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Good Ideas in Teaching Precalculus And...

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

Rutgers University - Busch Campus - New Brunswick
Friday, March 22, 2013
8:30 a.m. - 3:00 p.m.


(arranged alphabetically by presenter's last name)

Siham Alfred - Raritan Valley Community College
Critical Points of Polynomial Functions

With the widespread use of technology in the classroom, students can now explore more interesting questions.  In this session we look at a one parameter family of polynomials functions and construct a polynomial that passes through all its critical points.  The construction is very simple and the result is very pretty.  Come and let us explore it together.

Miguel Bayona – The Lawrenceville School
GeoGebra for the Mathematics Classroom

GeoGebra is a tool that every high school math teacher should have. In this workshop, participants will learn about this magnificent piece of software, its use and capabilities. At the end of the session, teachers will be able to use GeoGebra to enhance their classroom activities and promote student participation and exploration. Perfect for any level of mathematics, from basic geometry to sophisticated calculus applications. GeoGebra is free and works well in either platform. Discover its capabilities, and you will wonder how you got along without it all this time.

Eric Berkowitz – Parsippany Hills High School
Pictures are Worth 1000 Proofs

Proofs can be confusing, and so can algebraic identities that are not intuitive.  Why not show it in pictures?  Geometric figures can be used to prove many well-known algebraic and trigonometric identities, and students see them easily.

Amanda Caldwell – Indian Hills HighSchool, Oakland NJ
Using Schoology as a Classroom Resource

Student’s interactions and constant connectivity to electronics can be distracting to them. However, using this resource you can remain in contact with your students easily, send them updates, make class announcements, share resources, and much more. Schoology is a FREE resource that allows you to foster an environment where your students can interact with your class and resources constantly. Students can support each other, ask questions, form study groups, submit projects and work, etc. The possibilities are endless. Bring your laptop to interact with the site.

Kathleen Carter - North Hunterdon High School
Story Time in Math Class

Have you ever had story time in math class?  What does Dr. Seuss’s Sneetches have to do with Algebra?   Come find out how a Dr. Seuss story can illustrate some ‘big ideas’ for algebra  and precalculus students.   The session will introduce how a silly story may help students understand and remember some ‘big ideas’ about functions in algebra.

Michael Cedrone – Bayonne High School:
Bounded by Infinity: The Simple and Complex Beauty of Fractals

What are fractals? How do they help introduce concepts from Algebra to Calculus? And can you really bound infinity? Fractals are creative and useful tools to help explore geometric, algebraic and calculus concepts from similarity and congruence to sequences and series, limits and recursion, the complex plane and more. This brief intro to both the simplest and most complex fractals will showcase several fractals, and provide ideas on implementing them in the classroom.

Ihor Charischak – CLIME - Council for Technology in Math Education - an affiliate of NCTM
Common Core Math and Technology Standards - Perfect Together (or maybe not)

There are many pundits espousing the virtues of both the Common Core math and tech standards and there is much to be said for that. However, the picture is not as rosy as they predict. We'll look at some of these issues both pro and con and learn how technology will play an integral role in leading us to the “promised land” in math education.

Ken Collins – Charlotte (NC) Latin School:
Investigations to Improve Students' Understanding of Limits

This session will share several calculator based investigations that we have used in the classroom to help strengthen our students' understanding of limits. We will discuss some ideas for developing these investigations and offer reproducible copies to use in your classes. All levels of teaching experience are welcome.

Neil Cooperman – Millburn High School:
Projects for Geometry: It's Not Just Rules and Proofs

The first mathematics that the ancients began to explore was Geometry in an attempt to describe the world around them. The visual universe awed them, and they developed Geometry to explain what they were seeing. Today, we often lose sight of the beauty of Geometry as we focus on the rules, proofs, and problem-solving techniques to help students pass tests. These projects, which take little classroom time, can enhance what your students are studying and why they are learning it. Having your students observe Geometry all around them provides meaning, purpose and excitement to their studies and gives them a reason for expending all of their efforts.

Fred Decovsky - Teachers Teaching with Technology
Implementing the Common Core Standards with the TI-84 Plus C

Explore how to use the TI84Plus C graphing calculator and standards-based lessons to improve students’ understanding, to prepare for the Common Core and to create an engaging classroom environment. Gain hands-on experience using APPS, programs, data modeling and other features of the calculator.

Angelo DeMattia - Consultant
Turning Model Curriculum Assessment Items into Algebra Lessons

The major objective will be to use NJ State assessment items to help design more effective lessons in Algebra. The primary tool will be using the PAW process. That is, P is for Pictures (the visual part), A is for Algebra (the abstract part), and W is for words (the descriptive part). Ample examples will highlight the process that will help students attain a higher level of achievement on future NJASK/Algebra assessments as well as to help teachers experience the new connections to the Common Core Standards.

David Hoffman - Educational Consultant, Instructivision
Raising SAT Scores - Focus on Functions

Since 2005, the SAT has included questions requiring knowledge of functions.  This workshop will demonstrate all the variations of function problems your students will see on the SAT.  These problems can be used to teach function concepts and at the same time prepare students for the SAT. Remarkably, SAT problems are still designed to be completed in under a minute without a calculator. See for yourself!

Iftikhar Husain - University High School, Newark
Visual Approach to Mathematics on a Free Website

A free website presenting Pre-Algebra through Calculus and State Common Core Standards will be presented with animation. 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 the Visual Mathematics available free to all types of learners, the presenter has published the website and inviting volunteers to join.

John Kerrigan - Middletown Township Public Schools
Flipped Classroom at the High School Level

Are you looking for a way to make homework more meaningful? Looking for a way to provide students with more one-on-one interaction during class? Looking to provide your college placement and honors students with more of a challenge? Consider “flipping your classroom”. In this session, participants will learn ways to increase engagement in the mathematics classroom by using multimedia lessons. Tested strategies will be given for a wide variety of courses, from Algebra 1 through AP Calculus.

Lynne Kowski - Raritan Valley Community College
Can College-Level Remedial Math Programs Work?

A report on a study to test the efficacy of college-level remedial math programs, specifically in community colleges. In this study, chi-square independence test and logistic regression were used to compare the long-term academic outcomes of first-year community college students. Findings show that students requiring remediation in mathematics and successfully remediated into a college-level math class, experienced comparable outcomes to those not requiring math remediation, indicating that remedial math programs can be highly effective at resolving skill deficiencies.

Laura Kurmin – Wall Township High School:
Making Algebra 2 and Precalculus "Fun" through Meaningful Projects and Classroom Activities

During this session I will share a variety of alternative assessments and activities to help inspire the algebra 2 student and the pre-calculus student. Some activities include FACEing Math (creating a famous face through solving math problems), Math Concepts Go to the Movies (students use a movie to inspire classmates), MATHO (a competitive activity that can be differentiated for all levels of math students) and Picture This! GeoGebra Functions (the use of functions, specifically domain, range and transformations, to create an original, yet recognizable, design.) All activities are ready for you to use tomorrow. Some new activites will be added this year to include Algebra 2.

Joyce Leslie
How NOT to Teach Statistics

Statistics courses routinely teach students about the Normal Distribution (otherwise known as the Normal Probability Density function) without or before teaching about probability, random variables and probability density functions.  Statistics courses present the idea of a z-score – a “standardized value”, where z = (x minus mu)/sigma – without connecting this formula to the process of transforming other algebraic functions that students may know.  Formulas are presented without justification or proof and we teach students how to used “official tables” of the sum of probabilities without any explanation of how the table data generated (integrals of the probability density function).  In fact, since statistical analysis is done using computer-based packages like R and SAS, many students are not even given practice in using the formulas. This talk will suggest some historical and structural reasons for the problem, some ways to make statistics more meaningful to students, and curricular changes that are needed to prepare all students to understand and use statistics.

Irina Lyublinskaya – CUNY College of Staten Island
Teaching Geometry Proofs - Can Technology Help?

Teaching reasoning and proofs in high school geometry is one of the challenging tasks that we face today. Can technology help us with this task? In this presentation the presenter will share a set of problems that use symbolic geometry software that can be used to develop students’ proofs skills.

Amro Mosaad - Middlesex County Academy (Edison)
"HELLO my name is x+3" - Cooperative Group Activities for Teaching Polynomial and Rational Functions

Students’ understanding of polynomial and rational functions will be enhanced when they see them constructed.  By breaking the functions into their building blocks, you will be able to use cooperative group activities to engage students.  Students will collectively form polynomial and rational functions and see the connection between zeros and factors and determine other properties like domain, range, and asymptotes.   Worksheets will be shared.

Robin O’Callaghan and Brian O’Reilly – The College Board
Reasoning and Proof on the SAT

How can students demonstrate their ability to reason and to prove statements on a standardized test such as the SAT? How can they construct viable arguments and critique the reasoning of others? How does the SAT address the Standards for Mathematical Practice of the Common Core State Standards? Come hear the answers to these questions and more.

Peter Pace - Life Center Academy
Heir Today, Gone Tomorrow

An estate settlement problem in which participants will become heirs to an estate and do battle with the other heirs to see who can get the most goodies. Actually an algorithm for insuring that all heirs to the estate are treated fairly in the estate settlement.

Joseph G. Rosenstein – Rutgers University
Solving Problems Systematically

In this session we will explore a number of graph-related problems whose solutions require the solver to proceed in a systematic way. The material in this session will serve as an introduction to a soon-to-be-available textbook for average high school students. Its content is discrete mathematics, but its focus is on problem solving, reasoning, and systematic thinking, counting, and constructing.

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

Using trigonometric functions and calculus skills to determine the maximum range and the final velocity of a projectile based on knowing its initial velocity and maximum height. (Relate Physics to Mathematics).

Jay Schiffman – Rowan University
Modular Arithmetic in Precalculus and Calculus Courses

Modular arithmetic enables one to solve a number of diverse problems in pre-calculus, calculus, and discrete mathematics courses. In this workshop, participants will explore patterns in recursive sequences with regards to their divisibility and periodicity as well as form neat conjectures involving patterns in the derivatives of some trigonometric, exponential, and hyperbolic functions and the powers of the imaginary unit which is the square root of negative one. Please join us to explore a world of possibilities. You will conclude that examples of modular arithmetic permeate the K-16 curriculum.

Anita Schuloff – Paramus Catholic High School
Location of Complex Zeros on the Coordinate Plane

Real zeros of quadratic functions are easy to locate—they are found where the parabola intersects the x-axis. If you have ever wondered where on the coordinate plane the COMPLEX ZEROS are located, attend this session and find out!

Robin Schwartz - Math Confidence/College of Mt. St. Vincent
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 embrace the learning of 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. In fact, the comparison of multiple choice answers can help students to “think on their feet” while increasing accuracy, logic and frustration tolerance skills – assets in high school, college and the workplace. Worksheets will cover common secondary content incorporating Common Core  and SAT content (including algebra, geometry, trig and precalc) and will use multiple representations and technology to appeal to diverse learning styles creating a path to success for all.

Alice Seneres – Rutgers University
The Math of Student Loans

Many students need to take out student loans in order to attend college. Because these loans are a financial commitment that spans decades for the borrower, it is beneficial to have a mathematical understanding as to how the repayment process works. The math behind student loans is accessible and applicable to students with an algebra background; it involves exponents, percents, and compound interest. We will look at how the monthly payment of a student loan is determined, how to calculate the amount of interest that will be paid over the life of the loan, and the long-term effect of paying a small amount above the monthly payment each month.

Doug Smith – A.P. Schalick High School (Pittsgrove)
Coins, Cards, Counting, and the Common Core

What must students know in their future in probability and statistics for the new Common Core standards?  And the more important question, how are we going to fit this in?  Both will be discussed along with methods of demonstrating these probabilistic and statistical concepts for all grade levels.

Michael Weingart – Rutgers University:
The Prosecutor's Fallacy

The prosecutor asserts that based on evidence from the scene of the crime, the perpetrator had characteristics A, B, C, D, ... The defendant has all these characteristics. Since the probability that a randomly selected person has all these characteristics is only 0.00001, it is overwhelmingly likely, says the prosecutor, beyond reasonable doubt, that the defendant is guilty. Hmmm. There is a subtle fallacy pertaining to conditional probability lurking within the prosecutor's argument, and we will sort out what it is in this talk.

David Weksler – Consultant
More Math and Technology Stuff - It Just Keeps on Coming!

Innovation in software and Web-based applications for doing math on new hardware continue to evolve at an ever-quickening pace. A brief review of some of the new AND interesting (to this presenter) will be shared with participants. Additionally, the conversation about math education, technology, math concepts, history, etc., takes place all over the “social media” space. I’ll provide details - please consider joining this conversation and presentation.

Paul Westbrook – Rutgers University
The Math of Investing

Even our most accomplished students lack the basic financial skills crucial to success in life, yet they all take math and are all interested in money. I will demonstrate how to tap into that money interest and help kids become more mathematically and financially savvy by infusing investment applications into pre-calculus. Some of the applications that will be covered are: arithmetic versus geometric means, measures of central tendency, standard deviation, sequences and series and annuities, and weighted average, all applied to stocks and bonds. I will also address how the 2.5 credits of financial literacy education can be supported in math class.

Cathleen Zucco-Teveloff – Rider University
Using the Internet and Other Techniques to Teach Statistics

For this presentation, I will discuss techniques that I have found effective in teaching statistics. The focus will be on activities involving group work projects, conceptual flow charts and relevant internet data sources.  Participants will be given the opportunity to write and to share their own web-based application activity.

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