MATH 155: Mathematics, A Way of Thinking
Fall 1999, MWF: 12:10-1:00 pm, T: 1:00-1:50 pm, MC 406
Instructor: Rich Maresh, MC 522, 796-3655, (Home: 526-4988), Office Hours: MWF 10-11, W 2-3
Final Exam: Friday, 17 Dec 99, 9:50-11:50 am
Course Description: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:
Mathematics, One of the Liberal Arts. Miles, Thomas & Nance, Douglas. Brooks/Cole Publishing, 1997.
Core Skill Objectives:
THINKING SKILLS: The students will ...
(a) ... use reasoned standards in solving problems and presenting arguments.
COMMUNICATION SKILLS: The students will ...
(a) ... read with comprehension and the ability to analyze and evaluate.
(b) ... listen with an open mind and respond with respect.
LIFE VALUE SKILLS: The students will ...
(a) ... analyze, evaluate and respond to ethical issues from an informed personal value system.
CULTURAL SKILLS: The 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.
AESTHETIC SKILLS: The students will ...
(a) ... develop an aesthetic sensitivity.
It is also worth mentioning the NCTM (National Council of Teachers of Mathematics) "standards" for mathematics education, because they are also a list of some overall goals we strive for in this course:
The students shall develop an appreciation of mathematics, its history and its applications.
The students shall become confident in their own ability to do mathematics.
The students shall become mathematical problem solvers.
The students shall learn to communicate mathematical content.
The students shall learn to reason mathematically.
Course Objectives:
THINKING SKILLS: The students will ...
(a) ... explore writing numbers and performing calculations in various numeration systems.
(b) ... solve simple linear algebraic 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 the 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.
COMMUNICATION SKILLS: The students will ...
(a) ... write a mathematical autobiography.
(b) ... collect a portfolio of their work during the course and write a reflection paper.
(c) ... do group work (labs and practice exams), involving both written and oral communication.
(d) ... turn in written solutions to occasional problems.
LIFE VALUE SKILLS: The students will ...
(a) ... develop an appreciation for the intellectual honesty of deductive reasoning.
(b) ... understand the need to do one's own work, to honestly challenge oneself to master the material.
CULTURAL SKILLS: The students will ...
(a) ... explore a number of different numeration systems used by other cultures, such as the early Egyptian and the 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.
AESTHETIC SKILLS: The students will ...
(a) ... develop an appreciation for the austere intellectual beauty of deductive reasoning.
(b) ... develop an appreciation for mathematical elegance.
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.
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: Monday, September 13. Point value: 25. This will be a 3-5 page paper in which you explore your life as a math student. I think it is especially appropriate for education majors to reflect on your past mathematical life, and to consider what methods and styles worked for you in the classrooms throughout your K-12 career. Try to be specific and try not to make this a "blame the teacher" paper.
Portfolio: Due: Friday, December 10. Point value: 40. It is important to an artist or a photographer to assemble a "portfolio", a collection of their work which is representative of their skills and interests. The same is true for a student of mathematics. 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 choose 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 8 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. I believe that students learn in a variety of ways, and that while studying alone can be valuable, for many working on problems in small groups can enhance student learning significantly. Even though you will be working in a group of three or four people, each person should turn in a paper; I want to see each person's expression of the solutions to the problems - and if you each get a graded paper back it will give you something to study from. It is important that each person contributes their input into these labs. I will randomly assign groups, although I am willing to consider rearranging them as time passes, when, for example, a student drops the course. It happens.
The grading procedure is quite straight-forward. "A" = 90% or more of total possible points, "AB" = 87% or more, "B" = 80% or more, "BC" = 77% or more, "C" = 70% or more, "CD" = 67% or more, and "D" = 60% or more. We will probably end up with about 800 possible points. My advice is simple: if you wish to earn a decent grade, make sure that you keep up with your work and that you turn in ALL the papers which are to be graded. I find that the surest way to receive less than a "C" is to make sure you miss some classes and fail to turn in all your work!
Attendance is important in this class. There is really never a "good day" to miss because we will either be covering new material or working in groups on some problems. I will not formally reduce your grade for poor attendance, but I will take attendance throughout the course so that I can apply the 2-day rule when we take those practice exams (see above). I can also tell you that poor attendance is one of the best ways to hurt you overall chances of success.
Late assignments is also something you should avoid. For one thing, if I am going to be able to get your work graded in a timely fashion so that it will do you some good for study purposes, you need to get it turned in on time. Another reason is that since we will be moving from one topic to the next, it is important that you are not spending your time doing work you should have done a week or two earlier instead of focusing on what we are doing at the moment. Therefore, I have a rule on late assignments: 10% of the total point value of a given assignment will be subtracted from your score for each of the first 3 days past the due date. Beyond 3 class periods, I will no longer accept late work. In general it is better to turn in work even if it is not entirely finished than to hold on to it.
Final Comments: I believe firmly that you as the student are the learner, and that "to learn" is an active verb; you must be actively engaged in the learning process, and this is best accomplished by your DOING mathematics. I am not here to show you how much I know - I am here to be "a guide on the side, not a sage on the stage". Please feel free to ask questions in class, either of me or of your group-mates. Please feel free to come to my office to discuss problems you might be having. Please feel free to go visit the learning center for tutoring help if necessary. The bottom line is that you must take responsibility for your own learning. Please believe that "Mathematics is not a spectator sport!"
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 or Wayne Wojciechowski (MC 320, 796-3085) within ten days to discuss your accommodation needs.
Course Schedule
30 Aug Introduction, Syllabus, [1.1] p 5 #2, 4
31 Aug [1.2] Solving Problems p 10 # 5-8, 10, 11
1 Sep [2.1] Ancient Numeration Systems p 10 #14, 15; p 28 #1-10
3 Sep [2.2] Different Number Bases p 36 # 1-25 odd, 30
7 Sep LAB #1 Lab(1) Take-home Problems
8 Sep [2.3] Fractions and Decimals p 42 # 2-5, 7-10
10 Sep [2.4] Number Systems p 52 # 1-5, 8-10, 11, 16, 21, 22, 23
13 Sep [3.1] Set Notation p 70 # 1-15
14 Sep [3.2] Subsets p 79 # 1, 2, 4, 5, 8, 9
15 Sep [3.3] Set Operations p 84 # 1-45 odd
17 Sep [3.4] Venn Diagrams p 92 # 1, 5, 7, 11, 15
20 Sep [3.5] Set Properties p 97 # 1-13 odd
21 Sep [3.6] Applications of Sets p 101 #1, 3, 7
22 Sep LAB #2 Lab(2) Take-home Problems
24 Sep Review ...
27 Sep
EXAM #1 (100 Points)
28 Sep [4.1] Intro to Logic, [4.2] Logic: Terminology & Notation p 118 # 1-21 odd
29 Sep [4.4] Conditional Statements, p 131 # 1-6, 8-12, 29
1 Oct [4.5] Valid Arguments p140 # 3, 5, 6-12, 15, 19
4 Oct [4.6] Equivalent Statements p 148 # 7-14
5 Oct LAB #3 Lab(3) Take-home Problems
6 Oct [5.1] Algebra p 163 # 1-3, 12-14, 16-19, 25
8 Oct [5.3] Exponential Functions p 195 # 1, 3, 5, 13, 15, 17, 19, 21, 23
11 Oct [10.4] Compound Interest p 408 # 1-13 odd
12 Oct [10.5] Annuities p 414 # 1-11 odd
13 Oct [10.6] Loan Amortization p 419 # 1-9 odd
15 Oct ... more on Loan Amortizations
18 Oct LAB #4 Lab(4) Take-home Problems
19 Oct Review ...
20 Oct
EXAM #2 (100 Points)
25 Oct [6.1] Intro to Geometry, [6.2] Geometry Terminology p 224 # 1-6
26 Oct [6.3] Angles p 230 # 1-13 odd
27 Oct [6.4] Polygons p 242 #3-13 odd
29 Oct [6.5] Perimeter and Area p 255 # 1-15 odd
1 Nov [7.1] Geometry as an Axiomatic System p 270 # 1, 3
2 Nov [7.2] Non-Euclidean Geometry p 276 # 1, 2
3 Nov Perspective and Drawing
5 Nov LAB #5 Lab(5) Take-home Problems
8 Nov [8.1], [8.2] Introduction to Probability p 306 # 1-19 odd
9 Nov [8.3] Counting Rules p 315 # 1-17 odd
10 Nov [8.4] Counting and Probability p 319 # 1-9 odd
12 Nov [8.5] Compound Events p 328 # 1-29 odd
15 Nov [8.6] Odds, Expected Values p 333 # 1-11 odd (Turn in: # 4,6,8,10)
16 Nov LAB #6 Lab(6) Take-home Problems
17 Nov [9.1] Data and Graphs p 346 # 3-9 odd
19 Nov [9.2] Measures of Central Tendency and Position p 353 # 3, 6, 7, 9, 13, 15, 17
22 Nov [9.3] Measures of Spread p 361 # 1-25 odd
23 Nov [9.4] Normal Distribution p 372 # 1-23 odd
29 Nov [9.5] Statistical Inference p 384 # 1-17 odd
30 Nov LAB #7
1 Dec Review ...
3 Dec
EXAM #3 (100 Points)
6 Dec Work on Final Projects
7 Dec Work on Final Projects
8 Dec Review ...
10 Dec P
ractice FINAL EXAM (25 Points)
Friday, 17 Dec: FINAL EXAM, 9:50 - 11:50 pm (125 Points)