PRIMUS in 1998"
TL;DR: In this paper, the authors identify and analyze some recurrent problems with the implementation of cooperative and active learning strategies, such as the use of questions, management of instructor-centered activities, and giving up forms of control in the classroom.
Abstract: We identify and analyze some recurrent problems with the implementation of cooperative and active learning strategies. Specifically, we address the use of questions, management of instructor-centered activities, management of in-class group activities, and giving up forms of control in the classroom. We provide suggestions for dealing with each of these difficulties.
19 citations
TL;DR: In this article, a taxonomy of mathematical prose is presented, describing the precise function and meaning of specic types of mathematical exposition, and the merits and demerits of a style of mathematical writing that labels each passage according to its function as described in the taxonomy.
Abstract: This article begins the development of a taxonomy of mathematical prose, describing the precise function and meaning of specic types of mathematical exposition. It further discusses the merits and demerits of a style of mathematical writing that labels each passage according to its function as described in the taxonomy.
13 citations
TL;DR: In this article, the outcomes of an intensive one month mathematical modelling course and the use of posters in peer assessment of student work are described, and the results of the course are used to assess student's ability to use mathematics in problem solving.
Abstract: A well balanced mathematics curriculum consists of a mixture of concepts, context, and skills It is now recognized that one's ability to use mathematics in problem solving is equally important as developing mathematical skills Developing good problem solving skills is not easy In this paper we describe the outcomes of an intensive one month mathematical modelling course and the use of posters in peer assessment of the student work
13 citations
TL;DR: In this article, the authors focus on student learning rather than the deductive presentation of mathematics and provide a stimulus not only to discover theorems and proofs, but also to generate the meaning of definitions and axioms before their formed articulation.
Abstract: Focusing on student learning rather than the deductive presentation of mathematics is a stimulus not only to 'discover' theorems and proofs but also to generate the meaning of definitions and axioms before their formed articulation. Worksheets are provided that will enable an intuitive grasp to precede formal definition in the field of elementary group theory for groups, subgroups, isomorphism, cosets and normal subgroups.
11 citations
TL;DR: This article studied the grades of students under both methods in later courses with a calculus prerequisite, particularly in client disciplines such as physics and engineering, and found statistically significant patterns of differences in results.
Abstract: Freshman calculus at UIC was taught using traditional texts through 1994–95, but with the “Harvard” method fully adopted starting in 1995–96. We studied the grades of students under both methods in later courses with a calculus prerequisite, particularly in client disciplines such as physics and engineering. In some cases the results were indistinguishable, but we did find some statistically-significant patterns. One important example is an improvement of over a third of a grade-point in physics after reform calculus; there were lesser gains, but also some losses, in other courses. Not surprisingly, differences in results decline over time, with increasingly advanced level of courses.
9 citations
TL;DR: This paper examined students' grades in subsequent mathematics courses and observed statistically significant patterns, for example, two traditional lecture formats led to higher adjusted-means than two more time-intensive experimental methods.
Abstract: The lower remedial mathematics course at UIC was taught in fall 1995 using four different pedagogies; we examined students' grades in subsequent mathematics courses. Some measures were indistinguishable, but there were also statistically significant patterns. For example, two traditional lecture formats led to higher adjusted-means than two more time-intensive experimental methods. Other observed features were independent of method; for example, no version of the lower course led to substantial success through the calculus level.
8 citations
TL;DR: In this article, a study of students enrolled in college algebra courses is presented, where the predicted success of students is related to explanatory variables using a linear model, and Advising cut-off scores are discussed in terms of student-success rates as well as the mission statement and philosophy of the university.
Abstract: Placing undergraduate students in appropriate entry-level mathematics courses is a problem that all colleges and universities face. This article is a summary of findings from a study of students enrolled in college algebra. The predicted success of students is related to explanatory variables using a linear model. Advising cut-off scores are discussed in terms of student-success rates as well as the mission statement and philosophy of the university.
6 citations
TL;DR: In this paper, the authors address the problem of poor study habits of calculus students and present techniques to teach students to study consistently and effectively, explicitly showing students how to spend their time studying at least an hour a day, six days a week.
Abstract: The authors address the problem of poor study habits of calculus students and present techniques to teach students to study consistently and effectively. The approach explicitly shows students how to spend their time studying at least an hour a day, six days a week. It also helps them improve both their learning of new material and retention of earlier concepts in a highly organized fashion. Many students greatly appreciate the added structure, work harder than in previous courses, and witness newfound success as a consequence.
6 citations
TL;DR: In this article, some methods of describing and referring to mathematical objects and of consistently and unambiguously signaling the logical structure of mathematical arguments are discussed, as well as some methods for describing mathematical objects.
Abstract: This article discusses some methods of describing and referring to mathematical objects and of consistently and unambiguously signaling the logical structure of mathematical arguments.
5 citations
TL;DR: There is a growing trend in mathematics education to use history and original sources to motivate students to learn content as mentioned in this paper, and an added benefit of using these sources is that it allows instructors to allow instructors to...
Abstract: There is a growing trend in mathematics education to use history and original sources to motivate students to learn content. An added benefit of using these sources is that it allows instructors to...
4 citations
TL;DR: In this article, a summary of insights gained by the authors after a semester of collaborative teaching is presented, along with an overview of the challenges and benefits of collaborative learning. Butte
Abstract: This article presents a summary of insights gained by the authors after a semester of collaborative teaching.
TL;DR: In this article, the authors describe how constructing concept maps and writing accompanying interpretive essays can be used in a Calculus I course to improve students' understanding of important concepts and help teachers assess students' knowledge.
Abstract: This paper describes how constructing concept maps and writing accompanying interpretive essays can be used in a Calculus I course to improve students' understanding of important concepts and help teachers assess students' knowledge. This combined approach allows students to explicitly communicate their knowledge and offers them a chance to view mathematics as a creative activity.
TL;DR: In this paper, the results obtained using small groups and cooperative learning in the discussion sessions of large lecture classes in the mathematical sciences at Loyola University Chicago were described, covering an eleven year period from Fall, 1986-87, through Spring, 1996-97.
Abstract: This paper describes the results obtained using small groups and cooperative learning in the discussion sessions of large lecture classes in the mathematical sciences at Loyola University Chicago. It covers an eleven year period from Fall, 1986–87, through Spring, 1996–97, and provides data indicating where this approach worked well and where additional changes were needed. It also discusses the impact of these changes on class make-up, indicates the need for accurate placement tests, and offers some comments on implementing and using the approach.
TL;DR: In this article, the authors discuss the value of student designed, in-depth, modeling projects in a differential equations course and how to prepare them for it and discuss the benefits of using projects in teaching the calculus sequence.
Abstract: Much has been said about the benefits of using projects in teaching the calculus sequence. Here we discuss the value of student designed, in-depth, modeling projects in a differential equations course and how to prepare them for it. 1 This paper was written while the author was at Department of Mathematics and Computer Science, University of Puget Sounds Tacoma WA 98416 USA
TL;DR: In this article, the effects of incorporating a group final project into an elementary statistics course are discussed, including the implementation of, the evaluation of, and the students' reaction to the group's final project requirement.
Abstract: This paper discusses the effects of incorporating a group final project into an elementary statistics course. Issues discussed include the implementation of, the evaluation of, and the students' reaction to the group final project requirement. Emphases are given to the way in which the final group project is incorporated and the changes this incorporation brings upon the instructor's teaching and the students' learning. As an example, one of the students' group final projects will be presented and examined.
TL;DR: This article developed the idea of a Special Interest Area to complement the BS in mathematics at the University of Slippery Rock in Pennsylvania, USA, to answer two important questions facing undergraduate mathematics majors: What type of career can I look forward to and how can I prepare for it?
Abstract: Two important questions facing undergraduate mathematics majors are: What type of career can I look forward to and how can I prepare for it? While there are many career opportunities for math majors, most undergraduates are unaware of them. To help answer these questions, the Department of Mathematics at Slippery Rock University has developed the idea of a Special Interest Area to complement the BS in mathematics.
Abstract: The relatively young Monte Carlo method has been finding its way into more and more undergraduate courses in recent years. While the Monte Carlo method provides a relatively straightforward technique for approximating areas and volumes, students are seldom exposed to its true power in real-world simulations. This paper presents a relatively simple application of the Monte Carlo method used in actual Air Force studies, and suggests ways of incorporating the application into any appropriate course.
TL;DR: In this paper, the authors present the historical development of required undergraduate core mathematics courses and suggest that a new core course, discrete dynamical modeling, is needed to prepare students for success in the information age.
Abstract: New courses should be designed for the future needs of our students. This paper presents the historical development of required undergraduate core mathematics courses and suggests that a new core course, discrete dynamical modeling, is needed to prepare students for success in the information age. Topics associated with dynamical systems have previously been taught in upper-level, after-calculus courses. Discrete dynamical modeling is accessible to all first-year students, who through this course obtain the foundation for the reasoning, modeling, computation, and language of the new sciences of the 21st century. We propose that now is the time for this course to enter the core program for first-year students.
TL;DR: The Calculus Excellence Workshop as mentioned in this paper is an integral part of the course in Fall 1992 and has continued since that time, with a significant improvement in overall performance of students in this course has been realized.
Abstract: The overall goal of the South Carolina Alliance for Minority Participation (SCAMP) is to increase the number of students receiving advanced degrees in science, engineering and mathematics. One of the ways to achieve this goal is to assist students in the “gateway” courses in science, engineering and mathematics. Calculus I has been identified as one of the gateway courses at Benedict College in which students need special assistance and support. To help students successfully pass this course and to pursue advanced degrees in science, engineering and mathematics, the Calculus Excellence Workshop was instituted at the College. It was found that no single method works all the time. Flexibility is the key. Similar workshops have also been instituted at other SCAMP institutions. The Workshop became an integral part of the course in Fall 1992 and has continued since that time. A significant improvement in overall performance of students in this course has been realized. In this study we describe what i...
TL;DR: In this paper, the authors suggest an approach in courses for mathematics majors and minors similar to the approach becoming popular in applied courses -using student projects, where students are required to complete a statistical analysis of a problem in a semester-long project.
Abstract: This article suggests an approach in courses for mathematics majors and minors similar to the approach becoming popular in applied courses - using student projects. A natural place to introduce modern applications is in upper division, calculus-based probability and statistics courses for mathematics majors and minors. To provide students with an opportunity to design and study a real problem, students can be required to complete a statistical analysis of a problem in a semester-long project. The strategy and implementation is described in the article. 1 St. Joseph's University is a private, church affiliated university with approximately 3500 full-time students.
TL;DR: In this paper, the author shares anecdotes of how this symbolic double entendre causes difficulties for students, and then suggests ways instructors can clarify these ambiguities to make mathematics more understandable to students.
Abstract: In standard mathematical notation, it is common to have a given symbol take on different meanings in different settings. In this article, the author shares anecdotes of how this symbolic double entendre causes difficulties for students, and then suggests ways instructors can clarify these ambiguities to make mathematics more understandable to students.
TL;DR: In this article, a medley of proofs and topics related to the Pythagorean Theorem are presented, as well as a jumping off point for in-class research projects in geometry and the history of mathematics.
Abstract: This article presents a medley of proofs and topics related to the Pythagorean Theorem. It is a resource for teachers and students in high school and undergraduate liberal arts education as well as a jumping off point for in-class research projects in geometry and the history of mathematics.
TL;DR: In this paper, the authors present some aspects of the plan at Xavier University for assessing the mathematics major, including the relationship of department goals and objectives to those of the university, strategies to accomplish goals, assessment techniques, and feedback mechanisms.
Abstract: Although the assessment of student learning has become a very important issue in higher education, there appear to be few examples of plans for assessing programs for mathematics majors in the professional literature. This paper will present some aspects of the plan at Xavier University for assessing the mathematics major. In the spring of 1995, the department submitted its assessment plan which addressed the following topics: goals and objectives, relationship of department goals and objectives to those of the university, strategies to accomplish goals, assessment techniques, and feedback mechanisms. While the goals of the program and the strategies to accomplish these goals will be stated, the main component of this article is the list of assessment techniques. We relate the current status of implementing the plan along with changes we envision.
TL;DR: In this paper, the authors outline some practical advice for improving the level of student activity through properly directed faculty activity in a mathematics department at an undergraduate institution, which is an important gauge of academic atmosphere within the program.
Abstract: The level of student activity in a mathematics department at an undergraduate institution is an important gauge of academic atmosphere within the program. This article outlines some practical advice for improving the level of student activity through properly directed faculty activity.
TL;DR: In this paper, five examples of impossible constructions with Euclidean tools are given for training students the skill of transforming a geometric problem to an algebraic problem, which is called algebraic transformation.
Abstract: Five examples of impossible constructions with Euclidean tools are given for training students the skill of transforming a geometric problem to an algebraic problem.
TL;DR: In this paper, the authors cite a resource for a set of technology-based problems in calculus from science and engineering. But this resource is limited to a subset of problems in the calculus.
Abstract: We cite a resource for a set of technology-based problems in calculus from science and engineering
TL;DR: In this paper, the authors find that the current treatment in technical mathematics texts of approximate numbers, and their accuracy and precision, lacks insight and can be misleading and used without perspective, they can produce surprisingly inaccurate answers and cause confusion.
Abstract: We find that the current treatment in technical mathematics texts of approximate numbers (obtained by rounding), and their accuracy and precision, lacks insight and can be misleading. Rules on arithmetic of approximate numbers are only rules of thumb. Used without perspective, they can produce surprisingly inaccurate answers and cause confusion. However, elementary interval analysis can exactly determine the interval of possible error. Simple examples of interval analysis can be used in the classroom for a better understanding of the subject.
TL;DR: In this paper, the authors describe the development and evaluation of a multimedia statistical unit for a college general education mathematics course and show that female students adapted quickly and effectively to the use of videos, data displays and computer applications incorporated in the program.
Abstract: This paper describes the development and evaluation of a multimedia statistical unit for a college general education mathematics course. The findings indicate that students in the multimedia instructional program showed significantly higher statistical performance than students in a control group. The multimedia instruction seemed especially well suited to female students who, although initially apprehensive, adapted quickly and effectively to the use of videos, data displays and computer applications incorporated in the program.
TL;DR: In this article, the authors used various types of cumulative distribution functions to predict antagonists' behavior during a civil-rights case, and the results hinge on solving an equation that contains the cumulative distribution function for the jury's award in the case.
Abstract: This investigation evolved out of a Centre College student-faculty collaborative research project on Internet use and its benefits to empirical studies. As part of this project, the research team wrote a JAVA program, which simulated an individual's behavior when playing a competitive game. The simulation included an analysis of cumulative distribution functions, and subsequently motivated this study (the authors were two of the team members, the first a senior mathematics major). This paper uses various types of cumulative distribution functions to predict antagonists' behavior during a civil-rights case. The results hinge on solving an equation that contains the cumulative distribution function for the jury's award in the case. Analytically solving a simple triangular distribution model, and numerically solving the normal case, the paper predicts reduced litigation from innovative interpretations of a civil procedure rule, and compares three such rules. The approach provides a nice application ...