| Ideal Level | Standard Level | Unacceptable Level |
Achievement 1 | Can explain sets and functions in a classified way, and determine whether the cardinalities of two sets are equal | Can explain sets and a functions, and determines whether the cardinalities of two sets are equal | Cannot explain a set and a function, and cannot determines whether the cardinalities of two sets are equal |
Achievement 2 | Can explain the propositions and predicates, and correctly write a mathematical proof using proof by contraposition and contradiction, and the mathematical induction methods accurately. | Can explain the propositions and predicates, and write a mathematical proof using proof by contraposition and contradiction, and the mathematical induction methods. | Cannot explain the propositions and predicates, and write a mathematical proof using proof by contraposition and contradiction, and the mathematical induction methods. |
Achievement 3 | Can define sets and functions recursively and correctly. | Can define sets and functions recursively. | Cannot define sets and functions recursively. |