Math IVA: Bosky Frederick

Course Overview:

Math IVA - 2008-2009 - Bosky Frederick

In line with previous College Prep math courses, Math IVA stresses 1) problem solving as the central means of instruction, 2) a good command of basic facts based on understanding as well as memorization, 3) clear communication, both oral and written, and 4) appropriate use of technology.  We help students make connections among various topics and develop flexibility in their thinking.  This course, which serves as a bridge between the study of functions and the study of calculus and/or statistics at the college level, has four themes:
•    Calculus
    Sequences and series, limits, infinity, derivatives, and their relationship to graphs.  Basic techniques of differentiation.
•    Algebra, Geometry and Trigonometry
    Advanced solving, simplifying and factoring, including trigonometric equations and identities, transformations of functions and graphs, composite and inverse functions, the Factor Theorem, and a review of geometry and its application to contextual problems.
•    Discrete Mathematics and Statistics
    Counting techniques, permutations and combinations, probability, and a brief introduction to statistics.
•    New Objects and Representations
    Matrices, complex numbers, polar and parametric equations, and vectors.  All of these extend familiar notions of number, function and graphing.

In other schools, the most equivalent course is called Precalculus or Math Analysis, but these courses generally do much less geometry and calculus.  Math IVA builds on many familiar ideas from Math IIIA and introduces the important ideas of limit and derivative.  Students will discover formulas for derivatives of a wide variety of functions by matching their guesses with the graph of the derivative produced by the graphing calculator.  They will not know why these formulas are true at first, but having discovered them on their own, they will be more motivated to prove them analytically.

Because conceptual understanding depends on it, students learn symbol manipulation techniques without the calculator at first.  Some test questions can and should be done without a calculator.  On the other hand, use of a graphing calculator allows students to deal easily with "messy", "real-life" examples, and mathematical software helps them explore many examples quickly.  Graphing complicated 2-D and 3-D graphs was never this easy in our day!  Calculators, including the TI-84 plus (which most students got last year in Math IIIA), are allowed on the math portions of the SAT.

Each year the Math IVA text is modified and refined.  Errors are corrected and student suggestions are incorporated.

Bosky teaches two sections (period 6 & 7) of Math IVA, and Betsy Thomas teaches periods 1 & 2.  We cover the same material, but Betsy uses daily handouts instead of the text.  Class section sizes are 14 to 16 students.  Students use a binder to keep (in an organized fashion) assignment sheets, reference sheets, quizzes, tests, problem sets, and the text pages.

Assessment is not limited to tests.  Homework checks, problem sets, quizzes, and observation of student's group work all contribute to the student's grade.  The full period tests (generally two per quarter) are cumulative.  A test "rehearsal" is given as practice a few days before the exam.  Students having difficulty are encouraged to talk with any Math IVA teacher (or any math teacher for that matter).  Free periods are posted.

Other Section Resources:

Assignments

Find recent and upcoming assignments detailed here.

Class Resources

Notes, slide shows, handouts, and other useful items.

Useful Links

A collection of web links relevant to this class.