Tim O’Brien understands that math is more than numbers and equations—it’s a conversation. As Math Department Head and a Middle School Math teacher, O’Brien encourages collaboration and inquiry, allowing students to work together to break down problems and compare solutions. His teaching focuses not only on critical thinking and communication skills but also real-world applications of math, ensuring that students are prepared to apply concepts beyond the classroom.
O’Brien leans on his 20 years of experience and background in both math and English to blend logical reasoning with emotional understanding. Making math more relatable and accessible isn’t always easy, so O’Brien frequently collaborates across divisions to find ways to innovate the teaching process.
In the interview below, Tim O’Brien discusses Beaver’s approach to math.
How would you describe Beaver’s approach to teaching math?
We see math as more than a list of skills and aim for much more than traditional approaches that focus on presenting and drilling procedures for manual calculations. This means we instead place our focus on developing students in three key areas:
- Mathematical ways of knowing, thinking, and reasoning. This includes developing strategic and systematic problem-solving and computational thinking processes.
- Communicating complex mathematical ideas in written, verbal, and visual forms. We want our students to develop logical arguments and conjectures, analyze the same from others, and learn how to justify their conclusions with precision and clear evidence.
- Abstracting real scenarios and problems into mathematical models to make sense of them.
How do you expand learning outside of the classroom?
Our approach to teaching is guided by the goal of highlighting math’s place outside the classroom. School math–this traditional list of skills–has little place outside the classroom. This has been obvious to every student who has asked, “Why do I need to learn this?” Our perspective gives students readiness for real ways that math is applied in the world.
This also means we interact with real problems and place them at the center of our lessons. We invite resources from outside the classroom, including community members, or take our classes beyond Beaver’s campus to see math in action. Students quickly see that the math happening in their world is not something like polynomial division, but the kind of thinking they are working on every day in our math classes.
Beaver’s objective is to teach students to think about and do things in a mathematical way.
Tim O'Brien, Math Department Head, Middle School Math
Are there any assignments or projects that highlight your approach to teaching?
Even something as specific as the procedure for dividing fractions is learned as a part of the future-focused goal of reasoning through, making sense of, visualizing, and communicating about how division works. What is the problem 3/4 ÷ 2/3 asking us? If division is breaking things up into equal groups, how do you break something up into less than one group?
To begin, we start with the real situation before a division problem is even presented. A recipe calls for 3/4 cup of sugar. Unfortunately, your kitchen drawers are a mess, and all you can find is the 1/3-size measuring cup. How can you use the 1/3 measuring cup to scoop out the needed 3/4 cup of sugar for the recipe? How many 1/3s are in 3/4?
Students think through and answer this question with their prior knowledge and understanding, often relying on common denominators and diagrams. This is how we make it obvious that we are confronted with mathematical thinking outside the classroom regularly and how we develop our students as thinkers and doers of mathematics, not as calculators.
[In math,] students are often told to follow their teacher blindly. We want to hear the students’ voices.
Tim O'Brien, Math Department Head, Middle School Math
Discover math courses at Beaver…
Financial Algebra
Financial Algebra
Ever wondered, “How do I create a budget?” or “What’s the secret to mastering debt?” Want to unravel the mysteries of taxes and insurance, and discover the keys to paving your way through college expenses? In this course, you will be using skills you have previously learned in Integrated Math 3 (or Algebra II) to deepen
… your knowledge on personal finances. Get ready to transform your understanding of money, making it not just about equations but about owning your financial future with confidence!Students can opt to take this class at the Honors level
Prerequisites: Integrated Math 2 or Algebra 1 [read more]
Mathematics, Design, and Art
Mathematics, Design, and Art
Discover the beauty where mathematics, design and art intersect. Students will explore mathematical concepts and their applications in artistic fields, including geometry, symmetry, patterns, and proportions. Through hands-on projects and creative problem-solving, students will work with a variety of media to study and create connections between math, architecture, design, visual art, and more. This course provides
… a unique opportunity to deepen mathematical understanding while fostering creativity and innovation.Students can opt to take this class at the Honors level
Prerequisites: Integrated Math 2 or Algebra 1 [read more]
Matrices and Linear Algebra
Matrices and Linear Algebra
This course focuses on the theory and techniques of linear algebra. Topics include vectors in n-dimensional space, matrix theory, systems of linear equations, vector space theory, linear transformations, eigenvalues and eigenvectors, and optimization. This course includes economics and computer science applications.
Students can opt to take this class at the Honors level
Prerequisites: Integrated Math 2
… or Algebra 1 [read more]Probability and Combinatorics
Probability and Combinatorics
How likely is an event likely to happen? This is an essential question that is asked by professionals in a host of different fields. Probability helps to quantify a response, often relying on algorithms of combinatorics to count the number of favorable outcomes in a given scenario. Maybe you want to understand the efficacy of a
… revolutionary cancer treatment better, or think more critically about the P-values that deem a trial successful or unsuccessful. Maybe you are curious about the decision-making of professional poker players, or are interested to explore how meteorologists use this same theoretical math in their daily forecast of the weather. Maybe you see probability in sports, or combinatorics in computer science. Whatever the application is that interests you, here you will develop the advanced algorithms for counting which provide the groundwork for probability theory. In this course, you will develop an understanding of the mathematics that helps to inform the decisions we make every day.Students can opt to take this class at the Honors level
Prerequisites: Integrated Math 3 or Algebra 2 and Geometry
[read more]Student Directed Project – SDP
Student Directed Project – SDP
A Student-Directed Project empowers students to do an in-depth exploration of a topic of interest throughout the term.
The student designs, plans, and leads their research project in collaboration and with the guidance and support of a coach (faculty advisor). It allows students to delve deeper into their passion and to be the designer of their
… own learning. There is a wide range of Student-Directed Projects; they are multi-disciplinary, non-linear, and most importantly, student-created and led.That’s what makes them so interesting.
Here are some examples of past projects:
- Creating an architectural model using 3D architectural software
- Through their eyes: Photo and interview series of veterans
- Robosub electromagnetic linear accelerator
- Acoustic pinger for Robosub
- Virtual Reality game for visually-impaired persons
- Creating a concept album
- Dispute: Landlord-tenant board game
- Multimedia journalism: Producing a podcast series
- Perplex: English and Theater Study
- Sensors and fiber optics: Building a fiber optic dress
- Haptic technologies: Force-Feedback Virtual Reality
- Applications of integrals to analytical continuation of functions
Discrete Mathematics
Discrete Mathematics
Discrete Mathematics is concerned with processes and situations that are finite and discontinuous–things that have an end, can be measured, and given a whole-number value. In this course, students will have the chance to learn a range of discrete math topics that fall outside the spectrum of traditional high school mathematics. Existence problems deal with whether
… or not a solution exists, counting problems explore how many solutions may exist, and optimization problems focus on finding the most favorable solution to a particular problem. Topics covered may include finite sets and partitions, enumeration, probability, expectation, random variables, and elementary number theory, with an emphasis on applications of discrete mathematics.Students can opt to take this class at the Honors level
Prerequisites: Integrated Math 3 or Algebra 2 and Geometry
[read more]Foundations for Algebraic Reasoning
Foundations for Algebraic Reasoning
This course is designed for students who have not completed Algebra 1 through quadratics in middle school. Students will build a strong foundation in algebraic reasoning and grapple with real-world applications. Work will focus on solving linear equations and systems and the exploration of exponential and quadratic relationships.
Not offered at the Honors level.
… [read more]Integrated Math 2: Algebra, Geometry, and Data Science
Integrated Math 2: Algebra, Geometry, and Data Science
Integrated Math 2 students expand their algebraic reasoning and understanding of mathematical models including quadratic equations and exponential functions. Students also explore probability and build upon their knowledge of transformations, congruence, and similarity while developing logic skills through conjecture, argument, and proof. Investigations in this course build connections between all topics covered.
Prerequisites: Integrated Math 1,
… Algebra 1, or Foundations for Algebraic Reasoning. Offered at the Honors and Standard levels. Honors level requires departmental recommendation. [read more]Calculus – Derivatives & Integrals
Calculus – Derivatives & Integrals
The Derivatives course includes all of the topics of an introductory Calculus course including limits, derivatives and their applications.
The Integrals course includes all of the topics of an introductory Calculus course including definite integrals, indefinite integrals and their applications.
Prerequisite: Precalculus. Offered at the Honors and Standard levels. Honors level requires departmental recommendation.
… [read more]Statistics and Data Science
Statistics and Data Science
This course includes the gathering of data and a variety of sampling techniques, hypothesis testing, frequency distribution, normal distribution, correlation, linear regression, theoretical distributions, and inferential statistics. This course asks students to consider questions such as these: How is data summarized so that it is intelligible? How should statistical data be interpreted? How can we measure
… the inherent uncertainty built into statistical data? Students will be asked to collect, analyze and interpret real data to answer real questions in their areas of interest.Students can opt to take this class at the Honors level.
Prerequisites: Integrated Math 3 or Algebra 2 and Geometry
[read more]Advanced Topics (Honors)
Advanced Topics (Honors)
In this course, students will be asked to grapple with a range of topics that extend beyond fundamental calculus topics. Topics covered may include but are not limited to l’Hospital’s rule, linear approximations, differentials, Newton’s Method of Approximation, center of mass, arc length, surface area, and differential equations. Students will be asked to think creatively and
… apply their knowledge to complex real-world problems, and extend their knowledge of fundamental calculus topics. Students taking Advanced Calculus or others with a strong interest in pursuing advanced mathematics at the college level are strongly encouraged.Class offered at the Honors level only
Prerequisites: Advanced Calculus or departmental permission
[read more]PreCalculus – Trigonometry
PreCalculus – Trigonometry
Students in this course will learn about angle measurement, periodic behavior, and a range of applications related to both right triangle and circular trigonometry. Analytic geometry and polar coordinates are often included in this course, as well. Prerequisites: Algebra II and Geometry. Honors level requires departmental permission.
Prerequisites: Integrated Math 2 and Integrated Math 3. Offered
… at the Honors and Standard levels. Honors level requires departmental recommendation. [read more]PreCalculus – Functions
PreCalculus – Functions
In this course, students will take a deeper look at various families of functions: rational, radical, exponential, logarithmic, and polynomial. Students will learn about the ways in which domain, range, continuity, inverses, composition and transformation apply to those functions. Students will also have opportunities to analyze real-world data and generate predictive models. Topics from data science
… are often included in this course, as well.Prerequisites: Integrated Math 2 and Integrated Math 3. Offered at the Honors and Standard levels. Honors level requires departmental recommendation.
[read more]Advanced Calculus – Derivatives & Integrals (Honors)
Advanced Calculus – Derivatives & Integrals (Honors)
This course covers all of the topics of an introductory Calculus course, exploring concepts in depth with a greater emphasis on both the abstract aspects of calculus and its various applications in the real world. Students will be expected to enter the class with a firm grasp of all concepts covered in previous math courses.
Prerequisite:
… Precalculus and departmental recommendation. Offered at the Honors level only. [read more]Integrated Math 3: Algebra, Geometry, and Data Science
Integrated Math 3: Algebra, Geometry, and Data Science
Integrated Math 3 students continue to expand their algebraic reasoning and understanding of mathematical models including complex numbers, exponential equations, and polynomials. Students also explore sampling and build upon their knowledge of solid geometry and circle theorems while building connections between all topics covered.
Prerequisites: Integrated Math 2. Offered at the Honors and Standard levels. Honors
… level requires departmental recommendation. [read more]Math 8 – Relationships: Making and Modeling Connections with Geometry, Algebra, and Statistics
Math 8 – Relationships: Making and Modeling Connections with Geometry, Algebra, and Statistics
This course will focus on relationships across three domains: geometry, algebra, statistics. In geometry, students will examine the relationships of congruence and similarity through transformations and uncover the meaning behind the symbols of the Pythagorean Theorem by investigating the relationship between the three sides of a right triangle. Students will extend their algebraic understanding to include
… systems of linear equations and inequalities and expand beyond linear functions to investigate exponential and quadratic models. Students will analyze relationships between variables in real data by considering different visualizations including function models while examining regression and linear trends.Emphasis is placed on communication in verbal and written form, creative problem-solving, and thinking and reasoning skills. Willingness to take risks and productive struggle are also major themes of the course. Inquiry-learning through projects, technology, and collaboration support the curriculum.
Math 7 – Things Change: Linear Rates And Proportionality
Math 7 – Things Change: Linear Rates And Proportionality
This course will focus on number sense, proportional reasoning, and linear relationships. Students will extend their understanding of operations and properties of integers and rational numbers. They will also develop and use strategies for solving problems that involve proportional relationships. Students will build algebraic thinking as they learn to recognize various representations of linear relationships and
… investigate ways to solve equations.Emphasis is placed on communication in verbal and written form, creative problem-solving, and reasoning skills. Willingness to take risks and productive struggle are also major themes of the course. Inquiry-learning through projects, technology, and collaboration support the curriculum.
[read more]Math 6 – Fair vs Equal: Division, Decomposing, And Distribution
Math 6 – Fair vs Equal: Division, Decomposing, And Distribution
In this course, students will extend their understanding of the number system while exploring rational numbers and integers. Plus, they will make sense of algorithms for dividing fractions and decimals to explain why they work. Students will develop reasoning to solve and make sense of problems involving ratios, rates, and percents. In statistics, students will construct,
… interpret, and use calculation methods and models to describe distribution and variability.Emphasis is placed on communication in verbal and written form, creative problem-solving, and reasoning skills. Willingness to take risks and productive struggle are also major themes of the course. Inquiry-learning through projects, technology, and collaboration support the curriculum.
[read more]