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Calculus II - Course Options

Math for the Classically Educated Student.

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CALCULUS II IS A YEAR-LONG COURSE FOR STUDENTS IN 12TH GRADE.

While Calculus I is quite substantial, this second course in calculus broadens and deepens students’ understanding of this beautiful subject. Students continue to work through the Larson textbook as they learn new connections and real-world applications. After an overall review, we introduce some basic differential equations; we discuss infinite series, and power series representations of functions; we engage in a detailed study of parametric equations and polar coordinates and apply this to the classical study of conics; we begin to generalize to higher dimensions with basic vector material and the theory of vector-valued functions; we conclude with an introduction to functions of several variables and partial differentiation. 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.

Grade

Milestone

Purpose Served

K

Addition and subtraction facts

Math building blocks,

develop memorization skills

1st

Multiplication facts

Additional building blocks

2nd

Division facts

Additional building blocks

7th

Algebra I

Problem-solving, reasoning, logic

11th or 12th

Calculus I

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

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