Syllabus
1. Prerequisite: MATHS 202 with a C- or better grade.
2. Course Description: The study of a collection of topics from the theory of numbers that have specific applications in the elementary and middle school curriculum.
3. Course Objectives: This course is designed to prepare students to become more effective teachers of mathematics in the elementary and middle school. As a result of investigating important topics and problems, both historical and contemporary, in the theory of numbers, they will become better informed and prepared to make instructional decisions as teachers. Specifically, in this course preservice elementary and middle school mathematics teachers will be able to:
• form and test conjectures related to number theory
• recognize and use several forms of mathematical proofs (e.g., induction, contradiction)
• investigate the theory behind various procedures in number theory that are found in the elementary and middle school mathematics curriculum
• recognize famous problems and theorems that are important in the history and development of number theory
• explore famous unsolved problems in number theory
4. Course Rationale: Several professional organizations have identified content standards for teachers of mathematics. “Number and Operations” is one mathematics content area in which all teachers of mathematics need to be proficient. The National Council of Teachers of Mathematics and the Indiana Professional Standards Board state that teachers of elementary school mathematics must “have a well-developed number sense and an understanding of the use of number concepts, operations and properties, including basic number theory.” The Mathematical Association of America states that teachers of mathematics must “develop conjectures and intuitive proofs of number theoretic properties” and “investigate number sequences, patterns, and functional relationships”.
Thus, in this course, preservice elementary and middle school mathematics will explore and study selected topics in number theory. This is a required course for elementary education majors with a mathematics area of concentration. This theoretical study will provide a mathematical foundation in number and operation upon which they can draw in the future as they make instructional decisions in teaching basic number theory topics to elementary and middle school students.
5. Course Content: Topics in number theory which are included are:
• numeration systems
• figurate numbers
• magic squares
• prime and composite numbers
• the fundamental factorization theorem
• factors and divisors
• greatest common factors and least common multiples
• Euclid’s algorithm
• Pythagorean triples
• theory of congruences
• clock arithmetic
6. Course Format: Interactive lecture and discussion, in-class and out-of-class activities. A TI-73 graphing calculator is required.
7. Methods of Evaluating Student Performance: In-class assignments, out-of-class writing assignments and problem sets, small group projects/presentations, in-class quizzes and exams.
8. Evaluation of the Course: The instruction of the course is evaluated by departmental student evaluations and peer evaluations. The course is reviewed and revised periodically by the Department’s Teacher Education Advisory Committee and Undergraduate Programs Committee.
[E. Bremigan, January 2001]
[V. Mascioni, April 2004]