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
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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.)
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.