MathAMATYC Educator Ausust 2010
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 2, Number 1, August, 2010 Issue
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Michael Flesch is an instructor of Mathematics at Metropolitan CC in Omaha, NE. He has been teaching at the community college setting for twenty four years. He has taught courses from developmental mathematics through Calculus. He has developed several of the online courses in intermediate and college algebra, and statistics. He is currently the online coordinator for the mathematics courses at Metropolitan CC.
Elliott Ostler is a Professor of Mathematics Education at the University of Nebraska at Omaha. He has been teaching at the college and university levels 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 non-traditional pedagogies.
Analysis of Proctored versus Non-proctored Tests in Online Algebra Courses
Michael Flesch and Elliot Ostler
Reliable assessment is central to education and educational institutions for a number of reasons, not the least of which is that one of the primary purposes of assessment in an educational institution is to validate student knowledge (and by extension, verify the innate value of degrees and diplomas). In a product-based world, where institutions of higher learning offer services focused on a somewhat elusive product (a specified knowledge base in a given discipline or disciplines, acknowledged by degrees from those institutions), it is critical that the institutions be able to attest to the value of the products they offer. If an institution claims to provide a service, they must prove to society that they do so by some formally recognized assessment mechanism; otherwise, their reputation may come into question causing potential problems with recruitment, enrollment, and even accreditation. In large measure, accurate assessment methods help to insure the survival of educational institutions (Rowe, 2004).
James Metz, firstname.lastname@example.org, is an Associate Professor of Mathematics at Kapi’olani CC, Honolulu, HI. Besides teaching developmental mathematics classes he conducts workshops in South Africa with Teachers Without Borders.
Solving a Gambling Problem
The following Puzzler is from the National Public Radio show "Car Talk,” aired March 1, 2008:
Lost Wages in Vegas
Ray: This is from my Lost Wages series and it was sent in by Katherine Curtis. She writes, ‘A man is visiting Las Vegas, known for gambling casinos and the like, and he falls for the local hype and heads for a casino with hopes of hitting it big. He goes into this unusual casino that charges a dollar to enter, as well as a dollar to leave. He pays his dollar, plays the slot machines, loses half his money and in disgust pays his one dollar and leaves. The following day, he knows he’ll do better. He takes the money he has left and heads out to the same casino. He pays his buck, but just like before, he again loses half his money, and pays another dollar to leave. On the third day, he figures he’ll give it one more shot, but his money is dwindling fast. The same thing happens—after paying his one dollar entrance, he loses half his money, and then pays his last dollar to get out. He’s flat broke when he leaves.’ So the question very simply is, how much money did he start with?
Carla Thompson, Associate Professor, Graduate Educational Research and Statistics, University of West Florida, has over 30 years experience in teaching mathematics education in higher education in Oklahoma and Florida.
Patricia McCann, Assistant Professor, Mathematics, Tulsa CC, has over 20 years experience teaching mathematics in two-year colleges in Oklahoma.
Redesigning College Algebra for Student Retention: Results of a Quasi-Experimental Research Study
Carla J. Thompson
University of West Florida
One prohibitory component to graduation rates in college is the lack of student success in college algebra. The current national passing rate of college students enrolled in college algebra is approximately 40 percent. Lack of success in college algebra creating higher enrollments in remediation courses for students has also been linked to dropping out of college. This study explored these concerns by implementing an instructional plan of action aimed at redesigning the teaching and learning of college algebra in a two-year college mathematics program focused on the use of technology to determine the impact of course redesign on student performance and attitudes in college algebra as a key concern in the retention of students in college.
Chris Hughes received his Ph.D from the University of Reading (UK) in July 2005; his research was concerned with topographical water wave scattering. He was a part time instructor from January 2006-August 2006, and have been full time at Portland CC since September 2006.
A Placement Advisory Test
The primary method of placement at Portland CC (PCC) is the Compass Placement test. For the most part, students are placed correctly, but there are cases when students feel that they have been placed too low. In such cases we use our newly created Placement Advisory Test (PAT) to help us place them appropriately.
Vilma Mesa investigates the role that resources play in developing teaching expertise in undergraduate mathematics. Currently she is investigating the nature of mathematics teaching in community colleges. She has conducted several analyses of textbooks and has been involved in evaluation projects that study the impact of innovative teaching practices in mathematics for students in science, technology, engineering, and mathematics fields.
Examples in Textbooks: Examining Their Potential for Developing Metacognitive Knowledge
University of Michigan
Textbooks, like many other resources teachers have at hand, are meant to be an aid for instruction; however there is little research with textbooks or on their potential to develop metacognitive knowledge. Metacognitive knowledge has received substantial attention in the literature, in particular for its relationship with problem-solving in mathematics (Schoenfeld, 1992). In psychology, metacognition is defined as "knowledge of cognition in general as well as awareness of one’s own cognition” (Anderson, et al., 2001, p. 55). A further distinction is made in mathematics education to include individual’s monitoring, control, and regulation of cognition while engaged in solving problems (Flavell, 1976; Garofalo & Lester, 1985). In other words, it corresponds to the knowledge about what needs to be done to set up a problem, what resources to deploy and when, and how to determine that the problem has been successfully solved. In particular, I investigate the extent to which textbook authors make explicit the decision-making process for solving problems, how they indicate that an answer has been found, and that the answer is correct (Balacheff & Gaudin, 2010).
The Overtime Rule in the National Football League: Fair or Unfair?
Nicholas Gorgievski, Nichols College, and Thomas C. DeFranco
University of Connecticut
University of Connecticut
Kimberly S. Sofronas
In 1974, the National Football League (NFL) initiated a sudden death overtime rule for games ending in a tie score at the end of regulation time. The rule states,
The sudden death system of determining the winner shall prevail when the score is tied at the end of the regulation playing time of all NFL games. The team scoring first during overtime play shall be the winner and the game automatically ends upon any score (by safety, field goal, or touchdown) or when a score is awarded by Referee for a palpably unfair act (NFL Record and Factbook, 2005).
The rule further states that if neither team scores points during the overtime period, then the game ends in a tie. To better understand the overtime rule, the following example is given.
Victor Odafe, email@example.com is an associate professor of mathematics at Bowling Green State University Firelands, Huron, OH. He is interested in assessment strategies in mathematics and is currently exploring the use of cases in mathematics and mathematical preparation of teachers.
The Role of Student Reflection and Self-Assessment in College Mathematics
Bowling Green State University
When properly implemented, the vision of Beyond Crossroads will result in classrooms where students are actively engaged and responsible for their learning. They are able to share their thinking and the teacher, in turn, can use the emerging understanding as a foundation for learning. According to Beyond Crossroads, students will be expected to "engage in regular reflection and self-assessment of their performance” (AMATYC, 2006). To engage in regular reflection and self-assessment of their performance, students should consciously examine the knowledge they are acquiring, their involvement in the way they are acquiring it, and how that knowledge relates to what they already know. This process calls for active participation by students, and it is the position of Beyond Crossroads document (AMATYC, 2006) that requesting students to participate actively can enhance their performance. When students engage in regular reflection and self-assessment, the process provides both the instructor and the student with valuable feedback about student learning.
Heidi Burgiel, firstname.lastname@example.org, teaches at Bridgewater State College in Bridgewater, MA. Her interests include visualization in mathematics and teaching with technology.
Ward Heilman, email@example.com, also teaches at Bridgewater State College. He is responsible for the design and implementation of BSC’s Transition to Advanced Mathematics course.
Why Teach Transformations of Graphs?
Heidi Burgiel and Ward Heilman
Bridgewater State College
When planning a pre-calculus course, faculty must decide which topics to include and which to omit. We argue in favor of teaching transformations of graphs of functions by describing how a graphing activity used in our class reinforces student understanding of concepts ranging from input, output, and graphs to equations of conic sections.
Nadarajah Kirupaharan is an Assistant Professor of Mathematics at BMCC of The City University of New York. He received his Ph.D. in Mathematics from Texas Tech University in 2003. He has been teaching college mathematics for sixteen years. His research interests include mathematical modeling of epidemics. In 2004 he received the Best Paper of the Year Award in Difference Equations.
Leonid Khazanov is an associate professor of mathematics at the Borough of Manhattan CC of the City University of New York. His professional interests in the area of mathematics education include methods of addressing college students’ misconceptions about probability. He is also interested in finding effective strategies for improving developmental mathematics instruction.
What is the Best Way to Factor it? A Fresh Look at the Routine Problem of Factoring Quadratic Trinomials
Leonid Khazanov and Nadarajah Kirupaharan
Borough of Manhattan CC
Factoring polynomials is routinely taught in elementary algebra courses. In many courses, students are asked to master factoring in order to simplify and perform operations with rational expressions, solve quadratic and other polynomial equations as well as a variety of applied problems. Mastery of the techniques of factoring is often expected in upper-level mathematics courses. In an elementary algebra course, students often encounter a number of factoring techniques including factoring out the greatest common factor (GCF), factoring by grouping, factoring trinomials, and special factoring. While factoring quadratic trinomials with the leading coefficient 1 is usually mastered easily by the majority of students, factoring when the leading coefficient is other than 1 proves to be much harder for them. The reason is that there exists a simple algorithm for factoring quadratic trinomials with the leading coefficient 1. Students use the reverse FOIL. It works well for them because they need to focus only on the constant term and the middle coefficient. The leading term works out automatically by placing the variable in the first degree in each set of parentheses. When using this method, the key step is to find two numbers whose product equals the constant term and whose sum is equal to the middle coefficient, and then use these numbers to recreate the binomials whose product is the given trinomial.
After receiving his Bachelor’s Degree at Clemson University in South Carolina, Frank went on to Appalachian State University in Boone, NC to get his Masters Degree in Mathematics. He got his teaching career started at Maysville Community & Technical College in Kentucky and is now at Trident Technical College in Charleston, SC. Send comments in response to the article to firstname.lastname@example.org
Thinking Outside the Box, With a Box, When Teaching the Product & Quotient Rules in Calculus I
Frank Monterisi Jr.
Trident Technical College
One of the most important concepts in Calculus I is finding derivatives by either the Product or Quotient Rule. Sure, there are plenty of mnemonic devices available to help students remember what they are, but one of the biggest aspects of these rules is keeping track of all the functions and their derivatives, especially when the Chain Rule is involved. Therefore, to try to have the students grasp the concept of both rules instead of memorizing the formulas is to alter the way of teaching the Product and Quotient Rules. The rules are very much related, so the task of relating the two rules together was not that difficult of a task.
Teri Rysz is an Assistant Professor at the University of Cincinnati Clermont College. She has taught probability and statistics for more than 10 years, in large lecture halls and in small classes. She believes conceptual understanding is the highest priority in planning lessons for any size classroom.
A Lesson in Empirical and Theoretical Probabilities and the Law of Large Numbers
University of Cincinnati
When I was asked to participate in a best-practices presentation at our all-faculty retreat, I chose the following lesson about the Law of Large Numbers. After sharing my ideas with colleagues, I have received so many positive comments that I want to pass the lesson along to more people. Understanding the Law of Large Numbers is the main goal of the lesson; investigating the difference between empirical and theoretical probabilities is a launch pad.
Maria Brunett is a professor of mathematics at Montgomery College, Rockville, MD. She is always interested in innovative lesson plans for the college mathematics classroom. Outside of the classroom, Maria has been involved in organizing an annual day of encouragement and enrichment for middle school girls and their teachers.
Linear Programming with Legos®
One of the standards for instruction in Beyond Crossroads (AMATYC, 2006) is as follows: Faculty will design and implement instructional activities that actively engage students in the learning of mathematics. By combining several ideas, I have constructed a lesson plan that actively engages students as they learn about linear programming.
Heather Gould is a PhD candidate in mathematics education at Teachers College, Columbia University. She has taught and tutored mathematics at various schools within the State University of New York system, including Ulster County CC, Dutchess County CC, and Hudson Valley CC. Her academic interests include mathematics language acquisition, mathematics manipulatives, and pedagogical preparation of college instructors.
Mathcast: Podcasting for Effective Mathematics Teaching
Teachers College, Columbia University
Kids these days always have something electronic hanging off of them! Wouldn’t it be great to harness the power of these electronics to teach mathematics? Enter mathematics podcasting.