Mathematics

We recognize that mathematics is a language shared by all civilizations and all populations regardless of culture, religion, or gender, and our programs are designed to improve every student's quantitative literacy. We aim to foster strong critical thinking and mathematical reasoning in our students, with the goal of teaching them to view the world through a mathematical lens.

Requirements. In Grades 9-12, three years of math, through the 11th grade and including Algebra II, are required for a York diploma. York’s requirement meets University of California admissions requirements, which include a provision that students must complete a geometry course. Any student who wishes to take a credit math course over the summer must receive permission from the Math Department Chair and the Director of Teaching & Learning.

Algebra I

Algebra is the base upon which nearly all of mathematics is built; it is a leap from arithmetic to abstract, defining the rules for the study of mathematical symbols and how to manipulate them. Taken seriously, this is every student’s first foray into quantitative thinking. Students will work to develop fluency in the language and application of algebraic definitions and procedures, using those skills to solve for unknowns in increasingly complex equations. Emphasis is placed on developing student understanding of linear relationships and their applications to the real world.
Algebra II

Students will study a variety of different functions (such as quadratic, exponential, rational, trigonometric, etc.) learning their properties and graphical behavior. They’ll discover how each function relates to practical applications, putting theory into practice via math labs. Although graphing calculators are incorporated to enhance the curriculum, the emphasis remains on the thought process and on understanding mathematical concepts.
AP Calculus AB

Students will continue their understanding of the mathematical contexts and concepts within calculus, namely the three big ideas of limits, derivatives, and integrals, with the addition of a fourth: series. The depth and breadth is equivalent to a second year of college-level calculus. The course will include all of the concepts and techniques that appear on the AP Calculus BC exam, and all students enrolled in the course will be expected to take this exam in May.
AP Calculus BC

Students will continue their understanding of the mathematical contexts and concepts within calculus, namely the three big ideas of limits, derivatives, and integrals, with the addition of a fourth: series. The depth and breadth is equivalent to a second year of college-level calculus. Specifically, this course will focus on drawing connections between verbal, graphical, numerical, and analytic representations of functions. This course is designed to assist students in developing strategies and techniques to solve a diverse set of application problems, and then evaluate the reasonableness of solutions. Students will be required to use proper notation and will be able to communicate effectively with their peers and with the mathematical community. Technology will be used regularly throughout the course, with a special emphasis on graphing calculators, as a way of investigating and analyzing functions to help students draw conclusions that would have been impossible or too time consuming without supporting technology. The course will include all of the concepts and techniques that appear on the AP Calculus BC exam, and all students enrolled in the course will be expected to take this exam in May. Testing throughout the year will be designed to help prepare the students for this exam.
AP Statistics

AP Statistics introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Examples are drawn from applications in the natural and social sciences. Students collaborate with their classmates to learn statistics by doing statistics via in-class activities and simulations, computer labs, and projects. Students will master four broad conceptual themes: (1) Exploring Data (analysis of data through the use of graphical and numerical techniques to study patterns and departures from patterns); (2) Sampling and Experimentation (planning and conducting a study); (3) Anticipating Patterns (exploring random phenomena using probability and simulation for anticipating what the distribution of data should look like under a given model); (4) Statistical Inference (estimating population parameters and testing hypotheses).

Statistics and AP Statistics meet concurrently and cover the same content at the same pace. The main differences between these courses are that AP Statistics students also complete several projects and take the AP Exam.
Calculus

This course meets concurrently with AP Calculus AB and introduces students to the basic concepts of differential and integral calculus. It is roughly equivalent to one semester of college calculus. Although this course is not aimed at preparing students for the AP exam in Calculus AB, the topics covered will be very similar, but the assignments are shorter and the tests are easier than the Calculus AB class.
Geometry

Geometry is the study of shape, and draws on the right side of the brain. The subject appeals to visual thinkers who might otherwise cringe at its logic, though many students love geometry precisely because it is so logical. Students learn important definitions, postulates, and theorems connected with Euclidean geometry and apply them to solve geometrical application problems. A balance is sought between an intuitive understanding of what is true, and the need for a thorough, careful, deductive reasoning about one’s perceptions. Students learn how to order their arguments in clear, precise language when writing their proofs of geometry theorems. Students will also develop spatial skills in two and three dimensions, and review their algebra skills throughout the course. Students work on group projects and utilize computer exploration.
Math Modeling

Offered in alternating years
The overall goal of this course is to enable students to build mathematical models of real-world systems, analyze them, and make predictions about the behavior of these systems. A variety of modeling techniques will be discussed with examples taken from physics, biology, chemistry, economics, social sciences, and other fields. Mathematical modeling uses graphical, numerical, symbolic, and other techniques to describe and explore real-world data and phenomena. Emphasis is on the use of elementary functions to investigate and analyze applied problems and questions, on the use of appropriate supporting technology (e.g., Microsoft Excel or Google Sheets, Python, and other software or programming languages), and on the effective communication of quantitative concepts and results through relevant projects and presentations. This course is not intended to be a prerequisite for Calculus, though it will introduce and help students understand the basic topics of differential and integral calculus through application. Likewise, the class can be a math elective for students seeking an additional math class, for those hoping to solidify math concepts through modeling applications, or both.
Pre-Calculus

This course combines advanced Algebra II skills with trigonometry, data analysis, vectors, and an introduction to Calculus. In addition to strengthening Algebra II skills and problem-solving strategies, students learn to apply concepts to real-world problems through mathematical modeling. While the emphasis is on honing algebraic and graphical analysis skills, the course makes extensive use of the graphing calculator. Many of the same topics will be covered as in the Pre-calculus Honors class, but not as rigorously and at a different pace.
Pre-Calculus Honors

Pre-calculus Honors reinforces and expands upon the concepts encountered in Algebra II in order to prepare students for success in Calculus. Students will learn how to describe both new and already familiar functions verbally, algebraically, graphically, and numerically. Students also will learn how to transform these functions in order to model real-world data. In addition, students become familiar with other coordinate systems and with the use of vectors to model physical quantities. Experience with proofs will strengthen students’ ability to make conjectures, construct logical arguments, and justify their reasoning. Pre-calculus Honors covers Pre-calculus topics in greater depth, and its scope is much broader and includes numerous abstract and challenging enrichment topics. As a result, Pre-calculus Honors is intended for students who have a strong interest and aptitude for math, and who are ready, willing, and able to do the work necessary to tackle demanding problems at an accelerated pace.

Faculty

Jeff Hanna

Math/Science Department Chair

jhanna@york.org
Bio
It is easy to see why students at York love Physics. Walk into Dr. Hanna’s room and you are immediately engulfed in art, algebraic analyses, and experiments in action (just watch out for the projectiles!). From building mouse-trap cars to calculating the i and j components of the path of an angry bird, Dr. Hanna finds interesting ways to connect with students and show them that physics applies to things they do every day.

Great teachers are, by nature, giving and Jeff gives freely of his time and energy. He is continuously finding innovative methods to introduce concepts. Then he readily shares them with his colleagues as well as students. After school he can be found discussing vectors while running dust trails with the cross country team or in the design shop helping students fine-tune a robot for the FIRST Robotics Competition. Dr. Hanna’s enthusiasm for physics and his dedication to ensuring that students understand and can apply the concepts keeps the students continuously engaged.

Jeff has always been curious about how and why things function. His career path was inspired by his physics teacher, Mr. Khan, who helped him see that physics can be used to explain almost everything. After spending his high school years in Dallas, Texas, where everything is big, Jeff applied to the School of Mines in Colorado.

There he learned to appreciate big ideas, as well as big mountains, while earning his Bachelors degree in Physics and a Masters degree in Systems Engineering. He continued his studies at Cal Tech in Pasadena completing a second Masters, then a PhD in mechanical engineering that was focused on fluid dynamics. Dr. Hanna completed a postdoctoral project in fuel cell design at MIT before coming back to California and joining the York faculty.

When he’s not teaching, Jeff spends as much time as he can outdoors. A dedicated scientist he is always observing and learning, including recently why and how to avoid poison oak. On a typical weekend you will find him trekking through the wilderness with his wife and dog.
Haley Halasz

Math/Science Department

hhalasz@york.org
Scot Johnson

Math/Science Department; 11th Grade Class Dean

scotjohnson@york.org
Bio
USN Commander Scot Johnson (Ret.) was born in Barcelona. At a very early age, he was taken by Viking pirates, and given to the Johnsons, a family of retired riders who had settled near Minneapolis. On its next trip, the pirate ship was lost at sea with all its crew, and the Johnson’s kept him with the hopes he would become a farmer. But the call of the sea could not be ignored! After graduating from the University of Minnesota with a BS in Physics (High Distinction), young Mr. Scot left the frozen but serene plains of the Midwest for a life of duty and adventure as an officer of the US Navy. For thirty years he sailed the tempestuous Seven Seas in service of his country. The waters of Hawaii, Germany, Italy, Greece, Djibouti, Oman, Kwajalein Atoll, and Diego Garcia, Australia, Japan, Kenya, Midway Island, the Philippines, Singapore, and Sri Lanka have been theater and witnesses of his exploits. However, he has privately confided to us that the time he spent in Rota (Cádiz, Spain) will always have a special place not only on his aeronautical career but, most importantly, in his heart. Flying with his Electronic Reconnaissance Squadron, Commander Johnson kept a vigilant eye on the southern flank of the North Atlantic Alliance (His other eye was busy watching the flanks of...*). Between missions, Commander Johnson would sometimes drive his battle tested Ford Fiesta a few (nautical) miles east by south east, to Cape Trafalgar. From the rail of the lighthouse, he would behold the waters in which that action was fought, lamenting, sometimes even cursing, the two centuries which deprived him of the glory of being part of the greatest naval battle that -not counting Lepanto- the world has seen or will ever see.

Back to the USA, Mr. Johnson used his highly prestigious Burke Scholarship to earn an MS in Electrical Engineering (High Distinction) at the NPS in Monterey, taught the same subject at the U.S. Naval Academy in Annapolis and even sailed schooners to Great Antilles. He also served as a project manager for avionic software development.

Upon retiring from the Navy, Mr. Johnson went back to Minneapolis where he worked as an information technology consultant for the private sector. After seven long winters, his crew, formed at the time by Mrs. Johnson, wife, little Kevin, son, and Serra, family dog, mutinied, traced a line on the ice, and demanded an immediate descent of the Johnson’s Armada to more humane latitudes, thus giving York School a rare, indeed unique, opportunity to enroll in its ranks a truly exceptional scholar and experienced educator. Under the York flag, Mr. Johnson has taught all levels of math and science, created calculus and statistics College Advanced Placement Courses, coached the JETS Engineering Club, participated on the Admissions Committee and lead the Safety Squadron Committee which performed with much distinction in the York School Evasive Action of October 14, 2013. He is also the 11th grade Dean.

Mr. Johnson is very fond of hiking, golfing and, if I understood him correctly, of a pair of famous twins from Minnesota.

In conclusion, Scot Johnson is, not only a courageous, resolute and expert seaman, but a man of great culture and the best of friends.

* The following words were censored by the U.S. Navy D.M.I
Kim Kiest

Math/Science Department; 10th Grade Class Dean

kkiest@york.org
Bio
To inspire young men to go into STEAM (Science, Technology, Engineering, Art, Math) fields, one needs dynamic, challenging teachers. To inspire young women to do so, one needs not only challenging teachers, but role models. Kim Kiest fits the bill across the board. A riveting storyteller, Kim makes it one of her goals to accumulate personal adventure tales to bring back to the classroom. She has literally searched high and low in her quest, SCUBA diving under the Antarctic ice and climbing Mount Kilimanjaro. Between those extremes, she has battled dengue fever in the tropics and whale lice in Baja California. If there is a country with endangered species, marine animals, or both, Kim has most likely been there to see them, photograph them, and, if at all possible, play with them. In fact, she has traveled to all seven continents, returning to write articles for scientific journals based on the research she has performed. Kim brings to her classroom an endless wealth of great stories, a Seussian sense of humor, and a profound level of care for her students; it is no wonder that so many York alumni return to tell her that she has inspired them to pursue a career in science. Kim was raised in and near Portland, Oregon, where she showed horses and did her best to live outside the box. She completed her Bachelor of Arts degree at Scripps College in Claremont and her graduate degree at San Jose State University, earning an Masters of Science degree in Marine Science through Moss Landing Marine Laboratories. In addition to specializing in environmental science, Kim has a Master Gardener certification. In her spare time, Kim collects Zuni fetish carvings, Native American jewelry, Dr. Seuss artwork, and stuffed replicas of bacteria and viruses. At York, Kim teaches Biology, Anatomy and Physiology, Marine Biology, and Environmental Science. In addition, she is the 10th Grade Class Dean, the Environmental Sustainability Coordinator, the Chair of the Discipline Committee, and the Faculty Representative to the Board of Trustees.
June Trachsel

Math/Science Department

jtrachsel@york.org
Bio
It’s early May and the York campus looks like it’s been invaded by a small band of Ninja warriors. No…. it’s actually Mrs. Trachsel’s Calculus AB class, each wearing a headband with an individually chosen Japanese name written in authentic Japanese hiragana. Mrs. Trachsel has spent a year equipping them with the tools they need to be successful on the upcoming AP exam, and now her final task is to give each one that last tangible boost of confidence in a way that is uniquely June Trachsel.

When you first meet her, it’s easy to see why she is a favorite among the York students. Underlying her kind, soft-spoken persona is a gifted educator who is passionate about cultivating a curiosity about mathematics, whether real or imaginary. She is always challenging her students with interesting, applicable math problems, and believes in a more interactive approach to teaching. Can you imagine using calculus to determine the volume of odd shaped serving bowls? Well, her students can! When you walk into her classroom, you will see counters and walls covered with beautiful projects like origami polyhedra or calculus volumes using cross sections that her students have produced as she provides them with the experiences that will encourage them to love math.

June Trachsel grew up in Santa Maria, California and credits a special high school math teacher as her inspiration for entering the teaching profession. She earned both her B.S. in mathematics and her teaching credential at Cal Poly San Luis Obispo. After student teaching at Lompoc High, she came to York in 1989 as a sabbatical replacement, and has been here ever since. She has taught every math course in the York curriculum except Calculus BC, and has even taught eight grade science. She has also served in many roles within the York community, including Math/Science Department Chair, Head of Student Council, Work Job Coordinator, member of the Curriculum Committee and Admission Committee, and Coordinator for Mathletics just to name a few. And when her daughter, Corinne, joined the York student body in 2012, she took on a new role as a York parent.

Outside of school, one of June’s special passions is yoga—she even put together a dedicated room in her home just for her yoga activities. But what’s really intriguing is the connection that June makes between math and yoga—she embraces the tradition and values that come from the rich history of each one, while at the same time, celebrating the ways that makes them so relevant and useful in today’s world. And just as she shares her love of mathematics with each of her students, she also shares her zeal for yoga, and many students look forward to the yoga Health & Fitness class that she teaches every year.

Since June and I are both women of Asian heritage teaching in the math department here at York (and some might add that we are both “vertically challenged”), we are often mistaken for each other. Well, I can think of no greater compliment than being mistaken for June Trachsel!
Kande Williston

Math/Science Department

kwilliston@york.org
Bio
uiding others with kindness and motherly concern is the major activity in Kande Williston’s busy day. Whether she is guiding an Algebra II class through a conic sections dance, student council organizing for Fall Fair, or her own children on an outdoor excursion, Kande will be setting clear boundaries for what needs to happen, and displaying the fun that is possible within those boundaries.

After earning a Bachelors degree at the University of British Columbia in Vancouver, Kande was first exposed to teaching while working as an instructor at a science camp on Catalina Island. From there, she went back to UBC and obtained a teaching credential, taught in Ghana for two years, then in Gibsons, British Columbia, finally arriving at York in 2002. With her sister living nearby, and her husband working in Moss Landing, Kande chose York as the place to put down roots and start a family.

As a teacher, Kande is constantly trying new approaches to the material she is covering. This can involve experimenting with online graphing programs, using motion sensors for math labs, and trying out the flipped classroom experience. Her classroom is seldom quiet as students are encouraged to ask questions, openly collaborate with each other, and, whenever possible, music is incorporated into lessons. Students in Geometry, Algebra II, and Chemistry are the ones most likely to experience these activities, but she has also taught Physical Science, and Algebra I.

Kande created and led a popular Ultimate Frisbee club earlier in her years at York, and has acted as the faculty advisor to the Student Council for over a decade. As half of York’s Canadian contingent (with Murray Walker), Kande continues to “mark” papers and ask students to “sit” for exams.

Mathematics

Faculty

York School