Calculus Readiness Assessment

What is Calculus?

Calculus is a branch of mathematics concerned with studying change, such as problems where a variable changes with time or another variable of reference. Calculus is also called Infinitesimal Calculus because its calculations involve infinitely small quantities (called infinitesimals), such as the ratio between infinitely small quantities (called a derivative) or the sum of infinitely many infinitesimals (called an integral). Calculus is divided into two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus.

The concepts of calculus were formulated in the late 17^th century by Isaac Newton and Gottfried Wilhelm Leibniz. The theoretical foundations of calculus, studied in Real Analysis, were established much later, in the 19^th century, by Cauchy, Weiersstrass, and several others. Nowadays, calculus is considered a fundamental branch of mathematics because of its many applications in science, engineering, physics, biology, social science, and other branches of math.

What is Precalculus?

Precalculus is a course designed to builds the skills necessary to apprehend the concepts of calculus and gain proficiency in the methods of calculus. A typical precalculus curriculum includes:

1. Analytic Geometry: Analytic geometry provides a bridge between algebra and geometry, separate branches of mathematics learned in secondary school. Analytic geometry introduces a coordinate system (such as the Cartesian or the polar coordinate system) by which geometric objects (curves and surfaces) are represented as algebraic equations, and vice-versa.
2. Trigonometry: is a branch of mathematics concerned with relationships between angles and side lengths of triangles.
3. Elementary functions: An elementary function is a rule that assigns a single variable (real or complex) to another. Examples include polynomial, rational, trigonometric, hyperbolic, exponential functions, and their inverses.

A solid knowledge and proficiency in analytic geometry, trigonometry, and elementary functions are essential for success in calculus.

Calculus Curriculum and Drills

Calculus is typically taught over the course of 3 semester-long courses titled Calculus I, II, and III. At Wheaton College, each course is 4 credits and meets 3x/week.

Students who enroll in Calculus I or II must also enroll in a 0-credit drill session that meets weekly for 2 hours on Thursdays. Attendance is mandatory. Managed by instructors and teaching assistants, drill sessions provide a time and place for students to practice the theoretical concepts and methods learned during the MWF lectures through exercises and worksheets.

While most high-school level math can be grasped in real time (during lectures), the abstract concepts and complex methods of calculus cannot, as they need time and repetition to sink in. For most students, understanding and proficiency-building do not happen during lectures, but rather several hours or days later, through practice, repetition, and memorization. Because this type of learning is new to most students, drill sessions provide the time and place for it. At drill sessions, students sharpen each other’s skills by learning from each other. Furthermore, there are teaching assistants and instructors on hand to help.

Unlike many other types of knowledge, calculus cannot be learned by merely reading books, class notes, or solution guides. Like a precision sport, mastering calculus comes primarily through practice and repetition. Becoming stuck on a problem during drill is common and expected. When this happens, students should seek to overcome the roadblock by asking help from a friend, teaching assistant, or instructor. This method (called the Roadblock Effect) greatly promotes calculus learning and is most effective in a group study setting like a drill session.

Study Tips and Help

1. Regular study: Set up a dedicated times every week to work on calculus. Because calculus takes a few days to sink in, study well in advance of assessments (a few days before quizzes/exams).
2. Do not study in isolation: If possible, study calculus with other students. Make friends with other students in your course and meet with them to study.
3. Attend weekly help sessions: Every calculus TA holds a weekly 1.5-2-hour drop-in help session open to all calculus students on a weekday evening, where they are available to help and answer questions. Ask your instructor or consult the Math Portal screen (in front of Meyer 157) for the days, times, and locations.
4. Attend Wednesday evening study hall: Calculus TAs hold a 2-hour calculus study hall open to all calculus students every Wednesday evening. Consult the Math Portal screen (in front of Meyer 157) for the exact time and location.
5. Seek out help during Instructor office hours: Make an appointment to ask questions to your instructor during their office hours.
6. Private tutoring. Obtain the list of Math/Calculus tutors who can meet with you one-on-one as needed. Mary Erickson, Math and Computer Science Office Coordinator, can provide this list. Specialty area and fees for tutoring are included on the list.

Because calculus builds upon many different areas of mathematical knowledge (geometry, algebra, analytic geometry, trigonometry, and elementary functions), studying calculus is substantially different than studying math in high school, where the math curriculum is fairly sequential. In addition to the regular work of keeping up with the course, it is not uncommon for calculus students to have to engage in a fair amount of remedial study, as college students come from a variety of backgrounds with different levels of preparation. There is no shame in asking for help.