Cardinal Stritch University is a learning community in which the elements of scholarship and learning -- discovery, application, integration, and teaching -- are embraced by faculty, staff, and students. Stritch graduates are critical thinkers, ethical decision makers, and life-long learners.
Our mission is to transform lives. We do this through value-centered education. This is our business.
This course offers a variety of geometrical topics which may include taxicab geometry, conic sections, four-dimensional space, trigonometry in the unit circle, the geometry of the sphere, and geometric patterns in art. The topics will be determined by the instructor and the needs of the students.
Mt 322 Topics in Geometry Weekly Course Assignments.
In this course, benchmark tests give the student an opportunity to demonstrate fluency with basic vocabulary and computational strategies. In-class tests give the student an opportunity to demonstrate mastery of the various mathematical strategies and techniques -- particularly the construction of sound mathematical proofs. The Proof Book will provide a record of the student's growth in the ability to write coherent geometric proofs.
Beyond the content of individual courses, the major in mathematics is designed to prepare students for the 21st century by helping students to become problem solvers, effective communicators, users of appropriate technology, and team players. In this course, students will be engaged in a variety of activities which will help them to move toward achieving these goals.
As problems solvers, students will be learning to:
As effective communicators, students will be learning to:
As users of appropriate technology, students will be learning to:
As team players, students will be learning to:
Calculators and computers are legitimate tools for doing mathematics. One of the goals of the Department of Mathematics & Computer Science is that our students develop a facility with various forms of technology and learn to use these effectively to explore and solve problems. One of the specific goals of this course is to provide an opportunity for students to become proficient in the use The Geometer's Sketchpad. Throughout the semester, students will be given opportunities to use electronic communication tools (such as email and a graphical web browser). Class assignments will be regularly posted to the internet.
Each student will need to have access to computers and/or to work in the computer lab on some of the homework assignments and projects. Computer lab schedules are posted on the doors of the computer lab. Although other classes also meet regularly or occasionally in the labs, there is one lab which is always reserved for student use. You will need to plan to hold some of your outside-of-class group meetings in the computer labs.Back to TOC
See the Weekly Course Assignments for an outline of the sequence of topics and content to be covered in this course.Back to TOC
To be successful in this course, the student should have had at least two years of high school mathematics, including both algebra and geometry.Back to TOC
Students will do much of the work of this course in cooperative learning groups. These groups will work together on some homework problems as well as on in-class problems.
The objective of group work in this course is primarily to engage the students in thinking more deeply about important mathematical issues. Even though a lot of the work of the course is done in small groups, students are expected to learn to develop proofs and to solve problems on their own. Working with colleagues in this class and talking about problems in small groups are strategies for developing an understanding of a problem situations from several points of view. Learning theory research has shown that cooperative learning leads to deeper understanding and longer retention of material that is studied.
Working well in a group is an important skill. Some students enjoy the group work more than others, and all will benefit from further developing this skill. Most of our graduates are employed in workplace settings where they are expected to function as a member of a project team. Many of our graduates tell us that the skill they developed by working in cooperative learning groups is very beneficial in the workplace.Back to TOC
The faculty of Cardinal Stritch University are committed to developing writing and speaking skills for all students across all disciplines. Students will have opportunities in every class session to speak with peers informally in small-group and full-class discussions. Students will also have opportunities to give short presentations to their colleagues -- usually with respect to a proof that she/he is developing. This provides some experience in presenting work-in-progress, that is, not yet complete. Any written work that is turned in -- graded or ungraded homework assignments, tests, papers, and projects -- is to be written in standard English using complete sentences. Throughout the semester, students will receive feedback from the instructor (and from their peers) which is intended to assist in developing good speaking and writing skills.Back to TOC
Regular attendance is expected. Class discussion is dynamic, and hands-on computer activities are designed to stimulate discussion among students working in small groups. Getting someone's notes is a poor substitute for being present and involved in class discussion. However, if you must miss a class, it is your responsibility to find out what you missed.
Problem solving is not a spectator sport. During most class periods there will be time for large and/or small group discussions about selected problems. It is important to learn to ask helpful questions and to listen constructively to each other. Constructive participation sometimes means allowing others time and space to think about the problem.
Homework assignments will include reading the text, checking the library and other sources for information beyond that given in the text, and doing problems from each chapter. If the discussion is lively, with everyone contributing, I will collect and grade fewer problems and have fewer quizzes; if the discussion lags or is dominated by a few individuals, I may find it necessary to collect homework and/or give (unannounced) quizzes.
At the end of each class period, I will ask you to fill out a Class Participation / Self-Evaluation form. I will use these forms to check attendance, respond to your self evaluation, and give you a score for class participation. If you must miss a class for any reason (excused or unexcused absence), your participation score for that day will be recorded as 0. However, if you wish to make up for these absences, you may turn in written evidence that you have done some work to make up missed lab/class activities. This make up work must be turned in within two class periods of the missed classes.
One of the principal goals of this course is for students to learn to develop and write robust mathematical proofs. Throughout the semester you will be asked to write a lot of proofs. Some of these proofs will be turned in and graded individually. You are to collect these and other proofs that you develop into a Proof Book, a portfolio of your best geometric proofs. By the end of the semester, you shuld have 15 - 20 proofs in your Proof Book. These proofs should represent the entire scope of the course; that is, you should have many different styles of proofs, and you must include proofs from each chapter of the course. More will be said about the Proof Book toward the end of September.
Each proof that you write and turn in will be marked according to a rubric for grading proofs, which will be handed out in class. Each proof will be graded on logic, appropriate diagrams/tables, completeness, and clarity of explanation. These grading criteria are designed to give you constructive feedback so that you learn to develop more robust proofs. Writing proofs is one important form of written communication in mathematics.
A study guide for each test will be available about one week before the scheduled test date.
Ordinarily, I do not give make-up tests; exceptions to this policy will be considered on a case-by-case basis.
There will be two benchmark tests in this course. These are offered outside of regular class meetings. Each student should make an appointment with the instructor to take the benchmark test during the scheduled window-of-opportunity.
This benchmark will cover concepts and skills which are prerequisite for this course. The focus will be on the basic vocabulary and language of geometry. The study guide for this benchmark will be available about September 10.
This benchmark will cover basic concepts and proof strategies that are emphasized throughout the course. The study guide for this benchmark will be available about November 26.
Procedures for Benchmark Tests:
To pass the benchmark test, a student must get nine or ten of ten problems completely correct; there will be no partial credits. If a student passes on the first attempt, the score will be recorded as 100%.
If a student does not pass a benchmark test on the first attempt, he/she may demonstrate that that he/she has done some additional practice, and make an appointment with the instructor to try the test up to two more times.
If a student passes a benchmark test on the first or second re-test, the score will be recorded as the average of the scores made on each attempt.
If a student has not passed a benchmark after two re-tests or by the specified date, the score will be recorded as 0%.
Note: Each student's midterm grade will be based on five to ten graded proofs, one benchmark, one in-class test, and half the semester of participation. This represents 35% of the final course grade. Midterm is October 17, and the last day to withdraw from fall semester courses is November 8. If you have concerns about your progress or ability to keep up with course assignments, please feel free to discuss these with the instructor.
Inherent in the mission of Cardinal Stritch College is the strong belief in the principle of academic integrity. Students who cheat violate their own integrity and the integrity of the College by claiming credit for work they have not done and knowledge they do not possess. All students are expected to recognize and to abide by the policy on academic integrity found in the Student Handbook. Because you will be asked to do a lot of work in collaboration with your colleagues (i.e., your classmates), whenever I give you a take-home assignment or test on which I expect you to work on your own, I will make this very explicit.
If you have any special needs for alternative instruction and/or evaluation procedures, please feel free to discuss these needs with me so that appropriate arrangements can be made.
As a matter of courtesy, students are expected to turn off cell phones and pagers during class. If extraordinary circumstances require an exception to this policy, the student is expected to discuss this with the instructor before class begins.Back to TOC
My office is located in CH 34, just across the hall from the classroom where this course meets. I will be on-campus and regularly available for students most weekdays. If you wish to make an appointment with me, you may sign up on the sheets which are posted on the in the hallway just outside the door of my office. The best way to contact me is via email, which I check regularly (several times a day) both while I am on campus and from home.
If you need to reach me between classes: