# Mathematics

At Gould, our students work with faculty and use mathematics to find patterns and solve problems. Of course, true to our commitment to experiential learning, these truths are found in traditional classroom settings as well as on playing fields and mountains, in labs, and in the Marlon Family IDEAS Center where our student tutors host weekly Mathematics Help Center sessions.

## Mathematics Departmental Requirements

*Three years to include completion of courses equivalent to Algebra 1, Geometry, and Algebra 2. The TI-84 Plus calculator is required for ALL math students at Gould Academy.*

## Mathematics Courses Include:

This first year course covers such topics as algebraic expressions, linear equations, systems of equations, quadratics, and the introduction of functions. Emphasis is placed on learning algebraic skills and developing a deeper conceptual understanding of the material through problem solving and applications. Use of the TI-84 graphing calculator is introduced.

This course is an exploration of geometric concepts covering parallel theory, similarity, congruence, and properties and attributes of angles, triangles, polygons, and circles. Proof writing and algebraic skills are learned and practiced throughout the year. Real world applications and online manipulatives help students to explore and gain a deeper understanding of the geometric world. *(Prerequisite: Algebra 1)*

Functions are explored and serve as a common domain throughout this course. Working with linear, quadratic, polynomial, exponential, and logarithmic functions, new skills are learned and applied to a variety of real world situations. TI-84 calculators are used extensively to illustrate the functions graphically and to provide a visual representation for problem solving. Students are challenged to apply their skills and demonstrate their understanding both orally and in writing. *(Prerequisite: Geometry)*

This is a rigorous Algebra II course designed for students who have strong algebraic skills, the capacity to work both independently and collaboratively, and the ability and desire to work towards Honors Precalculus and AP calculus. New algebraic skills are attained through the exploration of functions including, linear, quadratic, polynomial, exponential, logarithmic, and trigonometric. Students enrolled in this course are required to maintain at least a B average. *(Prerequisite: Geometry and a strong Algebra 1 background)*

This course will extend the study of functions from Algebra II for those students preparing for a regular calculus course. Exponential, logarithmic, rational, and trigonometric functions will be explored. Also included with the trigonometry will be the unit circle and laws applied to triangle measurement. Applications and modeling are integrated into this skills-based course and there is extensive use of the TI-84 graphing calculator. *(Prerequisite: Algebra 2)*

This rigorous course is designed for students who are planning to take a college-level Calculus course. Strong computational skills are required, as well as an ability to think and work abstractly to solve problems. A variety of concepts and tools from both this and previous courses will be used to solve multi-step problems. Inverse, trigonometric and rational functions are some of the topics that will be explored. *(Prerequisite: Honors Algebra 2 and/or departmental approval)*

This course extends the concepts of precalculus and introduces the techniques of calculus, including limits, continuity, differentiation, and integration. Students use geometric, algebraic and trigonometric concepts to investigate real world applications. The course prepares students for a rigorous college calculus course and course content is reflected in topics studied in AP Physics. *(Prerequisite: Precalculus)*

This is a college-level, high intensity class that serves a twofold purpose: to prepare the students to take the Calculus AB Advanced Placement Exam in the Spring and to provide the calculus tools to students concurrently registered in AP Physics. The class will be taught at a relatively quick pace and the material will be covered in depth. Proofs of basic results from Calculus will be covered throughout the year. A graphing calculator will be used in the class to help students visualize and better understand the functions commonly used in Calculus. Students are expected to take the AP exam. *(Prerequisite: Honors Precalculus with an 85 average or better.)*

This is a college-level course that covers the four major areas typically included in a statistics course. Students will be introduced to the four broad conceptual themes: exploring data, sampling and experimentation, anticipating patterns, and statistical inference. Students are expected to take the AP exam. *(Prerequisite: Algebra 2 or above and departmental approval.)*

Students in Honors Senior Math will get a taste of the concepts from higher level mathematics, including logic, set theory, and number theory during the fall trimester. The emphasis will be on understanding the abstract concepts and learning to write clear and efficient proofs. During the winter and spring terms, the class will switch gears in order to prepare the students for the Calculus BC Advanced Placement Exam. Topics that will be covered include parametric and polar graphing, sequences and series, and advanced integration techniques. The graphing calculator will be used to assist students in preparing for the AP exam. *(Prerequisite: AP Calculus)*

Students will explore practical mathematical concepts relating to financial planning, money management, growing and protecting personal wealth, and will evaluate the risks and benefits associated with loans and investment instruments. The fundamental mathematical concepts students will apply include quantitative analysis, problem solving and linear algebra. Students will use spreadsheets to solve real-world problems involving the analysis and synthesis of data and formulas related to compound interest, cash-flow statements, budgets, credit cards and loans, financial aid, and will participate in a stock market game. The fall trimester will focus on financial planning and money management. The winter trimester will focus on income and asset protection. The spring trimester will focus on investing and personal wealth. This course is designed as a three-trimester sequence that can be taken for one, two, or all three terms. *(Prerequisite: Algebra 2)*

In this spring trimester course students will learn to analyze a variety of static structures, including pulleys and trusses. Through the proper use of free body diagrams students will master the ability to determine the stresses applied to these structures. They will also learn to determine where the center of mass is for basic and complex geometric objects. Homework and projects will include building and analyzing their own structures. *(Prerequisite: Algebra 2)*

Dynamic Functions will be a Geogebra based course designed to deepen students’ understandings of functions and their graphs. Students will be taught how to use the free online graphing program, and will work with Geogebra to solve a variety of tasks involving polynomial, exponential and trigonometric functions. The course will culminate with students making a math movie using Geogebra, demonstrating their understanding of function manipulation and movement. *(Prerequisite: Algebra 2)*

This course is designed to teach and develop mathematical problem solving skills and quantitative reasoning through non-traditional problems. Students are encouraged to collaborate, use the white-boards to draw pictures, and use manipulatives to attack a wide variety of problems. They learn different ways of approaching problems which can then be applied to anything from solving traditional math problems, to “real world” tasks. The text, *Crossing the River with Dogs*, was designed to “promote(s) the philosophy that students learn best by working in groups and the skills required for real workplace problem solving are those skills of collaboration. The text aims to improve students writing, oral communication, and collaboration skills while teaching mathematical problem-solving strategies.” *(Prerequisite: Algebra 2)*

## Mathematics Faculty

**alforda@gouldacademy.org**

Ms. Alford has been teaching in the mathematics department at Gould for more than 20 years. Before arriving at Gould, she spent a year in Tel Aviv, Israel, traveling, studying, and teaching vector calculus at Tel Aviv University under a program run by the University of New Haven. A passionate world traveler, Ms. Alford spent the 2009-10 school year teaching mathematics for School Year Abroad in Zaragoza, Spain. Her many passions include reading, baking, traveling, kayaking, hiking, and spending time with her husband, Doug, and their two children, Ben ’18 and Chaia.

**shifrinb@gouldacademy.org**

Mr. Shifrin teaches mathematics at Gould and lives on campus with his wife, Ms. Sara Shifrin, Director of the IDEAS Center, their daughter, Mia ’19, and son, Eli. As the Director of the Ninth Grade Program, he has created and implemented a program that enables each ninth-grade student to transition to Gould life and become a valued member of the community. Each student is recognized by students and faculty for who he or she is and who they want to become. As an experienced mathematics educator, Mr. Shifrin developed his own algebra utilizing an online content presenter, Heymath, to create a course of study that allows each student to learn at a pace and level that best suits their ability and need. He has also developed a course on financial literacy for seniors called Mathematics of Finance that integrates the principles of personal finance and mathematics to help students evaluate and make informed financial decisions. Mr. Shifrin has a great interest in the outdoors and utilizing experiential educational opportunities to help students understand how an individual can grow and impact a group. Outside of the classroom, Mr. Shifrin is passionate about soccer, holding a National B License from the United States Soccer Federation, which he used to coach at an elite level within the Olympic Development Program in Maine and New England.

**whittinm@gouldacademy.org**

Mrs. Whittington has more than 30 years of experience teaching mathematics in independent schools, almost 20 of them as Dean of Students. She embraces the values of the seven-day boarding school and brings those values into the classroom and dormitories and onto the playing fields. As the Director of International Student Programs, she works to strengthen and expand Gould’s global community. She works with the faculty to support the international students during their transition into the community and throughout their Gould experience. Ms. Whittington has coached field hockey and lacrosse during the course of her career at the Nichols School, Westminster School, Vermont Academy, Yale University, and Harvard University. As an experienced player, she enjoys coaching and sharing her passion for both sports. “Ms. Whit” and her husband, Mr. Tom Whittington, Dean of Academics, enjoy traveling on their own and with the 9th grade Four Point Program. Two of her favorite pastimes are bread baking and biking!