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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 16, 2018
8:30 a.m. - 3:00 p.m.


(arranged alphabetically by presenter's last name)

Lisa Barragato - Northern Valley HS, Demarest
Using Videos to Engage Students in Algebra (Algebra 1 and2)

Are you looking to add a little excitement to your lessons? Do you find that sometimes your students are not as engaged as you would have hoped? In this session we will utilize movie trailers, Ted Talks, and other online videos to help introduce new topics and develop lessons. Topics include exponential functions, sequences and series, rational functions, and more. Feel free to bring your own device to explore videos and develop your own lessons.

Angelique Bender and Sarah Kaeli – Lenape Valley Regional High School
How to Make Calculus Fun, Hands-on, and Tangible

This session will include a hands-on activity on volume by cross-section, a game on the computer on graphing with derivatives, a hands-on activity on volumes by revolution, and a fun way of grouping by using calculus.

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. We 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.

L. Charles (Chuck) Biehl - Consultant
A Teacher's Guide to Computational Geometry

Some geometry problems require algorithms and other mathematics to solve them. This session details some of these problems and focuses on two examples for high school: the Art Gallery problem, placing guards or cameras at vertices of polygons; and the Facility Location problem, calculating the best location for new facilities like restaurants and hospitals.

Kathleen Carter - North Hunterdon High School
Understanding Quadratic Functions

This session will analyze Quadratic Functions in its various representations to help students understand the characteristics of quadratic relationships.   First, the behavior of quadratic number patterns will be analyzed for writing recursive and explicit formulas.  Then, the characteristics of the graph of the parent function will be discussed as a foundation for the exploration of transformations.  The different forms of the equations of quadratics will be compared for purposes of graphing and modeling quadratic relationships.   The session will also demonstrate how the Desmos online graphing calculator can be incorporated to stimulate classroom discussion and analysis of quadratics.  Please bring a laptop or tablet to participate in the Desmos part of the presentation and a graphing calculator.

Dave Cesa – Charlotte (NC) Latin School:
Cold, Warmer, HOT: A Digital Strategy for Precalculus and Calculus

“Cold, Warmer, HOT!” is a digital hide-and-seek strategy that can be infused into Desmos animations and activities. This strategy helps students build better informal intuition about many key topics in Precalculus and Calculus before embarking on more formal problem solving processes. Some examples of topics to which this strategy may be applied include slope, conic sections, inverse functions, existence theorems (Intermediate Value Theorem, Mean Value Theorems), derivatives, integrals, polar curves, and Taylor series. We will share the motivation behind the strategy, many examples revealing how to implement the strategy most effectively, and some practical tips to help you create your own animations and activities utilizing the strategy.

Ken Collins – Charlotte (NC) Latin School:
Teaching Precalculus to Prepare Students for A.P. Calculus

The A.P. calculus curriculum and exam continue to evolve. There is a greater emphasis on understanding and applying fundamental concepts. The exam includes more “real world” problems where students have to interpret their calculus results in the context of the problem. We will offer some suggestions for pre-calculus teachers to help them better prepare their students for A.P. calculus. In particular, we will examine how to write pre-calculus questions that reflect the concept and word problem questions that have become more prevalent on the A.P. Calculus exam.

Neil Cooperman – Millburn High School:
Why Geometry?

The SAT’s have de-emphasized Geometry. The Common Core has minimized the topics in Geometry for preparation for College and Careers. Some schools are considering dropping Geometry as a required course for graduation and numerous states do not specifically require Geometry. Some guidance counselors believe that Geometry is not necessary for success in other math courses. This session will explore the relevance of Geometry (logic, reasoning, thinking outside the box, applications in nature, architecture, art and the sheer beauty of it) and why it is a core construct for future learning, not just in mathematics, but also in many other disciplines.

Fred Decovsky - Consultant, Teachers Teaching with Technology
Coding -- Not Just for STEM

Coding is an essential 21st-century skill. Coding can spark students' interest in programming and help them become better problem solvers. Tap into the world of computer programming using the TI-84 Family graphing calculators already in your classroom. Attendees will learn important programming commands and will write a few programs of your own.

Angelo DeMattia - Kean University
Visual Representations for Proportional Thinking and Algebraic Reasoning

How much of the Algebra that we teach will our students remember in a year?  In a month? In a day?  It is a common belief that visuals and manipulatives are used as a crutch on the road to learning the more abstract mathematics and that manipulatives are needed only for “babies” and the special needs students. This session will help rethink that belief and help your students create a mindset that enables them to use visual strategies - with an emphasis on spatial reasoning - that strengthen their quantitative literacy and reasoning skills. Come “see” for yourself!

Stephanie DiBari - Middletown High School North AND Eileen Fallon - Middletown High School South
dibarist@middletownk12.org and fallone@middletownk12.org
Formative Assessment with Desmos Activity Builder

The Desmos Activity Builder is an extension of the popular Desmos calculator tool that provides teachers with an easy way to create effective formative assessment tools. We will share examples of using Desmos Activities in a variety of high school math classes. Come see the new “Teacher Dashboard” in action, particularly the “anonymize” feature which allows discussion of student responses without identifying the students to the whole class; and the "pacing" tool which helps focus class discussions and keep students on task. We will also provide tips on how teachers can search for previously made activities available on Desmos or create their own original activities. Bring your own device so that you can participate.

Frank Forte – Raritan Valley Community College
Using Exploration and Technology to Teach Graph Translations

If you struggle to help students understand the rules of graph translations, we’ll look at ways that you can use technology and exploration in the classroom to help students discover how changes to the function affect the graph. The goal is to help students construct the rules on their own so they can move beyond memorization to a deeper understanding. We’ll also look at potential pitfalls when using this method so that you are well prepared to try this in your classroom. Bring some technology with the ability to graph – a graphing calculator, computer or phone that can load Desmos, etc.

Paula Gray – Bernards High School
The Beauty and Necessity of Correct Mathematical Writing and Notation

What does good mathematical writing look like? Why is it so important? We will discuss a writing rubric that has been developed and used at my school to assess and guide students in correct mathematical writing and notation. This is greatly emphasized on all PARCC and AP assessments. The rubric can be used when grading assessments and can be used to establish a writing SGO in any math class. Examples will be provided. To reinforce writing even more, TED (Think, Explore and Discuss) assignments that have been used at our school will be shared. In TED assignments, we explore challenging mathematical questions that are normally not ever seen in textbooks and appear on AMCs and other competitive tests. Students make formal presentations in class where correct notation, writing and structure are again emphasized and are part of the grading rubric. How must I write justifications for the Calculus AP exam? As a past reader, I will share with you the correct/acceptable writing of justifications in the open-ended questions on the AP exam. Finally, creative mathematical writing assignments where students can use math to create interesting mathematical stories will be shared with the attendees..Bring your flash drive with you and I will share the files with you.

Iftikhar Husain – University High School, Newark
Delivering Standards of Mathematics 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
Saving the Planet One Rational Function at a Time

How modeling geometric relationships with rational functions can be used to minimize materials required for construction.

Mike Kaplan – Ramapo High School, Franklin Lakes
Encouraging Deeper Thinking in the Math Classroom

In this session, we will reflect on and discuss strategies to encourage deeper thinking in the math classroom. These include questioning strategies, open-ended questions, student-centered learning and using technology (such as Desmos) to encourage students to think more critically about problem-solving. Participants will be encouraged to share their own lessons that encourage higher level thinking in their classroom.

Jeffrey Kaye – Millburn High School
Navigating Your Way Through the Fundamental Theorem of Calculus and Beyond

We will explore the precursors to the Fundamental Theorem of Calculus and how to immediately introduce the idea of net change to foreshadow and deepen students' understanding in preparation for the applications of the FTC.

John Kerrigan - Middletown Township Public Schools
Active Learning Strategies for the Math Classroom

This past summer I had the opportunity to teach Calculus II for Math/Physical Science Majors in the new "Active Learning Classrooms" at Rutgers University. This classroom layout forced me to convert my old "lectures" into opportunities for students to interact with the content, with one another, and with me. This talk will describe research-based methods for incorporating active learning opportunities in any mathematics classroom. Special emphasis will be placed on how to use technology and metacognition to make the syllabus, classroom introductions, formative assessment, reviews, and mini-lectures more active opportunities for students. Though the examples used will be drawn from primarily from calculus, the intent is for any participant to walk away and use these strategies in any high school-level math course.

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

This might be considered an odd title because all classes are at least somewhat diverse in student backgrounds and learning styles. However, I am drawing upon years of experience teaching a multi-level Calculus class with 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. I will share an approach that 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 an approach for reviewing functions through a calculus lens, and developing the derivative more slowly to naturally develop an understanding of two important ideas that students struggle with: the derivative is the slope of the tangent to a function at a single point and the derivative is function. 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.

Irina Lyublinskaya -- College of Staten Island
Exploring Sequences and Series with CAS

CAS provides new opportunities to investigate sequences and series and to discover some interesting patterns while avoiding tedious calculations. We will explore convergence of various sequences and series algebraically and graphically.

Eric Milou - Rowan University
The Status Quo in High School Mathematics is Unacceptable

Today, it seems as if nearly everyone agrees that high school mathematics needs to change. For far too long high school mathematics has not worked for far too many students. High school mathematics has not changed substantially in my lifetime, nor has it changed substantially for most students, teachers & schools. It is clearly an issue—and it is time to discuss and make serious changes.

Afroze Naqvi - Saskatchewan Polytechnic
Propositional Logic, Set Theory, and Mathematical Induction

The advent of the computer age at the end of the twentieth century has necessitated a closer study of topics in discrete mathematics because it provides the viable tools for dealing with many intricacies of problem solving involving computer science. In this session, I will explore the following topics in discrete mathematics: propositional logic, set theory, and mathematical induction proofs, including concrete examples.

Audrey Nasar - Borough of Manhattan Community College
Computational Thinking in Precalculus

Computational thinking involves learning how to use computers efficiently and effectively to solve problems. As such, it is historically taught within the computer science curriculum. In recent years however, there has been a strong push to teach computational thinking to a broader range of students as many of the problem-solving skills developed through computational thinking can be applied across other disciplines, including mathematics. This talk will demonstrate how computational thinking can be taught in precalculus through the analysis of several typical algorithmic problems.

Robin O’Callaghan and Fred Schuppan – Educational Testing Service
rocallaghan@ets.org and fschuppan@ets.org
Writing Fair and Effective Scoring Rubrics for Free-Response Questions

Math assessments, both inside and outside the classroom, include free-response questions. Questions that model precise language and that are written with a clear sense what is being measured will naturally lead to rubrics that result in fair and uniform scoring. Come learn about best practices in writing free-response questions and scoring rubrics and learn how to create your own effective scoring rubrics.

Ralph Pantozzi - Kent Place School South
Push Your Luck!

How far can you and your students go with probability? Far beyond expectations – through the study of expected value and probability distributions. Rather than a topic that comes after students have mastered other probability concepts, these ideas can help students develop a deep understanding of probability right from the start. When students move beyond thinking that probability means “no one knows what will happen” or “anything might happen” they learn how to make some wise decisions with probability in the classroom and in their lives. Join us in playing some games and simulating real choices where we will push our luck and understand that “luck” is only “probability taken personally”. Our investigations will be appropriate for students in any grade and have multiple extensions into further topics in Precalculus and beyond. Is it true that “fortuna audentes juvat”? Come find out for yourself.

Andrew Rosenbloom and Deanna Houlihan - Middletown High School South
rosenblooma@middletownk12.org and houlihandc@middletownk12.org
Flipped Mastery Learning in High School Mathematics

We would like to show our perspective of a “flipped classroom” and demonstrate the positive elements for both the advanced and classified students. In the area of mathematics, the flipped mastery approach to teaching and learning is very effective as content builds on prior learning and students have the ability to visit previous lessons as often as necessary. With mastery learning students are required to attain a pre-defined level of proficiency in a topic before they can move on to the next topic in a course. Describing our perspective on this innovative type of instruction aims to provide teachers with an additional resource as they prepare learning experiences to individualize instruction by regularly assessing student understanding; filling in gaps where necessary and challenging students when appropriate. Our perspective on this approach is from an Algebra II course.

Joe Rosenstein - Rutgers University (ret.)
Pascal's Triangle

In this presentation, we will look at a number of properties of Pascal’s Triangle, including the “choose numbers” that live on Pascal’s Triangle, and how they apply to a variety of counting problems.

Ahmed Salama - Passaic High School
The Benefits of Teaching the Application of Trigonometric Functions in Precalculus Classes

The presentation before his academic peers involved teaching students trigonometric functions through fantastic real-life applications such as: estimating the heights of objects, estimating the circumference of earth, musical symphonies, predicting weather, military operations, architecture and more.

Jay Schiffman – Rowan University
Mathematical Misconceptions that Permeate Many Textbooks Throughout the K-16 Curriculum

Many textbooks often divulge misinformation concerning key concepts. In this session, we will examine common misconceptions, poor notation and key phrases that are inhibiting students and teachers from having successful mathematical experiences. Among these include the concept of a function including the ordered pairs model, domain and range, the words factor, cross multiply, FOIL, reduce to lowest terms, plug in, cancel, evaluating limits by substitution and other morsels. In addition, we demonstrate anomalies which sometimes work, but quickly expire. The use of counterexamples and graphing calculators will be utilized to alleviate a number of these misconceptions.

Anita Schuloff – Paramus Catholic High School
Sequences, Quadratics, and Right Triangles

An amazing connection between a number sequence, quadratic polynomials, and right triangles.

Linda Treilman – Mercer County Community College
What's New for the SMART Board Software - Notebook 2017

Equation Editor for Mac and Windows users. Improved SMART Response (2) - more improvements coming for formative and summative assessments , SMART Lab activities, and some good tools to use in the math classroom to increase engagement, motivation and student understanding. (Participants are encouraged to bring their own mobile devices.)

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
Authentic Assessment in Algebra and Geometry

Need ideas for how to assess mathematics other than a traditional paper and pencil test? I will be presenting numerous formative and summative assessment ideas that complement the traditional assessment in Geometry and Algebra II. Some involve technology and many projects can be adapted to multiple classes. I will be bringing examples of student work and providing a handout with all the ideas and write ups students receive when assigning the project.

Amanda Zielenkievicz – Ramapo Indian Hills Regional District
Statistics, Standards, and Technology

Abstract: To Be Announced

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