Request for Designation as a Writing Reinforcement (WR) Course in Explorations

Name___Jeff Barton______

Course number and title__MA 335, Transition to Higher Mathematics______

Departmental endorsement______Yes______

Has this course been submitted for any other Explorations designation? ___No______
If so, which one? ______

Please list which of your course assignments or activities addresses each of the guidelines, state briefly how this is accomplished, and attach a syllabus for the course.

Criteria for writing reinforcement courses include the following:

  • Class time given to instruction on writing, with particular attention to discipline-specific forms of writing, research methods, and documentation

This course is designed as a transition from the calculus sequence to proof-based mathematics courses. Students learn several important methods of mathematical proof including direct proof, proof via contradiction, and induction. The construction of an appropriate counterexample is emphasized as a way of demonstrating that a statement is not true.

Assignments for the course are primarily exercises in proof-writing or the finding of counterexamples. Students engage in the research process through open-ended problems where they must first decide what is true and then use definitions, previous theorems from class, and the methods they have learned to produce an appropriate proof or counterexample.

  • Multiple writing assignments, including some use of questions on examinations which require substantial writing

Virtually all homework assignments and exams require students to write proofs and/or counterexamples; the complexity of the proofs and the sophistication expected of the students’ written work increases as the term progresses.

  • Required drafts of at least one assignment submitted for review subsequent to revision

The revision process may be handled differently by different faculty members. In my own MA 335 classes I often ask students to revise and resubmit their proofs after they have been critiqued by their peers (see amended syllabus for details of the peer review process). However, due to the nature of proof-writing, the same outcome may be accomplished by asking students to work a different, but essentially equivalent, problem. For example, if a student has received feedback on a proof that the product of two even numbers is even, then that feedback is directly applicable to a proof that the product two odd numbers is odd. All faculty routinely accomplish the goal of having students learn from feedback in this way, and we all incorporate many problems that are essentially equivalent on homework and exams throughout the course.

Return this form as one electronic file with a syllabus appended to by 30 May 2011.

Syllabus – MA 335, Transition to Higher Mathematics

Fall 2009

Instructor: Jeff BartonOffice: Olin 111

Office phone: 226-3027E-mail:

Office hours: M: 10:00-11:30, W: 10:00-11:30 and 12:30-1:30 (and by appointment)

This is a required course for the mathematics major. It is designed as a transition from the calculus sequence to proof-based mathematics courses. We will study methods of proof and learn how to prove theorems. We will gain experience in reading and understanding mathematical proofs, communicating mathematical ideas orally, and writing clear mathematical arguments.

Catalog Description:An introduction to the logic and methods used in advanced mathematics, with emphasis on understanding and constructing proofs. Prerequisite: MA 232.

General Course Goals: The overarching goals of this course are to 1) improve your critical thinking skills, 2) increase your facility in writing and understanding mathematical proofs.

Specific Course Objectives: This course is designed to help you to:

  1. understand symbolic logic and gain experience in using it;
  2. learn methods of proof including direct proof, contrapositive, contradiction, case analysis, and induction;
  3. understand the importance of counterexamples and gain experience in finding them;
  4. gain experience in reading mathematical arguments at an increasingly sophisticated level;
  5. enhance your ability to communicate mathematical ideas orally to your peers;
  6. develop your ability to create sound and well-written mathematical arguments;
  7. engage in investigative learning; and
  8. collaborate responsibly and productively in a mutually beneficial way.

Text: There is no text for this course.

Grades: Your grade will be computed based on the following percentages:

Attendance/engagement:10%

Presentations:15%

Workshops:25%

3 Midterm Exams:30%

Final exam:20%

Attendance: All students are expected to attend and participate in every class. Attendance will be taken at the beginning of every class.

Presentations: Each Tuesday will be spent with students volunteering to present problems at the board. Here’s how it will work:

  1. When students come to class on Tuesday, I will write a list of problems yet to be presented on the board.
  2. Students may then volunteer to work specific problems, and I will write their names beside the relevant problems.
  3. We will go down the list in order with one student presenting at a time and fielding questions about the problem.

Grading:

  1. Presentation grades will be based on completion.
  2. In extreme cases of unpreparedness, credit may not be given for a presentation.

Workshops: On Thursdays, students will spend time in small groups critiquing each others’ proofs. Workshop grades will be based on both the quality of a student’s proofs and the quality of the feedback students give to their peers. Here’s how the workshops will work:

  1. On Tuesdays, students will be responsible for bringing two carefully written, word-processed proofs to class along with hard copies of their proofs for each of their group members and the instructor.
  2. Before coming to class on Thursday, each student will be responsible for critiquing all of the proofs from his or her group members (a total of 6 to 8 proofs depending on the group size). Peer critiques will include both a numerical score and written comments on the positive and negative aspects of the proofs.
  3. In class on Thursdays, students will split into their groups and discuss each of the proofs and the comments on the proofs.

Grading:

  1. At the end of class on Thursdays, I will collect the proofs and critiques from two of the groups. (The groups will not be announced ahead of time.)
  2. I will critique and score each of the collected proofs using the same rubric that students use. Your grade for each proof will be given by

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  1. Each student will also receive a “critical reading” score based on the thoroughness of her or his critiques of other student’s proofs. Points will be deducted from the critical reading score for any fallacious proof accepted as true, any correct proof criticized as false, or a general lack of thoughtfulness in feedback.

The student workshop grade for that week will be a combination of the written proofs score and the critical reading score.

Rubric for Grading Proofs:

Is the mathematics correct? (Choose One) / Points
1)The proof contains a fatal error. This could be due to an attempt to prove a false statement or an attempt to give a counterexample to a true statement. This can also result from severe mathematical flaws while trying to prove a true statement or while trying to provide a counterexample to a false statement. / 0
2)The proof is mostly correct. The result is correct, and the method of proof is appropriate. Minor mathematical errors are all that prevent the proof from being entirely correct. / 3
3)The proof is entirely correct. The result is correct, the method of proof is appropriate, and the proof contains no mathematical errors whatsoever. / 5
Is the result communicated effectively? (Choose One)
1)The proof is difficult to read or follow, and/or stylistic errors are a significant distraction for the reader. A failure to clearly indicate what is to be proved or the method of proof at the beginning may be a reason for selecting this category. This may also result from errors in basic grammar, spelling, or punctuation. There may also be a lack of specificity in labeling variables, a serious omission of necessary steps, or a failure to label diagrams appropriately. / 0
2)The proof is fairly easy to follow. It is clear what is to be proved and what method of proof will be used. There may be minor stylistic errors. Such errors may include minor omissions of appropriate labeling or occasionally skipping a minor step that should have been included. Very minor grammatical errors may also be present. / 3
3)The proof is clear, concise, and easy to read. The method of proof is mentioned at the beginning, and it is clear what is to be proved. The level of detail is appropriate (i.e. an appropriate number of steps is shown), all variables and diagrams are clearly labeled, and there are no grammatical errors. One or two trivial errors (like an equation not being centered on the page) may be present in the presentation. / 5

Exams: There will be three midterm exams and a final. Exams may include an in-class and a take-home portion.

Honor Code: It is the responsibility of every student to be familiar with and abide by the BSC Honor Code throughout this course. Any student who is convicted of an honor code violation involving this class will receive a zero on the relevant assignment, project, or test.