MWF 1-1:50

MATH Building room 0201

J. Fey

Office in 3113 Mathematics Building

Phone: x53151 (voice mail)

E-Mail: JF7@umail.umd.edu

M 2-4, W 2-4, and other times by appointment

Room 3113 Mathematics Building

The broad purpose of MATH 110 is to survey some of the most common ways that mathematical ideas are used as models and to develop some skill in application of those models to important quantitative problems. This special section of MATH 110 (0501) shares that common overall purpose with all other sections of the course this Spring. However, the special section will explore several alternative approaches to that goal.

- Geometric models of size, shape, location, and motion
- Algebraic models of change
- Network optimization models
- Probability models of randomness

The goal of a collaborative, active class format is to engage every student in constructing a personal understanding of the key mathematical ideas - not memorizing in a rote fashion the mathematical techniques demonstrated by the instructor. The mathematical investigations will often include collecting and analyzing data from simple experiments, finding mathematical models that represent patterns in that data, and using models to make predictions which can then be tested.

Second, it is now fairly widely accepted that there are many different ways that one can demonstrate learning - not only by scores on timed examinations that emphasize computational problem solving. Therefore, each student will have some options (within certain limitations) in how their semester grade is determined.

**At least 50%**of the course grade will be based on the two hour exams and the final exam (weighting those scores in the ratio 2:2:3).- Weekly assignments - varying from individual and group written reports of
mathematical investigations, problems for homework, quizzes, and other learning
checkpoint activities - will constitute
**15 - 20%**of the semester grade. - Class participation - including regular attendance and active participation in the
cooperative problem solving activities of the class and regular writing in a journal
of reflections on content and learning throughout the course - will constitute
**15 - 20%**of the semester grade. - At your option, you can choose to have
**15 - 20%**of your semester grade based on a portfolio of work illustrating the topics and results of the course and your best work on those topics.

Because the class will involve frequent investigations that involve data collection, sketching of ideas, and written communication of results, it will make sense to have a notebook in which copies of individual papers can be entered neatly. Graph paper will be helpful. Some experiments will require rulers and angle measuring devices. For major sections of the course a graphing calculator will be an essential tool. While the regular sections of MATH 110 require only a TI-81 graphing calculator, many things we will do are aided by features of the somewhat newer TI-82 model that will cost only slightly more than the TI-81.

The focus of your journal entries should be your learning of mathematics - what you do, feel, discover, and wonder about. The journal entries will then comprise a reflective record of the questions and insights that help you make sense of the material covered in the course. In your writing you may choose to focus on any aspect of the course and its connections to your other mathematical, academic, and out-of-school experiences, as long as you are willing to let the instructor see what you have to say . There are no "right" or "wrong" journal entries.

As general guidelines to consider in crafting journal writing, you might consider the following questions:

- What did you learn from a class, activity, discussion, or assignment?
- What questions do you have about some current class topic or activity?
- What discoveries are you making about the ideas or methods of mathematics or about your own mathematical development?
- What thought processes have you gone through in solving a particular problem or investigating a question?
- What challenges or confuses you? What do you like or dislike?

Since this special section of MATH 110 will emphasize collaborative work on analysis of complex problems, with written and oral reports shared in full-class discussions, your work in the course will naturally lead to a portfolio of findings and reports. From time to time you will be asked to submit those reports for review, but you might also consider making a more complete portfolio of your work a significant component of the material on which your course progress is graded.

To construct a portfolio of your work, begin early to collect the problems posed and worked on in class and assigned as homework and your own write-ups of findings in work on those problems. As you gain new insights and see ways to solve previously unsolved problems, rework earlier results, crafting them into the sort of polished form you'd be pleased to present as reports to a supervisor at work. By the end of the course you should have assembled a collection of at least 15-20 such pieces of work, selected to illustrate the major ideas of the course. That is, your final submitted portfolio should include problems and results that would convey to someone else the main ideas of the course and your insights into those ideas. A brief commentary on each major section of problems and results should set the context and guide the reader.

To help you feel comfortable about the direction of your portfolio work, there will be two mid-term reviews of what you have assembled. You are, of course, welcome to discuss your progress with the instructor at any time. Grading criteria for portfolios will include breadth of the selection as indicators of course content, completeness and accuracy of your written work, and clarity of your presentation.

HTML coding by Tom O'Haver, Feb. 24, 1995.