> home > Education > Mathematics

Mathematics in Classical Education

Mathematics helps us with understanding, describing, explaining, and managing systems and situations all around us as they relate to our physical environment (physical sciences), technical accomplishments (engineering, automation, etc.), and human relations (applied statistics in sociology, anthropology, economics, etc.)

One very important aspect of mathematics is modeling: the creation of a model that describes a problem or situation. This process uses analysis and quantification to develop a mathematical representation (an equation, a functional relation, a system, etc.) that describes the situation or problem in a manner that is both sufficient and complete. Through the application of various mathematical techniques a solution is developed, and, based on critical testing procedures, the model may be accepted, rejected, or adjusted.

Another important aspect of mathematics is the continued development of an extensive, well-organized collection of acquired knowledge and abilities. Combined with a good understanding of the applicability and limitations of mathematics, students are able to relate new observations and discoveries to what they already know.

The mathematics course has three primary goals: the development of a vast repository of mathematical tools, the development of general reasoning skills, and the development of specialized reasoning and problem solving skills.

Our curriculum is designed to provide students with a thorough understanding of geometry, algebra, analysis (calculus), logic, statistics, and probability theory. Armed with an extensive collection of mathematical techniques, students will be ready to apply their knowledge to real-world problems. They will have learnt to analyze a problem, determine how to solve it, find the solution, and show that the solution is correct.

The world around us is inherently “messy”. Situations that present themselves are rarely isolated instances of textbook problems in a specific area of study. Instead, one usually has to combine techniques from various areas. The ability to accomplish that task is developed by presenting the students with an integrated approach to teaching mathematics. The journey through the various subjects follows a natural progression through levels of abstraction that corresponds to the ability of students to comprehend and work with those abstractions as they mature through the high school years. This integrated approach also follows the historical journey that mathematics took through the past 2000 years, enabling students to better understand why certain techniques were developed which in turn helps them to learn when and how to use them.

When teaching mathematics, integration between areas of study is carried over to integrating with other courses. History provides an important context for many discoveries in science and mathematics, and even in art and music. Instead of isolated events we encounter a dialogue between the different fields. Art shows the natural application of natural constants that we also encounter in mathematics (especially geometry), and the use of perspective is formalized in mathematical formulas that are further investigated in optics. The Pythagorean Theorem is a famous mathematical concept, but its origin is found in music and the development of string instruments. Further study has deepened our understanding of sound (as waveforms in physics) and harmony (in music). As students learn about these connections (and discover them in class), they will be able to better understand the beauty of mathematics and its role in helping us understand and appreciate God's creation.

Although the order in which subjects are presented differs from the typical mathematics curriculum in high schools, students will be very well prepared to excel on standardized college admissions tests such as the SAT or ACT. The integrated approach to teaching mathematics ensures that students are well prepared to enter the work force, or continue their education at any college or university in the US or abroad, be it in science, applied science (engineering), medicine, or the humanities.

This curriculum provides students with a very comprehensive education in mathematics. Students who consistently perform well in this curriculum should be well prepared for success on AP exams if they elect to take them.

In 9th grade, the course will cover:

Geometry (~ 50%)
- Synthetic geometry
- Analytic geometry
Algebra (~ 20%)
- Number theory
Analysis (~ 20%)
- Real analysis
Statistics (~ 10%)
- Descriptive statistics

In 11th grade, the course will cover:

Analysis (~ 55%)
- Pre-calculus
Discrete mathematics (~ 15%)
- Sequences
Algebra (~ 25%)
- Complex numbers
- Matrices and systems
Logic (~ 5%)
- Propositional and predicate logic

In 10th grade, the course will cover:

Geometry (~ 50%)
- Synthetic geometry (cont.)
- Analytic geometry (cont.)
- Trigonometry
Algebra (~ 7%)
- Polynomials
Analysis (~ 35%)
- Real analysis (cont.)
- Sequences
Probability theory (~ 8%)
- Counting problems
- Chances

In 12th grade, the course will cover:

Analysis (~ 53%)
- Derivatives
- Integrals
Discrete mathematics (~ 7%)
- Counting problems
Geometry (~ 15%)
- Solid geometry
Statistics (~ 10%)
- Descriptive statistics
Probability theory (~ 15%)
- Chances
- Stochastic variables

In 9th and 10th grade, most algebra instruction is presented as part of geometry and analysis.

In 11th grade no specific instruction in geometry is provided because it is closely integrated in the other subjects. Further explicit instruction in geometry is deferred to 12th grade because it requires concepts that are the topic of study throughout most of 11th grade.

Across all four years of high school, students will receive the equivalent of:

Geometry: 1.2 years
Algebra: 2 years
Analysis/calculus: 1.5 years
Statistics and probability theory: 0.5 years