Mathematics
The Mathematics Department seeks to contribute to students’ education through the study of abstract concepts and by developing problem-solving skills. By encouraging an intellectual progression from working concretely to handling abstractions, the Department’s offerings parallel and promote students’ cognitive development. Problem-solving and analytical skills are developed with an eye towards mastering the content material and the requirements of college level work. To this end, we incorporate technology, in the form of graphing calculators and interactive software, into our work. But Mathematics remains a human endeavor and we encourage cooperative work and varied forms of assessment (notebooks, journal entries, projects, etc.) as part of a program of appealing to multiple modes of learning. Mathematics also constitutes a search for patterns that extend beyond its problem-solving aspect. With that in mind, we strive to instill in students an appreciation for mathematics not only as a tool, but also as a means of appreciating the regularity and beauty of the universe. The study of mathematics supports the Dublin School mission as it can involve personal courage and often leads to individual understandings of the truth.
Algebra I
Algebra I serves as an introduction to abstraction and to the tools of higher mathematics. Students are first taught to work with abstract quantities while solving linear and absolute value equations and inequalities. This leads a study of different forms of linear equations and different methods to represent equations graphically on line graphs and coordinate planes. Finally, quadratic equations, their graphs and multiple ways of finding their solutions, are explored in depth. All of our studies are supplemented by real-world word problems.
Geometry
Prerequisite: Completion of Algebra I through the study of quadratics.
Geometry promotes deductive reasoning, through the study of proofs, along with a more concrete understanding of the mathematics of working with shapes in two and three dimensions. The course begins with an introduction to the terminology and concepts of geometry, which are developed through proofs, largely in two dimensions. As the year progresses, a third dimension is introduced and the concepts of surface area and volume are fleshed out.
Algebra II
Prerequisite: Completion of Algebra I and Geometry.
Algebra II is designed to strengthen and extend those skills introduced in Algebra I. A thorough review of basic algebra is pursued through quadratics. Students then work with exponents and exponential equations, culminating in an introduction to logarithms. The course relies heavily on the TI-83+ series of calculators, as students are encouraged to use technology to support the growth of their mathematical understanding.
Algebra II/Trigonometry
Prerequisite: Completion of Algebra I and Geometry.
Algebra II/Trigonometry further promotes students’ abstract skills and seeks to give them a substantial mathematical toolbox that will serve them in higher level math and science courses. Topics progress from a review of Algebra I through quadratics and on to higher order equations, logarithms and finally an introduction to trigonometry. Successful completion of this course will prepare students to go on to Precalculus.
Precalculus
Prerequisite: Completion of Algebra II/Trigonometry.
Precalculus completes the study of algebraic technique and is designed for students with substantial ambition in mathematics, science, engineering and related areas. Logarithms, exponentials and trigonometry, introduced in Algebra II, are studied in more depth and with particular regard to applications. Basic familiarity with those topics is assumed in this class. The course culminates with an introduction to the conceptual aspects of limits and both differential and integral calculus. Successful completion of this course will prepare students to go on to AP Calculus.
Advanced Placement Calculus
Prerequisite: Completion of Precalculus.
Advanced Placement Calculus is designed to offer a thorough introduction to the differential and integral calculus of a single variable. The course uses a variety of methods, numerical, graphical and analytical, to explore elementary functions. This is a demanding course, offering the possibility of college credit through the College Board’s AP program, and as such requires considerable commitment from students. It is expected that students enrolling in the course will have a thorough mathematical background, such as is offered in our Precalculus course. The AP exam in the spring is an integral aspect of the course.
Statistics
Prerequisite: Completion of Algebra II or Algebra II/Trigonometry.
Statistics is designed to give the student a basic working understanding of the topic, appropriate for future work in such fields as economics, sociology and biology. This course is very much a practical, ‘hands on’ course, featuring projects in related areas of physical, biological and social sciences. Topics covered include probability, various types of distributions, sampling, hypothesis testing, correlations and regressions.
Advanced Topics in Mathematics
For those students who have surpassed the normal high school mathematics curriculum and are invested in advancing in their studies of mathematics, a number of options are available dependent on interest in the form of independent studies or small classes. Topics that have been offered in the past include: AP Micro Economics, AP Macro Economics and AP Statistics. For a course of study of Set Theory, Number Theory, Abstract Mappings, advanced topics of Calculus of One and Several Variables, Infinite Sequence and Series and Vector Space Geometry, a score of a three or higher on the AP Calculus exam is a prerequisite.