Understands and applies recursion and iteration
Recursion and iteration are powerful mathematical tools for solving problems related to sequential (i.e., step-by-step) change, such as population change from year to year or the growth of money over time due to compound interest. To iterate means to repeat, so iteration is the process of repeating a procedure or computation over and over again. Recursion is the method of describing a given step in a sequence in terms of previous steps.
Recursive relationships may be described using informal notation such as NOW and NEXT. For example, NEXT = 1.08 NOW could describe a population that grows by 8% each year. Subscript notation may also be used (e.g., An+1 = 1.08 An), as well as function notation (e.g., S(n+1) = 1.08 S(n)). Students should understand and use a recursive view of functions (e.g., NEXT = NOW * 3 could represent an exponential function with constant multiplier 3, while NEXT = NOW + 3 could represent a linear function with slope 3.) Other topics studied should include arithmetic and geometric sequences and series, recursive formulas, and finite differences.