MathAMATYC Educator
A refereed publication of the American Mathematical Association of TwoYear Colleges
Editor: Pete Wildman, Spokane Falls CC
Production Manager: George Alexander, Madison Area Technical College
Volume 3, Number 3, May 2012 Issue
Earlier and Later Issues
AMATYC Members can view entire articles of this
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This Issue’s Features
Extending a Property of Cubic Polynomials to HigherDegree Polynomials
David Miller and James Moseley, West Virginia University
Using Dynamic Solution Exercises to Achieve Vertical Course Alignment
Elliot Ostler and Michael Flesch, Metropolitan CC
Open Educational Resources: A Faculty Author’s Perspective
Barbara Illowsky, De Anza College
The Effects of Requiring Study Group Participation Associated with Students’ Attitudes and Achievements in Developmental Math
Clayton D. Brown, Utah Valley University
The Keystone Approach: Integration of Methodology and Technology
M. ValiSiadat, Euguenia Peterson, CyrillOseledets, MingJer Wang, andGuoQuan "Jack” Zhang, Richard J. Daley College
Reflections on Teaching Statistics in a Hybrid Format
Victoria Ingalls, Tiffin University
MathAMATYC Educator's Departments
Use It Now
The Great Gorilla Jump: An Introduction to Riemann Sums and Definite Integral
Vicki Sealey, West Virginia University, and Nicole Engelke, California State University, Fullerton
Using "1 = 2” to Inspire and Learn
KirthiPremadasa, University of Wisconsin Marathon County, and GeethaSamaranayake, University of Wisconsin Whitewater
Notes on Parabolas Using the Mirage Illusion
Sid Kolpas, Delaware County CC, and Tom Voden, Glendale CC
A Gaming Application: The Pick3 Lottery
Greg Fiore, CC of Baltimore County
Walking Beyond Crossroads
Student Learning and the Learning Environment
Jack Rotman, Lansing CC
When am I ever going to use this?
HomeImprovement Company Growth
Frank C. Wilson, ChandlerGilbert CC
The Problem Section
Take the Challenge
Joe Browne, Onondaga CC

David A. Miller earned his PhD in mathematics from Oklahoma State University in 2006. He is currently an assistant professor of mathematics at West Virginia University. His research interests include undergraduate mathematics education, cognitive science, and illustrating mathematics through technology.
James Moseley earned his PhD in applied mathematics from Purdue University in 1979. He is currently an associate professor of mathematics at West Virginia University. His research interests range from largenorm asymptotic solutions of partial differential equations with an exponential nonlinearity to analytical and numerical solutions to engineering models and the related theoretical mathematics.

Extending a Property of Cubic Polynomials to HigherDegree Polynomials
David Miller and James Moseley, West Virginia University
In this paper, we will examine a property that holds for all cubic polynomials given two zeros. This property is discovered after reviewing a variety of ways to determine the equation of a cubic polynomial given specific conditions through algebra and calculus. At the end of the article, we will connect the property to a very famous method in calculus and extend the property for higherdegree polynomials.

Elliott Ostler is a professor of mathematics education at the University of Nebraska at Omaha. He has been teaching at the college and university level for nearly 20 years and works with teachers at all levels. His current research interests include the use of technology in the mathematics classroom, alternative assessment practices in math education, and nontraditional pedagogies.
Michael Flesch is an instructor of mathematics at Metropolitan CC in Omaha, NE. He has been teaching in a community college setting for 24 years. He has taught courses ranging from developmental mathematics through calculus and has developed several of the online courses in intermediate and college algebra, and statistics. Currently, he is online coordinator for the mathematics courses at Metropolitan.

Using Dynamic Solution Exercises to Achieve Vertical Course Alignment
Elliot Ostler and Michael Flesch, Metropolitan CC
This paper justifies the need for, and offers some suggestions on, the selection and implementation of mathematical problems known as dynamic solution exercises (DSEs). The intent of this article is to help provide insight into how mathematics teachers can go about making vertical articulation a cooperative and tangible part of the mathematics curriculum. A sample dynamic solution exercise is provided based on research at Metropolitan CC in Omaha, NE. Some strategies for selecting and building a DSE instructional environment are included.

Barbara Illowsky is the Mathematics Department Chair at De Anza College in Cupertino, CA, where she’s taught since 1989. She is the immediate past president of the CA Mathematics Council, Community Colleges, and was the first project director for the International Community Colleges Consortium for Open Educational Resources. She earned her PhD in education from Capella University, specializing in instructional design for online learning, her masters in statistics from the Wharton School, University of Pennsylvania, and her bachelors in mathematics from the University at Albany (formally the State University of New York at Albany).

Open Educational Resources: A Faculty Author’s Perspective
Barbara Illowsky, De Anza College
As the coauthor (with Susan Dean, retired De Anza College mathematics faculty) of a formally forprofit and now open (i.e., free on the web) textbook, Collaborative Statistics, I receive lots of questions about open educational resources (OER), which can be summarized as the follows: (1) What are OER? (2) Why do you support, actively promote, and speak about OER? (3) If a book is available for free, then is it really any good? (4) How can I find good OER for my courses? And (5) Why should I (the person asking me the question) bother when I might need to do more work if I choose an OER? (AKA What’s in it for me?)?

Clay Brown is an associate professor mathematics at Utah Valley University (UVU) in Orem, UT, where he has been teaching for 10 years. He received a MA in mathematics education from Central Washington University and a BA from Brigham Young University. He has received two UVU awards: Educator of the Year (2004) and University College Outstanding Educator of the Year (2006). Outside of teaching mathematics, his loves are his wife and 4 kids, sports, and gardening.

The Effects of Requiring Study Group Participation Associated with Students’ Attitudes and Achievements in Developmental Math
Clayton D. Brown, Utah Valley University
It is widely publicized that student attitudes and achievement in math in the United States require improvement (Arem, 2003). U.S. students have shown lackluster mathematics achievement scores compared to their international peers in other developed countries (Schmidt, McKnight, Cogan, Jakwerth, & Houang, 1999).
As a former high school math instructor, I observed that the attitude of many high school students and their parents was that the student should do as much math as possible in high school in hopes of "testingout” of college math so as to "never have to take math again.” As a college math instructor, I have known students who changed their major or career choice to avoid taking math as part of their graduation requirements. One study found that math serves as a "critical filter” for many students in determining their educational, occupational, and professional opportunities (Sells, 1978). Both high school and college students are showing evidence of being math avoiders (Arem, 2003). This math avoidance closes numerous doors of opportunity for too many students.

M. ValiSiadat is professor of mathematics and a department chair at Richard J. Daley College. He has two doctorates in mathematics, a PhD in pure mathematics and a DA in mathematics education. He
has more than twenty publications in mathematics and mathematics education and has had numerous presentations at regional and national mathematics meetings. He is the recipient of several national awards, including the Carnegie Foundation for the Advancement of Teaching, Illinois Professor of the Year Award, and the Mathematical Association of America’s Deborah and Franklin TepperHaimo Award.
Euguenia Peterson is an associate professor of mathematics at Richard J. Daley College. She holds a PhD degree in physics and mathematics, an MS in chemical engineering, and a MAT in secondary education. She joined the Daley College Mathematics and Science Departments in 1998. Her tenure project was based on the research in developmental mathematics classes. She has had several presentations and publications related to science and mathematics education.
CyrillOseledets is a tenured assistant professor in the Department of Mathematics at Richard J. Daley College. He holds a PhD in pure mathematics from the University of California, Riverside, and a developmental specialist degree from the Kellogg Institute at the Appalachian State University. He was formerly a fulltime mathematics professor at Syracuse University.
MingJer Wang has been teaching mathematics and physics at Richard J. Daley College as a tenured fulltime faculty. He holds a PhD in experimental nuclear physics from Case Western Reserve University with the thesis experiments carried out at Fermi National Accelerator Laboratory and Los Alamos National
Laboratory. He has also worked on experimental projects at UCLA and Saclay National Laboratory in France. His contributions to this study are experimental design, experiment coordination, and data analysis.
GuoQuan (Jack) Zhang is a tenured fulltime faculty member in the mathematics department at Richard J. Daley College. He obtained his PhD in applied mathematics from the Illinois Institute of Technology in
2007. His research interests are statistics and mathematics education.

The Keystone Approach: Integration of Methodology and Technology
M. ValiSiadat, Euguenia Peterson, CyrillOseledets, MingJer Wang, andGuoQuan "Jack” Zhang, Richard J. Daley College
This article is the result of a comprehensive research study investigating the impact of computerlearning technology as well as the impact of a synergistic teaching approach (Keystone Method) on developmental mathematics classes at the college level.
The study focused on mathematics skills of elementary and intermediate algebra students and measured their performance on departmentally designed common midterm and final exams as well as on a national standardized test (COMPASS). An analysis of the data for the period of study shows that students in experimental classes employing the synergistic approach attained higher performance outcomes compared with students taught under traditional methods with the use of technology. The higher outcomes in the experimental classes were not achieved with the attrition of weaker students. Moreover, investigating the impact of technology on traditional teaching in elementary algebra classes, the study found no significant gains in student learning outcomes in classes incorporating technology compared to those that did not use technology.

Victoria Ingalls (ingallsv@tiffin.edu) is an assistant professor of mathematics at Tiffin University and the mother of five daughters. She thoroughly enjoys teaching both mathematics and education classes in innovative and engaging manners.

Reflections on Teaching Statistics in a Hybrid Format
Victoria Ingalls, Tiffin University
Although this article recounts some major obstacles to teaching mathematics in such a format, the major emphasis of this article is on offering suggestions to other faculty members who may be benefit from another’s experiences in teaching a hybrid statistics course.

Vicki Sealey is an assistant professor of mathematics at West Virginia University. She serves as the coordinator for the calculus sequence and loves seeing students learn math. She researches student understanding of calculus topics with an emphasis on understanding Riemann sums and definite integrals.
Nicole Engelke is an assistant professor of mathematics at California State University, Fullerton. Her research focuses on how students learn and understand calculus concepts, particularly with contextual questions. She is actively involved in the special interest group of the Mathematical Association of America on research in undergraduate mathematics education.

The Great Gorilla Jump: An Introduction to Riemann Sums and Definite Integrals
Vicki Sealey, West Virginia University, and
Nicole Engelke, California State University, Fullerton
The great gorilla jump is an activity designed to allow calculus students to construct an understanding of the structure of the Riemann sum and definite integral. The activity uses the ideas of position, velocity, and time to allow students to explore familiar ideas in a new way. Our research has shown that introducing the definite integral as area under a curve first does not give students the foundations they need to be able to solve more difficult word problems involving definite integrals. Thus, this activity uses familiar ideas to build the foundations needed for understanding Riemann sums and definite integrals.

Kirthi Premadasa obtained his MS and PhD from Purdue University and has over 22 years of undergraduate teaching experience in Sri Lanka and the US. He is an assistant professor of mathematics at the University of Wisconsin Marathon County.
Geetha Samaranayake obtained her MS and PhD from Purdue University and has over 24 years of undergraduate teaching experience in the US. She is an associate professor of mathematics at the University of Wisconsin Whitewater.

Using "1 = 2” to Inspire and Learn
KirthiPremadasa, University of Wisconsin Marathon County, and GeethaSamaranayake, University of Wisconsin Whitewater
Mathematical fallacies have an embedded sense of awe and mystery that can be used effectively in a classroom to inspire students to tackle a fallacy and find the "hidden” violation. In doing so, the student may discover the consequence of a rule violation in a stimulating manner, thus making a lasting impact of the rule as well as providing the student with a chance to master all concepts surrounding a fallacy, with a high degree of motivation, as the search for the violation is pursued. Fallacies have a tendency to create a "puzzlesolver” state of mind in a student, which can be tapped to generate motivation among students and greater mathematical accuracy. Results of a twosemester study are presented, where firstsemester calculus students were provided with a number of fallacies covering three common algebraic violations.

Tom Voden earned a PhD in mathematics from the University of California, San Diego, in 2006. He was a fulltime math faculty member at San Diego City College from 2005 to 2007 and is currently at Glendale CC, where he enjoys his roles as Robotics Club advisor and Title V STEM success coordinator.
For the past 41 years, Sid Kolpas has taught at the junior high school, high school, and college levels. For the past 20 years, he has been a professor of mathematics at Glendale CC in Glendale, CA. In 2010, he received the Hayward Award for Excellence in Education from the California Community Colleges Board of Governors. In fall 2011, he started a new career at Delaware County CC, outside of Philadelphia.

Notes on Parabolas Using the Mirage Illusion
Sid Kolpas, Delaware County CC, and Tom Voden, Glendale CC
The present work is intended as a classroom note on the topic of parabolas. We present several realworld applications of parabolas, outline a short classroom lab activity using the Mirage Illusion, derive fundamental formulas and properties of parabolas, and suggest analogous discussions in the context of ellipses. The content is suitable for use in college algebra or precalculus as well as in ﬁ rstyear calculus courses.
Entire Article (PDF)

Greg Fiore (gfiore@ccbcmd.edu) is a professor of mathematics for the CC of Baltimore County, where he has taught for over 30 years. He has an MS in mathematics from Purdue University and an MS in computer science from Loyola University. He has authored several textbooks and published a dozen articles on math applications to science and other disciplines. Seven years ago, he developed a course entitled Mathematics of Gaming at CCBC, and has made presentations at national and local conferences on math in gaming.

A Gaming Application: The Pick3 Lottery
Greg Fiore, CC of Baltimore County
This article applies several basic probability tools including expected value, frequency tables, relative frequency, and the binomial distribution to examine the expected value of the Pick3 lottery game. Using the data and operating procedures published by the Maryland state lottery, calculations are made to demonstrate how this can be a positive expectation game in the short term.

Jack Rotman has been at Lansing CC since 1973, with a focus on developmental mathematics. He has an MA from Michigan State University and has been active in state and national professional organizations for almost 30 years, with over 20 presentations at AMATYC conferences. Jack has contributed to the AMATYC Crossroads and Beyond Crossroads and has chaired the AMATYC Developmental Mathematics Committee twice for a total term of 9 years. Currently, he is leading the AMATYC New Life for Developmental Mathematics, a project focused on reinventing developmental mathematics. Additionally, he is involved as a content liaison for the Pathways Grants of the Carnegie Foundations for the Advancement of Teaching.

Student Learning and the Learning Environment
Jack Rotman, Lansing CC
Learning is obviously a student responsibility … the learning environment is obviously the responsibility of faculty (supported by the institution). Beyond Crossroads Chapter 4 lists recommendations and standards in both areas. Current approaches to developmental mathematics offer methodologies that address those standards and bring a balanced methodology to the responsibilities of students and faculty.

Frank Wilson is the Math Division Chair at ChandlerGilbert CC. Educators worldwide use his activities and textbooks focused on helping learners make sense of mathematics and discover how to use it in everyday life.
Contact Frank at frank@makeitreallearning.com.

HomeImprovement Company Growth
Frank C. Wilson, ChandlerGilbert CC
Download Activity
Too often, students memorize mathematical procedures without understanding the "why” behind the "how.” As educators, our role is to help students understand the big ideas, make connections between related concepts, and learn to recognize mathematical concepts in realworld contexts. This issue’s When Am I Ever Going to Use This? activity is designed to help each of us do that.
The realworld context for this activity is homeimprovement
company growth. Data is provided regarding the number
of Home Depot and Lowe’s stores. Since many students have
interacted with one or both of these companies as a consumer, the context is familiar to them.


The Problem Section
Welcome to the Problem Section. We will strive to provide several interesting and usually challenging problems for you to consider in each issue. Content will be mathematics and puzzles connected in some way to the mathematics we teach in the twoyear college. Readers are invited (encouraged!) to submit problem proposals (with solution) for possible inclusion in this column. We also encourage readers to submit solutions to the problems posed here; we will publish the best or most interesting in a future issue.
Send all correspondence to Joe Browne at brownej@sunyocc.edu or at Mathematics Department, Onondaga CC Syracuse NY 13215.
The Problem Section is assembled by Fary Sami (at Harford CC, MD) and Tracey Clancy, Kathy Cantone, Garth Tyszka, and Joe Browne (editor) (at Onondaga CC, NY).


