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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 17, 2017
8:30 a.m. - 3:00 p.m.


(arranged alphabetically by presenter's last name)

Agnes Azzolino - mathnstuff.com
Trig Tricks with All Sorts of Technology

Take notes with Alt+Print Screen and a paint program.  See the Unit circle move.  "Derive" quadrantals and trig graphs with SketchPad. Graph all 6 functions w/special trig graph paper. "Prove" the Pythagorean identities with the Unit circle. Curve shift with Excel. Review with Windows Explorer.

Lisa Barragato - Northern Valley HS, Demarest
Exploring Geometry Concepts Using Hands-On Learning

Are you tired of teaching your students but then they don’t remember it in a few weeks or months?  Students retain information better and understand concepts more in depth if they are allowed to develop the concepts on their own.  In this workshop teachers will learn how to use protractors and rulers for students to explore triangles, quadrilaterals, parallel lines, and so much more.  

Angelique Bender and Sarah Kaeli – Lenape Valley Regional High School
Add a Little Color to Your Precalculus and Calculus Classes

Our presentation will demonstrate how we have used color as a vital tool in a number of lessons – two lessons will be discussed for each of precalculus and calculus.  At the end of each of these lessons, we observed an increased understanding of the topic compared to the time we taught it monochromatically.

Eric Berkowitz – Parsippany Hills High School
Making Connections Between Algebra and Coordinate Geometry

Warning: Topics are more closely related than they appear. We know that many topics are different from each other, but students can discover the connections to really help them make use of what they are learning.  Geometry and arithmetic can be used to help understand concepts throughout algebra and trigonometry.

L. Charles (Chuck) Biehl - Consultant
The Facility Location Problem: Algebra and Geometry Meet Discrete

Where to build a new hospital, fast food restaurant, or nuclear waste dump? This activity combines systems of linear equations, coordinate geometry, geometric construction, and a discrete model called a Voronoi Diagram, to help answer this question. Can be introduced as early as Algebra 1 and done in pieces over an extended time period; for Algebra 2 and precalculus, it can be a stand-alone modeling problem or project or a capstone activity for the embedded topics. The perfect activity for the question "What is this good for?"

Kathleen Carter - North Hunterdon High School
Incorporating Desmos in Algebra 2 and Precalculus Classes

The use of the online Desmos calculator engages students in activities that incorporate the Common Core Mathematical Practices.   The session will share Desmos activities that allow students to model using mathematics, explore transformations, and analyze functions and relations.   Activities allow students to make connections between graph, data table and equation. The session will also introduce the activity builder which gives teachers the flexibility to make their own activities in Desmos.

Dave Cesa – Charlotte (NC) Latin School:
Desmos for Calculus

Come see how the Desmos free online graphing calculator can enhance your Calculus instruction through animations, teacher demonstrations, and student activities. I will share some ready-made examples, plus help you create your own templates for dynamically modeling some of Calculus' Greatest Hits, including: exploring limits, sketching derivatives, related rates, the Fundamental Theorem of Calculus, Taylor polynomials, and polar curves. Bring your laptop or iPad with you to participate!

Ken Collins – Charlotte (NC) Latin School:
Series: From Precalculus to Calculus

The series question on the A.P. Calculus exam usually has the lowest mean score. One reason may be that calculus students may have a foggy understanding of series. We will share a number of classroom ready precalculus explorations that help deepen a student's understanding of series and even have some fun with them. Copies will be available to all participants.

Neil Cooperman – Millburn High School:
Productive Struggle and Student Discourse

Most of us learned successfully by listening and taking notes, but research shows that does not work for more than two-thirds of our students. Most students learn best in a “learning” environment and not as well in a “teaching” environment. Furthermore, scoring higher on the current evaluation models requires greater student engagement. Come and pick up a few more “tools of the trade” that will place increased responsibility on your students, enhance your observation scores, and simultaneously make your job easier and more fun.

Fred Decovsky - Consultant, Teachers Teaching with Technology
Composition and Inverses with Quadratic Functions

In this session we will look at the following ideas and make connections between the symbolic, graphical and numerical representation using the TI84 Family calculator:

  • Exploring the composition of functions, including domain & range
  • Finding inverse functions and relations
  • Graphing a function with a restricted domain and graphically confirming its inverse
  • Graphing inverses parametrically

We will also discuss strategies for effectively incorporating technology into the classroom.

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 that strengthen their quantitative literacy and reasoning skills. Come “see” for yourself!

Iftikhar Husain –
Delivering Standards of Mathematics Visually

The participants will be encouraged to answer Math Questions presented. The animated response will amuse the participants using the technology. Students can gain a deeper understanding of mathematical concepts of various levels all the while staying focused and motivated. It helps students to retain the stronger knowledge than they would have otherwise. Learners of all ages learn the math concepts intuitively. The topics discussed in this presentation are CCSS covering 8 Grade, Algebra I, Geometry, Algebra II and Trigonometry.

Mike Kaplan – Ramapo High School, Franklin Lakes
Using Technology to Enhance Calculus Instruction

This workshop will explore a number of on-line resources that can be used to make calculus concepts more meaningful, provide visual representations of concepts, and provide fun learning opportunities for students. Please bring laptops for participation!

Jeffrey Kaye – Millburn High School
Making the Connections Among f, f', and f''

Attendees will participate in a hands-on activity to explore the graphs of  f, f', and f'' to examine the relationships between them and to better understand their connections. This level of comprehension builds a strong foundation for introducing the first and second derivative tests and being able to answer AP level questions dealing with graphs or equations of any of these functions.

John Kerrigan - Middletown Township Public Schools
A Closer Look at the Redesigned SAT: Implications for HS Math Teaches and Preparation Resources

This session will highlight some of the key changes in the SAT since its revision in March 2016. Participants will engage in answering some questions from a recently released examination and discuss the pedagogy shifts necessary for students to do well on this exam. A special focus will be placed on key Algebra 1, Geometry, and Algebra 2 topics that frequently appear on the exam. As a group, we will look at resources for helping students prepare for the exam, including the Khan Academy's extensive suite of preparation materials.

Joyce Leslie
Identifying the Potential of Students with Serious Gaps in Mathematical Understanding

In this talk I will discuss my work with students who present major gaps in mathematical understanding. I will show examples of student work that shows the powerful reasoning capability in a student who first presented with severe deficits. The result of an initial diagnostic interview revealed a lack an understanding in many areas: number (positive and negative numbers, rational numbers), points on a coordinate plane, the graph of a point, the graph of a line, and solutions to equations with one unknown. I will discuss this in the context of my research on teaching such students. I will show participants video stories of pre-algebra students solving "guess my rule" problems. We will consider what the students in the video appear to know and the level of engagement that the students display as they work on the math problems. I will also discuss some of the results of research on student understanding of what it means to learn math, and how these expectations of "learning mathematics" may impact your own classroom.

Patrick Letourneau - North Hunterdon High School
The Beauty of Flipped Lessons

For teachers who are looking to find new, creative, unique ways to present material to students in order to appeal to specific needs of different learners. There will be 6 parts: 1 - All attendees will experience a flipped lesson firsthand! 2 -Introduction to what flipped lessons are, their purpose, their advantages, and their disadvantages. 3 - Descriptions of multiple ways to create flipped lessons (including use of Smartboard). 4 - Personal examples of flipped lessons. 5 - Creating a flipped lesson by working with a specific program (Windows Live Movie Maker and Smatboard). 6 - Question and answer time as well as sharing any personal ideas (although I take questions throughout the whole presentation!).

Robin O’Callaghan and Daniel Klag – Educational Testing Service
rocallaghan@ets.org and dklag@ets.org
Best Practices in Writing and Using Assessment

Math assessments are used for a variety of purposes, both inside and outside the classroom. To make the most of these assessments, it is essential that test writers (including classroom teachers) follow best practices to ensure the fairness and validity of their tests. Come hear about best practices for measuring what students know and can do.

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.

Ahmed Salama - PANTHER Academy, Paterson:
Learning Linear Equations through Kinematics

The goal of this presentation is to investigate the variety of means by which the motion of objects can be described. The variety of representations that we will investigate includes verbal, numerical and graphical representations. In algebra class, students should be able to utilize their understanding of kinematics to learn linear equations.

Jay Schiffman – Rowan University
The Binomial Theorem, Pascal's Triangle, Explorations and Patterns: A Happy Marriage with CAS

The binomial theorem is one of the most essential and beautiful results in mathematical lore. In this hands-on session, participants will view the essence of the binomial theorem, namely the binomial coefficients and their role in a plethora of dynamic and engaging mathematical situations. Our explorations will encompass figurative numbers which lie on the diagonals of Pascal's Triangle, explore whether the odd or even entries are more prevalent in the triangle and form patterns and then conjectures based on the analysis of such patterns all in the spirit of dynamic mathematics. The CAS enables one to expand binomials as well as to secure binomial coefficients. Please join us and witness many of the marvels of this configuration.

Anita Schuloff – Paramus Catholic High School
Some Calculus Lessons with Dynamic Software: Attach Tangents, Find Slopes, Extrema and Derivatives.

Geometer's Sketchpad is not just for geometry. Its graphing capabilities could be very helpful for most of your lessons. Learn how to present derivatives, concavity and optimization problems. Also to be presented is the ADVANCED TOOLKIT from the Keypress website which supplies tangents, min and max points and points of inflection for your graphs. Bring a laptop with a mouse so that you can follow along. I will supply you with the advanced toolkit file in an attachment to an e-mail.

Robin Schwartz - Math Confidence/College of Mt. St. Vincent
May, October, or January: When Will You Take the New SAT?

Robin Schwartz took the new SAT in May 2016 adding to her recent test experiences -- ACT (2012), “old” SAT (2009) and “ancient” SAT(1980). These recent exam experiences helped her to relive studying and test taking, fill gaps in her education, and relate better to students' experiences. Studying for the ACT/SAT helps students learn the content they need to successfully complete high school and/or avoid remediation. We will also discuss and profile examples of the SAT/ACT Math and show how improvement on these exams can help students (and adults alike) gain a new outlook and self-identity.

Kara Teehan - Middletown High School
Teaching Trigonometry without the Unit Circle-An All-Triangle Approach for Understanding

This session will explore an ideal method of teaching trigonometry that focuses on understanding, rather than memorization. The emphasis will be on using trigonometric relationships and special right triangles to develop an understanding of how to evaluate trig functions. This allows for students to never have to memorize the unit circle! Connections of this method to the unit circle will be explored. The value of teaching trig using this method will be emphasized using instances and examples from AP Calculus AB and BC where trigonometric function fluency is key!

Elaine Terry – Saint Joseph's University, Philadelphia
Assessing Background Skills of Students Enrolled in College Precalculus and Calculus

Calculus has been defined as the gateway to higher-level mathematics and other STEM subjects.  At the college level, this places precalculus and calculus in the position of being the two courses that determine 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 diagnostics tests administered in three college-level math courses 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
What's New for the SMART Board Software - Notebook 2016

Finally an Equation Editor for Mac users and Windows users who don't have Math Tools.  A new SMART Response (2) for formative assessments, new themes for SMART Labs and a review of some good tools to use in the math classroom. (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
Alternate Assessments Ideas in Algebra, Geometry, and Precalculus

This session will address creative ways to assess students other than a traditional test.  Many assessment ideas can be modified or enhanced to reach different levels.  These assessments go beyond creating a poster.  Samples will be brought.  Please note, there is an overlap with some of the ideas discussed in the Assessment presentation last year.

Amanda Zielenkievicz – Ramapo Indian Hills Regional District
Using EDpuzzle (Free) to Flip or Blend Your Class

EDpuzzle.com (Free) allows you to upload your own videos or use existing online videos on their platform. You can use parts of a video, speak over the existing audio, add quizzes or notes, and monitor student progress. You can prevent students from skipping ahead in a video, and much more! Monitor student progress with adding quizzes and checkpoints into the video to gain data about student progress. Please come prepared with your laptop and a video that you would like to use as we begin to utilize all of the exciting features that are available on this wonderful resource!

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