For class time and room, instructor contact information, and office hours, see Math 421 Homepage.
Text: Making Sense of Calculus, Volume 1: The Mathematics of Change and Variation by Sephen Monk, 2007 Draft edition, available at the University Bookstore.
We will operate on the hypothesis that if you have enrolled in this course, you are either definitely or potentially interested in becoming a secondary school mathematics teacher. There are three main goals in this class. They are interconnected and of equal importance.
The CONTENT GOAL is that you gain a deeper, more comprehensive and complex understanding of calculus, as a body of powerful mathematical ideas, as a way of understanding phenomena of change and variation, and as a subject studied in school.
The COMMUNICATION GOAL is that you learn to communicate your understanding, insights, and intuitions in relation to the ideas of calculus and that you do so with other people who may see calculus in ways very different from the way you do. This involves listening to others, asking questions, solving problems, making guesses, and supporting claims.
The LEARNING PROCESS GOAL is that you analyze and reflect on your experience as a student in this course in a way that will contribute to your understanding of the subject as well as your effectiveness as a mathematics teacher.
In Class: Learning to articulate your mathematical ideas, listen to others, and participate in group problem-solving are critical goals of this course. In class we will have both small group and whole class discussions. Groups will be randomly assigned the first day of the quarter. After that they will be changed every two to three weeks.
You are expected to attend every class, to participate fully and constructively in both small group and whole class discussions, and to take turns recording groupwork to be turned in. At the end of every class, each group should turn in a paper with the names of the group members present that day at the top. The work or discussion notes to be handed in will be specified during class.
Outside Class: You are responsible for several kinds of work outside of class.
Grades will be based on participation in class and your written work. There will be no tests (but we will meet during the scheduled final exam time for a final discussion). Grade distinctions beyond a basic grade of 2.8 will depend on the quality of your written homework and on how much additional work you want to take on, pursuing questions more deeply, reflecting on what you are learning, and pulling together the ideas of the course at the end of the quarter. The details of the grading system are as follows.
Basic Work: At least a 2.8 to a student who hands in competent versions of all written homework assignments on time, attends every class (except for excused absences) and participates fully and constructively in classroom activities. Deductions from the 2.8 will occur as follows. For each unexcused absence, 0.05 will be deducted, with our final two-hour meeting at the scheduled exam time counting double. You may have at most two excused absences for reasons such as illness or serious accident, and will have to do a makeup assignment for each. For a completely omitted homework assignment, 0.1 will be deducted. For each extremely late or seriously incomplete assignment and for repeatedly late assignments, deductions will be made in increments of 0.05.
Quality Points: Up to 0.6 additional grade points based on evalution of your written homework. I will write comments on homework and mark each assignment on a scale of + (superior), √ (OK), or - (lacking in some way). These evaluations will be based on the completeness, thoughtfulness, and depth of the work. An average of "OK" for the assignments for the whole quarter will earn at least 0.2 quality points.
Reflective Journal: Up to 0.4 grade points for keeping a reflective journal in which you report and reflect shortly after each class period on your experiences as a student in this class. Detailed requirements for the journal.
Synthesis Project: Up to 0.4 grade points for writing a synthesis paper near the end of the quarter reflecting on the entire quarter. More details will be posted here midquarter.
The total of possible points is 4.2, while of course the maximum possible course grade is 4.0. This allows a shortfall or omission in one area to be fully or partly made up by excellence in the other areas. For truly exceptional work on the journal or the project, I might add an extra 0.05 or 0.1.
Chapter 1, The Historical Development of Calculus: first two weeks.
Chapter 2, Investigating Situations of Change: Jan. 19-26.
Chapter 3, Spreadsheet Calculus: The Caculus of Sequences and Graphs:
Jan. 26-Feb. 7.
Chapter 4, Visual Calculus: Rates and Amounts: Feb. 9-23.
Chapter 5, Symbolic Discrete and Continuous Calculus: Feb. 28-Mar. 14.
Note that the final discussion of Chapter 5 will take place during the
scheduled final exam time for the course.
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Math 421 Homepage.
Most recently updated on January 1, 2011.