Mathematics

Math 155 Way of Thinking
Fall 1999

MWF 1:10pm - 2:00pm
MC 408
R 1:00pm - 1:50pm
MC 406

 Instructor: Dr. Milan Lukic
Office: MC 521
Office Hours: M-F 10 - 11
Phone: (608) 796-3659 (Office); 787-5464 (Home)
e-mail: mnlukic@viterbo.edu

Course Description

(from the catalog)
An investigation of topics including the history of mathematics, number systems, geometry, logic, probability, and statistics. There is an emphasis throughout on problem solving. Recommended for General Education.

Text

Miles, Thomas & Nance, Douglas, Mathematics, One of Liberal Arts, Brooks-Cole Publishing, 1997.

Core (General Education) Skill Objectives:

1. Thinking Skills:

   (a)

   Students will use reasoned standards in solving problems and presenting arguments.

2. Communication Skills: Students will ...

   (a)

   ...read with comprehension and the ability to analyze and evaluate.

   (b)

   ...listen with an open mind and respond with respect.

   (c)

   ...access information and communicate using current technology.

3. Life Value Skills:

   (a)

   Students will analyze, evaluate and respond to ethical issues from an informed personal value system.

4. Cultural Skills: Students will ...

   (a)

   ...understand culture as an evolving set of world views with diverse historical roots that provides a framework for guiding, expressing, and interpreting human behavior.

   (b)

   ...demonstrate knowledge of the signs and symbols of another culture.

   (c)

   ...participate in activity that broadens their customary way of thinking.

5. Aesthetic Skills:

   (a)

   Students will develop an aesthetic sensitivity.

Specific Course Goals:

Those happen to coincide with some of the NCTM (National Council of Teachers of Mathematics) ``standards'' for mathematics education. We have:
The students shall ...

1. ...develop an appreciation of mathematics, its history and its applications.
2. ...become confident in their own ability to do mathematics.
3. ...become mathematical problem solvers.
4. ...learn to communicate mathematical content.
5. ...learn to reason mathematically.
    

General Education Course Objectives:

1. Thinking Skills: Students will ...

   (a)

   ...explore writing numbers and performing calculations in various numeration system.

   (b)

   ...solve simple linear equations.

   (c)

   ...explore linear and exponential growth functions, including the use of logarithms, and be able to compare these two growth models.

   (d)

   ...explore a few major concepts of Euclidean Geometry, focusing especially on the axiomatic-deductive nature of this mathematical system.

   (e)

   ...develop an ability to use deductive reasoning, in the context of the rules of logic and syllogisms.

   (f)

   ...explore the basics of probability.

   (g)

   ...learn descriptive statistics, including making the connection between probability and normal distribution table.

   (h)

   ...learn the basics of financial mathematics, including working with the formulas for compound interest, annuities, and loan amortizations.

   (i)

   ...solve a variety of problems throughout the course which will require the application of several topics addressed during the course.

2. Communication Skills: Students will ...

   (a)

   ...collect a portfolio during the course and write a reflection paper.

   (b)

   ...do group work (labs and practice exams) throughout the course, which will involve both written and oral communication.

   (c)

   ...turn in written solutions to occasional problems.

   (d)

   ...write a mathematical autobiography.
    

3. Life Value Skills: Students will ...

   (a)

   ...develop an appreciation for the intellectual honesty of deductive reasoning.

   (b)

   ...listen with an open mind and respond with respect.

   (c)

   ...understand the need to do one's own work, to honestly challenge oneself to master the material.

4. Cultural Skills: Students will ...

   (a)

   ...explore a number of different numeration systems used by other cultures, such as the early Egyptian and Mayan peoples.

   (b)

   ...develop an appreciation for the work of the Arab and Asian cultures in developing algebra during the European ``Dark Ages''.

   (c)

   ...explore the contribution of the Greeks, especially in the areas of Logic and Geometry.
    

5. Aesthetic Skills: Students will ...

   (a)

   ...develop an appreciation for the austere intellectual beauty of deductive reasoning.

   (b)

   ...develop an appreciation for mathematical elegance.

Content:

This course is aimed at the needs of elementary education majors and as such is the first part of a three-course 12 credit sequence (MATH 155-255-355). This is a ``content'' course rather than a ``methods'' course (teaching methods are addressed in the latter two courses in the above sequence). It is what people generally call a ``Liberal Arts Mathematics Course'', meaning that it covers a wide variety of topics, has an emphasis on problem solving, and uses a historical and humanistic approach. Consequently, the course is considered appropriate for the general education requirements and is open to all students.
We plan to cover, with an appropriate selection, mainly the material from the first nine chapters of the textbook.

Course Philosophy and Procedure

Two key components of a success in the course are regular attendance and a fair amount of constant, every-day study. You should try to make sure that your total study time per week at least triples the time spent in class. Also, an active class participation, working in small groups, not hesitating to ask me for help both in class and in my office can greatly enhance the success and quality of your learning. You should also use the Learning Center facilities (MC 320) as much as possible.

Grading will be based on three in-class exams, a cumulative final exam, class participation, take-home problems, projects, group practice exams and portfolios. I have not decided yet about the distribution of points among those, but I can assure that you will be required to work hard, and that you will have every opportunity to show what you have learned. My grading scale is

A=90%, AB=87%, B=80%, BC=77%, C=70%, CD=67%, D=60%.

There will be a few assignments not generally included in a mathematics course, but which will, I hope, make your experience in this class more well-rounded than in a typical algebra course. These include the following:

Mathematical Autobiography: Due Tuesday, September 7. Point value 25. This will be a 3-5 page paper in which you will explore your life as a math student. Try to be specific, and to reflect what method and styles worked for you in the classrooms throughout your K-12 career.

Portfolio: Due Friday, December 10. Point value: 50. During this course you will be working many problems, some of which will be ``breakthrough'' efforts, when you finally understood how to do something or which you are proud of because your write-up was so well done. You will chose FIVE problems along the way which you want to include in your portfolio; for each of these problems you will include a nicely organized re-write of the problem along with a brief reflection paper on why you chose that particular problem and on what you learned from the problem. Each of the five problems (the write-up and the reflection paper combined) will be worth 10 points. I expect at least one page for each problem.

Group Labs: At a number of points during the course you will be working on a ``lab'' in small groups. Even though you will be working in a group of three or four people, each person should turn in a paper. It is important that each person contributes their input into these labs. However, I expect you to write the turn-in paper all by yourself.

I am looking forward to explore this fascinating subject with you, and for all of us to have an interesting and enjoyable semester.

Americans with Disability Act:

If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me and Wayne Wojciechowski in Murphy Center Room 320 (796-3085) within ten days to discuss your accommodation needs.

This syllabus is tentative and may be adjusted during the semester.
 

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