## What Mathematics Should Be

Developing mathematical literacy is an explorative, dynamic and creative process essential to making informed decisions in an ever-changing world. You will work collaboratively as you focus on developing mathematical reasoning in order to become a critical thinker and an adaptable problem solver. Our foundational courses focus on algebra, geometry, trigonometry, and data analysis.

By applying your mathematical knowledge and strategies to real life situations, you will be prepared to meet the demands of college and the challenges that lie beyond.

## Mathematics Curriculum

### List of 12 items.

• #### Math 1: An Intro to the Language of Mathematics

“The Universe is a grand book which cannot be read until one first learns to comprehend the language and become familiar with the characters in which it is composed. It is written in the language of mathematics.” --Galileo

How does the language of mathematics aid us in our problem-solving? You will develop a foundation in the language of mathematics and learn expedient algebraic pathways to solving real-world problems involving linear and exponential growth. Unlock the mystery of this language by translating words into symbols and problems into “puzzles” that are solved with the laws of mathematics. Your teacher will guide you and your group through instructional activities that gradually reveal “clues'' to unraveling the algebraic query of the day. You will strategize together by approaching the problem from the different vantage points that each student brings to the work.

Experience the satisfaction of a “team” tackling a challenge and succeeding, as well as the confidence built by independently solving problems through your own hard work and perseverance. You will see how systems of linear equations can be used in the debate about minimum wage, explore foundational concepts of functions with the decoding of encrypted messages, and examine human population growth and its impact on the environment with exponential functions. Algebra, or “al-jabr”, means the “reunion of broken parts’. This is exactly what we will do together in Math 1 by using the laws of mathematics to unite seemingly disjointed quantities in our constant quest to understand the universe.
• #### Math 2: Studying Spatial Relations Through Mathematical Reasoning

“Geometry will draw the soul towards truth.” --Plato

How does geometry draw the soul towards truth? Why did Abraham Lincoln in preparation for a career in law study one of the oldest text books in existence, The Elements, written in 300 B.C. by Euclid, the father of geometry? In your Math 2 class, you will discover the answers to these questions, among many others. When studying geometry, you will not only examine the spatial relations that dictate the laws of the universe, you will also develop the deductive reasoning skill necessary to prove that a conjecture is indisputably true, a skill that one can transfer to any discipline, as Lincoln demonstrated.

Working collaboratively with your peers, you will be guided through investigations that unveil structures and relationships among figures in two dimensional and three dimensional space. You will strategize together by approaching the problem from the varying vantage points that each individual brings to their work. What begins as an inquiry into an elementary concept--such as the sum of angles in a triangle equaling 180 degrees--evolves into a discussion of curved space and Einstein’s Theory of Relativity. Learn how early geometers measured the height of a pyramid and the distance to the moon. Experience the present-day utility of right triangle trigonometry in the building of ADA access ramps or in the designing of environmentally safe urban centers of the future. Join us in our Math 2 course and witness the magic of geometry in real-life application while always reaching into our algebraic toolkit to aid us in our problem-solving.
• #### Math 3: Building Fluency in the Language of Mathematics

“Algebra is nothing more than geometry, in words; geometry is nothing more than algebra, in pictures.” --Sophie Germain

The words of 18th century mathematician, Sophie Germain, reveals the interconnectedness of the two disciplines. In Your Math 3 course, armed with a strong foundation in geometry, you will further your understanding of algebraic laws in the context of several settings and with access to more mathematical tools. You will join your fellow students in the investigation and comparison of models of growth, from linear to polynomial to exponential and to logarithmic. Indirect variation and rational functions play a large part as we delve into the effective population of the Southern Elephant Seal.

Whether you are collaborating on a carbon-dating project to determine the age of fossil remains or studying the growth of a pandemic, you will view problems from the varying vantage points of different individuals and be an active member of a team working towards a single goal. Independent work will allow you to exercise the resilience and perseverance developed in your earlier years of mathematical study. You will revisit trigonometry, but not as a set of ratios in a right triangle, but as a function that models the periodic nature of much in the world around us. Math 3 will provide the tools needed to investigate further and in much greater depth the functions that you will see in pre-calculus as preparation for the study of Calculus.
• #### Math 3/Pre-Calculus: Navigating the Complex World of Functions

“We need to replace the idea that learning ability is fixed with the recognition that we are all on a growth journey.”--Jo Boaler

Students come to Drew in various stages of mathematical maturity and they may accelerate at any time in their progressive development of concepts, skills, knowledge and understanding in solving mathematical problems. As a result, Drew offers a condensed, one year course that covers the material in the two years of the Math 3 and Precalculus courses. This course keeps up a very rapid pace throughout the year and is designed for those students entering Drew in Math 1 and who demonstrate a fine mathematical understanding of abstract concepts throughout their first two years at Drew.

Moving quickly through material and in greater depth, you will challenge yourself and further cement your love of mathematics. Investigate functions that describe our world, from modeling the geography of land with polynomials to comparing the exponential growth of viruses to examining the periodic nature of coastal tides with trigonometry. All the while, you will simultaneously master advanced algebraic techniques for challenging problem-solving. The course prepares students for the study of calculus in their fourth year at Drew and is designed for those students who are interested in further study in mathematics and the physical sciences. The Math 3/Pre-Calculus student possesses algebraic fluency and the ability to digest abstract concepts quickly and thoroughly. This student is an independent, self-regulated and resilient student who has previously demonstrated excellence in the learning of mathematics.

Prerequisite: An “A” average in Math 1 and Math 2, placement test and teacher recommendation.
• #### Precalculus: Modeling the World with Function

“As long as algebra and geometry have been separated, their progress has been slow and their uses limited; but when these two sciences have been united, they have lent each mutual force, and have marched together towards perfection.” --Joseph-Louis Lagrange

When Rene Descartes, a 17th century French mathematician, scientist, and philosopher, devised the first link between Geometry and Algebra, he revolutionized mathematics by paving the path to Calculus. In Precalculus, you will follow Descartes’ lead and delve deeper into the study of functions, the relations that make the mathematical world “go round”. We can describe functions in four ways, but it is the graphical representation of these relations that allows us to investigate more effectively their behaviors as well as their transformations. After having acquired the algebraic skills necessary to manipulate mathematical symbols in Math 3, you will investigate the interplay between curves on a coordinate plane and the algebraic symbols that represent them. You will join your peers working together to explore the use of functions in modeling real-world situations in your quest to view the world through a mathematical lens. See a sinusoidal function demonstrating the movement of our oceans or an exponential function revealing the harrowing nature of radioactive decay as well as the rapid growth of a pandemic.

You will understand how mathematics is the “handmaiden” to the sciences as you work collaboratively in the completion of a “team” task. Celebrate your team’s joint success in problem-solving, as well as bask in the satisfaction of working independently with solid perseverance and resilience. You will do all this in your preparation for the study of one of mathematics’ most beautiful accomplishments - Calculus.

Prerequisite: Math 3
• #### An Introduction to Data Analysis: Big Data!

“Data has become a torrent flowing into every area of the global economy.” --McKinsey Global Initiative Report on Big Data

From the medical world to the world of scientific research, from satellites orbiting the globe to social network sites like Facebook or Instagram, from polling centers to United Nations commissions, data is being collected everywhere and all the time. An Introduction to Data Science teaches you to think critically about and with data. This course is a dynamic computation-based statistics and probability course that better prepares you for college and the job force.

By developing quantitative critical thinking skills, you will become a more informed participant in our modern democracy. You will engage with real data by learning the statistical, computational and graphical tools for reasoning about the world. By examining data from various sources, you will collaborate with your peers in creating hypotheses and fitting mathematical models to data. Together, you will work with algorithms to evaluate how well these models mirror reality while learning to program with data through R, an open-source programming language used in statistics. Join your peers in an inquiry-based course while engaging in a very diverse collection of relevant and authentic activities.

Prerequisites: Math 1 and Math 2
(This course is designed for students desiring an alternative to Math 3 that is validated by the University of California A-G math course requirements. This excellent option can be taken after Math 1 and Math 2 and in place of Math 3)
• #### Finite Math for Social Justice

“All students need to be able to use math as a window to see the world, and a mirror to see themselves and their experiences, their communities.”  -Robert Berry, NCTM past president

How can students recognize the power of mathematics as a tool for changing the world?  In this course, math is not a set of “rules” to be memorized in order to find answers to problems without connections to their lives. The purpose of the course is to give a survey of mathematical analysis techniques used to shed light on social issues confronting our present day society and to provide insight when seeking solutions to social injustice. You will work collaboratively to understand how true mortality rates from Hurricane Maria were estimated when only sixty-four were reported. How does an understanding of mathematics provide insight into the CDC’s precautionary constraints in the time of COVID? Incarceration rates among diverse segments of the population become more than just mere numbers. In this course you will gain understanding into how these rates are computed and what the implications have on our society. This course is for students who desire to use their math literacy to further broaden their vision of the world and inturn provide steps along the pathway to solving the problems of social injustice.

Prerequisites:  Math 3 or Introduction to Data Analysis.
• #### Statistics Honors: Modeling for Prediction

“The key is in remembering that a model is a tool to help us understand the complexities of the universe, and never a substitute for the universe itself.”--Nate Silver

How can we make informed inferences and accurate predictions using the tools of mathematics? Knowledge of statistics provides you with the necessary tools and conceptual foundations in quantitative reasoning to extract information intelligently from an abundance of data. In collaboration with your peers, you will investigate ways to depict data in an accessible and effective way, one which provides a clear mathematical snapshot of events. Learn the laws of chance as you delve into a study of probability, work on teams in your exploration of various statistical techniques of sampling and experimentation. Together you will enter the world of inferential statistics and begin to use statistical tools to make inferences with a heightened level of accuracy. You will measure the “significance” of various hypotheses regarding health, economics, politics, and sports, thereby paving the pathway to statistical prediction. Enjoy the collaboration of a team working together towards the solution to a messy problem, as well as the satisfaction of working independently, practicing perseverance and resilience in your quest for an elegant solution.

This course is designed for students who enjoy the challenge of a rigorous math course that is steeped in application and provides insight into the complexity of data analysis. Since the course is the application of statistical methods in the real world, the ideal student is proficient at comprehending word problems and possesses strong algebraic fluency. They are independent and resourceful critical thinkers who have demonstrated excellence in the study of mathematics.

Prerequisites: An “A” in Math 3 and Teacher Recommendation
• #### Calculus Honors: The Study of Change

“As its campfires glow against the dark, every culture tells stories to itself about how the gods lit up the morning sky and set the wheel of being into motion. The great scientific culture of the West--our culture--is no exception. The calculus is the story this world first told itself as it became the modern world.” --David Berlinski

How can the study of change lead to advancements in our understanding of the natural and physical world? You will answer this by delving deep into differential calculus as well as studying net change, area, and volume with integral calculus. The notion of a limit in a most fundamental sense forms the foundation of calculus. You will experience this mathematical mystery as it unveils the secrets of the infinitesimally small with respect to rate of change at a precise moment in time. Throughout this course, you will witness the historical movement from the static world of geometry to the dynamic world of calculus, which hallmarked The Age of Enlightenment.

Through both collaborative initiatives and independent study, you will investigate the spread of an Atlantic oil spill as its size increases over time, the amount of medication remaining in the bloodstream at an instant, or the exact moment when profit is at its maximum. All this is “the calculus”--and much more--as we continue our task of modeling the world with mathematics.

This course provides a rigorous, in-depth study of calculus on an honors level and is designed for students who are interested in studying mathematics in college as either a major or prerequisite for further studies in the sciences. The ideal Calculus Honors student has a passion for mathematics, a curiosity about the unknown and seeks out a rewarding challenge in math class. This student possesses keen mathematical insight, seeing patterns and making connections on an abstract level. The highly conceptual comes natural to the calculus student as does a fluency in algebraic skills. They are self-motivated, independent and resilient learners.

Prerequisite: an “A” average in Precalculus or Math 3/ Pre-calculus and recommendation of the department.
• #### Calculus Lab: Investigations & Applications

“The only constant in life is change.” --Heraclitus

How does the beauty of this dynamic branch of mathematics resonate in the world around us? How does it help us to make sense of motion and change, as witnessed in the orbits of planets, the behavior of fluids, or the profit analysis of goods? You will discover the foundational concepts of the mathematical study of change by working collaboratively with your peers to unveil the mystery of calculus. The emphasis on this course is in the “doing” of mathematics in the sense that it will be through activity and investigation that you become acquainted with these concepts. Moving from the conceptual to the concrete, you will work collaboratively to begin to use the tools of calculus to help model real-life problems from population growth to climate change to poverty and beyond. This is an introductory course for those students interested in studying science or mathematics. It provides a glimpse into the elegance and utility of calculus without the rigor of an advanced mathematics course.

Prerequisites: Pre-calculus
• #### Programming 1: An Introduction to Programming

If you are interested in getting started with a STEM field, this course is designed for you regardless of your programming skill. Using the Processing programming language, the course will introduce you to the fundamental concepts of programming and Computer Science.

Processing is designed for artists, designers, and game developers to create visual and interactive programs that include video games, data visualization, and digital artwork. Thus, all of your programs will be grounded in creating those same types of programs. The course will delve deeply into problem-solving building on your computational and abstraction skills, and you will learn the basics of Object-Oriented Programming.

Topics include data types, conditional structures, methods, arrays, objects and classes. You will engage in group lessons to get introduced to new concepts and then work independently in small groups through completing programming challenges in class. The goal of the class is to master the basics of programming along with gaining understanding of how computers work.
• #### Programming 2

Once you have mastered the concepts introduced in Programming 1, this class builds on those lessons and introduces new ones. Continuing with the Processing programming language, you will engage in larger projects with a full software development cycle - design, test, and iterate.

Larger projects require greater planning, so you will also be introduced to design concepts that will guide your development process. Programming topics include multi-dimensional arrays, switch statements, advanced geometry, and animating sprites. Focusing on project-based learning, the course will be broken down into several programming projects. Projects will range from video games to data visualization to digital artwork.

You will engage in group lessons to introduce new concepts and work on short practice exercises in small groups. The course’s emphasis will be on independent projects that are to be completed in and outside of class. The goal for the course is to advance your programming skills and knowledge by building meaningful and relevant projects.

Prerequisites: Programming 1 or by Teacher/Department Head permission. (Students must have a basic understanding of Object-Oriented Programming

### List of 5 members.

• #### Ms. Marian Ferrara

Mathematics Faculty
415.409.3739 x3761
• #### Emma Woods

Mathematics Department Chair
415.409.3739 x3729
• #### Mr. Michael Henley

Math Faculty
415.409.3739 x3745
• #### Carolynn Jimenez

Mathematics Faculty
415.409.3739 x3754

Mathematics Faculty
415.409.3739 x3762