A traditional calculus course consists of the following activities:
- Go to a lecture
- Watch some mathematics written onto a chalkboard or overhead projector slide
- Read a paper textbook
- Do some homework problems on paper
- Hand these papers in for credit
- Take a few exams
Distance Calculus operates on a very different paradigm.
There are no lectures.
Instead, the learning in Distance Calculus is active learning, rather than passive learning, like that in a lecture hall.
The "textbook" for Distance Calculus is the electronic textbook, Calculus&Mathematica™
(and its sibling project, Calculus&LiveMath™). Rather than simply reading the textbook,
you actively engage the textbook - the textbook has experiments for you to run yourself, to
actively investigate the calculus topics, with live graphs, algebraic computations, and
written explanations using the computer algebra systems
LiveMath™ Maker and/or
Mathematica®.
The Lessons
The Calculus&LiveMath and Calculus&Mathematica®
lessons are experiment-based electronic
notebooks where the students use LiveMath or Mathematica to investigate,
solve, interact, and develop the concepts of calculus. Different from a
"regular textbook", the Calculus&LiveMath®
and Calculus&Mathematica® materials ask the students
to think, theorize, and analyze the concepts and structures of calculus to a level
not possible with paper textbooks: the students actually work ON THE ELECTRONIC
TEXTBOOK, changing values, experimenting with examples, and developing ideas
about the concepts and calculations in calculus. As the courses progress the electronic textbook becomes a personal account of each students learning experience. The experience
from these materials is quite different from the "example, problem, example, problem"
common approach to learning calculus.
The Distance Calculus courses use the Calculus&LiveMath® and Calculus&Mathematica® materials as
its curriculum. Students enrolled in Distance Calculus will read, interact, experiment,
solve, write, and answer questions directly in these Calculus&LiveMath® and Calculus&Mathematica® notebooks,
which are then exchanged with the instructional team for feedback. Student mentors
and instructors comment, discuss, and interact with the students regarding their
assignments and general questions that come up during the completion of these lessons.
The Homework
"Homework" is the focus of this course, via the Calculus&LiveMath® and Calculus&Mathematica® notebooks.
Students primarly work on these assignments, and when needed, ask questions,
or are asked questions of, by the instruction team of student mentors and
instructors. The "Homework" notebooks are not typically turned in just one time:
there is a recursive process that submitted notebooks take
from student-to-instructor and back to student, back to instructors, and
so forth ... sometimes returning back to the student for more
work completion up to 10 times! This recursive process ensures that students move
at their own pace (with support and motivation from the instructional team), and
move to the next module when they are ready to do so.
Communication is the key. Instead of lectures, this course relies on person-to-person
communications using a variety of Internet communication tools, including:
- Chat Client (ex. AOL Instant Messenger®)
- Notebook transfers via the Web
The Pace
Students work at their own pace. The instructional team will spur students on, helping set individual goals. But if a student requires a few more days of work on a particular module to learn the content effectively, then those few days are afforded.
Exams are both electronic, and in written form. Students in Distance Calculus will set up "exam times" with a human monitor or proctor who will administer the exams. Examinations are not punitive. Students will take the quizzes and exams, except for the final exam, until the student passes the exam.
The instructional team is on duty the majority of each day. So if a Distance Calculus student wants to work on calculus in the morning hours before going to work, the instructional team will be on duty with either student mentors or instructors ready to answer questions and interact with students. If, on the other hand, a student wishes to work in the evening, there will be instructional staff on duty then, too. Weekends, holidays. This class never stops meeting.
The Units
Each of the courses offered in the Distance Calculus program are either three (3) or four (4) unit courses. Each of these courses are:
- University-level calculus courses ("engineering calculus", "regular calculus" or "survey of calculus".)
- Full three (3) or four (4) unit courses
- Transferable to most institutions: these are standard calculus sequence courses, interchangable with Freshman Calculus courses at most institutions.
- Satisfy engineering, science, computer science, and mathematics degree requirements
- Can generally be used to satisfy "business calculus" requirements, although the Distance Calculus (and "engineering calculus") is a "more difficult curriculum" than standard "business calculus" courses. Check with your transferring institution to make sure that they will allow this "course substitution".
The Method
Distance Calculus teaching methods were developed at the Ohio State University by Lee Wayand and Bill Davis, co-author of Calculus&Mathematica®, MathEverywhere Publishing (previously Addison-Wesley).