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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, 2019
8:30 a.m. - 3:00 p.m.


(arranged alphabetically by presenter's last name)

Angelique Bender - Summit High School - and Sarah Kaeli – West Morris Central High School
abender@summit.k12.nj.us and skaeli@wmrhsd.org
Transforming Students to be Transformations Experts in Graphing

In this presentation we will show you an easy and functional (no pun intended) way to approach transformations that can be applied to any family of functions. Function notation, reflections, translations and dilations will all be made approachable to students of a range of abilities using this technique. Suggestions for activities and incorporation of technology will be included. This is ideally geared toward Algebra 2 and Pre-Calculus but can be modified for Algebra 1 as well.

Eric Berkowitz – Parsippany Hills High School

Even if you've used Desmos as a graphing calculator, you may not have seen all that it can do. Come to learn about sliders, transformations, piecewise functions, solving equations, inverses, and trigonometry demos. I will show example of content ranging from early algebra to calculus. I will also include a segment on the teacher modules, which can be used to monitor your students as they go through a self-paced lesson. Be sure to bring a device with you.

Sabrina Bernath - The Frisch School, Paramus
The Good, the Bad, and the Ugly about Online Math Classes. Is there one for your student's needs?

In this session, we will examine the various reasons some high school administrators enroll students in online math courses. The necessary "hidden" skill set a student must process to be successful will also be discussed thoroughly along with specific cases presented with results discussed. Then various aspects of the online math classes offered by Virtual High School (VHS), Shmoop, and __________ will be explored in detail with screen shots provided of the different accompanying teacher dashboards. Participants of this session should leave with a great deal of knowledge and insight into this controversial but popular mode of math education.

L. Charles (Chuck) Biehl - Consultant
Modeling in Precalculus: Computational Geometry

Problems from computational geometry including the art gallery problem, facility location problem, and Steiner networks. Working on these problems involves many topics from pre-calculus including algebra, trigonometry, and coordinate geometry.

Kathleen Carter - North Hunterdon High School
From Data to Equations

Pattern recognition with numbers creates a rich discourse among students. Many struggle to move from the arithmetic to the algebra. This session will present instructional strategies to help students bridge the arithmetic patterns with explicit and recursive equations for linear, quadratic or exponential functions.

Ken Collins – Charlotte (NC) Latin School
Trends in A.P. Calculus and How They Affect Precalculus

A.P. Calculus continues to evolve. What is the focus of these recent changes? What impact does this have on how we teach PreCalculus? We will share some specific classroom-ready examples.

Neil Cooperman – Millburn High School:
Statistics: Learning by Doing!

Most teachers skipped or hated statistics in college and have avoided teaching it like the plague throughout their careers. I know; I was one! I thought it was so dry and boring. Well, I was wrong. Statistics is so much fun, if taught the right way. Avoid lecturing! Have your students solve problems hands-on. Students learn most from making mistakes, so give them plenty of opportunities to do so. This session is good for both AP and non-AP teachers. And, statistics is required throughout the curriculum, so since you have to teach it, you might as well enjoy it.

Stephanie Cooperman – President, Association of Mathematics Teachers of New Jersey (AMTNJ)
The Beauty of Harmonic Divisions of Golden Rectangle Designs

The Golden Rectangle has been employed by artists from the Renaissance to Modern Times to convey depth and proportion. This presentation will include background information and visuals displaying Harmonic Divisions in famous paintings. Participants will learn how to construct beautiful graphic designs based upon underlying grids of combined Golden Rectangles. The careful selection of vertices for forming the harmonic divisions, combined with engaging color choices, will establish dynamic compositions and perspective.

Students of varying abilities should have novel ways to "show off" that are entirely different from achieving high grades on tests, quizzes, and state testing. The cross-curricular themes - ancient civilizations, art history, technology and graphic arts - have significant impacts regarding personal interests and talents. The beautiful designs, produced by students working in pairs or groups, can be utilized for spectacular electronic bulletin board displays and whole-class presentations.

Fred Decovsky - Consultant, Teachers Teaching with Technology
Using Multiple Representations and the Graphing Calculator

Through specific activities we can discover ways to represent the same context in multiple ways: graphically, numerically, symbolically and verbally. The use of multiple representations helps with understanding relationships between variables, expressing these relationships in multiple ways, and reasoning about connections between representations.

Angelo DeMattia - Kean University
Some Fun and Challenging Problems from Marilyn vos Savant

How do we know our intuition has failed us? We are aware that some problems just don’t follow our brains’ wiring, but how do we know when this happens? Let’s explore some fun, puzzling, and challenging problems in probability and other areas of mathematics in order to begin the process of fine-tuning our reasoning skills - such as the Monte Hall Problem - and simultaneously connect to the CCSS and the Big Ideas in Math – including number sense and ideas in Algebra, Probability, and Statistics.

Meghan DeVaney - North Hunterdon High School
Dividing Polynomials: From Conceptual Understanding to Procedural Fluency

Students often struggle with algebraic manipulation of polynomials that are cubic or of higher degree. This session will share instructional strategies that help students develop better understanding of factoring and polynomial division for Algebra 2, Precalculus, and even Calculus. Students will develop greater flexibility in their procedural thinking and make connections to graphs of rational functions. If your students struggle with the algebra of polynomial division and rational functions, this session will help them “think deeply” about division and what the quotient can tell us.

Kevin Dziuba and Amanda Mihalic - Rancocas Valley Regional High School
Standards Based Learning and Assessment

Are the grades that students earn a good indicator of student knowledge? We will provide you with ways to allocate Common Core standards into units, and develop formative/summative assessments linked to those standards. We will discuss this both in general and how this could be applied in an algebra or geometry course. We will also offer methods for helping students to self-assess their content understanding.

Paula Gray and LuAnn Falletta – Bernards High School, Bernardsville
pgray@shsd.org and lfalletta@shsd.org
How to Have a Successful AP Calculus Classroom

If you teach AP Calculus then come and join us as we discuss and explore things that you can do to have a successful AP Calculus classroom. We will have ideas for novice and experienced teachers of AP Calculus and non-AP Calculus classes. Insight into the grading process for AP exams will be discussed as one of the presenters has been an AP reader. The inclusion of technology where appropriate will be addressed along with the importance of correct mathematical writing at any level of Calculus. Special projects, AP Roundtables, resources, films, books and post AP ideas will be included in this session.

Deanna Houlihan and Andrew Rosenbloom - Middletown High School South
houlihandc@middletownk12.org and rosenblooma@middletownk12.org
Maximizing the Co-Teaching Experience

Discover a new twist on co-teaching! Learn effective ways to differentiate instruction in the co-taught classroom while teaching students to own the strategies helpful to their learning style. Using multiple ways to differentiate instruction and personalize learning, in the co-taught classroom, helps your teaching team meet your students’ needs, interests and styles more efficient and effectively. The true co-teaching mindset shift leads to greater success for all students.

Iftikhar Husain – University High School, Newark
Preparing SAT (Math) Visually

One goal of the standards is a deeper understanding of math. The visual approach delivers concepts in a natural way and helps students stay focused and motivated.

David Hyman - Livingston High School
Strategy Games to Stimulate Critical Thinking

Using various non-traditional strategy games to stimulate critical thinking amongst the students. It’s all fun and games … even after they realize it's math!

Miklos Jalics – Morristown-Beard School
Singularities of Rational Functions and More

Many different types of problems will be presented in which students are asked to provide expressions for rational functions matching a certain criteria. Specific attention will be given to different types of singularities that occur coming from a removable discontinuity versus a vertical asymptote. The connections with limits will also be analyzed in conjunction with the rational functions.

Joyce Leslie with Elaine Weiland - Columbia High School, South Orange/Maplewood
Teaching Calculus to a Heterogeneous Class

This talk builds upon the talk of the same name that I gave in 2018. I have refined the methodology I described in the 2018 talk and I have been working with a colleague who is using this method for the first time.

After many years of teaching multi-level calculus classes I have been developing an approach which has been successful in focusing on the big ideas in calculus while strengthening student’s algebra skills – skills necessary for applying differential and integral calculus to interesting problems.

I will share how we review functions through a calculus lens, and develop the derivative to promote an understanding of two important ideas that students often struggle with: the derivative is the slope of the tangent to a function at a single point; and the derivative is also a function. This approach develops the idea and mathematics of the derivative incrementally; students develop and explore the algebra of the derivative as they explore this new and powerful idea.

I am drawing upon years of experience teaching a multi-level Calculus class with some students who are very weak in algebra (yes this happens even to accelerated students!), students who have approached learning math in meaningless and formulaic way, and students who found that 4 AP classes was too much, so they dropped from AP Calc to honors.

This year, another colleague, Elaine Weiland, is experimenting with the same approach in her calculus class and will join me to discuss her “first year experience” using it.

I will also share ideas in introducing integral calculus that appear to soften the tedium of adding the areas of a large but limited number of rectangles. Finally, I will conclude with suggestions for teachers that focus on better preparing students to learn calculus.

Eric Milou - Rowan University
Ending the College Remediation Crisis in Mathematics

It is abundantly clear that traditional mathematics courses are the most significant barrier to degree completion for all fields of study. Nationally, an estimated 60 percent of incoming two-year college students are placed into at least one developmental math course each year. Moreover, hundreds of thousands of students fail higher education math courses every year and many more students pass courses that do not prepare them for their future. This session will show the results of Rowan University's three-year initiative that (a) eliminated all non-credit basic skill algebra classes, (b) created new undergraduate math courses for non-STEM majors and (c) lowered the standardized assessment cut scores for entry into freshman undergraduate math classes. These new math courses were designed to align with students’ career and life needs and accelerate students’ entry into credit-bearing coursework. Our research provides recommendations for all colleges (including two-year colleges) and includes implications for high school mathematics.

Robin O’Callaghan and Fred Schuppan – Educational Testing Service
rocallaghan@ets.org and fschuppan@ets.org
Can Student Responses Inform the Writing and Scoring of Free Response Questions?

Math assessments, both inside and outside the classroom, include free-response questions. It is challenging to write effective free-response questions and to fairly and uniformly score them. Come learn how sample student responses can improve the writing of free-response questions and their scoring rubrics.

Joe Rosenstein - Rutgers University (ret.)
Counting Systematically

The New Jersey Mathematics Standards of 1996 and 2002 indicated that all students should be able to determine how many four-topping pizzas are possible if eight toppings are available.  In this session we will focus on the mathematics needed to be able to answer this question.

Audra Ryan - Middletown Public Schools
Using Google Expedition in the Algebra 1 Classroom

Let's take a trip! This workshop will use Google Expedition to seek interest and motivate students. To introduce Scatter Plots, we explore Yellow Stone National Park focusing on our tour of The Old Faithful Geyser. This real life experience enhances discussion when analyzing patterns in "eruption time" and "waiting time".

Ahmed Salama - PANTHER Academy
Learning Linear Equations in Algebra and Calculus Through Kinematics

The goal of this presentation is to explain how we concluded that we need to teach physics with algebra in order to establish a solid pre-calculus background. The variety of representations that we will investigate includes verbal, numerical and graphical representations.

Jay Schiffman – Rowan University
Examining Sequences in the High School Classroom

This hands-on workshop will focus on examining sequences which algebraic, geometric, Fibonacci-like and exponential in flavor. The TI-84 hand-held will be deployed to enhance the workshop and add a touch of data analysis to the presentation.  Please join us to engage, learn and explore. 

Anita Schuloff – Paramus Catholic High School
Generating Pythagorean Triples

Generating Pythagorean triples and their relationship to quadratic trinomials will uncover a fascinating sequence from the OEIS (Online Encyclopedia of Integer Sequences).

Robin Schwartz – Math Confidence/College of Mt. St. Vincent
Ideas for Math Class on Twitter: Sharing, Exchanging or Lurking

Twitter is a great place for Math educators to find tasks, routines and camaraderie. In this workshop, we will visit the #mtbos (Math Twitter BlogOSphere), #elemmathchat, #observeme, #iteachmath and other Twitter hashtags and people for inspiration and motivation for both teachers and students!

George Soliman – Raritan Valley Community College
Fibonacci Numbers are Fascinating, and That's No Fib!

The Fibonacci Sequence has many interesting patterns and applications, both mathematical and in nature. Come and see where Fibonacci Numbers hide, and their connection to the golden ratio and even Pascal’s Triangle. Get students to actually get excited about math when introducing these fascinating numbers!

Dianna Sopala – Northern Valley Regional High School
Making Learning Visual in the Algebra, Geometry, and Trigonometry Classroom

Our students are the Youtube, Netflix, and playing games generation.  Why are we still teaching them the same way as teachers taught students 50 years ago?  Students are more engaged in a highly collaborative, active, and visual mathematics classroom.  Participants will learn some strategies to teach students to effectively collaborate, visualize Algebra and Trigonometric concepts and to bring stagnant Geometry diagrams to life through videos and animation.

Kara Teehan – Middletown Public Schools
Teaching Algebra and Calculus in a High School Active Learning Lab

The speaker will discuss her experience teaching Algebra and Calculus in an Active Learning Lab designed for collaborative, cognitively demanding learning. The speaker will provide resources for active learning activities specifically for mathematics classes leading up to, and including, calculus. The speaker will provide images and information about designing a learning space conducive to active, engaging mathematics learning.

Elaine Terry – St. Joseph's University, Philadelphia PA
Preparation for Calculus: Assessing Background Skills of Students Enrolled in College Calculus

Calculus has been defined as the gateway to higher-level mathematics and other STEM subjects.  This places precalculus in the position of being the course that determines whether or not students are prepared to enter that gate.  College instructors find that many of the students enrolled in these two courses have deficiencies in skills that are necessary for completing problems. Data will be presented from diagnostic tests administered in a college-level calculus course to identify students’ strengths and weaknesses.  Examples of problems from precalculus and calculus will give insight into common errors that students make when attempting to complete problems.

Linda Treilman – Mercer County Community College
A SMART Board is a Great Tool for the Mathematics Classroom

To Be Announced

Paul Westbrook - Rutgers University
Using Statistics to Understand Investments

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 students become more mathematically and financially savvy by infusing investment applications with basic concepts in statistics. Some applications covered are: arithmetic versus geometric means, measure of central tendency, namely, standard deviation, weighted average, all applied to stocks and bonds.

Stacy Winters – Chatham Public Schools
Strategies and Resources to Reflect Student Thinking

We often get wrapped up assessing and listening for the right next step or the right answer that we often forget to ask students about their thinking. This workshop will explore resources that foster this type of thinking in the secondary math classroom including Math talks, WODB, Visual Patterns, Would you rather, legos, etc... These activities can be applied to any course content.

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