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Good Ideas in Teaching Precalculus And...

... Algebra, Calculus, Discrete Mathematics, Probability & Statistics, with Technology

Rutgers University - Busch Campus - New Brunswick
Friday, March 19, 2010
8:30 a.m. - 3:00 p.m.


Siham Alfred - Raritan Valley Community College
Create Mathematical Connections in Calculus

Many students come to us with the understanding that calculus is a series of skills that one should learn. In this session, we will see a handful of activities that emphasize teh improtance of concepts over skills. Students will be empowered to build and enhance their understanding of calculus concepts and will be given the opportunity in the classroom to make the necessary mathematical connections among the important building blocks of calculus.

Chris Alworth and Kim Barrett - Rumson Fair Haven Regional High School
What Precalculus Teachers Need to Know to Smoothly Transition to Calculus

This presentation will explain how to achieve greater success helping students make the transition from Precalculus to Calculus. By applying in your own classroom the innovative ideas, alternative teaching techniques, and topics to emphasize (with success proven examples) from this presentation, you can help increase students' proficiency with Precalculus while helping prepare them for Calculus.

Carrie Baker and Lindsay Segreto -- Rumson Fair Haven Regional High School
Name Reflection Project using Geometer’s Sketchpad

Join us in the computer lab to complete a Name Reflection Project of your own choosing using Geometer’s Sketchpad. The Name Reflection Project is a hands-on and interactive application of reflectional symmetry. Learn how to use Geometer's Sketchpad to complete this project in your classroom. Ideas for creating this project without Geometer's Sketchpad will also be discussed.

Eric Berkowitz – Parsippany Hills High School
Teaching Difficult Topics from a Different Angle

Some topics are just difficult to teach, and some are difficult for students to learn. I have had some success teaching a variety of topics by taking a non-traditional approach. This presentation will explore some of those ideas. Topics covered range from algebra through calculus.

L. Charles “Chuck” Biehl – The Charter School of Wilmington (DE):
Applications of Graph Coloring

It starts for early ages with map coloring. By high school, and with an algebra background, students can use the same fundamental concept to schedule meetings, safely store dangerous chemicals, design wildlife habitats, and even gain a basic understanding of how the master schedule for their school is determined. Start with small fun problems and end up solving meaningful scheduling and conflict problems from management science and operations research.

Neil Cooperman – Millburn High School:
What Is Alternative Assessment? It Is Not Just Assigning Projects!

Abstract and revised title will be posted later.

Fred Decovsky - Teachers Teaching with Technology
Investigating Domain and Range Using TI-Nspire.

What can the graph of a function or a relation tell you about its domain and range? In this session you will explore visual representations of relations to determine their domain and range using the dynamic features of TI-Nspire. See how ready-made standards-based lessons can be used to make discoveries and formulate conclusions that support effective learning and problem solving, engage students, and improve their understanding.

Angelo DeMattia - Consultant
Visualizing the Big Ideas in Algebra

Since too few students are able to demonstrate a deep conceptual understanding of algebraic relationships, this workshop will help teachers develop a more visually based lesson format. This will help students make an effective transition from the concrete/visual (i.e., modeling by drawing diagrams, pictures, etc.) to the abstract (i.e., use of variables). The use of graphing calculators will also be emphasized.

David Glatzer - Consultant
Coordinate Geometry: A Bunch of Good Ideas

Participants will explore a bunch of "favorite" coordinate geometry problems involving distance, slope, circles, and area. Extended constructed-response questions will be included. Have fun and walk away with new activities for your geometry or algebra class.

John Hanna - Teachers Teaching with Technology
Making the Switch to TI-Nspire

Considering using TI-Inspire? This session will highlight the similarities and especially the differences between the TI-83/4/9 and the TI-Nspire and TI-Nspire CAS. The newest features in both the handhelds and the software are important to you too, so if you are using v1.7 you'd be interested in this session, too.

Boaz Laor – Essex County Vo-Tech Schools (Newark):
Graphing Linear Functions

Understanding linear functions and how their graphs originate is fundamental for understanding how more complex functions behave. Analysis of linear functions (graphs, slopes, intercepts) can be taught without the emphasis on formulas and through understanding linear behaviors such as constant rate of change and the fact that any two points can be used to analyze the line. The session will share and engage the participants in a learning sequence that has been successfully used to teach this unit.

Joyce Leslie:
Teaching Algebra to Future Calculus Students ... and to All Future Students

In this presentation, I will discuss how I teach slope, lines, graphs and inequalities with an explicit goal of creating a foundation for precalculus and calculus. Some of the ideas I use are effective in helping students become interested in the algebra 1 topics and some of them just naturally arise as we discuss a particular problem? I will provide various examples of lessons (or lesson components) and the student questions they generated on the subject of slope, straightness of a line, continuous functions, distance-time graphs, closed intervals, and inequalities. Do calculus ideas regularly arise in algebra 1 class? I hope we can discuss this at the presentation. 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.

Irina Lyublinskaya -- CUNY, College of Staten Island
Teaching Precalculus and Algebra 2 with Symbolic Geometry

The presenter will share several problems developed for symbolic geometry technology that are focused on the development of students' skills in recognizing and using multiple represetnations while learning various topics in geometric transformations of functions and optimization usually covered in Algebra 2 and Precalculus.

Liz Marquez, Kathleen Carter, and Paul Westbrook
Satisfying the New Financial Literacy Requirement in Math Class, Part 1

Most high school students lack the basic financial skills crucial to success in life. New Jersey has responded to this problem by requiring 2.5 credits in financial literacy for high school graduation. This workshop will show math teachers how they can satisfy that new requirement and help students become mathematically and financially savvy. Classroom applications to be covered in Part 1 are linear regression and the cost of owning a car, and measures of central tendency and buying stock. Graphing calculator use will be included. (Part 1 and Part 2 can be taken independently.)

Liz Marquez, Kathleen Carter, and Paul Westbrook:
Satisfying the New Financial Literacy Requirement in Math Class, Part 2

Most high school students lack the basic financial skills crucial to success in life. New Jersey has responded to this problem by requiring 2.5 credits in financial literacy for high school graduation. This workshop will show math teachers how they can satisfy that new requirement and help students become mathematically and financially savvy. Classroom applications to be covered in Part 2 are sequences, series, and savings; spreadsheets and credit card debt; and percents and taxes. Graphing calculator use will be included. (Part 1 and Part 2 can be taken independently.)

Kevin Merges - Rutgers Prep
Fair Division - Apportionment - The Mathematics of Social Choice

Decision-making and apportionment will be introduced through a variety of methods including Borda counts and sealed bids. Apportionment will be explained as well as the various paradoxes that have emerged throughout the history of the United States. A wide vareity of real-life projects will be offered for classroom use, including ways to introduce technology as part of the lesson.

Robin O’Callaghan and Brian O’Reilly – The College Board
The SAT in a Flat World

How does the SAT Mathematics Test relate to a dynamically changing world? How can the SAT Skills Insight help students to improve their skills and reach their goals in college and beyond? How does the SAT prepare students to be flexible problem solvers and leaders in the workforce? Come hear the answers to these questions and more.

Anna Panova - Lawrence High School
Effective Ways of Using TI-Nspire CAS in an Inclusion Class

Computer Algebra System allows students with weak algebra skills to move beyond computation and concentrate on the concepts, not just the procedures. Come and learn how TI-Nspire CAS can be used in an inclusion setting class to help your students see patterns and understand difficult concepts. Effective ways of using TI-Nspire handhelds as a discovery tool in an Algebra 1 or 2 class will also be discussed.

Bob Riehs – New Jersey Department of Education:
The 21st Century High School Mathematics Classroom in New Jersey

Various factors make it necessary for mathematics teachers in the 21st century to teach differently than they themselves were taught. Today's students are "digital learners," available technology is changing almost daily, and expectations (including state and national standards) are changing. This session will attempt to help the participants make sense of these changes and develop a clearer vision of what evolutions in teaching would be consistent with these changes.

Joe Rosenstein – Rutgers University:
The New Jersey Mathematics Standards

Last year, the New Jersey Department of Education scrapped the draft math standards prepared by its own writing team and replaced it by a draft prepared by several staff members. Because of the negative response to this second draft, which was widely disseminated, and because of the impending development of national standards, the process of developing and adopting new math standards for New Jersey was shelved. However, over the past year the New Jersey Mathematics and Science Education Coalition has developed a new draft that builds on both the current standards and the two previous drafts. We will review and discuss the high school components of this new draft and compare them with the current New Jersey Core Curriculum Content Standards.

Ahmed Salama - PANTHER Academy, Paterson:
Mathematically, How Projectiles Work?

Use trigonometric functions and calculus skills to determine the range and final velocity of a projectile based in knowing its initial velocity and maximum height. This activity provides a good example of connecting physics and mathematics.

Jay Schiffman – Rowan University:
The Principle of Includion and Exclusion - A Powerful Combinatorial Tool

In this presentation, we will discuss the problem of finding the number of elements in the union of two sets, of three sets, and then, more generally, the number of elements in the union of a finite number of sets. Please join us, have fun, revisit Venn Diagrams and Pascal's Triangle and mathematical vocabulary (particularly "at least," "at most," and "exactly") and hlep alleviate student misconceptions that lead to serious overcounting.

Anita Schuloff – Paramus Catholic High School
See the Derivative Come Alive!

If you find that your students are having trouble visualizing the fact that the derivative of a function represents the slope of the function, then it’s time to make use of the Advanced Toolkit Option in Geometer’s Sketchpad. In this presentation, you will be shown how to attach a tangent line to a function, find its slope, superimpose the graph of the derivative onto the original function and show that the y-values of the derivative perfectly match the slope of the tangent line at each x-value.

Charles Schwartz – Rider University
An Inquiry Lesson in Precalculus

Abstract will be available later.

Robin Schwartz –College of Mr. St. Vincent / Math Confidence
When are we Ever Going to Use This Math?

In addition to content, math has other benefits: instilling values of discipline and excellence, improving memory and focus, as well as preparation for success in the "knowledge economy." The study of mathematics inspires critical thinking and improves problem-solving abilities while building confidence and persistence for personal and professional development. We will engage in hands-on activities and discuss how math can enhance focus, critical thinking, problem solving, and confidence.

Kathleen Shay – Middlesex County College
Classroom Voting in Mathematics

Classroom voting is an excellent and fun way to promote active learnign mathematics. Using electronic "clickers" or colored index cards, students vote for teh correct response to true/false or multiple-choice questions posed by the teacher. Following a vote, the teacher may lead a class discussion of the relevant concpts. Voting engages students in the lesson and provides instant feedback to the teacher about their understanding. This workshop will provide hand-on experience with clickers, examples of good voting questions in a variety of courses, and a look at the assessment date obtained from each vote.

Doug Smith – A.P. Schalick High School (Pittsgrove):
Probability with Pizzazz!

How to introduce experimental probability along with other fun ideas for your classroom. Come ready to play!!

Michael Thayer:
The Intersection of Music, Math, and Physics

We math teachers are always searching for interdisciplinary ways to approach "old" topics. The study of music offers a wide range of mathematical avenues that are appropriate for a precalculus or calculus class to explore. We will discuss several of these during this presentation, from the idea of musical temperament and its development from Pythagorean times, to the resonances that make musical instruments have their particular sounds (their "timbres"), among others. If you are interested in how music, math, and physics intersect, there will be a variety of things for you to think about!

Linda Treilman:
A SMARTer Board with SMART Notebook Math

Use a SMART Board to create lessons that illustrate mathematical concepts. Insert pictures that relate those concepts to real-life settings. The recent release of SMART Notebook Math Tools with an equation editor and and enhanced graphing features makes it even easier to create lessons that develop understanding. This session will focus on topics found in Algebra II and Precalculus such as transformations, conics, and trigonometry.

Michael Weingart – Rutgers University:
What Does Expected Value Really Mean?

If you were offered a choice of a guaranteed $1 million, or a 20% chance of winning $100 million (but an 80% chance of ending up with nothing), which would you choose? What about a guaranteed $100 versus a 20% chance of $10,000? This question always engages students when we study expected value. This talk will discuss ways not only to explain expected value to students, but also to get them thinking about what expected value really means (pun intended) and how to interpret the numbers they compute in order to make decisions.

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