	22nd AMATYC Annual Conference Long Beach, California , November 14-17, 1996
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On-Line Proceedings

The titles listed below represent the contributed papers of the Electronic Proceedings of the Twenty-Second Annual AMATYC Conference held on November 14-17, 1996 in Long Beach, CA. For each paper, the reader will find the title and author(s) with links to the paper in PDF format.

Contributed Paper and Author

Abstract and Documents

Personal Life Experiences and Work-related Factors Associated with Educators' Approaches to Multicultural Education

Beate Baltes
National University Educators have given immense attention to the importance of multicultural education. Several theoretical frameworks have been delevoped leading to many staff development programs. Since most educators consider themselves to be sensitive towards diversity, it is not uncommon for them to feel intimidated through more staff development programs that they are urged to attend.
These concerns could be addressed if educators were aware of their own philosophies of multicultural education and the personal life experiences and/or work-related factors that might have influenced their philosophies.

Acrobat PDF (28K)

Improving Quantitative Literacy
Dona Boccio
Queensboro Community College This paper addresses methods by which two-year college faculty can enrich curriculum to improve the quantitative literacy of their students. Examples taken from newspaper articles, advertisements, product labels, and schedules are discussed. These may be appropriate for a wide range of courses including developmental math, elementary and intermediate algebra, and finite math.
Acrobat PDF (170KB)

Bring Functions and Graphs to Life with the CBL
Frank Caldwell
York Technical College AMATYC's Crossroads in Mathematics includes function as one of its Standards of Content. This paper describes difficulties students experience with the function concept, studies conducted to determine the effect of technology on mathematics education, and the potential effect of the CBL and graphing calculators on students' learning of functions and graphs.
Acrobat PDF (37KB)

Multimedia in the Mathematics Classroom
Lynn Darragh
San Juan College The use of multimedia in the mathematics classroom of the future will allow the complete integration of mathematical topics and concepts with practical application and modeling. This paper illustrates a variety of multimedia techniques. Also included are ideas for classroom implementation.
Acrobat PDF (364KB)

Beginning Algebra Students' Images of the Function Concept
Phil DeMarois
William Rainey Harper College AMATYC's Crossroads in Mathematics lists function as one of the Standards of Content. This paper describes research focussed on the feasibility of using the function concept as a core idea in developmental mathematics. This research considers different aspects that make the function concept, building a view of function along both breadth (facets or representations) and depth (layers) dimensions. Pre- and post-course surveys along with task-based interviews are used to build a profile of developmental algebra students' concept image of function.
Acrobat PDF (96KB)

A Menu-Driven Developmental Mathematics Laboratory
Michele Diel
University of New Mexico - Valencia Campus This paper describes the Developmental Studies Computer Laboratory at the University of New Mexico, Valencia Campus. Challenges encountered and implimentation strategies are discussed. A list of activities and a copy of the author's syllabus for the Basic Mathematics Laboratory are included.
Acrobat PDF (28KB)

Algebra as a Laboratory Discipline: Implementation of Standards
Herb Garrett
Jim Brunner
University of Arkansas Implementation of an algebra program which strives to increase emphasis on reasoning, problem-solving, and communication while decreasing rote learning. Are you sick of grading homework and having to go over homework problems in class? This paper will demonstrate how your students can complete their homework and tests at the computer and provide class time for collaborative learning projects.
Acrobat PDF (301KB)

Getting Students Involved in the Learning of Mathematics, Through a Math Resource Center
Libby Holmgren
Johnson County Community College The Math Resource Center (MRC) at Johnson County Community College (JCCC) is a free center available to serve the 5500 students taking math each semester and the 27 full-time math instructors and 45 adjunct math instructors at JCCC. The obvious resources are free tutoring, videotapes on course work and calculator use, computer software, and group study sessions:

Tutorial assistance is provided by a total of 18 tutors to all JCCC math students for each of the 65 hours a week that we are open. (Between 2 and 6 tutors are available each hour.)
Videotapes on math course work and on using the TI calculators are available.
The center has its own computer room with 22-486's, with a variety of tutorial, and symbolic manipulators, spreadsheets, etc. We have our own technician. His responsibility is to keep everything running in the computer room, to add and delete programs as necessary, to assist students as they work, and to work with the math instructors on computer problems in their offices.

Some of the "not so obvious" resources are that we:

provide several types of space for students to meet together to discuss their math on either an impromptu or regular basis;
maintain an atmosphere that is nonjudgemental and encouraging,as well as quiet and studious;
provide resources for students to learn how to use graphing calculators so that time does not need to be spent in class;
provide a place where students discover that they are not the only ones who may need some assistance and that there are many people spending time on their mathematics;
provide the resources to instructors to facilitate more creative instructional strategies.
provide computers and math programs in an area reserved strictly for mathematics.

It is so exciting to see math students actively involved with their mathematics, and with each other while working with mathematics. It is great to be able to facilitate this occurrence!

Acrobat PDF (195KB)

What Can I Do With the TI-92 CAS-Based Calculator in Algebra?
Edward D. Laughbaum
The Ohio State University This paper lists several situations effectively modeled by the function:
M = a |x + e₁| + b |x + e₂| + ... d |x + e_n|+ f

Two examples are discussed in detail with instructions for investigating the model using the TI-92.

Acrobat PDF (558KB)

Using Converge and Derive in the Teaching of Calculus
Virginia Lee
Elaine Klett
Brookdale Community College Converge and Derive are two excellent and complementary software packages for teaching and learning Calculus. Converge is primarily a teaching tool and is equipped with routines which illustrate all of the important concepts in calculus. These powerful routines can be used by students to really understand the ideas being discussed. Derive, on the other hand, is a powerful symbolic manipulation program and students can use it as a tool for solving more complex problems and avoiding tedious calculations. If used at the appropriate times and in appropriate ways, these two programs together provide a genuinely exciting route through calculus. In this presentation, we will discuss the nature of each program and then guide the participant through examples chosen from supplements written for the students in Calculus I and Calculus II at Brookdale Community College. These supplements contain exercises completed in class with instructor guidance. In many cases, the exercises are preceded by development of the concept and a simple illustration by hand. Included in the mincourse will be a discussion of the appropriate times to use each program, motivations for including specific exercises, student reactions, and modes of testing.
Acrobat PDF (389KB)

The Characterization of Data
William Pletsch
Janet Heath
Albuquerque Technical-Vocational Institute The Rule of Four (each mathematical concept should be developed descriptively, numerically, graphically, and symbolically) will be applied to the manipulation and characterization of data. These data sets will include the linear, quadratic, polynomial, exponential, and Gaussian, exponential raised to polynomial power.
Acrobat PDF (165KB)

College Students and Elementary School Students as Partners in the Learning of Mathematics
Egon Mermelstein
Said Lamhaouar
College of Aeronautics

Philip Stanford
I.S. 391 Brooklyn It was hypothesized that minority college students with difficulty in mathematics who mentor minority 3rd, 5th, and 8th graders in mathematics would demonstrate increased performance in mathematics. Narratives from college and elementary students, suggest a reduction in math anxiety, improved communicatioon and a better understanding of mathematics.
Acrobat PDF (118KB)

A Transformational and Technological Approach to Precalculus: A Collaborative Effort
Harold Mick
C. Wayne Patty
Virginia Polytechnical Institute and State University¹ The purpose of this paper is to give an overview of the transformational approach to equations and graphs that the authors use in their text, Visual Precalculus. This approach is relatively unique in that its development begins in a purely geometric context and moves points in the direction from unknown graphs to known graphs. Transformations are mostly developed in the first chapter and provide a unifying theme throughout the text. The approach is particulary helpful with topics involving functions and plays an important role with inverse functions, symmetry, identities, and families of curves. The paper presents five examples showing the use and power of the approach as an unifying theme, and lists several objectives of the text.

This work was partially supported by a grant from the Virginia Quality Education in Science and Technology (V-QUEST). V-QUEST was Virginia's SSI grant and it was supported by the National Science Foundation under Cooperative Agreement No. 0SR9250058.

Making Functions Relevant with the CBL
Mary Robinson
University of New Mexico - Valencia Campus Students, quite often, have difficulty grasping the concept of function. Most textbook examples simply do not help students understand the concept itself. The CBL has proved a valuable tool to help students better understand the ins and outs of functions. Domain and range are put into a real context that makes more sense to students, and the relationship of input and output variables fall easily into place.
If enough CBLs can be acquired, letting the students do their own experiments is even more helpful. However, in many cases, limited numbers of CBLs are available. This workshop was designed to acquaint the participants with the benefits of using the CBL in connection with the TI/82 both when supplies are limited, and when they are not.

Acrobat PDF (73KB)

Real-World Activities and Applications for Beginning and Intermediate Mathematics Courses
Regina T. Shankland
Sara E. Williams
Mt. Hood Community College The Mathematics Division at Mt. Hood Community College has embraced educational reform and teaches a one-track mathematics curriculum for both the professional-technical student and the transfer student. The classes at Mt. Hood Community College are application-driven and students actively engage in team problem solving and discovery among other activities. The mathematics faculty at Mt. Hood Community College has been awarded an NSF Advanced Technological Education Grant (entitled ìApplication-Based, Technology-Supported, One-Track Mathematics Curriculumî). As part of the grant, Gina and Sara are collecting real-world application problems and hands-on activities. Drawn from business, industry, and other academic disciplines, these activities are designed to reach a broad audience. The presentation focused on the various uses of real-world applications in the classroom and in assessment. A sample application is also included in the paper. PaperAbstract: Real-World Activities and Applications for Beginning and Intermediate Mathematics Courses
Acrobat PDF (39KB)

Iteration and Fractals on the TI-82 Calculator
Thomas W. Shilgalis
Illinois State University This paper discusses iteration of elementary Functions to find fixed points; connections to some fractal figures. The use of the TI-82 is illustrated with several calculator programs listed.
Acrobat PDF (663KB)

Using and Creating Internet Math Resources: Putting the Mathematics Archives to Work
John St.Clair
Motlow State Community College This presentation examines the manner in which the Internet is used as a vehicle for the delivery of mathematics. An overview of the structure and content of the Mathematics Archives is presented. A list of specific strategies for delivering mathematical content via the web is given. A sample lesson is given to demonstrate how html is used to construct web pages.

Acrobat PDF (986KB)
HTML (WWW pages)

MichMATYC Algebra Curriculum Reform
David E. Steinfort
Grand Rapids Community College This paper focuses on the AMATYC Standards' impact on the Elementary and Intermediate Algebra curricula in Michigan community colleges. A grass-roots movement of forty-nine mathemtics educators produced algebra curruiculum reform which was endorsed by the MichMATYC membership. This paper looks at the problems, process, and results of the MichMATYC implementation of AMATYC standards.
Acrobat PDF (85KB)

Teaching Calculus with the TI-92
Sally Thomas
Orange Coast College This paper demonstrates the use the geometry application on the TI-92 in maximizing the area of a rectangle with a fixed perimeter. Detailed instructions for using the calculator are given as well as numerous screen snapshots captured from the calculator during the process.
Acrobat PDF (266KB)

Diversity Topics in the Developmental Curriculum
Barbara Tozzi
Brookdale Community College This paper presents the authorís experiences with including diversity topics in the Developmental Math (Computation) curriculum. Problems and labs based on newspaper articles, tables and graphics with diversity content, as well as alternate teaching techniques such as the "fishbowl" method of discussion, are included. Additional sources of information for data on diversity topics such as specific newspapers, magazines and Web Sites are noted.
Acrobat PDF (656KB)

How and Why the Computer Symbolic Algebra on the Hand-Held TI-92 Will Change Your Life Forever
Bert Waits
The Ohio State University What are the implications of student use of hand-held computer symbolic algebra (CSA) tools? What content that we teach today in algebra and calculus will become obsolete? How much paper and pencil algebraic manipulative skill is still necessary? What do we know about teaching and learning mathematics with CSA?
Dr. Waits shares the highlights from an article published in the Mathematics Teacher, A Computer for All Students - Revisited, copyright December, 1996 by the National Council of Teachers of Mathematics. Also included are a set of four detailed workshops in using the TI-92. These workshops were produced by Bernard Kutzler.

Acrobat PDF (225KB) Waits.pdf

Workshops:

Workshop 1 Acrobat PDF (504KB)
Workshop 2 Acrobat PDF (504KB)
Workshop 3 Acrobat PDF (411KB)
Workshop 4 Acrobat PDF (503KB)

Contributed Paper and Author	Abstract and Documents
Personal Life Experiences and Work-related Factors Associated with Educators' Approaches to Multicultural Education Beate Baltes National University	Educators have given immense attention to the importance of multicultural education. Several theoretical frameworks have been delevoped leading to many staff development programs. Since most educators consider themselves to be sensitive towards diversity, it is not uncommon for them to feel intimidated through more staff development programs that they are urged to attend. These concerns could be addressed if educators were aware of their own philosophies of multicultural education and the personal life experiences and/or work-related factors that might have influenced their philosophies. Acrobat PDF (28K)
Improving Quantitative Literacy Dona Boccio Queensboro Community College	This paper addresses methods by which two-year college faculty can enrich curriculum to improve the quantitative literacy of their students. Examples taken from newspaper articles, advertisements, product labels, and schedules are discussed. These may be appropriate for a wide range of courses including developmental math, elementary and intermediate algebra, and finite math. Acrobat PDF (170KB)
Bring Functions and Graphs to Life with the CBL Frank Caldwell York Technical College	AMATYC's Crossroads in Mathematics includes function as one of its Standards of Content. This paper describes difficulties students experience with the function concept, studies conducted to determine the effect of technology on mathematics education, and the potential effect of the CBL and graphing calculators on students' learning of functions and graphs. Acrobat PDF (37KB)
Multimedia in the Mathematics Classroom Lynn Darragh San Juan College	The use of multimedia in the mathematics classroom of the future will allow the complete integration of mathematical topics and concepts with practical application and modeling. This paper illustrates a variety of multimedia techniques. Also included are ideas for classroom implementation. Acrobat PDF (364KB)
Beginning Algebra Students' Images of the Function Concept Phil DeMarois William Rainey Harper College	AMATYC's Crossroads in Mathematics lists function as one of the Standards of Content. This paper describes research focussed on the feasibility of using the function concept as a core idea in developmental mathematics. This research considers different aspects that make the function concept, building a view of function along both breadth (facets or representations) and depth (layers) dimensions. Pre- and post-course surveys along with task-based interviews are used to build a profile of developmental algebra students' concept image of function. Acrobat PDF (96KB)
A Menu-Driven Developmental Mathematics Laboratory Michele Diel University of New Mexico - Valencia Campus	This paper describes the Developmental Studies Computer Laboratory at the University of New Mexico, Valencia Campus. Challenges encountered and implimentation strategies are discussed. A list of activities and a copy of the author's syllabus for the Basic Mathematics Laboratory are included. Acrobat PDF (28KB)
Algebra as a Laboratory Discipline: Implementation of Standards Herb Garrett Jim Brunner University of Arkansas	Implementation of an algebra program which strives to increase emphasis on reasoning, problem-solving, and communication while decreasing rote learning. Are you sick of grading homework and having to go over homework problems in class? This paper will demonstrate how your students can complete their homework and tests at the computer and provide class time for collaborative learning projects. Acrobat PDF (301KB)
Getting Students Involved in the Learning of Mathematics, Through a Math Resource Center Libby Holmgren Johnson County Community College	The Math Resource Center (MRC) at Johnson County Community College (JCCC) is a free center available to serve the 5500 students taking math each semester and the 27 full-time math instructors and 45 adjunct math instructors at JCCC. The obvious resources are free tutoring, videotapes on course work and calculator use, computer software, and group study sessions: Tutorial assistance is provided by a total of 18 tutors to all JCCC math students for each of the 65 hours a week that we are open. (Between 2 and 6 tutors are available each hour.) Videotapes on math course work and on using the TI calculators are available. The center has its own computer room with 22-486's, with a variety of tutorial, and symbolic manipulators, spreadsheets, etc. We have our own technician. His responsibility is to keep everything running in the computer room, to add and delete programs as necessary, to assist students as they work, and to work with the math instructors on computer problems in their offices. Some of the "not so obvious" resources are that we: provide several types of space for students to meet together to discuss their math on either an impromptu or regular basis; maintain an atmosphere that is nonjudgemental and encouraging,as well as quiet and studious; provide resources for students to learn how to use graphing calculators so that time does not need to be spent in class; provide a place where students discover that they are not the only ones who may need some assistance and that there are many people spending time on their mathematics; provide the resources to instructors to facilitate more creative instructional strategies. provide computers and math programs in an area reserved strictly for mathematics. It is so exciting to see math students actively involved with their mathematics, and with each other while working with mathematics. It is great to be able to facilitate this occurrence! Acrobat PDF (195KB)
What Can I Do With the TI-92 CAS-Based Calculator in Algebra? Edward D. Laughbaum The Ohio State University	This paper lists several situations effectively modeled by the function: M = a \|x + e₁\| + b \|x + e₂\| + ... d \|x + e_n\|+ f Two examples are discussed in detail with instructions for investigating the model using the TI-92. Acrobat PDF (558KB)
Using Converge and Derive in the Teaching of Calculus Virginia Lee Elaine Klett Brookdale Community College	Converge and Derive are two excellent and complementary software packages for teaching and learning Calculus. Converge is primarily a teaching tool and is equipped with routines which illustrate all of the important concepts in calculus. These powerful routines can be used by students to really understand the ideas being discussed. Derive, on the other hand, is a powerful symbolic manipulation program and students can use it as a tool for solving more complex problems and avoiding tedious calculations. If used at the appropriate times and in appropriate ways, these two programs together provide a genuinely exciting route through calculus. In this presentation, we will discuss the nature of each program and then guide the participant through examples chosen from supplements written for the students in Calculus I and Calculus II at Brookdale Community College. These supplements contain exercises completed in class with instructor guidance. In many cases, the exercises are preceded by development of the concept and a simple illustration by hand. Included in the mincourse will be a discussion of the appropriate times to use each program, motivations for including specific exercises, student reactions, and modes of testing. Acrobat PDF (389KB)
The Characterization of Data William Pletsch Janet Heath Albuquerque Technical-Vocational Institute	The Rule of Four (each mathematical concept should be developed descriptively, numerically, graphically, and symbolically) will be applied to the manipulation and characterization of data. These data sets will include the linear, quadratic, polynomial, exponential, and Gaussian, exponential raised to polynomial power. Acrobat PDF (165KB)
College Students and Elementary School Students as Partners in the Learning of Mathematics Egon Mermelstein Said Lamhaouar College of Aeronautics Philip Stanford I.S. 391 Brooklyn	It was hypothesized that minority college students with difficulty in mathematics who mentor minority 3rd, 5th, and 8th graders in mathematics would demonstrate increased performance in mathematics. Narratives from college and elementary students, suggest a reduction in math anxiety, improved communicatioon and a better understanding of mathematics. Acrobat PDF (118KB)
A Transformational and Technological Approach to Precalculus: A Collaborative Effort Harold Mick C. Wayne Patty Virginia Polytechnical Institute and State University¹	The purpose of this paper is to give an overview of the transformational approach to equations and graphs that the authors use in their text, Visual Precalculus. This approach is relatively unique in that its development begins in a purely geometric context and moves points in the direction from unknown graphs to known graphs. Transformations are mostly developed in the first chapter and provide a unifying theme throughout the text. The approach is particulary helpful with topics involving functions and plays an important role with inverse functions, symmetry, identities, and families of curves. The paper presents five examples showing the use and power of the approach as an unifying theme, and lists several objectives of the text. This work was partially supported by a grant from the Virginia Quality Education in Science and Technology (V-QUEST). V-QUEST was Virginia's SSI grant and it was supported by the National Science Foundation under Cooperative Agreement No. 0SR9250058.
Making Functions Relevant with the CBL Mary Robinson University of New Mexico - Valencia Campus	Students, quite often, have difficulty grasping the concept of function. Most textbook examples simply do not help students understand the concept itself. The CBL has proved a valuable tool to help students better understand the ins and outs of functions. Domain and range are put into a real context that makes more sense to students, and the relationship of input and output variables fall easily into place. If enough CBLs can be acquired, letting the students do their own experiments is even more helpful. However, in many cases, limited numbers of CBLs are available. This workshop was designed to acquaint the participants with the benefits of using the CBL in connection with the TI/82 both when supplies are limited, and when they are not. Acrobat PDF (73KB)
Real-World Activities and Applications for Beginning and Intermediate Mathematics Courses Regina T. Shankland Sara E. Williams Mt. Hood Community College	The Mathematics Division at Mt. Hood Community College has embraced educational reform and teaches a one-track mathematics curriculum for both the professional-technical student and the transfer student. The classes at Mt. Hood Community College are application-driven and students actively engage in team problem solving and discovery among other activities. The mathematics faculty at Mt. Hood Community College has been awarded an NSF Advanced Technological Education Grant (entitled ìApplication-Based, Technology-Supported, One-Track Mathematics Curriculumî). As part of the grant, Gina and Sara are collecting real-world application problems and hands-on activities. Drawn from business, industry, and other academic disciplines, these activities are designed to reach a broad audience. The presentation focused on the various uses of real-world applications in the classroom and in assessment. A sample application is also included in the paper. PaperAbstract: Real-World Activities and Applications for Beginning and Intermediate Mathematics Courses Acrobat PDF (39KB)
Iteration and Fractals on the TI-82 Calculator Thomas W. Shilgalis Illinois State University	This paper discusses iteration of elementary Functions to find fixed points; connections to some fractal figures. The use of the TI-82 is illustrated with several calculator programs listed. Acrobat PDF (663KB)
Using and Creating Internet Math Resources: Putting the Mathematics Archives to Work John St.Clair Motlow State Community College	This presentation examines the manner in which the Internet is used as a vehicle for the delivery of mathematics. An overview of the structure and content of the Mathematics Archives is presented. A list of specific strategies for delivering mathematical content via the web is given. A sample lesson is given to demonstrate how html is used to construct web pages. Acrobat PDF (986KB) HTML (WWW pages)
MichMATYC Algebra Curriculum Reform David E. Steinfort Grand Rapids Community College	This paper focuses on the AMATYC Standards' impact on the Elementary and Intermediate Algebra curricula in Michigan community colleges. A grass-roots movement of forty-nine mathemtics educators produced algebra curruiculum reform which was endorsed by the MichMATYC membership. This paper looks at the problems, process, and results of the MichMATYC implementation of AMATYC standards. Acrobat PDF (85KB)
Teaching Calculus with the TI-92 Sally Thomas Orange Coast College	This paper demonstrates the use the geometry application on the TI-92 in maximizing the area of a rectangle with a fixed perimeter. Detailed instructions for using the calculator are given as well as numerous screen snapshots captured from the calculator during the process. Acrobat PDF (266KB)
Diversity Topics in the Developmental Curriculum Barbara Tozzi Brookdale Community College	This paper presents the authorís experiences with including diversity topics in the Developmental Math (Computation) curriculum. Problems and labs based on newspaper articles, tables and graphics with diversity content, as well as alternate teaching techniques such as the "fishbowl" method of discussion, are included. Additional sources of information for data on diversity topics such as specific newspapers, magazines and Web Sites are noted. Acrobat PDF (656KB)
How and Why the Computer Symbolic Algebra on the Hand-Held TI-92 Will Change Your Life Forever Bert Waits The Ohio State University	What are the implications of student use of hand-held computer symbolic algebra (CSA) tools? What content that we teach today in algebra and calculus will become obsolete? How much paper and pencil algebraic manipulative skill is still necessary? What do we know about teaching and learning mathematics with CSA? Dr. Waits shares the highlights from an article published in the Mathematics Teacher, A Computer for All Students - Revisited, copyright December, 1996 by the National Council of Teachers of Mathematics. Also included are a set of four detailed workshops in using the TI-92. These workshops were produced by Bernard Kutzler. Acrobat PDF (225KB) Waits.pdf Workshops: Workshop 1 Acrobat PDF (504KB) Workshop 2 Acrobat PDF (504KB) Workshop 3 Acrobat PDF (411KB) Workshop 4 Acrobat PDF (503KB)