This is an interactive session with TI-83 graphing calculators in which six carefully selected data sets, some old and some new, will be analyzed and modeled using polynomial, exponential, and logistic models. (One data set comes from Rene Descartes' data on the volume of a chambered nautilus, one from experimental data of different weights on a spring, and several from the Statistical Abstracts of the United States.) The distinguishing characteristics of each model will be identified and how each model is used in a Calculus or Precalculus course will be discussed. Handouts will be provided.

This panel discussion will present three perspectives on how high school teachers can better prepare students for success in college mathematics courses.

Utilize a graphing calculator and parametric equations to graph the conic sections and their active inverses. Perform transformations easily, including rotations.

Imagine a the functionality of a TI-80 AND a TI-83 in one calculator with a price under $55. Come and test drive one. A calculator will be raffled off at the end of the session.

ABSTRACT AVAILABLE SOON

Notes, animations, web pages of supposer stuff, spreadsheets and documents. See precalculus "at present and in the future".

The SRA (Special Review Assessment) is an alternative assessment taken by high school students who do not achieve proficiency on the High School Proficiency Assessment (HSPA). After a brief introduction, the session will be an open exchange between the presenter and the audience about HSPA SRA Mathematics PATs (Proficiency Assessment Tasks), samples of which can be examined on the NJPEP.org website. The presenter is HSPA SRA Coordinator for the New Jersey Department of Education.

Matrix algebra tends to be confusing, and often seems of no practical value. This presentation will suggest a method to remedy both of these issues simultaneously by exploring applications that will make the mechanics of matrix operations come clear.

Many high school mathematics concepts are taught with little or no context. Examples include applications of proof in algebra and geometry, as well as combinatorics and analytic geometry, including trigonometry. This session will provide sample lessons and resources to provide teachers with activities usually labeled as "discrete math" which can serve to provide a springboard for more effectively engaging students, for enabling deeper understanding of these topics, and for supplying more meaningful and contemporary applications of traditional topics in the algebra, geometry, and precalculus curricula. The activities in this session utilize the concepts of Steiner trees, path problems, and efficient hamiltonian circuits.

This session will look at three areas where discrete math can be used in dealing with homeland security. We will take a look at Visual Cryptography in a manner which young people can get a taste of steganography. Then we will look into the problem of the minimum number of people necessary to secure a cave which is an easily understood application of graph theory. Finally we will talk a bit about graph theory as it applies to epidemics with emphasis on a deliberate unleashing of a biological weapon as well as the possible immunization of the population.

This presentation will show how geometric transformations lead to algebraic transformations, and how analyzing functions through a transformational approach improves understanding and connects the many varied topics of precalculus through a unified theme.

Participants will take a look at some simple programming techniques (Input/Output, If...Then...Else, For) which can be used throughout the curriculum. Bring a TI-83+ calculator, if you have one. Bring any programs you'd like to share.

Come hear about creative ideas for alternative assessments for students in Algebra 1, Geometry, and Algebra 2. Examples and sample rubrics will be provided. These projects include daily, multiple day, and marking period projects. These ideas can be adapted to specific levels.

This hands-on session will explore engaging activities for Advanced Placement Statistics. Ideas for introducing and developing several topics, including descriptive statistics, probability, experimental design, and inference, will be presented. Many of the activities can be modified easily for the pre-AP classroom. Participants are asked to bring a TI-83+ to the session.

This session will have participants doing activities that are motivating to students. The hands-on activities will use ready-made lessons that integrate probability and data analysis concepts into the high school curriculum. These activities will address the Probability & Statistics strand of the recently revised NJ Core Curriculum Content Standards in Mathematics.

Driving on congested roads can be an interesting experience as well as a frustrating one.

Analysis of traffic flow results in a real life application of consistent/dependent systems of equations. Braess' Paradox is a fascinating analysis of how traffic can actually get worse when new roads are added to an existing network. Finish with a nice example of how mass transit has its problems also. Drive on in!

In this presentation, we consider different perspectives through which students' questions about mathematics topics (Why is a negative times a negative a positive? Why is anything raised to the zero power equal to 1? Why is a division of fractions given by multiplication by the reciprocal?) can be explored. Discussion will include history of mathematics and reconciling mathematicians' perspectives on these issues with teaching for understanding.

During the past 15 years of teaching introductory statistics, I've developed a number of activities and projects for my students to do both in and out of the classroom. In this session, I'll present some of these projects for teachers of statistics to use, modify, or adapt to their classrooms. I'll also talk about what works, what doesn't, and where to find real data for classroom use.

Participants will be shown how a slice of cake can be used as motivation to introducing the concepts of area and volume in Algebra 2 or Calculus. Each participant will receive a piece of graph paper and a slice of cake. After tracing the cake, a linear model will be found on the calculator. The area and volume will be computed geometrically and through the use of calculus. Yes, participants will be able to eat the cake at the end of the presentation! Please bring your TI-83.

We will explore applications of parametric functions by solving word problems. We will create equations and watch paths representing the motion of bugs, balls, and a person on a ferris wheel appear on a graphing calculator screen to solve the problems. Bring a TI-83 or TI-83+ calculator, if you have one.

This unique and exceptionally creative use of the TI-83 family of graphing calculators enables one to Explore Algebra with Creative Designs. The activities are designed to help students visualize concepts, predict results, and make connections between algebra and geometry. The activities encourage students to strive for greater depth and meaning, and develop a classroom environment where students interact with each other and also work independently. Students make their own t-shirts, which inspire and motivate other students in the learning process. Teachers can make their own classroom posters and borders demonstrating various mathematical concepts. Bring a TI-83+ calculator, if you have one.

An exploration via rational functions, as to whether a tin can manufacturing company is using the minimum possible surface area for their can. How "can" you make improvements? The discovery and development of volume and surface area of a cylinder. How the radius and height affect volume and surface area of a cylinder. Participants will actively derive a surface area function as it relates to the volume and radius of the cylinder. Using graphing calculators, participants will determine if their cylinder utilizes the minimum possible surface area for its volume. Using some of the same ideas participants will determine the maximum possible volume of a can given a fixed surface area. Bring in a canned food container and a graphing calculator and see what you "can" do.

What happens when medication is consumed? Suppose we look at taking a cough medicine. We will model what happens using exponential functions when only one dose is taken. We will model using infinite geometric series when many doses are taking how the body eliminates the medication. We will use the TI-83 to model this problem, using an analytic approach to finding a model and the regression utilities of the calculator to create a model.

Polynomiography is the art and science in visualization of polynomials. Informally speaking it allows you to take pictures of polynomials and subsequently color them in many ways using your creativity and artistry. It can be used to produce beautiful artwork. But the process of visualization in polynomiography can also be used to teach mathematical notions, properties, theorems, and algorithms at high school or college level. Here is a sample of what can be taught via polynomiography: the notions of convergence, limit, and continuity; polynomial roots; algorithms for polynomial root-finding and iteration functions such as Newton's method; theorems on polynomials, e.g. location of zeros; symmetry and mappings; geometric constructs such as Voronoi regions; the algebra and geometry of complex numbers; fractals and much more. I will demonstrate some of these using polynomiography software on a PC and will also introduce an interactive version of the software that can be accessed via the internet at www.polynomiography.com.

In this hands-on session, participants will have an opportunity to try out the software discussed in the presentation described above.

The Math Forum has a new project to support the use of software for mathematics education. We will be developing a community digital library where teachers, teacher educators, software developers, and students can all work and learn together on the effective use of technology in the classroom.

The scope of the Math Tools digital library: pre-K to calculus. All platforms will be included: computer, graphing calculator, PDA, etc.

Special features:

• quick help with using math software,
• reviews and opportunities to discuss software tools and related classroom activities and problems,
• stories of how others have used them, and
• convenient opportunities for you to contribute your ideas.

The Math Forum will work with interested community members to develop a Technology Problem of the Week to help with adoption and implementation in the classroom. Issues concerning technology in mathematics education and guidance for effective usage will be addressed through education research summaries and public forums.

The Math Tools digital library will offer a new kind of opportunity for users to conveniently get information and support, to receive recognition for their own contributions, and to help shape software to meet their needs. We'll describe the project in more detail so you can see what is new and exciting, show off our prototype web site, and explain how you can get in on the ground floor.

The Math Tools project is a part of the National Science Foundation's NSDL initiative.

Some of the simplest puzzles can be brought into the mathematics classroom and used as springboards for discussing a wide variety of topics dealing with numbers, variables, and shapes at many different levels, covering everything from a review of basic skills to challenging problem solving. This presentation takes you through several examples that start as hands-on activities but lead to intriguing arrangement, transformation, and counting problems that require the skills of algebra and geometry and a lot of visualization and imagination.

Evan Maletsky has served for many years as professor of mathematics at Montclair State University. He is an active speaker, author, and editor with NCTM and an author of numerous mathematics textbook series, professional books, and other publications. This spring, Dr. Maletsky was the recipient of the NJ MAA 2002 Distinguished Mathematics Teaching Award.

Radian measure is always a mystery to trigonometry students. By using adding machine tape and paper plates, the mystery will be solved. A development of the unit circle and graphing will also be highlighted.

Recursion and Mathematical Induction are important topics in mathematics. We will look at two activities that can be used to introduce applying recursive thinking to problem solving. There are many famous problems whose solutions involve recursive thinking. First, we will investigate the Tower of Hanoi problem. Next, we will use a recursive process to create a fractal pop-up card. Finally, we will find a surprising connection between these two activities.

The five major ideas of calculus - functions, limits, derivatives, antiderivatives and integrals - can be made accessible to students in the first week of the course through a visual approach. Experience visual activities using paper and pencil and Geometer's Sketchpad that will introduce students to these ideas and get them asking the fundamental questions of calculus in the first week.

The goal of my presentation is to examine the concept of limit from four different perspectives; namely analytically, graphically, geometrically, and computationally. We will discuss limits of both functions and sequences. The TI-89 graphics calculator will be available and used to exhibit both graphical and symbolic phenomena. Our aim is to promote further understanding as well as to gently nurture both the faculty member and student to achieve a successful learning outcome in this most crucial yet maligned idea at the core of analysis.

The concept of limit is central to any calculus course. The derivative and the definite integral are defined in terms of limits. A thorough treatment as well as understanding of the ideas involving limits is paramount for further study in mathematical analysis. As mathematics educators, we constantly attempt to achieve a delicate balance between the beautiful yet subtle theory involved versus the routine computational techniques that our students somewhat master. A large number of first year calculus students are unable to distinguish between computing limits and merely substituting a value for the independent variable. Perhaps this is the fault of a large variety of problems dealing with nice (i.e. continuous or polynomial in particular) functions that lend themselves to such manipulation and overall misconception. The ideas of proximity and nearness in contrast to exactness escapes the average first year student. This has consequences down the road when a number of our students enroll in a theoretical course such as advanced calculus or real analysis where a great deal of trepidation is experienced. At this stage, the students discover what a cursory knowledge they possess of deep mathematical concepts including limits. This raises the question of the role of the mathematics educator and their expectations for students. Moreover, the ability for faculty to achieve their goals and present a meaningful treatment of the concept of limit is a continuous and ongoing activity.

(Please note that this session will be very similar to a session that took place last year entitled: Calculus Before Algebra: Using Technology to Put Calculus in its Place)

During this session, participants with have the opportunity to explore activities that exploit simulation and visualization technologies (SimCalc) developed with National Science Foundation support. This technology enables teachers to consider ideas involving the Mathematics of Motion and other topics that underlie calculus, topics that have historically required long series of prerequisites that have filtered out many students. This is done by making the content come alive in new ways that connect to students' real experience of motion and change in their worlds. Further, these approaches contextualize, energize and organize other core mathematics that students often find difficult or irrelevant in their lives, ideas such as rate, ratio, proportion, function, slope, linearity, graphs and their interpretations, signed numbers, areas, algebraic representations, and so on -- ideas that are at the heart of the new standards.

In this session, you can see how I was able to take care of writing in the math classroom, covering all the standards, and still not using class time to accomplish this. On top of this, I'll show you how to grade these writing assignments so you can still have time to see the latest of "The Bachelorette", and eat and sleep, too!

It's not as bad as it sounds, and I guarantee you that the students will like it! Well, as much as they like mathematics, anyway. . .

Failing algebra students benefit greatly when classroom time is replaced by hours in the computer lab using tutorial software. Take some free software back to your school.

As a teaching professional, you demand excellence from your students, yourself and your community. You are committed to giving your students the skills and confidence they need to reach for the highest standards. And while you guide your students along the journey of academic achievement, you look for guides for your own journey of professional growth. National Board certification may be just the challenge you are looking for. It is a symbol of commitment to excellence in teaching. Endorsed by NEA and NCTM, the National Board establishes high and rigorous standards for what accomplished teachers should know and be able to do. Most candidates will say that pursuing National Board certification was the best professional development experience they have ever encountered. Learn about the National Board of Professional Teaching Standards and how you can become a National Board Certified Teacher.

Geometric planes become more familiar if students can relate them to real life. Build a model and conquer the abstract! Learn about planes, lines and points. Bring scissors.