# 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.)*

Linear Algebra is the study of multi-dimensional vector spaces using matrices. Emphasis is put on solving large systems of linear equations, and the theoretical implications of such. The course studies spaces closed under the operations of addition, and scalar multiplication, and begins the process of abstracting mathematical operations in order to extend simple mathematical concepts beyond the scope of the numerical systems most high school students are used to. (*Prerequisites: Honors Precalculus and departmental approval)*

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)*

This course serves as final trimester of AP Calculus, covering the topics on the AP BC exam that were not covered in AP Calculus AB.*(Prerequisites: AB Calculus)*

Abstract Algebra is the study of abstract mathematical structures which behave similarly to the number system students are typically used to, while also having novel characteristics. While many of the concepts in Abstract Algebra are relatively “simple,” because they often don’t have an obvious analog in day-to-day life they are theoretically rich and push students to think about the mathematics they are used to in different ways. *(Prerequisites: Honors Precalculus and departmental approval)*

While most high school students study Euclidean Geometry, few have the chance to study it in the way the Greeks did, building logical structures with nothing but a compass and straightedge. In this course, students will work through Euclid’s Elements, and see geometry as the incredible mental leap that it was in its original formulation.*(Prerequisites: Honors Precalculus and departmental approval)*

## Mathematics Faculty

**shifrinb@gouldacademy.org**

Mr. Shifrin teaches mathematics at Gould and lives on campus with his wife, Sara, their daughter, Mia ’19, and son, Eli ’23. As 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.

**blaussn@gouldacademy.org**

Mr. Blauss studied Mathematics and Physics at Colgate University and the University of Rochester, and has since taught both at a succession of schools. An avid outdoorsman, he has thru-hiked the Appalachian Trail, built a wooden sea kayak, spent a year as an outdoor educator at the Chewonki Foundation, 10+ seasons in the Appalachian Mountain Club’s Alpine Huts and Construction Crew, and spent many years working as a carpenter. He is willing to argue about almost anything. Having recently moved to Bethel with his wife, Elke (who teaches Biology at Telstar), he is consistently thrilled at the chance to learn something new about the world, and aspires to become his hero, Merlyn, from *The Once and Future King.*

**kramern@gouldacademy.org**

**zutshia@gouldacademy.org**

Mr. Zutshi teaches upper-level mathematics at Gould, including AP Calculus and AP Statistics. He is a dorm parent in Davidson Hall and is the advisor for both Model United Nations and Yearbook. He also coaches the Math Club Team in various regional and national math contests.

Prior to Gould, he ran his own tutoring business in Boston, specializing in test prep and mathematics, including college-level calculus and statistics. Before that, he had a career in law and in financial services, having worked as a corporate attorney and, prior to law school, an actuary.

Mr. Zutshi is a graduate of Belmont Hill near Boston. In college, he taught math for Belmont Hill’s summer school program, and later at a Mary Institute and St Louis Country Day School (MICDS) in Missouri, where he also coached wrestling and football.

He studied Applied Mathematics at Harvard and received his law degree from Washington University in St Louis. He joined the faculty at Gould in 2018.