MATH 155: Mathematics, A Way of Thinking
Spring 2005, MWHF, 10-10:50 A.M., 417 Murphy Center
Instructor: Terry R. Witzke
Home Phone: 608-788-4875. E-Mail: firstname.lastname@example.org
Final Exam: Tuesday, 10 May 2005, 7:40 AM to 9:40 AM
Course Description: An investigation of topics, including the history of mathematics, set theory, logic, number systems, basic algebra concepts, linear graph functions, geometry, counting methods, basic probability and statistics, consumer mathematics. There is an emphasis throughout on problem solving. Recommended for general education requirements, B.S. degree.
Text: Mathematical Ideas, 10th edition, by Miller, Heeren
, and Hornsby (
CORE SKILL OBJECTIVES:
These skills are related to the General Education core abilities document. They are also written to refer to the various INTASC standards for the purposes of the Elementary Education program.
Thinking Skills: The students will engage in the process of inquiry and problem solving that involves both critical and creative thinking.
(a) ...explore writing numbers and performing calculations in various numeration systems.
(b) ... solve simple linear algebraic equations.
(c) ... explore a few major concepts of Euclidean Geometry, focusing especially on the axiomatic-deductive nature of this mathematical system.
(d) ... develop an ability to use deductive reasoning, in the context of the rules of logic and syllogisms.
(e) ... explore the basics of probability.
(f) ... learn descriptive statistics, including making the connection between probability and the normal distribution table.
(g) ... learn the basics of financial mathematics, including working with the formulas for compound interest, annuities, and loan amortizations.
(h) ... solve a variety of problems throughout the course which will require the application of several topics addressed during the course.
Life Value Skills: The students will analyze, evaluate and respond to ethical issues from informed personal, professional, and social value systems.
(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.
Communication Skills: The students will communicate orally and in writing in an appropriate manner both personally and professionally.
(a) ... write a mathematical autobiography.
(b) ... do group work (labs and practice exams), involving both written and oral communication.
(c) ... turn in written solutions to occasional problems.
Cultural Skills: The students will understand their own and other cultural traditions and respect the diversity of the human experience.
(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.
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.
FURTHER COURSE NOTES:
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). This 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.
MATHEMATICAL AUTOBIOGRAPHY: Due: Monday, January 31. Point value: 25.This will be a 3-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.
GRADING PROCEDURES: The grading procedure is quite straight-forward. "A" = 90% or more of total possible points, "AB" = 85% or more, "B" = 80% or more, "BC" = 75% or more, "C" = 70% or more, "CD" = 65% or more, and "D" = 60% or more. My advice is simple: if you wish to earn a satisfactory grade, make sure that you keep up with your work and that you turn in ALL the papers which are to be graded. The surest way to receive less than a "C" is to miss some classes and fail to turn in all your work! See the testing schedule included in the course schedule. The number of tests should give an adequate sampling of your understanding of course content.
ATTENDANCE POLICIES: 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. You will be give one point for each class you attend and these will be added to your point totals for this course.
LATE ASSIGNMENTS: Turning in assignments late 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.
RESOURCES: Tutoring is available in the Learning Center,third floor, Murphy Center. I also want you to consider arranging to see me if you have a problem with some material. Sometimes we can resolve in a few minutes a difficulty that can cause problems for weeks. Don’t wait to get the help you need. I want you to be successful in this class. Get involved. This can be a rewarding experience for you.
WEB SITE: www.interactmath.com Need to install Math XL using Internet Explorer.
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 classmates. 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.
Spring 2005 Math 155 Course Schedule
17 Jan <1.1> Problem Solving and Inductive Reasoning p 7 # 15-51 odd
19 Jan <1.2> Number Patterns p 17 # 9-47 odd
20 Jan <1.3> Problem Solving Strategies p 26 # 5-45 odd
21 Jan <1.4> Calculating, Estimating, Reading Graphs p 36 # 19-51 odd
24 Jan Lab #1
26 Jan <2.1> Basic Set Theory p 54 # 1-45 odd, 53-73 odd
27 Jan <2.2> Venn Diagrams and Subsets p 61 # 1-51 odd
28 Jan <2.3> Set Operations p 73 # 1-53 odd, 81-91odd
31 Jan <2.4> Cardinal Numbers and Surveys p 79 # 1-27 odd
2 Feb Lab #2
3 Feb <3.1> Statements and Quantifiers p 99 # 1-51 odd, 61-73 odd
4 Feb <3.2> Truth Tables, Equivalent Statements p 111 # 1-49 odd, 61-67 odd, 71
7 Feb <3.3> The Conditional Statement p 120 # 1-49 odd, 61-69 odd, 79, 81
9 Feb <3.4> More on the Conditional p 128 # 5-49 odd
10 Feb <3.5> Arguments and Euler Diagrams p 132 # 1-29 odd
11 Feb <3.6> Arguments and Truth Tables p 145 # 1-23 odd, 27, 33, 35
14 Feb Lab #3
16 Feb Group Practice Exam #1
17 Feb EXAM #1 (Sections from Chapters 1, 2, 3)
18 Feb <4.1> History of Numeration Systems p 158 # 1-29 odd, 35
21 Feb <4.2> Hindu-Arabic System p 167 # 1-31 odd, 41-49 odd
23 Feb <4.3> Number Bases p 176 # 1-53 odd
24 Feb Lab #4
25 Feb <5.5> Fibonacci Sequence, Golden Ratio p 237 # 1-19 odd, 25-31 odd
28 Feb <7.1> Linear Equations p 322 # 1-31 odd, 37-43 odd
2 Mar <7.2> Applications of Linear Equations p 335 # 11-41 odd
3 Mar Group Practice Exam #2
4 Mar Exam #2 (Sections from Chapters 4, 5, 7)
7 Mar -Mid-Semester Break-
14 Mar <9.1> Points, Lines, Planes, and Angles p 499 # 1-65 odd
16 Mar <9.2> Curves, Polygons, and Circles p 506 # 1-45 odd
17 Mar <9.3> Perimeter, Area, and Circumference p 518 # 1-51 odd, 57-69 odd
18 Mar <9.4> Triangles: Congruence, Similarity, Pythagoras p 530 # 1-55 odd
21 Mar < 9.5> Solids: Volume, Surface Area p 542 # 1-33 odd, 43-53 odd
23 Mar Lab #5
30 Mar <11.1> Counting Principles p 635 # 9-55 odd
31 Mar <11.2> Using the Fundamental Counting Principle p 644 # 5-49 odd
1 Apr <11.3> Permutations and Combinations p 655 # 15-49 odd
4 Apr <11.5> Counting Problems Involving “Not” and “Or” p 699 # 5-37 odd
6 Apr <12.1> Basics of Probability p 681 # 5-51 odd
7 Apr <12.2> Events Involving “Not” and “Or” p 689 # 1-33 odd
8 Apr <12.3> Events Involving “And” p 698 # 1-51 odd
11 Apr <12.4> Binomial Probability p 705 # 1-27 odd, 37-45 odd
13 Apr Lab #6
14 Apr Group Practice Exam #3
15 Apr Exam #3 (Sections from Chapters 9, 11, 12)
18 Apr <13.1> Frequency Distributions & Graphs p 731 #5-33 odd
20 Apr <13.2> Measures of Central Tendency p 744 #9-41 odd
21 Apr <13.3> Measures of Dispersion p 753 # 5-39 odd
22 Apr <13.5> Normal Distribution p 769 # 3-41 odd
25 Apr <14.1> Money and Interest p 798 # 7-25 odd, 31-43 odd
27 Apr <14.2> Consumer Credit p 809 # 1-41 odd
28 Apr <14.3> Truth in Lending p 820 # 1-29 odd
29 Apr <14.4> Purchasing a House p 829 # 1-31 odd
2 May Lab #7
4 May Group Practice Exam #4
5 May EXAM #4 (Sections from Chapters 13, 14)
6 May Review (Preparation for the Final Exam)
10 May FINAL EXAM: 7:40-9:40 A.M., 417 Murphy