Prerequisite: Precalculus or Saxon Advanced Math 2nd Edition
Helpful pre- or co-requisite: Calculus for Everyone

NOTE: Planned optional Dual Credit (MAT 141 Calculus I & MAT 142 Calculus I Recitation) through Kepler's Partnership with Colorado Christian University's Dual Credit Program via CCU Academy. See details below. Parents and students should schedule a meeting with Mrs. Santoro before enrolling in CCU's Dual Credit Program.

Calculus I is a classical Christian approach to the liberal arts of mathematics and geometry. Galileo observed, “Mathematics is the language in which God has written the universe.” As a language, mathematics implies communication—something more than formulas on a page. While textbooks and lectures can impart knowledge, true fluency requires dialogue, practice, and participation. To speak mathematics well, one must engage it conversationally.

This course provides a solid framework of instruction and skill development, while guiding students beyond the mechanics into deeper understanding through discussion, reflection, and the canons of rhetoric. Calculus I invites students into the Great Conversation of the liberal arts, where mathematics is studied not only as a tool for science but as a language of order, beauty, and truth. Drawing on Shormann Math’s structured lessons, the narrative clarity of Calculus for Everyone, and carefully curated AP/collegiate‑level problems, the course situates calculus within the Western tradition as both the crown of the quadrivium and a means of contemplating God’s creation. It aligns with dual‑credit standards while maintaining a distinctly classical Christian emphasis on mathematics as both technical mastery and language fluency.

Course Organization:

This course consists of two semesters (32 weeks) and offers 1.0 high-school credit and optional 4.0 collegiate credits through CCU (see details below). Each semester students will be assigned lessons, discussion posts, quizzes, and exams, and attend live recitations as active members. Students should expect to expend time and effort in line with an honors/advanced/AP Calculus course. The optional collegiate course MAT 141/142 is 4 credits: 3 credits are MAT 141 and the last credit is the MAT 142 piece, which is the recitation session, or participation grade. Expect to work about 3 hours per credit hour outside class to master this material; so, 12 hours per week.

Course Description:

Derivatives of polynomial and trigonometric functions, applications of the derivative, the definite integral, the fundamental theorems of calculus, and applications of integration.

This course will:

• Examine limits and applications of limits.
• Examine how limits can be used to prove basic differentiation formulas.
• Examine differentiation rules.
• Explore the tangent line problem.
• Expose the students to applications of differentiation including optimization problems.
• Explore related rates problems.
• Introduce students to methods of calculus that aid in curve sketching.
• Introduce students to antidifferentiation (integration) techniques, Riemann Sums, and The Fundamental Theorem of Calculus.
• Expose students to separable differential equations.
• Explore Biblical connections to calculus.

While the emphasis in this course is on Calculus, in the classical manner, students will either review or gain a basic understanding and increase their fluency in the following major mathematical topics: number, ratio, algebra, geometry, analytical geometry, measurement, trigonometry, statistics, computer math.

Course Objectives:

On completion of Calculus I with a passing grade, you should be able to meet the following learning outcomes:
✓ Demonstrate an understanding and ability to apply basic differentiation and integration
skills to computational problems in theoretical and real-world situations.
✓ Demonstrate the ability to interpret, make appropriate calculus judgments, and draw logical conclusions based on quantitative information.
✓ Demonstrate the ability to translate problem situations into symbolic representations and to use those representations to solve problems.

Additionally, students should be able to

• To look at the quadrivium's mathematical arts of arithmetic and geometry from a biblical and classical approach.
• To appreciate how God reveals Himself in math concepts and how they reflect His Glory in Creation.
• To build upon Pre-Calculus knowledge
• Within the rigor of the materials and calendar, to contemplate the truth, beauty, and goodness via journaling and actively participating in discussions of mathematics.
• To study the language of mathematics with a goal of improving fluency.
• To gain understanding and wisdom in the arts of mathematics using Cicero's Five Canons of Rhetoric to participate in various methods of discussion.
• To appreciate the integration of major math concepts in other subjects.

Required Curriculum:

• Shormann, D. (2025). Calculus 1. DIVE, LLC. (Please note: students must purchase the non-refundable, 12-month school license through Kepler and not through DIVE.)
• Stokes, M. (2020). Calculus for Everyone: Understanding Physics and the Mathematics of Change. Roman Roads Press.
• Additional readings, videos, and worksheets, as directed by instructor

Highly Recommended:

• Hass, J., Heil, C., & Weir, M. D. (n.d.). Thomas’ Calculus: Early Transcendentals. (Any edition or format.)
• Khan, S. (n.d.) Khan Academy: Calculus 1. https://www.khanacademy.org/math/calculus-1
• Khan, S. (n.d.) Khan Academy: Precalculus. https://www.khanacademy.org/math/precalculus

Required Resources:

• Hand-held graphing calculator (most instruction will be via TI-Nspire™ CX II CAS)
• Ability to quickly produce a single, well‑formatted PDF of handwritten work, including during class when needed. Photos must be cropped to the written content, without large white borders or background distractions, so the final document is clear and professional.
• Working camera, headset, microphone, and stable internet connection

Virtual Classroom/Attendance:

Attendance is a vital part of this course; therefore, students must attend class sessions and actively participate in discussions. Unless stated otherwise, students are expected to have completed the assignments before coming to class. Although the recitations will be recorded, a student cannot participate while watching a recording. In-class recitation problem sets or quizzes must be completed in class for credit. All live classes will take place on Zoom or other-directed virtual classroom. Students must always have cameras on unless given prior approval for an extenuating circumstance. To participate, the student must have a stable internet connection, a working webcam, headset, microphone, and screen large enough for viewing material (a phone is not recommended.) Technological issues occur but must be addressed and fixed as soon as possible. Recurrent technological issues may risk the student being dropped from the class.

NOTE: In addition to a classical overview of the history and philosophy of calculus, the first quarter includes a high-speed and intense review/preview of the major math concepts: number, ratio, algebra, geometry, analytical geometry, measurement, trigonometry, calculus, statistics, and computer math. Adequately blocked time is necessary to diligently develop or polish skills and habits and avoid “cram, test, forget” mentality. Depending on student's math knowledge and fluency, consider blocking sufficient time to build math habits, especially in the first quarter. Students pursuing dual credit may need additional time and extra problems to build competence and longer retention.

The successful student usually:

• Practices mathematics regularly, preferably daily, to cultivate diligence in practice, reinforce concepts and build lasting fluency; “cram‑test‑forget” is not the goal.
• Is self‑motivated and studies calculus as part of forming the mind toward truth, beauty, and goodness under God’s created order, while also laying a solid foundation for Calculus II.
• Manages time wisely, exercising prudence in planning and maintaining a steady weekly workflow rather than relying on last-minute efforts.
• Engages the homework assignments and recommended resources with a desire for understanding, treating the exercises as tools for growth and not as graded tasks to complete.
• Is prepared to discuss the material; works on homework ahead of time so there is time to ask for support from fellow students and instructor.
• Has earned a B or higher in Precalculus. (Note, this course is not recommended for students who struggled to pass Precalculus. The greatest challenge in Calculus I is often not the calculus itself, but the ability to recall and apply algebraic skills accurately and in context.)

Assignments & Assessments:

• Final Exam (25%)
• Quarterly Exams (30%)
• Weekly Homework Quizzes (20%)
• In-Class Recitation: Demonstrations, Problem Sets, Presentations, and Quizzes (15%)
• Discussion Posts (5%)
• Attendance (5%)

Biblical Integration:

This class approaches mathematics from a biblical worldview, attending to truth, beauty, and goodness as we explore how mathematical ideas reflect the order and glory of God’s creation. Shormann Math provides a distinctly Christian foundation by presenting math as the “language of science and a God-given tool” for understanding the world He made (Shormann, n.d.-a, p. 2). It’s emphasis on history and Christian intellectual heritage helps students grasp not only how to do mathematics, but why it matters (pp. 2-3).

In the Shormann Calculus framework, Dr. Shormann encourages students to develop Christlike humility and joy in their studies, recognizing that mathematical understanding rests on a kind of “reasonable faith” consistent with Hebrews 11:1 (Shormann, n.d.-b, p. 4). Likewise, Dr. Stokes reminds us that calculus is central to Western thought and that understanding its purpose and development brings clarity to both scientific and philosophical ideas (Stokes, 2020, p. xxvi).

Students will engage these themes through weekly discussion posts that connect formal calculus concepts with the broader ideas presented in Calculus for Everyone. Initial responses should thoughtfully address the prompt, and replies should extend or deepen classmates’ insights. Contributions ma include observations in everyday life, conceptual breakthroughs, questions about challenging ideas, or reflections that integrate mathematical understanding with a biblical perspective. These discussions aim to cultivate curiosity, strengthen conceptual understanding, and foster a collaborative learning community.

Colorado Christian University's Dual Credit Program

Dual Credit Program | CCU Academy.
This dual-credit course must be completed with a grade of C- or higher to be considered for college transfer credit. Calculus I (MAT 141/142) is a 4-credit course. Payment and registration are two separate actions. Parents and students should schedule a meeting with Mrs. Santoro before enrolling in CCU's Dual Credit Program.
Be advised that a course's dual credit status with CCU is subject to change and is not confirmed until the CCU Academy course enrollment is approved and enrollment opens in the fall. While not yet approved, we do not foresee issues and will not hold the course without dual credit approval.

References:

Shormann, D. (n.d.-a). Shormann Math Algebra 1: Core ideas, course description, and table of contents. DIVE, LLC.

Shormann, D. (n.d.-b). Teacher Guide for Shormann Calculus. DIVE, LLC. https://store-a78f1.mybigcommerce.com/content/Teacher%27s%20Guides/Teacher%20Guide%20for%20Shormann%20Calculus.pdf

Stokes, M. (2020). Calculus for Everyone: Understanding Physics and the Mathematics of Change. Roman Roads Press.