Math for the Classically Educated Student.
CALCULUS I IS A YEAR-LONG COURSE FOR STUDENTS IN GRADES 11-12.
As Veritas students settle into the rhetoric stage, they are ready to build mighty ideas upon the solid foundations they have built. Calculus empowers students to do so by expanding upon the algebra, geometry, and trigonometry that they have spent their dialectic years studying. When students study calculus — the mathematics of change — they gain the ability to think like a mathematician and see new logical relationships as concepts come together to form a more complete picture of the world around us. As the capstone of our mathematics curriculum, the Larson textbook used in this course caters to students in the rhetoric stage by demonstrating the connections and real-world applications of concepts both old and new. This first course in calculus is a substantial and thorough introduction to the three main ideas of calculus: limits, derivatives, and integrals. After a review of prior function concepts, students proceed to develop a concept of limits. They then apply this concept to define the derivative and explore its applications, only to return to define the integral, exploring its relation to the derivative. Finally, students will discuss numerous integration techniques and applications. Learning can happen through both the You Teach and Live Online formats.
The Veritas Approach to Math
Unlike some classical educators, we believe math is a crucial subject. It’s necessary for a well-rounded, rigorous classical education. In the grammar years, math provides content for developing memorization tools. In the dialectic years, subjects like Algebra I and Geometry develop students’ reasoning skills. In the rhetoric years, Pre-calculus, Calculus, Statistics, and Business Math lead students to value math in real-world applications.
At Veritas, we’re convinced that math has been dumbed down in America.١ Most students are more capable than we think. Our mission is to help make sure your children don’t become a dismal math statistic. For more than 25 years, we’ve been proving that our math standards shouldn’t come from what we were raised with. After all, if the education we ourselves received was as education should be, why would we be doing something different for our children? A study of historical٢ and international math standards helps us see this clearly.
Maybe the best way to understand our approach is to mark some milestones.
Addition and subtraction facts
Math building blocks,
develop memorization skills
Additional building blocks
Additional building blocks
Problem-solving, reasoning, logic
11th or 12th
Mapping change, thinking numerically, living today٣
Veritas recommends Saxon Math for K–6th, Jacobs for Algebra I and Geometry, Foerster for Algebra II and Pre-Calculus, and Larson for Calculus.
Saxon, with its incremental advances and continual review, works best with the grammar stage. Thankfully, Harold Jacobs understands the dialectic student and has written a superb curriculum for them with Algebra I and Geometry. One of his former students, Paul Foerster, writes where Jacobs left off, providing us our favorite texts for Algebra II and Pre-Calculus. Finally, Larson, a most prolific producer of Calculus texts, provides the capstone to our math curriculum.
Some prefer to stick with Saxon into the secondary school years. We are fine with that—even offering live class options using Saxon—but prefer texts written with more of a classical pedagogical approach.
Today, all math education needs to address the use of technology. At Veritas, it’s simple: use technology as a tool, not a crutch. Learning to work a two-variable algebraic equation is important. When mastered, however, why waste time plugging and chugging the numbers to develop a graphing solution? Let a machine do the number crunching. Students simply need to know how to do it.
Math is crucial to classical education. Don’t let anyone tell you otherwise.
١Americans are lagging in math: http://www.pewresearch.org/fact-tank/2017/02/15/u-s-students-internationally-math-science/
٢A Brief History of American K-12 Mathematics Education: https://www.csun.edu/~vcmth00m/AHistory.html
٣Is Calculus necessary? http://www.math.harvard.edu/~knill/pedagogy/use/index.html