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AMATYC Review Fall 2005
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The AMATYC Review

A refereed publication of the American Mathematical Association of Two-Year Colleges

Editor: Barbara S. Rives, Lamar State College
Production Manager:John C. Peterson
Vol. 27, No.1, Fall 2005 issue, Abstracts
Authors
James Metz
Joscelyn Jarrrett
Lisa Evered and Sofya Nayer
Ayoub B. Ayoub
Patricia Hale and Charles Hale
D. Patrick Kinney and Douglas F. Robertson
James Metz
Ben Hill
David M. Behrman
Jawad Sadek and Russell Euler
Nancy J. Sattler
Edited by Sandra DeLozier Coleman
Alain Schremmer
Edited by Brian E. Smith
Reviewed by Marion S. Foster, and Tomball College
  • The Problems Section (no abstract available)
Edited by Stephen Plett and Robert Stong
James Metz

The AMATYC Review

Fall 2005, Vol.27, No.1

The AMATYC Review

Fall 2005, Vol.27, No.1

Solving Triangles

Joscelyn Jarrrett

Joscelyn A. Jarrett is a professor of mathematics at Gordon College in Barnesville, Georgia, He received an MS in mathematics from the University of Toronto and a PhD in mathematics education from the University of Iowa. E-mail: j_jarrett@gdn.edu
This article discusses the four categories of triangles that are standard in most textbooks when "solving" triangles: (a) Given the lengths of two sides and the measure of an angle opposite one of the two given sides, (b) Given the lengths of two sides and the measure of the included angle, (c) Given the lengths of all three sides, d) Given the lengths of one side and the measure of two angles. It then introduces two new categories of solving triangles: (e) Given the measures of two angles and the perimeter of the triangle, and (f) Given the measures of two angles and the area of the triangle. These two new categories require the use of two non-standard theorems which are stated and proved in the article. One of the two theorems is an extension of the Law of Sines to include the perimeter. The other provides a relationship among the area, angles, and the perimeter of a triangle. Furthermore, the article gives four applications of the use of these theorems in solving problems of the two new categories introduced.

 

The AMATYC Review

Fall 2005, Vol.27, No.1

Nurturing Mathematical Talent through Student Research

Lisa Evered and Sofya Nayer

Lisa Evered is a professor of mathematics at Iona College in New Rochelle, New York. She has taught mathematics at every level from elementary to graduate school and is the author of articles about education of the mathematically talented. E-mail: levered@iona.edu
Sofya Nayer is an associate professor at Borough of Manhattan Community College in the City University of New York. She has a degree in engineering and a doctorate degree from Teachers College, Columbia University E-mail: yakovn@hotmail.com
The tedium that characterizes many routine calculus activities necessary for average students often results in the loss of the most talented to the field of mathematics. One way to overburden teacher to nurture mathematical talent within a typical calculus class is to encourage student research. This article illustrates how student research facilitated the learning and stimulated the interest of two urban community college students. The contrast between the creative studentÕs thought and more pedestrian approaches is useful In understanding the nature of mathematical talent.

 

The AMATYC Review

Fall 2005, Vol.27, No.1

Cramer's Rule Revisited

Ayoub B. Ayoub

Dr. Ayoub is a professor of mathematics at Abington College of the Pennsylvania State University. His interests include number theory, collegiate mathematics and mathematics history. He received The Pennsylvania State University's 1990 George Atherton Award for Excellence in Teaching. E-mail: aba2@psu.edu
In 1750, the Swiss mathematician Gabriel Cramer published a well-written algebra book entitled Introduction á l'Analyse des Lignes Courbes Algèbriques. In the appendix to this book, Cramer gave, without proof, the rule named after him for solving a linear system of equations using determinants (Kosinki, 2001). Since then several derivations of this rule have appeared (Chadha, 1996; Larson et al., 2004; Shirm & Adams, 2002). In this article, the author will introduce another proof of Cramer's rule based on the expansion in cofactors of a determinant.

The AMATYC Review

Fall 2005, Vol.27, No.1

The Battle of the Zero Divisors

Patricia Hale and Charles Hale

Patricia Hale is an associate professor of mathematics starting her sixth year of teaching at California State Polytechnic University, Pomona. She teaches mathematics courses primarily for elementary and secondary preservice teachers. Her interests include mathematics education, group theory, and women in mathematics. E-mail: phale@csupomona.edu

Charles Hale is a lecturer in the mathematics department at California State Polytechnic University, Pomona. His interests are mathematics education, mathematics history and non-Euclidian geometries. Additionally, he likes to water-ski, camp, hike and eat, not necessarily in that order. Lastly, he is the proud father of Jessica, who has been accepted to Stanford's graduate program. E-mail: crhale@csupomona.edu

The mathematical reasons that we cannot divide by zero are not easy for most students to understand; in fact, even those students who have more than just a basic understanding of algebraic concepts still have difficulty. This is most problematic for college students who are prospective teachers since they need to develop a deep understanding of division because both national and state standards usually require these topics be taught to elementary school children. Unfortunately, many of our prospective teachers are never given the opportunity to develop a deep understanding of the reasons why division by zero is undefined; what indeterminate means in this setting; and what is meant when we say a solution does not exist because it would approach infinity. In this paper we give examples of prospective teacher's understanding of division by zero and a particular model that has helped our college students come to an understanding of why division by zero is undefined.

 

The AMATYC Review

Fall 2005, Vol.27, No.1

Identifying Students' Reasons for Selecting a
Computer-mediated or Lecture Class


D. Patrick Kinney and Douglas F. Robertson

Pat Kinney is a mathematics instructor at the Wisconsin Indianhead Technical College in New Richmond, Wisconsin. He has a PhD in mathematics education from the University of Minnesota. Previously, he taught mathematics at the General College of the University of Minnesota. E-mail: pkinney@witc.edu

Douglas F. Robertson is a professor in the General College, the developmental education unit of the University of Minnesota, where he has taught mathematics and computing since 1974. E-mail: droberts@umn.edu

Students in this study were enrolled in either an Introductory Algebra or Intermediate Algebra class taught through computer-mediated instruction or lecture. In the rst year of the study, students were asked what they believed helped them learn mathematics in the instructional format in which they were enrolled. They were also asked what they would nd dicult about learning mathematics in the instructional format in which they were not enrolled. Based on studentsÕ written responses, a set of 12 survey items was developed. The items were administered at the end of the fall semester the following year. There was a signicant dierence at the p = 0.05 level on nine of the twelve items when comparing results from computer-mediated and lecture students who were consistent in their preference for either computer-mediated or lecture instruction. Students who selected computer-mediated instruction indicated that the software should provide step-by-step instructions and allow the students to control the pace and to navigate backwards to review. They also viewed the software as a more visual way of learning than a teacher lecturing and indicated that software holds their attention better than a teacher lecturing.

 

The AMATYC Review

Fall 2005, Vol.27, No.1

The AMATYC Review

Fall 2005, Vol.27, No.1

Regarding Basic College Mathematics, A
Subversive Comment and a One Act Play

Ben Hill

Ben Hill is a mathematics instructor at Lane Community College in Eugene, Oregon. He has taught mathematics, statistics, or cultural anthropology at Oregon Coast Community College, the University of Maryland Asian Division, and the University of North Dakota.
He holds an MS in mathematics and a PhD in curriculum and instruction from the University of Oregon. His research interests are in cultural aspects of education. E-mail: hillb@lanecc.edu

Among math educators, it is a truism that basic college math skills are needed in every career eld. But actually this is a false professional myth. Hardly anyone makes direct use of mathematics beyond arithmetic in the course of everyday life. Moreover, math’s status as an almost universally required college subject is not inevitable. Algebra and calculus could conceivably be relegated to specialists in the same way that Latin has been. This is not a research paper, but an opinion piece intended to provoke reection and discourse. In a personal and sometimes humorous tone, the author argues that basic college math in fact deserves its position in the college curriculum, though for reasons other than those commonly asserted. By way of conclusion, ideas from the essay are explored in a ctional vignette between one teacher and one student, presented in the form of a one act play.

 

The AMATYC Review

Fall 2005, Vol.27, No.1

The AMATYC Review

Fall 2005, Vol.27, No.1

Classroom Issues with Series Tests

Jawad Sadek and Russell Euler

Jawad Sadek is an associate professor of mathematics at Northwest Missouri State University in Maryville. His main interests include complex analysis, problem solving, his students' questions, and soccer. E-mail: jawads@mail.nwmissouri.edu

Russell Euler is a professor in the Department of Mathematics and Statistics at Northwest Missouri State University. His interests include analysis, geometry, and number theory. Presently he is the Problems Editor for the Elementary Problems and Solutions section of The Fibonacci Quarterly. E-mail: reuler@mail.nwmissouri.edu

We find infinite series in calculus to be one of the most confusing topics our students encounter. In this note, we look at some issues that our students find difficult or ambiguous involving the Ratio Test, the Root Test, and also the Alternating Series Test. We offer some suggestions and some examples, which could be a supplement to the set of the exercises in the standard calculus texts, to help alleviate these difficulties. Precisely, we discuss the issue of the relationship between the Ratio Test and the Root Test as well as some misconceptions that students may have when applying the Alternating Series Test. In particular, students often fail to understand the importance of checking that the sequence is nonincreasing. We also point out how they may even confuse the concept of alternating terms.

 

The AMATYC Review

Fall 2005, Vol.27, No.1

AMATYC Members Offer Their Perceptions of
Interactions That Occur in Developmental Mathematics Courses

Nancy J. Sattler

Sattler presently teaches on-line and has taught mathematics for over 20 years at Terra State Community College in Fremont, Ohio. She chairs the AMATYC Distance Learning Committee and is past-president of OhioMATYC, presently serving as its historian, newsletter editor, and webmaster. E-mail: nsattler@terra.edu

This study investigated teacher perception of interactions used in on-line developmental mathematics courses at two-year colleges. A total of 98 AMATYC teachers were surveyed.

The following conclusions were inferred from the study's findings: (a) The teacher responding to the survey was apt to be a female between the ages of 50 and 59, had taught an average of 14 years, and had an average class size of 24 students; (b) The course taught was more likely to be a beginning or intermediate algebra class and was offered asynchronously; (c) The course management system used most often was more likely to be Blackboard, followed by textbook publishers systems, and WebCT; (d) The textbook company used was more likely to be either Prentice Hall, Addison Wesley, or Academic Systems; (e) The mean perception of Student-to-Teacher interactions varied depending on the type of interaction. There was no difference in the mean perception between the different course management systems Blackboard, WebCT, and textbook publishers. However, there was a significant difference in the mean perception between different

  • in-person meetings; teachers had the greatest success with tests, final exams, and orientation
  • on-line meetings; teachers had the greatest success with tests, final exams, and quizzes.
  • tools used; teachers had the greatest success with electronic mail, audio-conferencing, and interactive video;

(f) There was no significant difference in the mean perception of the different student-to-student interactions however e-mails were used the most frequently according to the on-line developmental mathematics teacher; and (g) There was a significant difference in the mean perception of the student-to-content interactions with textbooks being used the most often but instructor made video and course packet/handouts having the higher mean perceptions. General conclusions informing the field of study include: (a) on-line teachers continue to use traditional methods of assessment; (b) teachers desire some type of interaction with their students; and (c) distance classes are a blending of the old with the new.

The AMATYC Review

Fall 2005, Vol.27, No.1

Book Reviews

Edited by Sandra DeLozier Coleman

THE MYSTERY of THE ALEPH, Mathematics, the Kabbalah, and the Search for Innity, Amir D. Aczel, Washington Square Press publication of POCKET BOOKS, a division of Simon and Schuster, Inc., New York, 2000, ISBN 0-7434-2299-6.

 

The AMATYC Review

Fall 2005, Vol.27, No.1

Mathematics For Learning

With Inammatory Notes for the Mortication of Educologists and the Vindication of Just Plain Folks

Alain Schremmer

In the Spring 2004 issue of The AMATYC Review, Schremmer introduced his idea for an open-source serialized text: Mathematics For Learning. The Preface to the text appeared in the Spring 2004 issue with a new chapter in each subsequent issue of The AMATYC Review. This issue contains Chapter 3. There are six sections in this chapter: "States," "Transactions," "Usual Representations: Signed-Number-Phrases versus T-accounts," "Adding Signed-Number-Phrases," "Subtracting Signed-Number- Phrases," and "Effect of Transactions on States."

The AMATYC Review

Fall 2005, Vol.27, No.1

Software Reviews

Reviewed by Marion S. Foster, Tomball College

Edited by Brian E. Smith

MyMathLab/CourseCompass Course Management System

Producer and Distributor: Pearson Education Math and Statistics
Web addresses: www.coursecompass.com and www.mymathlab.com

System Requirements: Specic system requirements vary depending on your course. Most MyMathLab courses require a Windows® operating system and a supported version of Microsoft® Internet Explorer or Netscape®. However, courses for calculus and statistics also run on certain Macintosh® operating systems with supported versions of Netscape.

Internet connection: Cable/DSL, T1, or other high-speed for multimedia content; 56k modem (minimum) for tutorials, homework, and testing. Price: No charge to instructor for course creation. Students have to obtain a student access code. This may be provided with text adoption or purchased online. Contact Pearson Education for details.

The AMATYC Review

Fall 2005, Vol.27, No.1



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