2008 Program

2008 Abstracts

2008 Sharing Sessions

2008 Schedule
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2008 Registration Form

Agnes Azzolino – mathnstuff.com
asquared@mathnstuff.com
Spreadsheets for Algebra and Precalculus
(Computer lab session – Space limited to first 20 participants)

This hands-on lab session for the spreadsheet beginner will introduce participants to spreadsheets and how they can be used in algebra and precalculus classes. This will include an introduction to Excel® including cell, formula, select/copy/paste, hide/unhide, graphs of curves and histograms, etc. as time permits.

Eric Berkowitz – Parsippany Hills High School
eberkowitz@pthsd.k12.nj.us
Mix it Up – Review Many Topics Simultaneously

Need a way for students to remember what they learned last week? Last month? Last year? Why review only one topic at a time? Don't give students a chance to forget anything. Come hear some suggestions on how to pose questions that pull from different areas of the curriculum simultaneously. This idea can be used at any level, but the examples presented will focus on advanced algebra through calculus.

L. Charles “Chuck” Biehl – The Charter School of Wilmington (DE)
cbiehl@charterschool.org
Systematic Counting: How to Count without Using the “F” Word

Permutations, combinations, and combinatorics in general are a formula (the "F" word) nightmare for students and a conceptual nightmare for teachers. Learn how to teach counting with the concepts first and foremost, and the formulas last, if at all, depending on the class.

Brother Patrick Carney – DePaul Catholic High School (Wayne)
br.patrickcarney@dpchs.org
There’s Math in Them There Codes

Taking advantage of students' interest in codes, this session uses a hands-on approach to both information-simplifying codes (such as zip codes) and secret codes to teach mathematical concepts in the high school curriculum such as combinations, checking one's work, modular arithmetic, solving simultaneous linear equations, and many more.

Ihor Charischak – DMCpress.org (Stevens Inst. Of Technology, retired)
ihor.charischak@verizon.net
The Jinx Puzzle, Measuring the Earth, Shooting Globs and Other Classroom Adventures

Stop by this session and take in some amazing stories about how the internet along with dynamic software such as Geometer's Sketchpad, spreadsheets, and other microworlds have made a significant difference in helping students gain a deeper understanding of powerful mathematical ideas in Algebra and Geometry. See http://dmcpress.org for more details.

Neil Cooperman – Millburn High School
cooperman@millburn.org
Creative Projects for the “Pre”-Calculus Classroom

This session will explore a variety of projects and alternative assessments that are appropriate for students in Geometry, and Algebra II, as well as Pre-Calculus. The difference in the meaning between “projects” and “alternative assessments” will be examined. We will discuss methods of scoring and grading these assignments that are simple, easy, short, and designed not to make you crazy. Issues pertaining to the pros and cons of group projects vs. individual projects will also be investigated.

Suzanne Cranwell – Rumson-Fair Haven Regional High School
Kristin McCarthy – Rumson-Fair Haven Regional High School
scranwell@rfhrhs.org, kmccarthy@rfhrhs.org
How Geometer’s Sketchpad Has Changed Our Classrooms
(previously presented at 2007 conference)

Revolutionize and energize your classroom with the integration of this dynamic and exciting teaching tool. From the simple (one teacher work station) to the more adventurous (a work station for each student), see how the Geometer’s Sketchpad can enliven the way you teach Algebra, Geometry and Precalc. A variety of demonstrations and projects will be presented to heighten your appreciation of this software’s potential.

Bill Crombie – MetroMath Fellow, Rutgers University
Jessica Alvarez – Woodrow Wilson High School, Los Angeles, CA
bcrombie@aol.com, jxa2788@lausd.k12.ca.us
A Calculus Problem for the Algebra I Classroom

In this session, participants will work through a student activity which explores a fundamental relationship between area and slope. The problem task involves data analysis, conjecture development, and the construction of a mathematical proof. The problem, implemented as a TI-Nspire document, is an Algebra I version of the Fundamental Theorem of Calculus. This material is part of an on-going program which develops advanced topics in secondary mathematics from an elementary standpoint.

Fred Decovsky – Teachers Teaching with Technology
fdecovsky@aol.com
Using Cabri Jr. APP in Algebra and Geometry

This session will look at investigations using the Cabri Jr. application on the TI-83+ and TI-84+. See how pre-made lessons can be used as well as how easy it is to construct your own. Give your students the opportunity to discover many geometric properties. Learn how to incorporate this interactive geometry program into your geometry and algebra lessons to enrich instruction and extend your students' comprehension.

Angelo DeMattia – Consultant
adema@comcast.net
Statistical Simulations for the Calculator-Challenged

Simulations help bridge the gap between Exploratory Data and Statistical Inference. This session will help you to construct that connection by creating and demonstrating probability and statistical simulations on the TI-83/84 graphing calculator. Probability simulations will be designed to estimate probabilities while statistical simulations will be used to generate approximate sampling distributions – in order to determine which results are reasonably likely/rare. Bring your graphing calculator!

David Glatzer – Consultant
glatzer7dj@aol.com
Ideas and Activities to Enhance the Learning of Geometry

Activities will include using a variety of special grids and questioning techniques. Specific topics will include coordinate geometry, perimeter and area, similar polygons, and the Pythagorean Theorem. Be prepared to have fun and walk away with new activities for your classroom.

Iftikhar Husain – University High School (Newark)
husains4ever@aol.com
Visual Mathematics

Participants will receive an activity CD to be able to appreciate the power of Geometer's Sketchpad. The presenter has integrated the technology into mathematics as a visual learning tool to enhance, expand and embrace the existing curriculum. In order to make Visual Mathematics more useful to all types of learners, the author has a collection of activities ready for the classroom for basic Algebra, Algebra I, Geometry, Algebra II, Precalculus, and Trigonometry.

Daniel Ilaria – Springfield Public Schools
dilaria@springfieldschools.com
Teaching Calculus Using TI-Nspire

Learn how the TI-Nspire calculates derivatives and integrals. Participate in classroom lessons that use the document capabilities of the Nspire to demonstrate calculus concepts.

Jeff Killion – Cherry Hill High School East
jkillion@chclc.org
Calculus and the Economics of Baseball

Bring your graphing calculator and learn about an interesting activity which ties together Calculus topics, economic theory, and (hopefully) heated conversation about how Major League Baseball can help all of its teams stay afloat in an era of astronomical player salaries. We will spend some of the session “channeling our own Bud Selig” to create a fictional revenue-sharing system for baseball.

Joyce Leslie – Columbia High School (Maplewood)
jleslie501@aol.com
Help Students Learn Calculus by Creating Problems

In my Calculus Honors and AP classes, I have the students create problems and functions that are associated with a story or phenomenon that is being described. I find it very interesting that these problems turn out to be a wonderful assessment tool for me and for them – they discover their own gaps in understanding when they create problems and I learn more about their understanding than I do with any other assessment tool.
When time permits I also have a year-long competition (often a battle of the sexes) in which the teams make up problems (that they must be able to solve) to challenge the other teams. The most points can be won if they stump the other teams. They sometimes get so caught up in this challenge that they spend time at home creating terrific problems that focus on what they know everyone finds difficult. The result is that they all focus on the difficulties and collectively get better and better.
I will show some student examples and talk in detail about how this works.

Irina Lyublinskaya – College of Staten Island & Teachers Teaching with Technology
ilyublin@comcast.net
Teaching Precalculus Using TI-Nspire

Precalculus concepts become clear using multiple representations. The new technology (TI-Nspire) allows for a real variety of approaches (numeric, graphic, symbolic, and verbal) that appeals to all learners. Come check it out.

Robin O’Callaghan and Brian O’Reilly – The College Board
rocallaghan@collegeboard.org, boreilly@collegeboard.org
The SAT as a Means of Mathematical Communication

It is well known that the SAT Mathematics Test plays an important role as a national assessment. However, this important examination also plays a role in promoting meaningful mathematical discourse. Come see actual questions from the SAT and find out how they facilitate learning, thinking, and effective mathematical communication.

Ralph Pantozzi – Mount Olive Board of Education
rpantozzi@mtoliveboe.org
How Fast is Your Shadow?

"Related Rates" is more than a Calculus topic. In this session, we will examine how students from Algebra 1 through Calculus can examine how a change in one quantity can make a change in another, and then another. Using a traditional and a non-traditional related rates context involving shadows, we will look in new ways at the chain rule, average rates of change, functions, function composition, similar triangles, slope, and how units are used in computation. Teachers of Algebra 1 through Calculus will have a productive time catching shadows.

Carol Richards – Rowan University (Camden)
richards6686@comcast.net
The X, Y, Z’s of Teaching Precalculus

This presentation is directed to the teacher who is new to teaching precalculus. Most teachers new to the subject merely follow the textbook and the course of study. As such, you may be doing your students a grave disservice; especially if they plan on taking calculus the following year. In this fast-paced workshop, you will be given specific topics to emphasize and the skills to make a lasting impact. Numerous interactive examples will be presented and discussed, as well as some novel techniques to reinforce learning....i.e., games, songs, little-known history, etc.

Robert Riehs – New Jersey Department of Education
robert.riehs@doe.state.nj.us
2008 Revisions to the NJ Core Curriculum Content Standards in Mathematics

This session will include recently adopted revisions to the math standards, a clarification (including sample assessment items) of some of the individual Cumulative Process Indicators (CPIs), and an opportunity for participants to suggest further revisions as part of the five-year revision process.

Joe Rosenstein – Rutgers University
joer@dimacs.rutgers.edu
Finding the Best Network, Path, and Circuit

Vertex-edge graphs can be used to solve a variety of problems that arise in everyday life – such as finding the best route from one site to another (“path”) or finding the best car-pool route to efficiently drop off all the kids and get back home (“circuit”). In this session we will discuss how each of these types of problems can be solved mathematically, and compare and contrast the algorithms that are used to solve them.

Ahmed Salama – PANTHER Academy, Paterson
salamamath@yahoo.com
The “Art” of Transforming Functions

By doing various transformations to functions, students will be able to use graphing calculators (TI-84) to obtain art figures that are relevant to geometry and other SAT problems. Come find out more.

Jay Schiffman – Rowan University
schiffman@rowan.edu
Different Models of the Function Concept

Far too many students at both the high school and collegiate levels possess only cursory understanding of the function concept, which is central to further study in mathematics. In this session, the function concept as represented via the relation model and the arrowed diagram model in addition to the “cookbook” graph test will be illustrated. In addition, some neat ideas related to discrete mathematics are emphasized to further enhance conceptual understanding.

Peter Schuenzel – Morris Hills High School
pschuenzel@mhrd.k12.nj.us
The Smarts on the SMART Board
(Computer lab session – Space limited to first 20 participants)
(previously presented at 2006 conference)

Learn how to get the most out of using a SMART Board (an interactive whiteboard connected to a computer). Come and discover some of the possibilities of how this technology can enhance students' interest and understanding. Basic set-up, presenting a lesson, using a variety of programs and the Internet in a mathematics class will be covered. Some of the programs utilized will be Fathom, the Geometer Sketchpad, Graphmatica, Word and PowerPoint.

Anita Schuloff – Paramus Catholic High School & Montclair State University Gifted/Talented Program
aschuloff@yahoo.com
Very Strange Ellipses and Hyperbolas

Re-writing the polar form of the equation of an ellipse into rectangular form can be tedious. However, some ellipses can have their parameters transferred directly to the rectangular equation. A demonstration of this phenomenon will be done using Geometer’s Sketchpad. Did I also mention that certain hyperbolas (with a small twist) have this same property? Come see this amazing theorem.

Charles Schwartz – Rider University
schwartz@rider.edu
Building Conway’s Pencil Models
(previously presented at 2007 conference)

John H. Conway invented a class of models built of hexagonal prisms. Participants will learn to build these models out of pencils and rubber bands, and will explore the symmetries of these models and the relationship between these models and models made of cubes.
You may preview these models by going to my web page – http://www.rider.edu/172_5403.htm, and clicking on the link “Conway’s Pencil Models.”

Robin Schwartz – Math Confidence & College of Mount St. Vincent
mathconfidence@aol.com
Empowering Students Who Ask, “When Are We Ever Going to Use This Math?”

When Math is presented as a life skill that broadens career choice and inspires critical thinking, students learn reasoning and problem-solving skills while building confidence and persistence. While many students will not major in science or engineering in college, all students benefit from the challenge and discipline of Math. This positive attitude can help teachers, administrators and students to meet the challenges of ‘teaching to the test’ by viewing it as an opportunity to address common errors and misunderstandings (without formally reviewing) thereby increasing accuracy, logic and frustration tolerance skills – assets in high school, college and the workplace.

Neil J. A. Sloane – AT&T Shannon Labs, Florham Park
njas@research.att.com
The On-Line Encyclopedia of Integer Sequences

The On-Line Encyclopedia of Integer Sequences (OEIS) is a database of some 135000 number sequences. A typical entry gives the initial terms (anywhere from 10 to 10000 terms) of the sequence, formulae, references, links, computer programs for producing the sequence, etc. To find the OEIS, Google "sequences". It is freely available on the Web and is used by people all over the world who are interested in numbers – from high-school students to research mathematicians. Many people have reported that their interest in mathematics blossomed once they found out about the OEIS. The talk will be illustrated with numerous examples, emphasizing sequences that have arrived in the past few months, and taken from number theory, combinatorics, graph theory and geometry. The talk will also demonstrate two features that have recently been added to the OEIS: the ability to display the graph of a sequence or to hear it played on a musical instrument.

Doug Smith – A.P. Schalick High School (Pittsgrove)
smithd@pittsgrove.k12.nj.us
“Probably” A Few of My Favorite Things

A few of my favorite things I give to my stat students when we get to probability. One to confound, one to edify, and one that's just amazing to discuss. It will probably be a good session (well, I'm 95% confident, anyway).

Michael Weingart – Rutgers University
weingart@math.rutgers.edu
The Mathematics and Statistics of Polling and Predicting Election Results

In an election year we frequently read or hear of the latest poll which claims to measure how popular each political candidate is among some large group of voters, such as all voters in a state, or in the country. A closer look shows that these polls are usually based on relatively little data. How is it, then, that pollsters predict election results with any accuracy at all? The answer is part statistics, part polling methodology. In this session we will investigate the mathematical, statistical basis for making such predictions with reasonable accuracy. This is an excellent topic for engaging students in an election year.

David Weksler – Consultant
wex@pobox.com
TAPPED IN–An Online Environment for Teacher Professional Development
(Computer lab session – Space limited to first 20 participants)
(previously presented at 2007 conference)

Tapped In <http://www.tappedin.org> is a free, online environment for teacher professional development established with funding from the National Science Foundation in 1997. Approximately 21,000 members participate in online discussions on educational issues of all kinds. Several discussions focus on math education (focus on K-3 classrooms, K-20 issues, use of technology within math education) and members may, in fact, even lead discussions on topics not currently covered.
The "Good Ideas in Teaching Precalculus and..." conference is a great annual event at Rutgers. Online discussions at Tapped In are ways of extending the discussion of good teaching ideas and allowing for professional interaction in a virtual setting year-round. Learn more about how Tapped In can support you professionally and personally.

Peter Winkler – Dartmouth College
peter.winkler@dartmouth.edu
Energizing Students with Puzzles
(PLENARY SESSION)

Two well-known weaknesses of high school math are 1) that it's old, and 2) that it's known. Here's a suggestion: to keep kids who wish to pursue the new and unknown from phasing out in math class, try using mathematical puzzles.
Puzzles come in many varieties: simple questions with surprising answers; questions which seem to be hard to answer, but turn out to be easy; questions which seem easy, but no one knows the answer. Examples of each will be provided, and some ideas on how to get students engaged in trying to solve them.
Peter Winkler is professor of mathematics and computer science, and Albert Bradley Third Century Professor in the Sciences, at Dartmouth. His specialties include discrete mathematics, probability, the theory of computing, and their applications. Prior to joining Dartmouth in 2004, he directed the mathematical research groups at Bellcore (now Telcordia Technologies) and Bell Labs (now part of Alcatel-Lucent) for 15 years. He is the author of "Mathematical Puzzles: A Connoisseur's Collection" (AK Peters Ltd, 2004) and "Mathematical Mind-Benders" (2007), each of which contains easily explained puzzles whose solutions involve creative reasoning.

Janina Wozniak and Betty Meeks-Manning – Hackensack High School
j.wozniak@hackensackschools.org, b.manning@hackensackschools.org
Growing a Geometric Garden

This hands-on, long-term activity applies various mathematical concepts to gardening. In the spring, my students will design their own garden using geometric principles, grow plants on the windowsill, measure & record the growth daily, and eventually transplant them onto the school campus grounds where they will continue to care for the plants. Some mathematical topics applied are designing the garden layout using symmetry, collecting and analyzing data through a scatterplot, and using number sense to understand financing the project. This activity can be interdisciplinary if the students of the art teachers help create garden sculptures for the geometric garden. For this session, participants need to bring a graphing calculator. Everyone will leave the session with activity ideas ready for classroom use.

Cathleen Zucco-Teveloff – Rowan University
cathy.zuccoteveloff@prodigy.net
Using Web-Based Activities to Teach Earth Algebra
(Computer lab session – Space limited to first 20 participants)

I will discuss how I used a variety of web-based media sources to expose students to environmental applications that can be used in elementary/intermediate algebra classes. I will share exercises created for such applications as capture-recapture proportion modeling, average rate of change modeling for energy availability, exponential growth modeling for developing nations and exponential decay modeling for radioactive materials.