New Course of Studies Introduction

The new course of studies booklet was just printed. Here’s the new introduction to the Math Department’s section:

Mathematics is the language of the universe. It is everywhere, and every subject is permeated by mathematics. It is beautiful, logical, abstract, relevant, and practical. Furthermore, a background in mathematics can lead you just about anywhere. Math majors have chosen careers from law, medicine, computer science, and engineering to philosophy and the visual and performing arts. Increasingly, many more professions require knowledge of higher mathematics for full success.

The world of mathematics is full of breathtaking examples of elegant beauty, brought forth from the luminary minds of people such as Noether, Erdos, Newton, Escher, Turing, and Lovelace. The Williston Mathematics Department strives to expose all students to that beauty while also realizing that many, if not all, students will need mathematics for its practical applications. The students of today are entering a quantitative world that demands an understanding of our subject. Through their studies of mathematics and with the support of a dedicated faculty, Williston students at all levels build habits of mind that translate into the many other areas of life that require problem solving.

A defining characteristic of humanity is our curiosity, and through our study of mathematics we continue the perpetual journey of understanding our existence. Mathematics is the bridge between the arts and the sciences, and we believe that everyone can find joy in mathematics.

The primary goal of Williston’s Math Department is to help prepare students for college mathematics. The course sequence—Algebra I, Geometry, Algebra II—teaches the foundation of mathematics that all students need. Once they have mastered the foundation, students can delve more deeply into mathematics through a variety of upper-level courses. While the content of these courses varies, the primary goal of each course is the same: to help students become more successful problem solvers.

In addition to different course options, students will encounter various tools and learning situations. Sometimes students will use computers to explore mathematics, or calculators to assist with graphing and computation. Students taking Geometry will participate in laboratories designed to provide time for extended work. At other times students will work in small groups to investigate a topic. All of these experiences encourage a flexible approach to mathematics.

Whether students dislike math or enjoy puzzle-thinking, have strong backgrounds or weak ones, they will find teachers dedicated to supporting their efforts to become better problem solvers. Each course offers the opportunity to review basic skills and to master the core knowledge of the subject. Students are challenged to move beyond memorized rules to discover the source of rules, to examine why they work, and to theorize about how they are used to solve problems.

As Roger Bacon proclaims, mathematics is a gateway. Like most gates it must be unlocked; and one cannot be pushed through it but must enter with one’s own effort.

Squares, Cubes, and Alpha Centauri

I love all kinds of space.

The space in front of me:

The student who sends me the best solution to this problem by 4/29 will get $50. The only requirement is that your solution must be in video form.

Can you fill a cube with a finite
number of cubes of all different sizes?

The space above be:

Last week we were 70,000 years away from the nearest star system to our own, Alpha Centauri. Today we are 20 years away. Learn more here.

The space all around me:

Next year I will be leading a spring break trip to New Zealand. Applications are due by Monday, May 2nd. Complete trip information is online at


US Mathematics Students of the Trimester – Winter 2016

I am excited to announce a new award, the Upper School Mathematics Students of the Trimester!


You can watch a video of the presentation right here.

Each math faculty member was free to choose whichever student of theirs they thought best exemplified what they are looking for in a model mathematics student. The official description of the award is as follows:

“Awarded to students who exemplify the math department’s core values of competence, confidence, and perseverance while helping their peers realize the relevance and importance of an exceptional mathematical education both for its beauty and for its practical application.”

The following students have been recognized as the Upper School Mathematics Students of the Trimester for Winter 2016.

Please join me in congratulating these outstanding mathematics students!

Bernstein,-ZachZach Bernstein – Zach has always been a strong student, but during the second trimester he rose to new heights, completely dominating every topic we encountered. His command of the material has been impressive. I have relied on him to answer difficult questions, and also to lead with his quiet presence. Zach is humble, never calling attention to himself, but he’s always ready to lend a helping hand to his fellow students. Great work Zach!
Bradway,-EthanEthan Bradway – Ethan made such incredibly progress in the winter term, and so much of that progress was due to his fantastic work ethic and careful preparation. His verbal reasoning ability improved by a huge margin from where it was in the fall, and Ethan’s determination to succeed was self-evident. It was a huge pleasure to watch Ethan’s growth as a math student this past winter.
Fokas,-WillWill Fokas – Will has worked hard for the entire year in pre-calculus so far. He makes a wonderful math student of the trimester due to the effort he puts in both inside and outside of class. Outside of class he is dedicated improving his math skills by regular practice. During class Will is a leader. He volunteers to answer questions, show work on the board, and is always helping his classmates when they get stuck. He is not afraid to answer challenging questions and contributes great ideas to class discussions.
Harris,-ChloeChloe Harris – Chloe has demonstrated a relentless effort to understand the concepts in Trigonometry, Probability and Statistics. She is motivated to achieve mastery of the content regardless of the difficulty level. Chloe relies on solid study habits and, at the same time, continues to build her problem solving strategies and organization techniques. It has been great to see her progress and wonderful to have her positive influence in the classroom. [2nd time winner!]
Hill,-RobbyRobby Hill – Robby has been a consistent leader in the class. Not only does Robby ask insightful questions, but he pushes his classmates to also examine the material in more depth. Robby has proven himself a very capable mathematician. [2nd time winner!]
Iwama,-FukaFuka Iwama – Fuka’s quiet determination is apparent every day. I look forward to grading her homework because it is always completed with detail and care, showing her desire to understand concepts deeply. She takes the time to connect concepts, writing notes revealing her thought processes as she works her way through the solution of a problem. Her presentations of her solutions are well-organized and quite beautiful! Her dedication to gaining a strong understanding of the theory behind the content is just as apparent in class as she shares her ideas and questions her peers, pushing herself and them to defend the reasoning behind their thoughts. As seen by her face lighting up in class, Fuka finds joy in studying and gaining insight into mathematical mysteries, the best reward for her dedicated work!
Ramirez,-ChrisChris Ramirez – Chris had a fantastic trimester in the Algebra II classroom. He is a dynamic learner who is quick to volunteer answers to the most challenging questions. He easily infers previously learned material into new concepts and enthusiastically ties concepts together. His written work is excellent. It demonstrates the depth of his knowledge as well as his ability to work with great accuracy. His 98 on the trimester 2 assessment was outstanding work!
Robbins,-ZazhZack Robbins – Zack is a leader in our Precalculus class. He pushes himself to understand the most difficult material in the class and is always eager to explain his thought process to his peers. He helps create a dynamic learning environment. It has been a pleasure working with Zack this year.
Soley,-MayaMaya Soley – Maya exemplified preparation, passion, dedication, creativity, and positive contribution to the class experience in Video Game Programming and Design. The competency she built through her meticulous completion of classwork enabled her to execute complex and interesting original game designs that will raise the bar for future sections of this class.
Triana,-SofiaSofia Triana – TSofia made a remarkable effort this trimester in Calculus. While she struggled with the material in the first trimester, Sofia worked steadily to master both the material that had been a challenge and the new material. Because of her careful preparation for class along with attentive participation in class and coming for extra help, Sofia moved to producing honors level work. I look forward to her great work in the spring trimester!
Zawacki,-MollyMolly Zawacki – During the second trimester, the topics in AP Computer Science have presented a challenge to all students. Among these topics are polymorphic methods, interfaces, and the theory of inheritance among super-classes and sub-classes. Throughout these topic explorations, Molly has demonstrated the ability to quickly understand and deftly apply these concepts in programs and assessments. She is well on her way to studying Computer Science at the college level. Congratulations Molly! [4th time winner!]
Zhao,-DerrickDerrick Zhao – Derrick has been a consistently strong AP Calculus student all year long. Derrick has the ability to learn material very quickly. He also is able to apply what he has learned to help him figure out new and more complicated problems on his own.

Past students of the trimester can be found right here: Fall 2013, Winter 2014, Spring 2014, Fall 2014, Winter 2015, Spring 2015, Fall 2015