FOUNDATIONS

Mathematics (updated 8-16-02)

Level 1

Level 2

Level 3

1. Computation: Performs the basic mathematical operations (addition, subtraction, multiplication, and division) without a calculator; understands decimals and fractions

2. Analysis: Divides material into component parts and analyzes the relationship between the parts and the whole; abstracts principles

3. Synthesis: Finds creative solutions by reassembling parts into a new whole; applies mathematical principles to new situations of moderate difficulty and complexity

4. Geometrical Thinking and Measurement: Understands the geometrical concepts, such as parallelism, perpendicularity, congruence, similarity, and symmetry, which underlie the three-dimensional world of buildings and moving objects

5. Communication in Mathematical Terms: Presents mathematical results or ideas coherently and convincingly

NOTE: Both part A and part B must be demonstrated to complete validation for Mathematics at Level 2.

A. Algebraic Thinking: Understands algebraic functions which relate directly to applied mathematics such as statistics, at a level equivalent to MATH 102: College Algebra

B. Statistics: Is aware of the pervasiveness of statistics in interpreting information in the modern world; recognizes basic uses and misuses of statistical representation and inferences; demonstrates responsible use of statistics (either data which the student has assembled or data from an external source) used as supporting information; understands and employs elementary principles of probability as used in predicting such future events as election results, business forecasts, and outcomes of sporting events

Demonstrates superior understanding and creativity in one of the following ways:

a. Designs and completes a project in any discipline requiring unusually sophisticated use of mathematics (statistics or some other branch) in a supporting capacity

b. Demonstrates unusual ability to teach mathematics

c. Completes a creative project exploring the relationship between mathematics and the arts (music, poetry, architecture) or some other area of human activity