|
If you have any questions, please ask during class, after class, or during my Office hours |
Or E-mail me at schumacherc@kenyon.edu | |||
| Back to Carol Schumacher's Homepage |
The Art of Mathematics: The central purpose of this course is to introduce you to mathematics as the discovery and study of patterns. The course is meant to make you think about mathematics in a completely new way and to broaden your view of what mathematics is. The course will consist of a series of hands-on mathematical explorations of various types. There will be essentially no lectures. In the words of the authors of the series Discovering the Art of Mathematics: "Students in the course will be actively involved in authentic mathematical experiences that
- are both challenging and intellectually stimulating,
- provide meaningful cognitive and metacognitive gains, and,
- nurture healthy and informed perceptions of mathematics, mathematical ways of thinking, and the ongoing impact of mathematics not only on STEM fields but also on the liberal arts and humanities.
Main texts/materials are freely available on line on the website Discovering the Art of Mathematics.
Supplementary text (required), The 5 Elements of Effective Thinking, Burger, Edward B. and Michael Starbird, Princeton University Press, 2012, is available at the Kenyon bookstore.
Grading: The grade will be calculated based on 5 components:
| Day-to-Day work: Class preparation, class participation, and in-class presentations | 30 % of the final grade |
| Lab Notebooks, Writing assignments, and Homework challenges | 25% of the final grade |
| Student-faculty conferences | 15 % of the final grade |
| Reflections on Productive Failure | 10 % of the final grade |
| Final project (done in pairs) | 20% of the final grade |
Day to day work: Art of Math is different from other math courses you have had. Because the purpose of the class is to change the way that you think and reason about mathematics, it is essential that you become immersed in the work of the course. It is not enough to respond to what your instructor does or tells you. You and your fellow students are the ones that make things happen in class. Without your active participation, nothing will happen. Perhaps more than in any class you take, you will get benefit out of the course in direct proportion to how much effort you put in. Thus day to day work is the most substantial portion of the grade. This part of the grade has several components:
The persons presenting their work to the class are not the only ones with responsibilities in a presentation. The students sitting at their desks have as central a role to play. Students presenting their work are not meant to replace a seasoned, polished lecture that would be given by an experienced instructor. They are counting on their fellow students to help them by making clarifying suggestions and asking questions. I will feel free to ask questions of persons who are sitting down.
Inquiry-Based Learning: The classroom approach used in this class is called Inquiry-Based Learning, or IBL. IBL is a pedagogical strategy in which students are led to develop mathematical concepts and discover mathematical connections for themselves. The faculty member serves as mentor and moderator. The time in class is structured as a collaborative learning experience in which everyone works together to deeply understand the mathematical ideas.
Working with your fellow students: There is a lot of evidence that, when students actively discuss mathematical ideas with other students on a regular basis, they learn more deeply and the knowledge stays with them longer than when they work in isolation. Also working with others is much more fun than working alone! Thus you will be working in small groups every class, and I encourage you to work together outside of class as well as in class.
Office hours and MSSC hours: The work in this class will involve lots of conversation: between faculty member or LT and the students and among the students themselves. Thus frequent work in office hours and at the MSSC is an expected part of the course. I encourage you to plan Art of Math work time around my office hours and around Robin Belton's hours at the MSSC. This allows you to work with others and to chat with Robin or me when you feel stuck or confused.
Lab Notebooks: In this course, you will be expected to learn to discuss mathematical ideas orally and in writing. Thus I expect you to keep a daily "Lab Notebook" in which you describe your various attempts to solve the assigned challenges, a clear summary write-up in which you explain final success in solving a given challenge, and your thoughts/notes on the discussion questions that go with the work on the challenges. You will be asked to turn in your lab notebook at several points during the semester. These won't be graded, in the usual sense, but I will assign a score (0, 1, 2, or 3) based on how well you are keeping notes about your activities.
Writing Assignments: during the semester you will be asked to write a few short essays about themes relating to the course. Shorter pieces may be written in class; longer ones you will write outside of class and turn in. These may take various forms.
Cooperative learning for written assignments: I encourage my students to discuss their work with me and with each other. This is true for written work as well as for work on mathematical challenges. If you work with other students on an assignment, you should note this on your paper. (There is no penalty, this is just a matter of academic honesty.) However, write-ups are individual. Be sure that the group discussions stop before the writing begins. Discuss the ideas in a group, then go off by yourself to write. For instance, it is not OK for a group to work out a problem together, copy it down, and turn in identical write-ups----even if all members of the group contributed equally to its production. Individual digestion of the ideas and individual writing must be the end of the process. (See Academic Integrity, below.)
Homework challenges: As we work on things in class, I will assign pieces of the larger mathematical exploration to be worked out (or completed) outside of class and turned in at the beginning of the next class.
Student-Faculty conferences: Twice during the semester, I will meet with each student individually and ask them to talk to me about their work and to discuss their mathematical understanding of the themes and challenges we have been working on in the class. Each of these conferences will be 20 minutes long and must be scheduled individually within a designated two-week period. (I will have extended office hours and during these weeks to accommodate the conferences and will require students to sign up in advance for their conferences.)
Reflections on Productive Failure: One of the 5 Elements of Effective Thinking laid out in the book of the same name is "fail to succeed." This play on words embodies the idea that successful people understand that anything worth doing requires perseverance and determination and that there are often failures along the way. Mistakes are great teachers that help us identify and attack holes in our understanding. They also highlight important opportunities to push forward to and achieve more the next time. In this class you will not only be encouraged to make mistakes, you will be graded on how thoroughly you fail at something and on how you make use of your mistakes to get better at the challenges placed before you. This portion of the grade will be based on two writing assignments in which you look back over the work you have been doing in the class, identify one or more places you didn't succeed in your objective but where those failures helped you to see how to improve. Part of the purpose here is for you to be on the lookout for places where you try something that doesn't work. Watch for these moments. Then deliberately and carefully pause to see what you can learn from your failed attempts. Describe the incident and the process in your lab notebook. If you do this, writing these reflections should come easily.
Final Project: Around the beginning of November, you and a partner will be asked to look at the Discovering the Art of Mathematics books and pick a mathematical exploration that we have not done in the class. (I may have some guidance about possible good choices, but you are free to ask to do something else, if you wish.) You will need to clear the topic with me in a written (short) proposal. Then you and your partner will work out the challenges in the exploration, write a summary/reflection of your work and make a poster summarizing your work. This will be presented to your classmates during the regularly scheduled final exam period. (Tuesday, December 15, 8:30-11:30 a.m.)
Academic Integrity: You are encouraged to work with other students. It is, however, understood that all written work that you turn in must finally be your own expression. In working alone or with other students, it is understood that your only additional sources of information will be the textbooks or other materials specifically made available to the class by Prof. Schumacher, any notes you took in or for class, and brainpower. (And, of course, Prof. Schumacher or Robin Belton, who are happy to consult with you at any time.) You are not to consult other written or human sources ---this prohibition includes all things like books, journals, online sources and your friend the math major. For further information see the student handbook or consult Prof. Schumacher.
Disabilities: If you have a physical, psychological, or learning disability that may impact your ability to carry out assigned course work, feel free to discuss your concerns in private with me, but you should also consult the Office of Student Accessibility and Support Services (SASS) at 740-427-5453. The Coordinator of SASS, Erin Salva (salvae@kenyon.edu), will review your concerns and determine, with you, what accommodations are appropriate. It is Ms. Salva that has the authority and the expertise to decide on the accommodations that are proper for your disability. Though I am happy to help you in any way I can, I cannot make any special accommodations without proper authorization from Ms. Salva. Except in extraordinary circumstances, accommodations must be arranged with Ms. Salva and with me at least one week before they are to take effect.
Title IX; responsible employee: As a member of the Kenyon College faculty, I am concerned about the well-being and development of my students and am available to discuss any concerns you may have. However, I need for you to know that as a Kenyon faculty member I am obligated by federal law to share certain information with the college's Title IX coordinator. This is to ensure our student's safety and welfare are being addressed, consistent with the requirements of that law. These disclosures include but are not limited to reports of sexual assault, relational/domestic violence, and stalking.