17. Analyses and evaluates the mathematical thinking and strategies of others
In problem solving situations, candidate can explore the thinking of students with a variety of solution strategies and identify the usefulness and appropriateness of a strategy for learning more mathematics. Evaluation and teaching mutually interact for planning.
Candidate normally evaluates others mathematical thinking but does not fully explore the strategies of students to ascertain understandings and conceptions. These evaluations inform the teaching.
Candidate occasionally evaluates the thinking of students but does not use the information as part of lesson planning or as part of teaching. Purely used as an evaluation tool for grading.
Candidate uses assessment as a grading tool and only checks for a single strategy. Expects others to solve problems as they are shown. Multiple problem solving strategies are not in evidence.
18. Mathematical Problem Solving is used to build conceptual understanding
Candidate demonstrates ability to expertly lead classes in mathematical problem solving. Focus is on in-depth conceptual understandings. Students are expected to develop and test generalizations.
Candidate demonstrates ability to lead classes in mathematical problem solving. Conceptual understanding is part of the focus with guided practice of generalization development and testing as a class.
Candidate demonstrates ability to lead classes in mathematical problem solving with “teaching as telling” as a main feature. Generalizations and testing are provided to students.
Candidate teaches examples from text. Problem solving is a by-product of text exercises without depth in exploration of concepts. View of problem solving is procedural.