MAE 301 Foundations of Secondary School Mathematics

Fall 2006 Syllabus

This course has several goals. First, to ensure that you have fully mastered the secondary school curriculum. Second, to develop an understanding of the interconnections among the different branches of secondary school mathematics. Third, to develop an understanding of the connections between the secondary school curriculum and your college level mathematics curriculum. Fourth, to enhance your problem solving abilities, and to develop an understanding of the processes involved in learning and understanding mathematics and in mathematical problem solving.

Instructor: Professor Bernard Maskit

Office: Math 5-112

Phone: 632-8257

e-mail: bernie@math.sunysb.edu

Office Hours: Mondays: 12:00 - 3:00 p.m., by appointment only

Tuesdays: 2:00 - 4:00 p.m.

Wednesdays: 2:00 - 3:00 p.m.

There is no textbook for this course; class notes can be found at http://www.math.sunysb.edu/~bernie/classnotes.pdf

Class worksheets, which will also contain homework assignments, will be distributed in class.

MAE 301 is part of a sequence of courses leading to certification as a teacher of mathematics in grades 7-12. In light of the professional nature of this course, neither excessive absence nor excessive tardiness will be tolerated.

First Exam: There will be an in-class exam on Wednesday, September 20. The questions on this exam are taken directly from the New York State A and B Mathematics Regents exams. The passing grade on this exam is 85; students who do not achieve a passing grade will have two opportunities to pass an equivalent exam. While we will attempt to follow the course outline below, to some extent, the amount of time spent on any one topic will depend on the exam scores on questions related to this topic.

Other examinations: In addition to the regents exam mentioned above, there will be a midterm exam and a final exam.

Calculators: New York State requires graphing calculators on its Regents exams; you will not be able to solve some of the problems on examinations in this course without a graphing calculator. However, overly fancy calculators, such as those that do symbolic manipulations, or have telephones, or have overly extensive memories, will not be permitted.

Homework: Homework will be assigned in most classes, usually as part of the classroom worksheet. In general, the homework will be due the following class. A selection of the assigned homework problems will be graded. At the end of the semester, the lowest two homework grades for each student will be dropped.

Classwork: Class assignments will vary. For some, you will be required to work in groups assigned by the instructor; for some, you will be permitted to work in groups of your own choosing; for some, you will be required to work alone.

Grading: The final grade has two components.

Component 1:

First Exam: 10%

Midterm Exam: 20%

Final Exam: 40%

Classwork and

Attendance: 15%

Homework: 15%

Component 2: If you do not achieve a grade of at least 85% on the First exam (or on a subsequent make-up exam), your final grade will be at most C-.

Note: If you have a physical, psychological, medical or learning disability that may impact on your ability to carry out assigned course work, you are urged to contact the staff in the Disabled Student Services office (DSS). They will review your concerns and determine, with you, what accommodations are necessary and appropriate. All information and documentation of disability is confidential. Note that we cannot make special arrangements for students with disabilities except for those determined by DSS.

Tentative Course Outline

  1. Introduction, Natural numbers and their properties, sets, prime numbers, integers
  2. Formal logic, Boolean algebra, sets and circuits, logic in natural language, the language of mathematics
  3. Functions, Cartesian products, relations, equivalence relations
  4. Fractions, rational numbers, infinite decimals,
  5. Regents exam
  6. real numbers, complex numbers, quarternions and vectors
  7. Cardinality --- The transfinite world
  8. Real functions, approximations, Mean Value theorem and Taylor's theorem, the use of calculators and computers
  9. Continuation of measurements; use of trigonometry
  10. Mathematical induction
  11. Polynomials, factorization, the Euclidean algorithm, division, roots
  12. Combinatorics: factorials and the binomial theorem
  13. Basic probability: coin tosses, dice, Bernoulli trials
  14. Basic statistics: sampling, plots, mean, median, mode, standard deviation
  15. Regression and related concepts
  16. The laws of exponents, exponential functions
  17. Probability distribution functions; the normal curve
  18. Review
  19. Midterm exam (covers material up to and including exponential functions)
  20. Logorithms
  21. The basic figures of geometry, congruence, areas, perimeters and volumes
  22. The Euclidean motions: translations, rotations and reflections
  23. Circles, chords, diameters, tangents
  24. Constructions with triangles and circles
  25. The parallel postulate; similarities and dilations
  26. Polar coordinates and the trigonometric functions
  27. Tesselations of the plane
  28. Review