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MathAMATYC Educator May 2010
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MathAMATYC Educator

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

Editor: Pete Wildman, Spokane Falls CC
Production Manager: Jim Roznowski, Delta C

Volume 1, Number 3, May, 2010 Issue
Earlier and Later Issues

AMATYC Members can view entire articles of this issue
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This Issue’s Features

What Community College Developmental Mathematics Students Understand about Mathematics

James W. Stigler, Karen B. Givvin, and Belinda J. Thompson

Using a Square to Complete the Algebra Student: Exploring Algebraic and Geometric Connections in the Quadratic Formula

Connie H. Yarema and T. David Hendricks

Controlling Population with Pollution

Joseph Browne

Odd-Boiled Eggs

Kenneth Kaminsky and Naomi Scheman

MathAMATYC Educator’s Departments

In My View

Reflections on Teaching Developmental Mathematics: Motivation Through Enlightenment

Félix Apfaltrer and Marcos Zyman

Walking Beyond Crossroads

Student Perspectives on Mathematics Writing Assignments

Todd Cadwallader Olsker

Use This Now

Suuroji Puzzles: Sudoku-like Logic with a Twist

Marcus Jorgensen

How to Build a Pyramid

Keith Brandt

Reading and Understanding Expressions: Replacing the Order Of Operations

Herbert Libow

Pedagogy on Integral Notation: Defending the Differential

Michael W. Ecker

Multivariable Economic Applications in Applied Calculus

April Allen-Materowski, Warren B. Gordon, and Walter O. Wang

When Am I Ever Going to Use This

Working with Piecewise Functions

Frank C. Wilson

Book Review

Mathematics and Democracy: The Case for Quantitative Literacy

Roxane Barrows





What Community College Developmental Mathematics Students Understand about Mathematics

James W. Stigler, University of California, Los Angeles
Karen B. Givvin, University of California, Los Angeles
Belinda J. Thompson, University of California, Los Angeles

Abstract
The nation is facing a crisis in its community colleges: more and more students are attending community colleges, but most of them are not prepared for college-level work. The problem may be most dire in mathematics. By most accounts, the majority of students entering community colleges are placed (based on placement test performance) into "developmental” (or remedial) mathematics courses (e.g., Adelman, 1985; Bailey et al., 2005). The organization of developmental mathematics differs from school to school, but most colleges have a sequence of developmental mathematics courses that starts with basic arithmetic, then goes on to pre-algebra, elementary algebra, and finally intermediate algebra, all of which must be passed before a student can enroll in a transfer-level college mathematics course.

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yarema

Connie Yarema teaches mathematics courses for non-science majors and pre-service secondary mathematics teachers at Abilene Christian University, Abilene, Texas. She is interested in outreach mathematics - focusing on establishing communities of practice using lesson study, a Japanese professional development model for in-service and pre-service teachers.

Using a Square to Complete the Algebra Student: Exploring Algebraic and Geometric Connections in the Quadratic Formula

Connie H. Yarema, Abilene Christian University
T. David Hendricks, Abilene Christian University

hendricksDavid Hendricks teaches mathematics courses and is the chair of the mathematics department at Abilene Christian University, Abilene, Texas. He is interested in cryptography, preparing pre-service teachers, and working with in-service teachers.

Abstract
Recommendations and standards from various stakeholders in the mathematical preparation of teachers, such as The Mathematical Education of Teachers (http://www.cbmsweb.org/MET_Document/chapter_2.htm) and Beyond Crossroads (http://beyondcrossroads.matyc.org/doc/CH6.html), call for courses that emphasize connections within topics in mathematics, especially those that are most familiar to pre-service teachers.  However, these recommendations are applicable for any student taking an algebra course at a post-secondary institution, including developmental algebra courses.  One familiar topic to students who take an algebra course in college or who will teach an algebra course in high school is the quadratic formula.  Algebra students often see the derivation of the quadratic formula based on the method of completing the square using algebraic procedures.  However, the history of mathematics indicates that these procedures originated from geometric concepts.  Presenting both algebraic and geometric representations as the quadratic formula is derived helps pre-service mathematics teachers and algebra students, in general, visualize concepts and make sense of algebraic procedures.  It also sets up a natural extension for students to make meaning of the quadratic formula itself by connecting its algebraic symbolism to a geometric representation.

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browne

Controlling Population with Pollution

Joseph Browne, Onondaga CC

Abstract
Population models are often discussed in algebra, calculus, and differential equations courses. In this article we will use the human population of the world as our application. After quick looks at two common models we’ll investigate more deeply a model which incorporates the negative effect that accumulated pollution may have on population.

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kaminsky

Odd-Boiled Eggs

Kenneth Kaminsky, Augsburg College
Naomi Scheman, University of Minnesota

scheman

Abstract
At a Shabbat lunch in Madrid not long ago, the conversation turned to the question of boiling eggs. One of the guests mentioned that a Dutch rabbi he knew had heard that in order to make it more likely that boiled eggs be kosher, you should add an egg to the pot if the number you began with was even. According to the laws of Kashruth, Jews may not consume eggs containing blood spots. When observant Jews make an omelet or bake challah, they break each egg separately and discard any that are bloody before they add them to the rest of the ingredients. But when you boil eggs, there is no easy way to tell beforehand if the eggs you are cooking have blood spots or not. Once the eggs are boiled and opened, the spots can be seen, but by then it is too late. All the eggs must be discarded, and a pot in which bloodied eggs are cooked is no longer kosher.

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felix

Reflections on Teaching Developmental Mathematics: Motivation Through Enlightenment

Félix Apfaltrer, Borough of Manhattan CC, CUNY
Marcos Zyman, Borough of Manhattan CC, CUNY

zyman

Abstract
The Motivating Beauty of Mathematics. Most college instructors agree that there is a need to motivate students to learn mathematics. But there is a profound disagreement on how exactly to do this. Can we actually motivate our students to learn basic algebra? Is the instructor to emphasize the usefulness of mathematics in the "real world”? Are we to motivate students by exhibiting our own motivation and passion for the subject? Are we to convey the beauty of mathematics at such an early stage? Needless to say, these questions pose considerable complexity, and to some extent, the answers are yes, yes, yes, and yes. However, as faculty, we need to find a theme, indeed a style in our teaching of developmental mathematics. Although engaging students in the developmental classroom requires all of these considerations, we contend that the coherence, logical structure, beauty, and breadth of mathematics should be kept at the center of our motivational efforts.

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cadwallader

Student Perspectives on Mathematics Writing Assignments

Todd Cadwallader Olsker, California State University, Fullerton

Abstract
AMATYC’s document, Crossroads in Mathematics, encourages mathematics faculty to "foster interactive learning through student writing,” among other activities in its section on standards for introductory college mathematics. However, as Meier and Rishel (1998) point out, these student writing assignments must be carefully designed in order to successfully foster student learning and engagement. Without a connection to the class material, a writing assignment will be less en-gaging to students and will be less successful in achieving an increase in student understanding.

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jorgensenMarcus Jorgensen is an assistant professor in the Developmental Mathematics Department at Utah Valley University (UVU). Prior to UVU, he served as Dean of Computing, Mathematics, and Science at Spokane Falls CC. Marc is a retired United States Coast Guard captain where much of his career was spent in the field of education and training.

Suuroji Puzzles: Sudoku-like Logic with a Twist

Marcus Jorgensen, Utah Valley University

Abstract
During a break at a conference of the Southwest Association for Developmental Mathematics, I overheard a colleague say that he wished that Sudoku puzzles used more mathematics so that that he could use them in his classes. I was intrigued with the idea and set out to see if it was possible to combine the logic of Sudoku with some mathematics. Kakuro, or cross-sums, puzzles do use some math but I wanted a little more. Eventually, I came up with what I call Suuroji puzzles (Suuroji uses the beginning letters of the Romaji forms of the Japanese words for mathematics and logic). I have used them in my developmental classes as a way for students to practice some basic operations as well as factoring and problem solving.

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brandt

How to Build a Pyramid

Keith Brandt, Rockhurst University

 

Abstract
As we teach our courses, we often look for new examples, exercises, and projects that illustrate important mathematical concepts. Questions of an applied nature are particularly useful because they help motivate the study of mathematics. A few years ago a student of mine, who happens to be a cabinet maker, posed a question regarding the construction of a chute. The essential ingredients in his question are contained in the following problem:

A construction crew is remodeling the second floor of an office building and will build a chute to guide debris into a truck below. The chute will have four walls, a large square opening at the top (say with side b1 ), a smaller square opening at the bottom (say with side b2 ), and length . Determine the dimensions of the walls of the chute. In particular, determine the miter angles to be cut along the edges of the walls so that they fit together properly.

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Herbert Libow has worked in the fields of physics, engineering, and teaching throughout most of his professional career. One of his prime interests is improving the language of algebra. On leave from Santa Monica College in Santa Monica, California, he can be reached at h.rlibow@ca.rr.com. Comments, questions, and conversations are welcome.

Reading and Understanding Expressions: Replacing the Order Of Operations

Herbert Libow, Santa Monica College

Abstract
This concept paper presents a system for reading the meaning of expressions that mimics what those who use math think when reading expressions. Concurrently, this system overcomes the difficulties inherent in the Order of Operations.

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Michael W. Ecker (DrMWEcker@aol.com or MWE1@psu.edu) is an associate professor of mathematics at Pennsylvania State University's Wilkes-Barre campus. Having taught math since 1972, he received his Ph.D in mathematics from the City College of New York in 1978. He was the founder of The Mathematical Review problem section in 1981, a position he held until 1997. He is the author of over 500 newsletters, columns, reviews, and articles, many computer-related, as well as five books and/or solutions manuals. His other passions include racqutball, sweets, and Renee (Wife 2.0).

Pedagogy on Integral Notation: Defending the Differential

Michael W. Ecker, Pennsylvania State University, Wilkes-Barre Campus

Abstract
It seems that at least once every decade, somebody publishes a diatribe against the differential dx in the integral notation, integral. When I wrote a solution manual for a survey math text back in 1993, I noted that the author refused to use the differential in the text where he had an introduction to integral calculus. Although I would not have included calculus in such a course at all, I would have at least used correct notation. I wound up insisting on including the differential in my solutions, despite the poor editor’s understandable plea for consistency with the author.

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allen

Multivariable Economic Applications in Applied Calculus

April Allen-Materowski, Baruch College – CUNY
Warren B. Gordon, Baruch College - CUNY
Walter O. Wang, Baruch College - CUNY

gordon
wang

Abstract
The applied calculus course is generally a less theoretical version of the traditional calculus course aimed at non-science majors. In many colleges, students enrolling in this course are business majors, often majoring in economics or finance. A frequent complaint of students is the paucity of realistic applications relevant to these disciplines. The literature study revealed few realistic multivariable applications to these disciplines. The applications found included the usual, hackneyed, maximize profit/revenue, minimize cost, or determine if demand functions are complementary/substitutes exercises. A review of texts in economics and finance found interesting applications and/or interpretations  to level curves, homogeneous functions and Euler’s theorem. The authors claim no originality in the following discussion; however, these applications need a wider audience in the mathematical community with the goal of ultimately benefitting students.

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wilson

Working with Piecewise Functions

Frank C. Wilson, Chandler-Gilbert CC

Abstract
Math teachers everywhere are familiar with the common student question, "When am I ever going to use this?” Many students are disinterested and unmotivated in mathematics because they don’t see it as relevant to their own lives. Brain research has shown that when new information makes sense and is perceived as relevant by the learner, retention of the new information greatly increases. One way to increase relevance (and student learning) is to teach students how to apply mathematics in meaningful real world situations.

Greeting Card Activity

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Roxane Barrows is Associate Dean of Arts & Sciences at Hocking College in Nelsonville, Ohio. She has been teaching mathematics for over 20 years. She obtained her BS in Business Administration from Ohio State University, MS in Mathematics at Ohio University, and is currently working on her dissertation in Higher Education Administration at Ohio University.

Mathematics and Democracy: The Case for Quantitative Literacy

Roxane Barrows, Hocking College

Abstract
Mathematics and Democracy: The Case for Quantitative Literacy, edited by Lynn Arthur Steen, is a very timely book. Mathematics, mathematics education, and to a lesser degree, quantitative literacy have never been under as much scrutiny as they are today. Many mathematicians and non-mathematicians believe that too much attention has been placed on abstract mathematical concepts and not enough on numeracy. Steen, rightly so, believes that the majority of citizens need an understanding of quantitative literacy to succeed in life and the workplace, not abstract mathematics. To support his idea, he emphasizes that mathematics and numerical literacy are two different subjects and that being able to understand mathematics in the context in which it is being used is essential. The non-mathematical world is slowly coming to the realization that mathematics literacy is important and Steen does an excellent job of illustrating how fundamental quantitative literacy is for virtually everyone in our society regardless of occupation and/or economic status. He reminds the reader that quantitative data are everywhere in our society: (a) increases in gas prices, (b) changes in SAT scores, (c) low interest car loans, and (d) sports reporting (p. 1). Nearly everyone can relate to one or more of these examples, but many in our society do not know how to use the data for meaningful analysis, which is problematic. The first chapter sets the stage for the rest of the book; a collection of articles, by differing authors, about quantitative literacy.

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10/13/2016
Part One: Have You Seen a Number?

11/3/2016
Part Two: The Game of Algebra

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