Office: NSM A-117
Office hours: 4 hours per week TBA
This course covers the theory and applications of Rational numbers. Topics central to the course are Number systems, representation of numbers, equivalence classes, rationality and irrationality, properties of the rational number system, applications of the central ideas to proportional reasoning, and developing intuitive models for the standard rules and algorithms. The course meets for 3 hours of lecture per week.
MAT 543 or concurrent enrollment. Students must have graduate standing and one year of full time secondary teaching.
After completing MAT 506 the student will be able to
State definitions of basic concepts
Understand the rational number notation and equivalence classes
Recognize irrational numbers and prove that some numbers are irrational
Construct proofs of mathematical assertions
Construct intuitive, concrete explanations and models of standard rational number rules and algorithms
Engage in problem solving using foundations of Rational numbers and proportional reasoning
Be knowledgeable of the current research and theories of proportional reasoning instruction
Create short units of instruction that address common misconceptions of Rational numbers and proportional reasoning
Students should be able to demonstrate through written assignments, tests, and oral presentations that they have achieved the objectives of MAT 506.
Evaluations are based on homework, class participation, short tests, scheduled presentations and group projects that cover students' understanding of topics.
Students' grades are based on homework, class participation, short tests, and scheduled presentations and group work. The instructor determines the relative weights of these factors.
No single text will be assigned, as no single book exists that is suitable for the course. Library research by students and class handouts will be used instead.
Week 1: Common misconceptions about fractions and proportional reasoning group discussion
Week 2: Delving into theory. Building the Rational numbers from scratch, number systems, representing numbers and equivalence classes
Week 3: Continuing the development of the theory of Rational numbers. Equivalence classes
Week 4: Incompleteness of the Rational Numbers: Irrationality and Rationality
Week 5: Arbitrarily close: The density of the Rational numbers in the real number system
Week 6: Developing concrete models for the addition and subtraction of fractions
Week 7: Developing concrete models for multiplication and division of fractions
Week 8: Creating number sense with rational numbers and choosing group project topics
Week 9: Problem solving using proportional reasoning and the structure of the Rational numbers
Week 10: Problem solving using proportional reasoning and the structure of the Rational numbers
Week 11: Problem solving using proportional reasoning and the structure of the Rational numbers
Week 12: Teaching and learning issues in proportional reasoning
Week 13: Teaching and learning issues in proportional reasoning. Discuss math Ed papers about proportional reasoning.
Week 14: Group Presentations
Week 15: Group Presentations
Students are required to attend all scheduled classes.
Due dates of assignments and projects will be announced in class. No late work will be accepted.
The instructor sets all test dates. Students will be notified well in advance. The final group project is due on the last day of class.
The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)