Fall 2011 ArizMATYC Conference Sessions

Listed below are the presentation made at the conference held at Estrella Mountain College and any resources that the presenter(s) provided.

Planar Reflections: Reflecting a Point (or Curve) Across a Dynamic Tangent Line, Frank J. Attanucci, Scottsdale Community College

Let C be a smooth curve in the plane and let P be any (fixed) point in the same plane as C. Let L be a line in the plane that is tangent to C at the (dynamic) point Q. Let R be the reflection of P across L. Of course, as Q moves along C (thus changing the orientation of the tangent line), R also moves in the plane. In this paper, I first find general equations that describe this “dynamic reflection” of P across L; then by considering some specific examples (based on choices for C and P), one discovers new(?) ways in which “familiar curves” can be generated. I also discover some surprising results when P is a “well-chosen” parameterized curve and not merely a point. I finish by indicating possible directions in which the investigations contained this paper could be continued.

    • Session Paper (PDF)
      Reflecting the Focus of an Ellipse across a Dynamic Tangent Line


      Reflecting the Focus of a Parabola


Avoiding Curriculum Whiplash, Andy Burch , Estrella Mountain Community College

It has been my experience while teaching MAT121 that students often suffer from curriculum whip lash. We cover factoring, then solving quadratics. We cover rational expressions, then solving rational equations. This continues throughout the course with solving equations always appearing as an after thought. For the past 2 semesters, I have been trying a new order of topics that makes solving equations a more prominent focus, which we will discuss in this session.

A Balance Between Conceptual Understanding and Procedural Skills in Mathematics – A Proposed Model, Paul Vaz, Arizona State University

Efforts to reform the instruction of mathematics continues to be a major research topic. Over the past several years, research has indicated that learning mathematics with understanding has a positive effect on the learner’s mathematics proficiency. Researchers have established that conceptual understanding and procedural fluency build on each other. In this presentation, a model for planning the delivery and the assessment of the learning process has been proposed.

Reviewing the Basics While Teaching Beginning and Intermediate Algebra,
Sherri Messersmith
, McGraw-Hill Author

Rules of exponents, radicals, factoring, and applied problems are difficult topics in algebra courses often because of weak prerequisite skills. This session will present activities that can be done in five minutes or less that will strengthen students’ basic skills and improve their chances of mastering course content.

WebWork: A free online homework system, John Neuberger/ Nandor Sieben Northern Arizona University

We will demonstrate the online homework system called WebWork, which is a free alternative to systems such as WebAssign and MyMathLab. We will guide participants in a hands-on experience in using the system’s basic functions. There exists a National Problem Library containing a huge number of exercises covering all levels of mathematics. WebWork is supported by the MAA. After the workshop, interested faculty can ask for a trial account on the MAA-hosted WebWork server for free.

Projects for College Mathematics in MyMathLab, Denise Nunley ,Glendale Community College & Alicia Collins, Mesa Community College

This presentation will be using the custom question builder for MyMathLab to demonstrate how projects as a form of alternative assessment can be used within the MyMathLab setting. The project presented will be for use in the Finance section for a College Mathematics (Math for Liberal Arts Majors) Course. Participants will be able to copy this project to their MyMathLab course after attending this presentation.

Motivating STEM Engagement Through Robotic Clubs, Michael Little Crow, Scottsdale Community College

Teaching mathematics through real world experiential activities has been an elusive goal of mine throughout my thirteen year teaching career. Working with Professor Bill Johnson’s robotics club at Scottsdale Community College is brining that goal within reach. Learn how you can incorporate robotics into math and teacher education.

Improving the Mathematical Readiness of College-Bound Students, Brian Beaudrie, Northern Arizona University

Studies show that almost two-thirds of entering college students who are required to take remedial courses in college never graduate. This presentation will discuss a practical strategy to help middle-achieving high school students avoid the financial costs, time, and discouragement associated with required mathematics remediation courses when entering post-secondary education.

Graphing Trig Functions using the Order of Operations, David Dudley, Scottsdale Community College

We will look at how the order of operations can be exploited as an organizing framework for graphing trigonometric functions. We will also re-examine using the Law of Cosines for solving the ambiguous case.

Real Problems – Comparing Health Insurance Plans with Piecewise Functions, David Graser, Yavapai College

Many students will have to make decisions regarding health insurance in the next few years. These decisions require a basic understanding of the terminology used in the industry as well as the ability to compare different plans. This past summer I developed a project for my college algebra students to help them model the total annual cost of two health insurance plans as a function of the total annual medical charges incurred. In this presentation I’ll present this project and the technology assignments I use to help my students complete the project efficiently.

Arizona Mathematical Association of Two Year Colleges