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Mathematics

The CATS Academy Math Department is comprised of eight teachers who offer a wide range of exciting and challenging courses. Our teachers pride themselves on reaching all levels of math learners through engaging lessons, projects and hands-on learning.

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  • Worcester Polytechnic Institute Math Competition
  • Worcester Polytechnic Institute Math Competition
  • Talk on campus from Mira Bernstein on math and gerrymandering

Mathematics electives

CATS Extra: Integrated Mathematics

Building on the math knowledge that CATS Extra students already have, Integrated Mathematics advances students’ math knowledge in the areas of geometry, algebra, trigonometry, discrete mathematics, and probability and statistics.  The theme of the course is patterns. Students create, model, analyze, and explain the different patterns that occur in each of the math disciplines.  Connections are explored between the different areas of mathematics so that students understand how each can be represented as a data table, equation, picture, and description.  Students complete projects throughout the year to demonstrate their understanding of the concepts. In this way, students expand their mathematical vocabulary and communication skills while furthering their study of mathematics.

Integrated Mathematics I

In this course, students study the foundations of Algebra and Geometry. Students build an understanding of variables, expressions, and equations. They learn to write and solve linear equations and then apply equations to angles, triangles, and polygons in Geometry. Students learn to work with equations of lines and segments on the coordinate plane, as well as solve systems of equations using various methods. Students also explore basic statistics.

Integrated Mathematics II

In this course, students continue their study of Algebra and Geometry, completing the second semester of each subject. Students study similarity, right triangles, trigonometry, area, and volume. They also study exponents, quadratic functions, and polynomials. Students continue their study of statistics, including probability, and explore patterns and sequences as well. Prerequisites: Integrated Math I or Placement Test

Geometry College Prep

In this course, students explore shapes and their relationships to the two and three-dimensional world. Topics include triangles, quadrilaterals, polygons, circles, area, volume, congruency, similarity, and trigonometry.  Students pay particular attention to measurements and calculations of real world applications. This course also further develops students’ algebraic skills as students apply their Algebra I knowledge to geometric concepts.

Geometry Honors

The Geometry Honors course covers the same material as the Geometry CP course but moves at a faster pace and introduces additional topics. There is an increased emphasis on formal geometric proofs and logic. Theorems, postulates, and axioms are discovered and applied to proving why other concepts are true.  Prerequisites: B+ or better in Algebra I and recommendation of teacher. ESL Level 3 or higher.

Algebra II College Prep

This course builds on what students have learned in Algebra I. Students in the course develop advanced algebra skills such as solving systems of equations, factoring advanced polynomials, and understanding imaginary and complex numbers. Students also study matrices, rational functions, and conic sections. The focus for all of the topics is on problem-solving and developing formal mathematical language in English. The mathematical training in this course is important as preparation for the ACT and SAT, as well as future courses in Pre-calculus and Calculus. The text for the course is Big Ideas Math: Algebra II, and the course makes use of the TI-84 graphing calculator. Prerequisites: Successful completion of Algebra I and Geometry

Algebra II Honors

The Honors Algebra II course covers the same material as the Algebra II College Prep class, but moves at a faster pace and covers additional topics. As Honors students, you will receive more challenging assignments and projects, with the goal of developing your critical thinking skills and formal mathematical thought processes. Prerequisite: Returning students: Recommendation of current math teacher; New students: Placement test results.

Pre-Calculus College Prep

This course provides students with the skills they need to study calculus. It highlights the key methods from algebra, trigonometry, and geometry that are needed for further study. The central unifying concept is the mathematical function. The course focuses on both conceptual understanding and problem solving ability and provides students with a deep understanding of exponential, logarithmic, polynomial, rational, and inverse functions.  It also offers an introduction to sequences and series. The textbook for the course is Functions Modeling Change: A Preparation for Calculus 5th ed. by Connally et. al., and the course makes extensive use of the TI-84 graphing calculator. Prerequisite: Successful completion of Algebra II

Pre-Calculus Honors

The Honors Pre-Calculus class covers the same material as the College Prep class but moves at a faster pace and covers additional material as a preview of calculus. Some additional topics include polar functions, sequences and series, and an introduction to limits and derivatives. Honors students also receive more challenging assignments and projects with the goal of further developing their critical thinking and logic skills and keeping them fully engaged. Prerequisites: Returning students: A- or higher in Algebra II College Prep; B or higher in Algebra II Honors; ESL Level 3 or higher; recommendation of previous instructor. New students: ESL Level 3; successful completion of Algebra II; placement test results.

Discrete Mathematics College Prep

Discrete Math utilizes a first year college textbook and provides an introduction to a survey of topics in mathematics, including problem solving, set theory, logic, number theory, probability, statistics, and graph theory. Students have not previously had the opportunity to study this content in the Algebra, Geometry, and Algebra II sequence. This greatly enhances students’ understanding of topics included in the broader field of mathematics. Students taking this course enhance their ability to make sense of problems and persevere in solving them, reason abstractly and quantitatively, construct viable arguments and critique the reasoning of others, model with mathematics, use appropriate tools strategically, and look for and express regularity in repeated reasoning. Prerequisites: Successful completion of Algebra II or instructor approval

History of Mathematics

Through this course students gain a greater appreciation of mathematics as a human endeavor created by a diverse group of individuals whose life experiences and environments are integrally tied to the discoveries they made.  An historical perspective is applied to analyze the conventions and norms of communication adopted by mathematicians, the messages these norms convey, and their implications for the role of mathematics in society. Students focus on the development of the number systems, the development of algebra, and math in modern society. Pre-requisites: ESL 4 or higher; completed Algebra II with a B or higher

Introduction: Abstract Mathematical Thought Honors

Introduction to Abstract Mathematical Thought provides an introduction to a survey of topics not previously covered in the traditional high school algebra to calculus sequence, including formal logic, set theory, number theory, and graph theory. This greatly enhances students’ understanding of topics included in the broader field of mathematics. While the topics in this course have some overlap with those covered in Discrete Mathematics, there is a much greater focus on constructing formal mathematical proofs. Students will learn a variety of proof-writing techniques and approaches, including direct proof, proof by contradiction, proof by contrapositive, and proof by induction and disproof by counterexample. By viewing the mathematical world as a series of conjectures that must be proven or disproven, as opposed to theorems that are simply applied, students gain an insight into and appreciation for how the mathematics was developed. By the end of the course, students will have developed both the skills and mindset necessary for discovering new mathematics. Students use the textbook: Chapter Zero: Fundamental Notions of Abstract Mathematics by Carol Schumacher. Prerequisite: Recommendation of current math teacher.

Calculus Honors

Calculus Honors is an introduction to differential and integral calculus with a single variable. Students are introduced to limits, derivatives, integrals, the fundamental theorem of calculus, the mean value theorem, differential equations, optimization problems, and a variety of other topics and their applications to real-world problems. The course includes most of the material in AP Calculus but at a more relaxed pace, and the AP exam is not a component of this course. Prerequisites: Returning students: Recommendation of previous instructor. New students: ESL Level 3; placement test results

Multivariable Calculus Honors

Students in this course continue their study of calculus begun in AP Calculus AB and complete their preparation for the BC level of the Advanced Placement examination in calculus to be taken in the spring. Coverage includes integration by parts and by partial fractions, improper integrals, first order separable differential equations, infinite series and power series, and parametric and polar coordinates. Students continue their study of mathematics by extending their knowledge to the calculus of three-dimensional space. Partial differentiation and multiple integration are the main areas of study. Students must have a TI-84 Plus graphing calculator and must take the College Board BC Calculus exam at the end of the year. Prerequisite:  Successful Completion of AP Calculus AB and recommendation of Calculus Instructor

Introduction to Statistics

This course provides a basic introduction to statistics. It is recommended for students who are interested in business, social science, human resources, and criminal justice, and it provides an excellent preparation for any career. Topics include descriptive statistics, probability, probability distribution, normal distribution, hypothesis testing, estimates and sample sizes, the chi square distribution, correlation, and regression. The course is a critical thinking course as well as an analytical one, where students do many short-term projects and a long-term project. This course also provides an overview on how to collect, analyze, interpret, and display data from various real life sources and topics, emphasizing pop culture, politics, and the sporting world. Prerequisites: successful completion of Algebra II

Statistics Honors

Students expand their understanding of data collection and the role of statistics in making inferences from data. Applications from many realistic contexts such as business and economics, the social and physical sciences, healthcare, education, engineering, and leisure activities are examined throughout the course. Students use realistic data that they collect and analyze for class assignments and projects. The course includes most of the material in AP Statistics but at a more relaxed pace, and the AP exam is not a component of this course. Prerequisites: Returning students: A- or higher in CP Math course; B or higher in previous Honors Math course; ESL Level 3 or higher; recommendation of previous instructor. New students: ESL Level 3; placement test results

Game Theory

Game theory utilizes both popular and more contrived games as well as an accessible text to provide a fun and engaging introduction to the fundamentals of strategic decision-making. Through the analysis of games, students begin to understand the different roles that players can take, the behavior that constitutes the optimal strategy for playing these roles, and the behavior that constitutes the optimal strategy for assisting or countering these roles.  Using this knowledge, students interpret the current behavior of teammates and/or opponents in an attempt to determine their roles, recall the optimal strategy associated with these roles, predict the future behavior of other players based on their optimal strategy, formulate their own optimal strategy to best assist teammates and/or counter opponents, recall the role associated with this strategy, and implement the strategy by behaving in accordance with the calculated role. Furthermore, students gain an appreciation for how these concepts can be applied to fields including but not limited to business, economics, political science, computer science, logic, biology, and philosophy. Prerequisites: ESL Level 3 or higher; Algebra I; instructor approval

Applications of Game Theory: Traditional Game Desi

Using concepts learned in Game Theory, students research popular board games with the aim to design, refine, and construct an original board game. Additionally, students learn how to sell a refined and marketable game to a publisher. This process is ultimately split into four major phases: research, development, refinement, and sale. Prerequisites: Game Theory or permission from instructor

Advanced Placement electives

AP Statistics

The purpose of AP Statistics is to demonstrate a range of relevant everyday issues that can be addressed with the help of statistical analysis. This course is meant to expand the understanding of data collection and the role of statistics in making inferences from data. Applications from many realistic contexts such as business and economics, the social and physical sciences, healthcare, education, engineering, and leisure activities are examined throughout the course. Students use realistic data that they collect and analyze for class assignments and projects. Preparation towards the AP Examination highlights the four major disciplines within the Statistics class: Exploring Data, Sampling, Probability, and Inference. The primary textbook used is The Practice of Statistics for AP, 4th Ed. by WH Freeman. Students also use the following resources: www.collegeboard.com and www.apstatsmonkey.com and use TI-84 Plus C Silver Edition Calculators. Prerequisites: Returning students: ESL Level 4 or higher; A- or higher in previous math course; recommendation of previous instructor. New students: ESL Level 4 and placement test results

AP Calculus AB

Students prepare for the Advanced Placement Test in order to gain college credit while learning topics in Single Variable Calculus. Students are introduced to limits, differential equations, the derivative, points of tangency, slope fields, optimization problems, the fundamental theorem of calculus, mean value theorem, integration, application of calculus, and a variety of other topics that will provide real world examples as to the importance of calculus. The textbook for the course is Rogawski’s Calculus for AP. Taking the Advanced Placement test is a mandatory component of this course. Upon completing this course, students are eligible to take Multivariable Calculus or an independent study in mathematics. Prerequisites: Returning students: ESL Level 4 or higher; A- or higher in previous course; recommendation of previous instructor. New students: ESL Level 4; placement test results

“IN MATH CLUB WE CAME UP WITH A SERIES OF LECTURES TO HELP STUDENTS BECOME BETTER PROGRAMMERS AND SELF-TAUGHT PROBLEM SOLVERS”

Uljad from Albania

Progressed to New York University (#30 National University) to study Engineering with a major scholarship. He also received two acceptances to two top 100 national universities.

Faculty

Mary Carroll
Math Department Chair &
Math Teacher
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Mary Carroll

Math Department Chair &
Math Teacher

BA, Mathematics, Carleton College, Minnesota. MA, Liberal Studies, Reed College, Oregon

Mary Carroll is the Chair of the mathematics department. She works with teachers to provide a challenging math curriculum to suit the needs of all students. She also teaches Multivariable Calculus Honors, AP Statistics and Honors Statistics. Prior to joining CATS Academy, Mary taught high school mathematics in Costa Rica, Turkey, Spain and the Dominican Republic, as well as the US. She has a Master’s degree in Liberal Studies from Reed College in Oregon and an undergraduate degree in mathematics from Carleton College in Minnesota.

Jeff Napior
Director of CATS Innovation,
Chair of Technology Department &
Math Teacher
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Jeff Napior

Director of CATS Innovation,
Chair of Technology Department &
Math Teacher

BS, Aerospace Engineering, Cal Poly, San Luis Obispo
MS, Aeronautical Science, Embry Riddle Aeronautical University

Jeff Napior runs the CATS Innovation Lab where students benefit from a 'design-make-use' philosophy. This approach leverages open-ended exploration and tacit learning, therefore helping students complete projects typically related to the STEAM disciplines. Jeff worked for fifteen years as an aerospace engineer. He has hands-on experience with the electrical integration of flight vehicles ranging from fighter jets to orbital-class rockets. He has professionally trained US Navy aircraft technicians, tutored high school students and provided post-GED math lessons to incarcerated persons. Jeff is a huge sci-fi fan and an avid reader.

Mike Cerbarano
Math Teacher
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Mike Cerbarano

Math Teacher

BS, Mathematics, Bridgewater State University

Michael Cerbarano is a member of the mathematics faculty at CATS Academy. He is currently teaching Geometry and Algebra II. Prior to joining CATS, Michael served and is still serving as an adjunct mathematics professor at Massasoit Community College. Michael brings over eight years of higher education experience in both lower and upper-level mathematics courses. Michael received his BS in Mathematics at Bridgewater State University in 2009.

Justin De Santis
Math Teacher
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Justin De Santis

Math Teacher

Justin De Santis is a Math teacher, specializing in discrete mathematics, proof writing and game theory. He is also the coach of the CATS Boston Ultimate Frisbee team. Originally from New York, Justin is entering his fourth year at CATS Academy. Prior to joining CATS Justin spent five years living in Maine working as a high school math teacher, math team advisor, and tennis coach at Lee Academy. When not delivering inspiring math classes Justin can be found on campus enjoying a meal in the dining hall, or tossing an Ultimate disc next to the soccer field. “As a math enthusiast, I feel so fortunate to be a part of the incredibly passionate and dedicated faculty here at CATS. I could not be more grateful to be given this opportunity to impart the wisdom of a subject I love to those who will sculpt the future of our world."

Kadijah Figarsky
Math Teacher
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Kadijah Figarsky

Math Teacher

BS, Mathematics, Keene State College
MS, Mathematics, University of Connecticut Storrs

Khadija Figarsky joined CATS Academy in the fall of 2017. She teaches both Algebra II CP and Integrated Mathematics. Before joining the CATS faculty she worked in the field of neuroscience research at an NYU School of Medicine affiliated institute. Khadija started teaching math in graduate school, where she was a teaching assistant and adjunct faculty member, teaching numerous college-level courses. Khadija has lived on three continents, and she is fluent in three languages — English, French, and Arabic. And having studied and lived abroad, she is familiar with the unique needs of international students. Khadija holds an MS in Mathematics from the University of Connecticut Storrs and a BS in Mathematics from Keene State College. She is excited to be working with such a dynamic and diverse international student population at CATS.

Dominique Lomax
Math Teacher
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Dominique Lomax

Math Teacher

BA, Mathematics Willamette University
MAT, Mathematics, Willamette University

Prior to joining CATS Academy, Dominique taught at a school in China for three years. Here she taught AP Calculus and Pre-calculus. Once returning to America she worked at various schools that had an international student body or an international focus. Dominique comes to CATS Academy with four years’ of teaching international students both in China and America. She understands how to support international students as they learn, not only mathematics, but the English used in mathematics. Dominique received her BA in Mathematics with a minor in Chinese Studies from Willamette University and her MAT from Willamette University's School of Education.

Annie Schneider
Math Teacher
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Annie Schneider

Math Teacher

Annie Schneider joined the CATS Mathematics department for the start of the 2018-2019 school year.  She teaches Algebra I and Algebra II.  In addition to teaching, Annie resides on campus in Wheatley Dormitory where she works as a house parent.  Annie is also the head coach of the varsity girls' basketball and varsity girls' volleyball teams. Prior to joining CATS Academy, Annie taught high school mathematics and coached at Milton Academy and at the Williston Northampton School.  She has a bachelor’s degree in liberal arts with a major in mathematics and secondary education and a minor in Psychology from Assumption College in Worcester, MA.

Mustapha Coker
Math Teacher
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Mustapha Coker

Math Teacher

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