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Math 302: Mathematical Modeling

Oldfather 203, 4:30 - 5:45 Tu-Th

Section 001, 3 credit hours

Fall Semester, 2011

Steve Dunbar

Welcome to Math 302. You are part of a course whose purpose is to learn mathematics that will make you a better elementary teacher of mathematics. (Middle school math teachers will also find the course beneficial.) The overall goal of the course is to develop in you the “habits of mind of a mathematical thinker.” That is, the course will emphasize careful reasoning, problem solving and communicating mathematics both orally and in writing. The course will pay careful attention to connections among all areas of mathematics. To get the most out of this course, be an active participant and give every assignment your best effort. Accept the challenge to achieve at a high level, but also to seek help when you need it. You are welcome to contact me with questions at any time.

The prerequisites of the course are: ``Admission to the College of Education and Human Sciences. Open only to middle grades teaching endorsement majors with a mathematics emphasis and/or to elementary education majors who want a mathematics concentration.''

The class will meet Fall Semester 2011, at 4:30 - 5:45 pm on every scheduled Tuesday and Thursday.

Text: Mathematics for Elementary Teachers with Activity Manual, Third Edition, together with Mathematics for Elementary Teachers Activity Manual Third Edition, Sybilla Beckmann, Addison-Wesley, available at least through Amazon.

I will publish all additional materials for the course on the web at
http://www.math.unl.edu/~sdunbar1/Teaching/MathematicalModeling/
mathmodel.shtml
and also on the UNL Blackboard site: my.unl.edu in the course MATH MODELING MATH302 SEC 001 FALL 2011.

Office and Availability:
Office Hours: Tuesday-Thursday, 3:30 am - 4:20 pm, 308 Avery
Phone: 472-7236 (24 hour University Voice Mail)
Math Department: 472-3731 (8:00 AM - 5:00 PM)
Email: sdunbar1@unl.edu , URL: http://www.math.unl.edu/~sdunbar1

Course Goals:

  1. Use mathematics for realistic problems from the school curriculum. The mathematics for these models mix arithmetic, algebra, sequences, functions, mathematical terminology, concepts and principles.
  2. Help teachers develop the habits of mind of a mathematical thinker, that is, get a much better understanding of what it means to think about mathematics, communicate mathematics, to reason and to solve problems.
  3. Become proficient in using the Mathematical Practices of the Common Core State Standards.
  4. Help teachers use the Mathematical Practices of the Common Core State Standards in their classroom.
  5. A paraphrase of a statement from Matt Larson, Superintendent of Mathematics at LPS is ``To teach effectively at a grade level, you must understand the mathematics that comes in the previous 4 grades and the successive 4 grades.'' Therefore, a course goal is to introduce you to mathematics at multiple levels, not necessarily directly at a grade level you presume you may teach.

Class Policies:

  1. I require attendance in each class period and I will record attendance each class period. Class participation is an extremely important component of the course because class will be conducted essentially as a ``lab course'' with very little lecturing. Missing a class day is missing approximately 3% of the course material. You will be allowed up to 2 unexcused absences. For each unexcused absence beyond that, I will subtract 2% from your final course percentage. Legitimate reasons or emergencies may cause one to be late or result in an unplanned absences so I agree to allow up to 2 absences. For excused absences, I will subtract 0.5% from your final course percentage. If, for any reason, you must miss a day or arrive late, please try to contact me prior to class. Doing so is not just a courtesy; it is a trait that is expected of a professional.
  2. Collaboration and group work on homework is allowed, but each student must turn in the assigned homework.
  3. The mid-terms are tentatively scheduled for class time, October 13, 2011 and November 22, 2011 and the Final Exam is scheduled for Monday, Dec 12, 2011.

Assignments and Grading

Habits of Mind Problems: The purpose of these challenging mathematics problems is to develop the habits of mind of a mathematical thinker. Your best 10 HoM homeworks count as your HoM grade. Solutions must be written up neatly with careful attention paid to explaining your reasoning. Group work is permitted, even encouraged, and you are welcome to seek help from me. The use, or more properly abuse, of outside resources (people outside class, copying a solution from a web location, etc.) is considered academic dishonesty.

Readings: At various points during the semester, you will be given an article to read that we will discuss in class. In preparation for class, you are to prepare a one page “report” on the ideas advanced in the article. Each “report” is worth 5 points.

Favorite Five: Provide a “final solution” for five problems that were worked in class or worked as a homework problem. Select problems that you found challenging and that you are proud of or “like best.” (Perhaps they help demonstrate what you have accomplished). This assignment is worth 25 points.

Math Modeling Project: You will have one extended (50 point) project where you will use the mathematics you have been studying to model an applied problem and present your solution. The project will be done in groups.

Math Exams: You will have two 100 point exams during the semester and a 150 point Final Exam. The Final Exam is comprehensive.

Grades All assignments are due on agreed upon due dates. Points may be deducted for late assignments. The grading scale and point allocations are as follows:

Habits of Mind Problems (10) 100
Active Participation 50
Readings 25
Favorite Five 25
Math Modeling Project 50
Math Exams (2) 200
Math Final Exam 150
Total 600

Grade Scale
A+ 95% B+ 84% C+ 74% D+ 64%
A 90% B 80% C 70% D 60%
A- 87% B- 77% C- 67% D- 57%

Thus, your final grade will be based on approximately 10 Habits of Mind problems carefully written up as homework assignments worth approximately 16%, active participation worth approximately 8%, readings and written work worth approximately 16% including an extended project worth 4%, two mid-term exams worth approximately 32%, and one comprehensive final exam worth approximately 25% of the course grade.

Department Grading Appeals Policy: The Department does not tolerate discrimination or harassment on the basis of race, gender, religion, or sexual orientation. If you believe you have been subject to such discrimination or harassment, in this or any math course, please contact the department. If, for this or any other reason, you believe that your grade was assigned incorrectly or capriciously, appeals should be made to (in order) the instructor, the department chair, the departmental grading appeals committee, and the college grading appeals committee.

Week 1 Aug 23 Introduction Aug 25 KenKen puzzles  
Week 2 Aug 30 8.1, Factors, Multiples Sept 1 8.1, Finding Factors  
Week 3 Sep 6 8.2, GCD and LCM Sept 8 8.2, GCD and LCM  
Week 4 Sep 13 8.3, Prime Numbers Sept 15 8.3, Prime Factorizations  
Week 5 Sep 20 8.4, Even and Odd Sept 22 Number Patterns  
Week 6 Sep 27 Fibonacci Numbers Sept 29 Fibonacci Numbers  
Week 7 Oct 4 Recursions Oct 6 Recursions  
Week 8 Oct 11 Review Oct 13 Mid-Term Exam 1  
Week 9 Oct 18 Fall Break Oct 20 Direct Proportion  
Week 10 Oct 25 Inverse Proportionality Oct 27 DRT Problems  
Week 11 Nov 1 9.8, Linear Relations Nov 3 Linear Graphs, Tables  
Week 12 Nov 8 Quadratic Expressions Nov 10 Quadratic Equations  
Week 13 Nov 15 Exponential Growth Nov 17 Exponential Growth  
Week 14 Nov 22 Mid-Term Exam 2 Nov 24 Thanksgiving Break  
Week 15 Nov 29 9.5 Sequences Nov 26 Functions  
Week 16 Dec 6 Review Dec 8 Review  

Finals Week Dec 12-16: Final Exam Mon, Dec 12, 10:00 - 12:00 PM

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Math 302: Mathematical Modeling

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Steven R. Dunbar
Department of Mathematics and Statistics
University of Nebraska-Lincoln
Lincoln, NE, 68588-0323 USA
email: sdunbar@math.unl.edu
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