MATH 5325: Structure of Number Concepts
Spring 2011


TIME:                   Mondays 7:00-9:30 PM
PLACE:              CS 107
INSTRUCTOR:   Elaine Young
PHONE:              825-2819
OFFICE:             CI-360
OFFICE HOURS: by appointment


The course will offer an in-depth and relational investigation of numbers and number systems, operations and algorithms, and quantitative and qualitative reasoning. Number theory topics will enhance the mathematical understanding and ability of secondary mathematics teachers within an environment that is conducive to mathematics education pedagogy.


Graduate standing; teacher certification or experience teaching mathematics in grades 6-12; and/or permission of the instructor.


Required text: Navigating through Number and Operations in Grades 9-12, NCTM, 2006
Required supplies: Scientific calculator; Word and Excel (or comparable software)


  • Gain a perspective of the historical background of number theory
  • Explore other number bases through historical/cultural class presentations
  • Calculate and convert between different number bases
  • Recognize and work with common number sets
  • Write elementary proofs for number theory topics such as divisibility
  • Make connections between number theory topics
  • Deepen mathematical understandings of 6-12 grade TEKS in number and operation
  • Understand and use theorems and algorithms of number theory
  • Explore a number theory topic in depth for final research project & presentation


The course will consist of lecture, collaborative groups, and class presentations. Students are expected to participate in collaborative groups and whole class discussions by contributing knowledge and thoughtful evaluation of the contribution of others.



Class presentation
Pre/post tests

Participation: Attendance is required and is part of the grade. If you must be absent, please contact the instructor and your group as soon as possible. Participation points may be recovered through make-up work with permission of the instructor. Participation includes ctive participation in collaborative explorations, group discussions, and class presentations.

: Readings, problems and class presentations will be assigned for homework. Late homework will only be accepted with prior approval from instructor and may be assessed penalty points.

Class presentation
: Each student will research and present a class presentation about a number theory related topic.

Pre/post tests
: A pre-test will pre-assess student needs and achievement as well as provide information for the grant project evaluation. The post-test will be a cumulative final exam covering course topics and seeking feedback for course improvement and grant project evaluation.


Class Presentations
Pre-test; ancient mathematics
History of number theory
Base 10; place & face value
Egyptian number system
Other number bases; base 5
Babylonian number system
Real number system; interesting subsets
Binary/hexadecimal number systems
Prime & composite numbers; FTA; simple proofs
Sieve of Eratosthenes
Factors & multiples, factorization
Prime numbers
Duodecimal number system
More proofs  
Euclidean algorithm
Sequences & series
Mayan number system
Countable & uncountable sets
Hotel Infinity presentation
Modular arithmetic
Diophantus presentation
Irrational numbers; continued fractions; constructible & transcendental numbers
Incan number system


Written work: Written hardcopy assignments must be typewritten or neatly printed with pages stapled together (no folding, paper clips, or plastic covers please). I reserve the right to penalize sloppy, unorganized, unstapled, misspelled or poor grammatical work.

Late Work: Students are encouraged to always turn in work on time. However, if situations dictate that work will be late, please notify the instructor and turn it in as soon as possible (do not wait until the next class, bring it to my office or email or fax it). Late work deadlines and points awarded may be adjusted at the discretion of the instructor.

Make-up Work: In the case of an excused absence, make-up work may be allowed. Make-up work and available points are at the discretion of the instructor.

Group Work: Each student will be assigned to a collaborative group and be expected to participate and contribute to group work efforts. In the event of a conflict or problem, the group or individual may request a change. Final decisions about changes are up to the instructor.

Help: The best source of help for this course is the people directly involved in this course: your peers or instructors, in class or during office hours. CASA is available for tutoring help; the Writing Center is available for help with written assignments.

Attendance: Attendance is expected and is reflected in individual and group participation. If you must be absent, please communicate with me and your group before class or as soon as possible. Email is encouraged,, or call my office at 825-2819 and leave a message. I will reply with details of what you missed in class and any assignments.

Participation: Participation includes class attendance and participation in collaborative explorations, group discussions, and class presentations. This daily grade can be made up for documented excused absences (see instructor for details).


Conway, J. H. & Guy, R. K. (1996). The book of numbers. New York: Copernicus.

Bransford, J.D., Brown, A.L., & Cocking, R.R. (Eds.). (2000). How People Learn: Brain, Mind, Experience, and School. Washington, DC: National Academies Press.

National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

Ore, O. (1967). Invitation to number theory. Washington: Mathematical Association of America.

SBEC Technology Standards for Beginning Teachers. [Online]

Silverman, J. H. (2001). A friendly introduction to number theory. Upper Saddle River, NJ: Prentice Hall.

Texas Education Agency. (2007). Texas Essential Knowledge and Skills. [Online]

Academic Integrity/Plagiarism
University students are expected to conduct themselves in accordance with the highest standards of academic honesty. Academic misconduct for which a student is subject to penalty includes all forms of cheating, such as illicit possession of examinations or examination materials, falsification, forgery, complicity or plagiarism. (Plagiarism is the presentation of the work of another as one’s own work.) In this class, academic misconduct or complicity in an act of academic misconduct on an assignment or test will result in a zero grade.

Dropping a Class
I hope that you never find it necessary to drop this or any other class. However, events can sometimes occur that make dropping a course necessary or wise. Please consult with me before you decide to drop to be sure it is the best thing to do. Should dropping the course be the best course of action, you must initiate the process to drop the course by going to the Student Services Center and filling out a course drop form. Just stopping attendance and participation WILL NOT automatically result in your being dropped from the class. Friday, 5 April 2011, is the last day to drop a class with an automatic grade of “W” this term.

Classroom/professional behavior
Texas A&M University-Corpus Christi, as an academic community, requires that each individual respect the needs of others to study and learn in a peaceful atmosphere. Under Article III of the Student Code of Conduct, classroom behavior that interferes with either (a) the instructor’s ability to conduct the class or (b) the ability of other students to profit from the instructional program may be considered a breach of the peace and is subject to disciplinary sanction outlined in article VII of the Student Code of Conduct. Students engaging in unacceptable behavior may be instructed to leave the classroom. This prohibition applies to all instructional forums, including classrooms, electronic classrooms, labs, discussion groups, field trips, etc.

Grade Appeals
As stated in University Rule 13.02.99.C2, Student Grade Appeals, a student who believes that he or she has not been held to appropriate academic standards as outlined in the class syllabus, equitable evaluation procedures, or appropriate grading, may appeal the final grade given in the course. The burden of proof is upon the student to demonstrate the appropriateness of the appeal. A student with a complaint about a grade is encouraged to first discuss the matter with the instructor. For complete details, including the responsibilities of the parties involved in the process and the number of days allowed for completing the steps in the process, see University Rule 13.02.99.C2, Student Grade Appeals, and University Procedure 13.02.99.C2.01, Student Grade Appeal Procedures. These documents are accessible through the University Rules Web site at For assistance and/or guidance in the grade appeal process, students may contact the Office of Student Affairs.

Disabilities Accommodations
The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please call or visit Disability Services at (361) 825-5816 in Driftwood 101.

If you are a returning veteran and are experiencing cognitive and/or physical access issues in the classroom or on campus, please contact the Disability Services office for assistance at (361) 825-5816.