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AMATYC Review Spring 2007
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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


Spring 2007 issue, Vol. 28, No.2

Table of Contents

Change: It Comes Straight from the Heart,

Richelle (Rikki) Blair

Rikki Blair is President-elect of AMATYC, editor of Beyond Crossroads, and professor emeritus of mathematics at Lakeland Community College. Her professional interests are curriculum development, incorporating active student learning experiences into the classroom, and increasing professional development opportunities for faculty. She received her PhD from Kent State University in curriculum and instruction.

An important component of transitioning from a classroom instructor to a practicing teaching professional is a commitment to continuous growth and lifelong learning. The professionalization process is dynamic, producing a state of professionalism with changes in one’s values, philosophy, and classroom activities. When considering a change in behavior or practice, the power of past practices, rules, or paradigms to influence current judgments and choices cannot be underestimated. In order to embrace a particular change in behavior or practice, it must be seen, felt, touch the heart, and resonate with one’s own values. Mathematics professionals who find implementing change challenging may find the strategies and step-by-step process of the Implementation Cycle of Beyond Crossroads helpful. The goal of the document is to empower the mathematics professional to embrace change and strengthen the learning and teaching of mathematics.(back to top)

Moving Beyond Crossroads: Opportunities and Paradoxes

Lynn Arthur Steen

Lynn Arthur Steen is a professor of mathematics and special assistant to the Provost at St. Olaf College in Northfield, Minnesota. A former president of the Mathematical Association of America, Steen is the editor or author of several books including Math and Bio 2010, Achieving Quantitative Literacy, Mathematics and Democracy (2001), Why Numbers Count, On the Shoulders of Giants, Everybody Counts, and Calculus for a New Century. Steen holds a PhD in mathematics from the Massachusetts Institute of Technology as well as several honorary degrees.

Beyond Crossroads addresses many of the challenges facing American higher education and offers members of AMATYC an ideal opportunity to respond energetically and constructively to these challenges. Notwithstanding the many efforts to improve secondary schooling, most students enter postsecondary education well behind where they should be in mathematics. If two-year colleges are to succeed in preparing students for life and work in the 21st century, AMATYC members will necessarily play an increasingly central role. (back to top)

Beyond Crossroads: Putting Standards into Action

Gregory D. Foley

Gregory D. Foley is senior scientist for secondary school mathematics improvement for the Austin Independent School District, Austin, Texas. Greg has taught elementary arithmetic through graduate-level mathematics, as well as upper division and graduate-level mathematics education. He has presented over 200 lectures, workshops, and institutes throughout the United States and internationally, and has directed a variety of funded projects. In 1998, Foley received the AMATYC Award for Mathematics Excellence.
Beyond Crossroads is a call to action. Within this call, AMATYC has updated its 1995 Crossroads standards, developed a new set of guiding principles, and created a blueprint for implementing these revised principles and standards. The principles guiding Beyond Crossroads are a significant overhaul of their predecessors and are bold statements that embrace changes in practice to improve student learning. The Standards for Intellectual Development now include linking multiple representations, and the Standards for Content add measurement to the geometry standard and data analysis to the probability and statistics standard. Beyond Crossroads has a clear focus on implementation, with six of the ten chapters devoted to the new Implementation Standards. This action-oriented focus on implementation is reminiscent of NCTM’s Agenda for Action. Many of the critical themes of Beyond Crossroads—problem solving, quantitative literacy, technology, accommodating
diverse needs, professionalism, and public support—have their roots in the Agenda for Action. The article concludes with a critical question: Will we heed this latest call for change and act on it? We have at our disposal the materials and methods we need; now we must act on what we know. This requires hard work, tenacity, and mutual support.
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Four Steps to a Standards-Embracing Department

Alan Jacobs, Sally Jacobs, Ted Coe, and Connie Carruthers

Alan Jacobs, recently retired from the mathematics department of Scottsdale Community College, Scottsdale, Arizona, served as a section writer and reviewer for Beyond Crossroads. He is past mathematics department chair at Scottsdale CC and coauthor of The Maricopa Project. He received the AMATYC Teaching Excellence Award in 2005.

Sally Jacobs, recently retired from the mathematics department of Scottsdale Community College, Scottsdale, Arizona, was a contributing writer for Beyond Crossroads. She was involved with implementation of various reform initiatives at Scottsdale CC and was the faculty liaison between Maricopa faculty and mathematics education research projects at Arizona State University.

Ted Coe, evening chairperson of the mathematics department at Scottsdale Community College, Scottsdale, Arizona, was a contributing writer for Beyond Crossroads.

Connie Carruthers, professor of mathematics and daytime chairperson at Scottsdale Community College in Scottsville, Arizona, received a BA at University of California and a MS at California State University, Northridge.

How did it happen that both full-time and adjunct faculty at Scottsdale Community College embrace a standards-based curriculum from beginning algebra through differential equations? Simply put, it didn’t just happen. Not only did it take well over a decade, but it was also the result of a sequence of initiatives, decisions, discussions, targeted faculty development, and a willingness to take risks. This article summarizes that sequence of initiatives in four steps:

  1. Invest in a manageable change, with a plan to bring the entire department along. We made this investment when we adopted a reform-calculus book in 1994.
  2. Engage the adjunct and full-time faculty in activities that build mutual respect. We began joint professional development seminars that led to learning communities.
  3. Implement your initiative to solve the problem only when you have agreement about what the problem is. The key word is "agreement.” Our initiatives were most successful when we were patient enough to come to agreement.
  4. Build on past successes. After several initiatives you develop a department process. Use your unique department process on each new initiative. (back to top)

Quantitative Literacy—Beyond Crossroads Gets It Right

William G. Steenken

William G. Steenken retired from GE Aviation, Cincinnati, OH in 2001 after a 29 year career, but continues to consult with them on a regular basis. He holds a PhD in Mechanical Engineering and is the author of over 34 papers in the field of Inlet/Engine Compatibility and Engine Operability. He has been involved with education since 1977 through service on school, and mathematics and science advisory and coalition boards. For the last ten years, he has been deeply involved in supporting the efforts to improve K–12 mathematics and science education at the policy level in Ohio.

In this article, Steenken conveys some thoughts about when parents and our citizenry will believe that today’s students know mathematics. It will be when students have significant Quantitative Literacy (QL) skills as set forth in AMATYC’s new standards, Beyond Crossroads. He supports the strong call for QL to be imbedded across all curricula and as a method for assuring that students who leave two-year programs are prepared for the world that will confront them. He further supports the need for faculty to see QL as a daily part of their lives, especially as they make the Implementation Cycle presented in Beyond Crossroads as a method for assuring continuous improvement in their professional activities. He ends with a statement that Beyond Crossroad’s strong call for QL will be met with strong support from industry and the business world. (back to top)

Setting a Course for Change Based on Beyond Crossroads

John A. Dossey

John A. Dossey is the Distinguished University Professor of Mathematics (Emeritus) at Illinois State University. Prior to his 30-year career at Illinois State University, he taught middle and senior high school mathematics. John served as President of the National Council of Teachers of Mathematics (NCTM) and Chair of the Conference Board of the Mathematical Sciences (CBMS). He received his BS and MS degrees at Illinois State University and his PhD from the University of Illinois at Urbana-Champaign.

The article provides a vision of how Beyond Crossroads can serve as a departmental guide to inducing systemic change at a two-year college. Curricular change does not mean just changing the content taught, it also means changing the way it is taught, the way learning may be assessed, and the ways in which faculty and administrators may evaluate curricular effectiveness. Beyond Crossroads provides a starting point, the rest remains in the hands of faculty committed to providing the best program possible for their students. (back to top)

Implementing Change in College Algebra

William E. Haver

Bill Haver is professor of mathematics at Virginia Commonwealth University (VCU). He received his PhD in the area of infinite dimensional topology from SUNY Binghamton. He has also held appointments at the University of Tennessee (UT), the Institute for Advanced Study, and the National Science Foundation. He is chair of the Curriculum Renewal Across the First Two Years Committee of the Mathematical Association of America. He has taught college algebra at the UT, VCU, Rutgers University, Bates College, and J. Sargeant Reynolds Community College.
In this paper, departments are urged to consider implementing the type of changes proposed in Beyond Crossroads in College Algebra. The author of this paper is chair of the Curriculum Renewal Across the First Two Years (CRAFTY) Committee of the Mathematical Association of America. The committee has members from two-year colleges, four-year colleges, and research universities. CRAFTY recently organized 11 workshops, each bringing together representatives from partner disciplines to explore the mathematical needs of students in their discipline. The recommendations from the various disciplines were remarkably consistent and lead to College Algebra Guidelines that provide a vision of what all students enrolled in College Algebra should experience. The Guidelines contain specific recommendations concerning topics in functions, equations and data analysis that need to be contained in the course. They also address appropriate pedagogical and assessment practices. These are at a more specific level than Beyond Crossroads. However, there is a very strong correlation between the College Algebra Guidelines and the Basic Principles of Beyond Crossroads. College Algebra indeed provides an important place to begin the implementation proposed in Beyond Crossroads. (back to top)

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Beyond Crossroads: Impressions of a Statistics Educator

Richard L. Scheaffer

Richard L. Scheaffer received his PhD in statistics from Florida State University, whereupon he joined the faculty of the University of Florida and remained on that faculty ever since. Now professor emeritus of statistics, he was chairman of the department for a period of twelve years. Research interests are in the areas of sampling and applied probability, especially with regard to applications of both to industrial processes. He has published numerous papers in the statistical literature and is co-author of five college-level textbooks covering aspects of introductory statistics, sampling, probability, and mathematical statistics.

Beyond Crossroads recognizes that success in the modern world demands higher-level thinking across the mathematical sciences. Broad quantitative literacy skills are essential for the college graduates of today and tomorrow if they are to be informed citizens and productive workers. Such skills include the quantitative aspects of daily life and work that allow educated people to make intelligent decisions based on knowledge rather than being manipulated through guile or fear. Quantitative literacy is largely akin to statistical thinking, because many of the quantitative areas of life and work involve understanding data—how it is collected, what it represents, and what conclusions can be drawn from it. In that respect, the document is in concert with the American Statistical Association’s Guidelines for Assessment and Instruction in Statistics Education (GAISE). All colleges should seriously consider how following the recommendations of Beyond Crossroads can
impact their mathematics programs for students in their first two years. (back to top)

Developing and Implementing a Quantitative Reasoning Program at BMCC

Klement Teixeira

Klement Teixeira is a deputy chair of the mathematics department at Borough of Manhattan Community College, CUNY, in New York City. He earned an MA in mathematics specializing in probability and statistics from City College, CUNY, an MS in mathematics at the Courant Institute of Mathematical Sciences, New York University, and a PhD in mathematics education from the Steinhardt School of Education, New York University.

The case study approach is commonly used in the fields of law, medicine, and business administration to help apply theory to practice. This approach is equally useful in the teaching and learning of mathematics since various categories of coping strategies used to alleviate math anxiety become more meaningful when they are used to assist "real” students. A number of case studies were developed to apply the coping strategies presented in Beyond Crossroads to students who have found themselves at the "crossroads” between success and failure. Each case represents a student at the author’s institution who is confronted with a potentially stressful situation when attempting to study mathematics. (back to top)

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Using Chapter 6 of Beyond Crossroads as a Catalyst for Curriculum Change

James W. Hall

James W. Hall is a Parkland College Professor Emeritus. He was department chair of mathematics at Parkland College for 7 years and has written numerous textbooks in undergraduate mathematics. He is also writing team chair for Chapter 6 on Curriculum and Program Development in Beyond Crossroads. He celebrated his first hole-in-one on May 15, 2006 near his home in Sun Lakes, Arizona.

This article is written from the perspective of a department chair who recognizes that there are often significant barriers within the department to changing the curriculum. This article makes the case that changes are needed and suggests actions that can be the catalyst for change. (back to top)

Time to Re-evaluate: Am I Implementing the Standards?

Nancy J. Sattler

Nancy Sattler is an adjunct mathematics teacher at Terra Community College in Fremont, Ohio. She has been a member of AMATYC’s Distance Learning Committee since its inception and was a section writer for Beyond Crossroads.

Beyond Crossroads states that mathematics faculty should (a) select technology that is accessible to students enrolled in their distance learning mathematics course, (b) advise students on the expectations of their distance learning mathematics course and orient them to the distance learning environment of their course, (c) provide students with course information outlining course objectives, concepts, ideas, and learning outcomes for their distance learning mathematics course, (d) engage in ongoing professional development to enhance their mathematics course presentation and support their teaching practice in the distance learning environment, and (e) assure that learning outcomes in mathematics distance learning sections are consistent with those of similar mathematics courses taught in the classrooms. Nancy Sattler, past chair of the Distance Learning Committee, explains how she is addressing Beyond Crossroads strategies in her online mathematics class as Terra Community College changed from quarters to semesters and the curriculum changed. She adheres to the philosophy that technology should facilitate a kind of learning that is durable, has substance, is engaging to students, and provides mathematical insights through a high level of understanding of the mathematics being taught. (back to top)

Building Consensus and Providing Guidance among Professional Societies?

Johnny W. Lott

Johnny W. Lott is the director of the Center for Teaching and Learning Excellence at The University of Mississippi. He is a past president of the National Council of Teachers of Mathematics and was professor of mathematics education at The University of Montana until his
recent move to Ole Miss.

Beyond Crossroads has as a stated objective having "two-year college mathematics faculty and institutions collaborate with professional societies, government agencies, and educational institutions to build consensus and provide guidance to practitioners.” Issues involving two-year faculty and university faculty members in conversations about common issues has at times been challenging. With school teachers (typically members of the National Council of Teachers of Mathematics (NCTM)) at the pre-collegiate level in the mix, the conversation becomes even more difficult. With students taking dual enrollment courses at high school and all levels, the Mathematics Association of America (MAA) writing placement examinations in conjunctions with Maplesoft for use throughout the collegiate levels, and teacher preparation being distributed across two- year colleges and four-year schools, the conversations are needed and desirable. In order for the conversations to happen, suggestions include working with the NCTM/MAA Joint Committee on Common Concerns, possibly adding a member of the Board of Directors of NCTM who is a two-year college person, adding a specific member of the Board of Governors for the MAA to represent two-year colleges and adding a representative from the pre-collegiate level and the four-year level to the American Mathematics Association for Two-Year Colleges (AMATYC) Board of Directors. None of this will be easy, but each could help move the conversations along. Beyond Crossroads is a document with a wide vision of what could happen in this arena. It will take the concentrated work of the three named professional organizations to make this happen. (back to top)

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Commentary: Beyond Crossroads

Joan R. Leitzel

Joan Leitzel is President Emerita, University of New Hampshire; Professor Emeritus, The Ohio State University. Dr. Leitzel is an accomplished leader, having served as President of the University of New Hampshire, Senior Vice Chancellor for Academic Affairs at the University of Nebraska Lincoln, Director of the Division of Materials Development, Research, and Informal Science Education at NSF; and Associate Provost at Ohio State. She received her Ph.D. in mathematics at Indiana University and was a Professor of Mathematics at Ohio State for 25 years. She is a former chair of the Mathematical Sciences Education Board at the National Research Council.

The Commentary salutes AMATYC for its significant contributions to standardsbased education in mathematics and discusses possible audiences for Beyond Crossroads, in addition to the primary audience of faculty members and departments in two-year institutions. Because Beyond Crossroads focuses on lower division college mathematics, it helps clarify the connections between secondary school mathematics and baccalaureate programs. Consequently, it can be a valuable tool for both high school teachers of mathematics and faculty in baccalaureate programs and can help with efforts to create a more coherent curriculum across grades 9–16. Beyond Crossroads is also seen to be a potential resource for those working on assessment and placement instruments at several levels, for those providing professional development to teachers of middle school and high school mathematics, and for those attempting to implement content standards in instruction. In this Commentary, Beyond Crossroads is viewed as more than a resource for two year institutions and is highlighted as potentially important to several areas of mathematics education. (back to top)

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Assessment: Key to Teaching and Learning

Judy Marwick

Judith Marwick is vice president of instruction and student services at Kankakee Community College in Illinois. Earlier, she was department chair and professor of mathematics at Prairie State College. Judy served as a writing team chair for Beyond Crossroads and was chair of the AMATYC Placement and Assessment Committee from 1999–2003. She holds an MS in mathematics from Purdue University and an EdD in community college leadership from the University of Illinois.

Assessment of student learning is key to all educational endeavors and required by governmental and accrediting bodies. Faculty initiate and implement assessment strategies to be sure that students are learning what is being taught. Classroom assessment is generally easier for faculty to embrace than course or program level assessment because classroom assessment techniques can be developed by individual instructors and implemented within a single classroom. Course and program assessment requires collaboration among all faculty involved in teaching a section of a course or within a program or sequence of courses. While it may be difficult to reach a consensus about what is most important for students to learn or how best to measure their learning, the discussion and introspection among colleagues wrestling with these issues is of great value.

Faculty at community colleges have never stopped at what is easy. In fact, they move mountains and make a difference in students lives every day. Assessment should be seen as one more endeavor that, while difficult to implement, has the potential for significant results. (back to top)

Using Assessment of Student Learning As A Catalyst for Change

Myra Snell

Myra Snell is a professor of mathematics at Los Medanos College, Pittsburg, California. She currently is co-coordinator of the LMC Developmental Education Program and co-coordinator of the Teaching and Learning Project, which oversees campus assessment activities.

Implementing intentional change is at the heart of Beyond Crossroads. Using assessment of student learning as a vehicle for improving learning is one of the underlying principles integrated throughout the AMATYC standards and expanded upon in Chapter 5. In this article three case studies from Los Medanos College in Pittsburg California illustrate how assessment can motivate positive change that improves student learning across a developmental math program. Improvements in learning resulted from collaboratively establishing clear goals for learning, responding to assessment results with definitive changes to classroom activities, and professional development that integrates math education research and classroom-based research. (back to top)

Math Anxiety Case Studies: A Beyond Crossroads Companion

Fred Peskoff

Fred Peskoff is chairperson of mathematics at Borough of Manhattan Community College, City University of New York. He has made numerous presentations both nationally and internationally on math anxiety and its impact on students and faculty. His work has been published by the Harvard Graduate School of Education. Peskoff won the 2003 AMATYC Teaching Excellence Award for the Northeast Region.

The case study approach is commonly used in the fields of law, medicine, and business administration to help apply theory to practice. This approach is equally useful in the teaching and learning of mathematics since various categories of coping strategies used to alleviate math anxiety become more meaningful when they are used to assist "real” students. A number of case studies were developed to apply the coping strategies presented in Beyond Crossroads to students who have found themselves at the "crossroads” between success and failure. Each case represents a student at the author’s institution who is confronted with a potentially stressful situation when attempting to study mathematics. (back to top)

AMATYC’s Role for Improvement of Future Learning

Linda P. Rosen


Linda P. Rosen is President of Education and Management Innovations, Inc. Previously, Rosen served as Senior Advisor to Secretary of Education Richard W. Riley and as the Executive Director of the National Commission on Mathematics and Science Teaching for the 21st Century (known as the Glenn Commission). She was also the Executive Director of NCTM and the Associate Executive Director of the Mathematical Sciences Education Board.

The educational landscape has shifted significantly in the past few months with a new call for national standards and national tests as well as for accountability in higher education. Beyond Crossroads must be implemented with full understanding of these shifts and with agility to adapt to further seismic changes.

A brief history puts the magnitude of recent shifts in context. Those in mathematics education often claim the title as "godparent” of the standards movement after the 1989 release of the NCTM Curriculum and Evaluation Standards. Yet, when President George H.W. Bush and the nation’s governors announced America 2000 to create "world class standards” and achievement tests, politicians laid claim to "godparent” status. In the 1990s, the business community also laid claim as the "godparent” of the standards movement.

Of course, parentage is unimportant as long as high quality, well-conceived standards get put into practice. And, therein lays the problem for K–12 and for higher education: defining high quality standards and, more importantly, implementing them.

The Commission on the Future of Higher Education recently identified three As for the renewal of higher education: access, affordability, and accountability. It is the third A—accountability—that is pertinent to the release of Beyond Crossroads. Knowing that administrators and policymakers are weary of calls for excellence without commensurate, steady progress towards that vision and know-ing that external pressures on them to "deliver” are increasing, it behooves AMATYC to take seriously the need to improve every component of mathematics education in the first two years of college. (back to top)

Why is it Essential to Involve Stakeholders in Implementing Beyond Crossroads?

Sue Parsons

Sue Parsons is currently the Director of Teacher TRAC and Learning Community Programs and an associate professor of mathematics at Cerritos College. She served on the National Academy of Science MSEB Board 2001–2004. She also served as AMATYC West Region Vice President, Co-PI on an AMATYC NSF Teacher Preparation grant, and as a writing team chair for the AMATYC Beyond
Crossroads Project.

Most two-year mathematics faculty initially won’t gravitate toward the chapter on stakeholder involvement in implementing Beyond Crossroads. Faculty most likely will search out the chapter on curriculum and instruction. In fact, some mathematics faculty may not consider the relevancy of other stakeholders as an important factor for improving their students learning in mathematics. The thought may exist that, "I am a two-year college mathematics professor. Why do I need to collaborate with entities outside my department? Why do I need to be involved with other stakeholders? I am well versed in my content area and have the mathematical background to teach two-year college students.” Part of implementing Beyond Crossroads is the recognition that improving student learning in mathematics will not be fully realized without meaningful involvement of many stakeholders. The article addresses questions and discussion that are meant to emphasize that we, as mathematics faculty members, are stakeholders and Beyond Crossroads is a call to action for all stakeholders to work together to improve student success in mathematics courses and programs in the first two years of college. (back to top)

Book Reviews

Edited by Sandra DeLozier Coleman

THE CALCULUS WARS: Newton, Leibniz, and the Greatest Mathematical Clash of All Time, Jason Socrates Bardi, Thunder’s Mouth Press, an imprint of Avalon Publishing Group, Inc., New York, 2006, ISBN 1-56025-706-7.

TOM STOPPARD: PLAYS 5—Arcadia, The Real Thing, Night and Day, Indian Ink, Hapgood, Tom Stoppard, Faber and Faber Limited, London, 1999, ISBN 0-571-19751-5. (back to top)

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Software Reviews

Reviewed by Patrick J. DeFazio, Onondaga Community College

Edited by Brian E. Smith

powerOne™ Graph v4.2
Producer and Distributor: Infinity Softworks, Inc.
Web addresses:
Price: Retail Price $59.99

As a qualified educator, administrator or director, you may be eligible to purchase a single copy of powerOne™ Graph graphing-scientific calculator software or powerOne® Finance financial calculator software for a 75% discount for your personal use.

Platforms: Palm® OS

PowerOne™ Graph v4.2 by Infinity Softworks, Inc. is a graphing calculator software title for Palm® handheld devices. Its functionality is robust and it is both expandable and customizable through downloads from Infinity Softwork’s web site. The software includes capabilities for computation, conversion, graphing (with analysis), business, matrix, probability, statistics, regression, and more. The user can select their desired input mode (algebraic, RPN, chain, order of operations) to meet their individual needs. Entries are made through the touch screen using the stylus and pop-up keypad calculators (when needed), or through Palm’s® Graffiti writing software. Data and results can often be copied and pasted to/from the system clipboard and the software documentation indicates that a user can also export results to spreadsheet and word processing applications (which may require add-ons). Use of the Palm® device’s wireless communications is also enabled to allow the user to "beam” selected data, functions, or results to others.

This review outlines the main calculator interface, illustrates the use of a statistics template, and then demonstrates a few of the more commonly needed graphical features. Screen shots were obtained using a PC emulator. It should be noted that the resolution of the images from the emulator do not adequately indicate the resolution obtained when using the software on a Palm® handheld. [Ed.: Because this journal is printed in black and white, the color features of the software cannot be seen.]

The main calculator interface (see Figure 1) has many features that make calculation input and access (to the many additional software features) very easy. Calculations are entered through the use of the keypad and function buttons (on the function bars). These buttons call individual functions (or function categories) and appear in two rows that the user can scroll to see additional available buttons. The buttons can be customized to include templates as well. The list of available function buttons may change with the use of alternate skins (from the website). The user can also select functions through the functions

button (located next to the function bars) which opens a menu of function categories (Math, Number, Trig, Prob, Stat, Matrix, Vars, etc). Selecting one of these categories opens a new menu of individual functions. The default input mode is "algebraic” allowing the user to enter the entire calculation in the view window at once. When ENT is selected the calculator returns the final result using the normal order of operations. However, different input modes can be selected (RPN for those accustomed to HP calculators, for example).

Within the view window are some additional features. The H3 in the screen shot in Figure 4 indicates the memory location where the current calculation results are stored. When thebutton within the view window is tapped with the stylus a calculations log opens showing a recent list of calculations and results. These can be individually recalled to the view window for use in the current calculation. The D in the view window pictured in Figure 1 indicates that the calculator is in decimal mode. This can be selected to open a menu that allows the user to change the base for calculations or convert results (to binary, octal, or hexadecimal). Fraction and mixed number modes/conversions are also available here. (See Figures 2–4.)

The powerOne button at the top of the main calculator screen provides access to the preference settings. It also contains the copy/paste commands that access the Palm® system clipboard. Additional features mentioned in this review may also be accessed through this button.

New data (variables, constants, matrices, tables, etc.) can be entered through the"My Data” navigation button at the top of the main calculator screen. User created macros (specific equations for recall in other calculations) can also be entered here. Many useful constants come stored in the "My Data” area including e, , the speed of light, gravity acceleration, electron mass, and others. Tables are easily created by selecting New from the "My Data” screen. The user can name the table, enter its imensions (see Figure 5), and then, using the pop-up keyboard calculator (which automatically appears when needed), input the individual entries, as shown in Figure 6. After completion and returning to the "My Data” screen the table can later be edited, duplicated, beamed, or have notes attached (Figure 7). The ability to attach notes is a nice feature that would be very useful if multiple tables are needed for an assignment or project.

Templates are a nice feature of this software. Some templates come pre-installed, others can be created by the user or obtained from Infinity Softworks Inc.’s website. Access to the templates is obtained through the "My Templates” navigation button at the top of the main calculator screen. When this button is selected with the stylus a menu of templates (sorted into categories) is opened. Business, calendar, conversion, and many statistical templates are available here. Some of the statistical choices are shown in Figure 8. The 2-Var Stats template was chosen in Figure 9 to illustrate the process.

The two columns of the Sample table are selected from drop down lists as the data source. When OK is tapped by the stylus the template runs and approximately two screens of statistics are shown in Figures 10 and 11. Tapping the button at the top of this screen provides a nice summary of all of the statistics calculated in this template, as indicated in Figure 12. Selecting Graph from this screen shows a plot of the data with an automatically fitted window. From there, Analysis can then be selected with Regression and Quadratic chosen from the subsequent menus to produce a graph of the quadratic regression function (see Figures 13 and 14). Details of the regression function can be found using the button as demonstrated in Figure 15.

The function f(x) = sin(x) + 1 will be used to demonstrate a few of the graphical features of the software (graphing, finding extrema, tangent lines, and intersections) that are in common use in a mathematics classroom. Some very nice features of this handheld device software (color, naming, categorizing, notation, and use of stylus) that differentiate it from many popular graphing calculators are also highlighted.

Selecting the "My Graphs” navigation button at the top of the main calculator screen brings up the "My Graphs” screen (see figure 16). This is where a list of previously entered graphs is contained. A listing of all graphs can be shown, or just those from selected (user created) categories. Graphs displayed on the list can be selected or deselected through checkboxes. In addition, different colors and line styles may be assigned to different graphs from this location. Window settings for graph viewing can also be set here for an individual graph or an entire category of graphs. The ability to use different colors does allow multiple graphs to be viewed on the same set of axes with greater clarity than on a typical monochromatic calculator screen.

Select New with the stylus to create a new graph. Once the type of graph (Function, Parametric, Polar, Sequence, or Data) is selected (Figure 17) the "New Graph” screen is revealed with three tabs (Figure 18). The "Data” tab is the location for entering the function to be graphed. Commonly needed keys and commands are on a keyboard menu. Selecting f(x) brings up a menu of categories of functions (Math, Number, Trig, Prob, etc.) shown in Figure 19. Selecting one of these categories brings up a menu of individual functions (sine, cosine, tangent, etc.), as indicated in Figure 20. The menus are easy and convenient and well suited for quick entries using the Palm® stylus.

The "Details” tab (Figure 21) is the location for assigning the new graph a name (optional) and a category (optional), as indicated in Figure 22. These options could be very useful for an instructor wishing to categorize multiple graphs by different courses or for a student categorizing graphs by assignment. Naming a graph by its homework exercise would also prove a beneficial use of this feature. Graphs without names are listed by their function rule. Color and line styles can also be assigned here. The "Prefs” tab (Figure 21) allows the user to select window settings. One additional (and very nice) feature found on this screen is the Notes option. Selecting Notes from the New Graph screen opens a text input area allowing the user to enter annotations, comments, or questions that can be saved with the graph (see Figure 23). This would be very useful as a pedagogical tool.

Now that the graph’s information has been entered, return to the "My Graphs” screen. The drop menu at the upper right-hand corner allows the user to have only the graphs in a desired category to be shown (Figure 24). The desired individual graph(s) are checked, window settings adjusted (if desired) (see Figure 25), and then Graph is selected to view the graph shown in Figure 26.

The Palm® stylus works very well as an input/selection device for many common graphical analysis procedures. The steps required for obtaining local extrema and tangent lines, tracing, zooming, and determining points of intersection all highlight this fact. These can all be initiated from the "Graph” screen, most from the Analysis menu. Other tools are available on this menu as well, including Roots, Derivative, and Inflection.

Select Maximum from the Analysis menu and then use the stylus to drag open a box defining a region for the software to calculate the maximum function value within. The results are displayed on the graph screen (Figure 27). Additional boxed regions can then be defined with the stylus to find additional maximums.

Select Tangent from the Analysis menu and then use the stylus to choose a point on the graph (or enter a desired x value). This will display the slope and y-intercept for the line tangent to the graph at the desired point, as shown in Figure 28. Additional points can be selected (and additional tangent lines found) by tapping additional points on the graph with the stylus or entering the desired x values through a pop-up keyboard. The user can also slide the stylus along the graph to see the tangent lines instantly change.

Zooming can be controlled by selecting Zoom In (or Zoom Out) and then tapping the desired focal area of the graph with the stylus. Alternatively, the user can select Zoom Box from the Zoom menu and define the box by dragging the stylus over the desired area of the graph. Tracing (evaluating) is accomplished by selecting Trace/Eval from the Analysis menu and then using the stylus to tap the desired point on the graph, as indicated in Figure 29. Again, the stylus can also be slid along the graph to see the function values instantly change.

The intersection of two graphs can be found by having both graphs shown on the same axes, selecting Intersection from the Analysis menu, and then using the stylus to drag open a box around the desired point (see Figure 30).

This review has illustrated some of the abilities and features of this very functional software title. The main interface and subsequent menus and screens are clear and easily navigated. The Palm® stylus is an intuitive input device and the software utilizes it well. Pop-up keyboards and calculators provide an easy way to enter data for those who frustrate easily with PDA-type handwriting recognition. The ability to add-on or customize this software adds to its strength as an educational tool. In addition, the full color and higher resolution screen outclass the common graphing calculator screens that are widely used. Any mathematics instructor or student currently owning a Palm®device would find this software very useful.

Reviewed by Patrick DeFazio, Assistant Professor, Department of Mathematics, Onondaga Community College (Syracuse, NY). DeFazio received his BS (Mathematics) from the State University of New York (SUNY) at Fredonia and both a BA (Philosophy) and MA (Mathematics) from SUNY Brockport.

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Brian E. Smith
AMATYC Review Software Editor
Department of Management Science
McGill University
1001 Sherbrooke St. West
Montreal, QC, Canada H3A 1G5

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The Problems Section

Edited by Stephen Plett and Robert Stong

New Problems

The AX Problem Set consists of four new problems.

Set AV Solutions

Solutions are given to the four problems from the AV Problem Set that were in the
spring 2006 issue of The AMATYC Review.
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