Mathematics

Members of the Math Department aim to teach students to use critical thinking, reasoning, and problem-solving effectively. Real-world applications are integrated throughout the curriculum, whereby students develop the skills required to be critical thinkers and tomorrow’s leaders.

Algebra I is the first mathematics course at Notre Dame. The Algebra I course set forth here is not the algebra of 30 years ago; the focal point of this course is the algebra content strand. Algebra provides tools and ways of thinking that are necessary for solving problems in a wide variety of disciplines, such as science, business, social sciences, fine arts, and technology. This course will assist students in developing skills and processes to be applied using a variety of techniques to successfully solve problems in a variety of settings.

Geometry is the second course in mathematics for high school students. Within this course students act as true mathematicians and have the opportunity to make conjectures about geometric situations and prove in a variety of ways — both formal and informal — that their conclusion follows logically from their hypothesis. This course is meant to employ an integrated approach to the study of geometric relationships. Integrating synthetic, transformational, and coordinate approaches to geometry, students will justify geometric relationships and properties of geometric figures. Geometry is meant to lead students to an understanding that reasoning and proof are fundamental aspects of mathematics and something that sets it apart from the other sciences.

Algebra II is the third course for mathematics at Notre Dame and is an extension of the two courses that preceded it. While developing the students’ algebraic techniques, this course is also intended to continue developing alternative solution strategies, problem-solving, and algorithms. Within this course, the number system will be extended to include imaginary and complex numbers. Students will also be exposed to the study of quadratics, graphs, polynomial and rational functions, exponential and logarithmic functions, sequences, probability/statistics and trigonometry. Overall, this course will allow students to learn to approach problems algebraically, graphically, and analytically through logical thinking and reasoning.

Pre-Calculus is designed for students who have shown an aptitude and ability to handle algebraic, geometric, and trigonometric concepts. The course begins with an extensive review of trigonometry in order to best prepare the students for calculus. Topics covered include linear functions, nonlinear functions, graphing and solving trigonometric functions, evaluating limits- both graphically and algebraically, continuity and differentiation. Overall, this is an integrated course, which will show students how to apply the process of logical thinking and reasoning to both mathematical and non-mathematical situations.

AP Calculus AB is taught over a full high school academic year. It is possible to spend some time on elementary functions and still cover the Calculus AB curriculum within a year. This course is designed for students who have shown an aptitude and ability to handle algebraic, geometric, and trigonometric concepts. The course begins with a review of algebraic and trigonometric topics, covered in previous courses, to prepare the student for calculus. Subsequently, topics covered include evaluating limits (graphically and algebraically), continuity, differentiation, applications of the derivative, graphs of the derivative, integration, applications of integration, and various other subsets within these topics. If students are to be adequately prepared for the Calculus AB examination, most of the year must be devoted to topics in differential and integral calculus. Differentiation and integration is explored with a variety of functions. Overall, this is an integrated course that shows students how to approach all concepts, problems, results, and applications numerically, graphically, analytically, and verbally. Students are required to take the AP Calculus AB Examination in May.

AP Statistics is an introductory college-level statistics course that introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data.  AP Statistics prepares students to collect, analyze, and extrapolate data. Course topics include data-based predictions, variation and distribution, patterns and uncertainty, conclusions, and decisions. Students learn about the major concepts and tools for collecting, analyzing and drawing conclusions from data. AP Statistics can prepare students for dozens of college majors beyond statistics, including criminal justice, aerospace engineering and environmental studies, just to name a few. 

PSAT preparation is incorporated into each year’s program of study. The Math Department provides PSAT preparation for all freshmen, sophomores, and juniors taking the PSAT exam in October. Preparatory activities continue throughout the year. By the time students sit for the SAT in the spring of their junior year of high school, they will have received nearly three academic years worth of study and exposure to the exam. Additionally, our partnership with Fordham University enables students to track their performance progress over time, as well as develop both study and test-taking strategies that will bolster their performance on these exams. SAT preparation is incorporated into the senior curriculum as well, and is done in the week leading up to a College Board scheduled exam.

A few words from the Math Department:
Keeping up with the work is very important. We, teachers and parents, are here for help and support, but success lies mainly in the hands of the student. This may seem like an awesome responsibility, but the simple truth is: we cannot do the work for them. So, to realize success, each student is urged to: participate actively in class, question for clarification, make up work missed due to an absence, take advantage of the practice that doing homework assignments affords, and lastly keep an open mind and stay positive when work becomes especially challenging.