SYLLABUS for EMAT 4500/6500: Connections in Secondary School Mathematics Spring 2001

Instructor: Heide G. Wiegel hwiegel@coe.uga.edu, Lisa Sheehy lsheehy@coe.uga.edu, Inchul Jung ijung@coe.uga.edu

Class Time: Tue / Thu 3:30 Ð 4:45 p.m.

OBJECTIVES

The course is designed to

• survey, from an advanced point of view, selected topics from the current secondary school curriculum;
• explore the connections among the topics and to other subjects (e.g., sciences, the social sciences, the humanities);
• use a variety of mathematical models in solving problems from different domains;
• highlight technology as well as hands-on approaches;
• acquaint you with two contemporary textbook series;
• provide opportunity (-ies) to develop a topic for presentation and teaching;

Textbooks:

1. Schrage, G. (1996). Analyzing Subject Matter: Fundamental Ideas of Combinatorics. Portsmouth, NH: Heinemann.
2. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston. VA: Author.

High School Textbooks:

1. Interactive Mathematics Program. Integrated High School Mathematics. Years 1-4. Key Curriculum Press.
2. Contemporary Mathematics in Context. Core-Plus mathematics Project. Years 1-3. Everyday Learning Corporation.

TOPICS (tentative)

1. Introduction and warm-up: Looking back at the Functions chapter;
2. The Ant on the Wheel: An in-depth investigation of the cycloid and related functions;
3. It's a Small World: An in-depth investigation of growth functions (exponential vs. logistic); Sample presentation of an IMP unit;
4. Discussions and selected combinatorics problems from Schrage, G. (1996). Analyzing subject matter: Fundamental ideas (pp. 167-220). Portsmouth, NH: Heinemann.
5. Group projects and presentations: Textbook investigations (Core-Plus and IMP) Additional topics as time permits
6. Variations on triangular numbers and other figural numbers;
7. From all sides and angles: Area of a Triangle

Students' Work

UNITS (tentative)

• IMP-Year 1: The Pit and the Pendulum (Unit 4, statistics, physics, poetry)
• IMP-Year 2: Is there really a Difference? (Unit 2, probability) or Do Bees build It Best? (Unit 3, geometry)
• IMP-Year 3: Fireworks (Unit 1, algebra, physics)
• IMP-Year 4: High Dive (Unit 1, algebra, trig, physics; connects to the Ant-on-the-Wheel problem)
• CorePlus-Year 1: Graph Models (Unit 4, Graph theory)
• CorePlus-Year 2: Matrix Models (Unit 1, discrete math) ?
• CorePlus-Year 2: Network Optimization (Unit 5, with reference to Unit 4, Year 1, graph theory)
• CorePlus-Year 3: Modeling Public Opinion (Unit 2, discrete math)
• CorePlus-Year 3: Discrete Models of Change (Unit 7)

TENTATIVE SCHEDULE

 Week Tuesday Thursday Assignments due Week 1: 1/8-1/12 Introduction Ant on Wheel Expl. 8, # 2 and # 6; 1/11/01 Week 2: 1/15-1/19 Ant on Wheel Ant on Wheel Week 3: 1/22-1/26 Ant on Wheel Ant on Wheel Ant on Wheel 1/24/01 Week 4: 1/29-2/2 Ant on Wheel Small World Week 5: 2/5-2/9 Small World Small World (Several smaller assignments) Week 6: 2/12-2/16 Small World Small World Week 7: 2/19-2/23 Logistic Model Logistic Model/ Combinatorics Week 8: 2/26-3/2 Midpoint: 3/1/01 Combinatorics Combinatorics Week 8a: 3/5-3/9 Spring break Spring break Week 9: 3/12-3/16 Combinatorics Test Week 10: 3/19-3/23 Combinatorics Combinatorics Week 11: 3/26-3/30 IMP 1 IMP Q&A, Brian Lawler Combinatorics Week 12: 4/2-4/6 IMP 2 IMP 3 Tue: IMP 1 Week 13: 4/9-4/13 IMP 4 Core Plus 1 Tue: IMP 2, Th: IMP 3 Week 14: 4/16-4/18 Core Plus 2 Core Plus Q&A, Jon Challen (tent.) Tue: IMP 4, W: CorePlus 1 Week 15: 4/23-4/27 Core Plus 4 (Core Plus 3/more about recursion) Tue: CorePlus 2, Th: CorePlus 4 Week 16: 4/30-5/4 Reading day Final Exam 3:30-6:30

COOPERATION

Working together in pairs or groups is encouraged. Here are some rules:

1. Everyone turns in his or her own version of assignments. That is, I will NOT accept any group write-ups. Exception: If you have to share a computer, so can each include the hardcopies with both your names.
2. Be responsible for your own learning. Don't let somebody else do your work.
3. Be responsible for your partner's or group members' learning. Don't do all the work.
4. Reference all help (persons and / or written materials).

The Department of Mathematics Education
University of Georgia