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Geometry

The first semester of Year II contains the topics of a standard high school course in plane and solid geometry, specifically, distance, angles, area, Pythagoras theorem, congruent triangles, polygons, dilations, similarity, and transformations.  Students are given rigorous weekly homework assignments that help them learn to formulate mathematical proofs and derive general formulas.  Emphasis is placed on mathematical thinking and methods of proof.  Our work is supported by weekly access to a computer lab, where we investigate the fundamental ideas of geometry through cooperative learning using the software, Geometer's Sketchpad.

PreCalculus

Second semester, the fast-paced Precalculus portion of ATYP’s math sequence covers the topics of a standard high school course in Trigonometry and Analytic Geometry, specifically equations, inequalities, graphs, functions which include polynomial, rational, exponential, and logarithmic functions; trigonometry which includes angles, right triangle trigonometry, circular functions, identities and equations; polar equations, parametric equations and conic sections. The course makes extensive use of graphing calculators, which help to promote each student's conceptual understanding of the various topics.  Students are given challenge problems each week to promote problem solving skills.

Classes

This class meets one afternoon per week from 1:20 – 3:50 pm.  The day of the week varies each year depending on number of students and instructor availability but has typically been held on a Tuesday.  A break is held half-way through the class meeting to allow the students to stretch, use the restroom and get a snack from the vending machines (money needed).  The classes meet in a classroom on the Western Michigan University campus with an instructor that is qualified in mathematics and understands gifted youth.  Each instructor creates their own assessment tools that are used throughout the year.  Typically, there are 2 tests given each semester and a nationally normed standardized test is given at the end of each semester to assess the student’s knowledge of the topics studied.  Grades are given and sent to the student’s school at the semester break and at the end of the year.  A study session is run by a high school/college student grader each weekend that allows the students to discuss the homework and generate ideas for solutions.

Homework

Homework is assigned in a rotational manner.  For the first semester, the homework is divided into two parts.  Approximately half of the problems come from the material that has just been studied (the students complete the odd problems one week and the even problems the following week).  The remaining problems come from the material discussed the previous week.  During Precalculus each homework assignment will have three parts.  Approximately one-third of the homework questions will come from material that has just been discussed in class.  Approximately one-third of the homework questions will come from material that was discussed the week before.  So, they will have done some problems for this section the previous week, gotten some feedback on how they handled those problems, and (hopefully) internalized the concepts more thoroughly.  The last one-third of the homework questions come from material discussed two weeks prior.  Thus, this material should be mastered as they solve these questions.  This approach helps solidify the concepts being taught in an individual manner and without unnecessary repetition in class.

Calculator Policy for ATYP
A graphing calculator can enhance the understanding of mathematics by allowing student access to harder problems and alternate ways of representing data. However, students are not encouraged to use a graphing calculator until a few months into the program. This is to make sure the student understands basic principles and theorems before allowing the calculators to do the work for them. ATYP encourages students to make use of concepts introduced in the book and not to reach for a calculator to do basic mathematics operations.

This being noted, ATYP utilizes graphing calculators in all years of its mathematics program. Most current graphing calculators are acceptable. If a student already owns a graphing calculator, then check with the instructor to make sure that it is compatible with ATYP’s program. If a student needs to purchase a graphing calculator for ATYP’s program, then both a TI-83+ and a TI-84+ are acceptable. Since KAMSC is recommending that their incoming freshman have a TI-84+ calculator, by purchasing a TI-84+ you may be able to use your calculator throughout more of your school career. A calculator with a keyboard or one containing a computer algebra system does not help a student learn mathematics and, as such, should not be purchased for this program.

Kelly Schultz
Kelly.Schultz@wmich.edu