Informal Assessment sometimes interprets enthusiasm and confidence in mathematics for cognitive competence. Presented are two case studies of interviews conducted to study the affective and reflective capacities underlying children's mathematical thinking during a nonroutine problem-solving task. (MDH)

Since thinking is most often performed in problem-solving situations, teachers can become observers by providing situations in which students can practice and demonstrate intelligent behaviors. Some indicators include: perseverance, precision of language, problem finding, decreased impulsivity, metacognition, checking for accuracy, transference,…

Suggests that, although questions are often used to help students or stimulate student thinking, questions can also be used to help evaluate student thinking and attitudes about problem solving. Sample problems and questions are given. (PK)

Presents an activity for representing a given number in as many ways as possible using short periods of time to develop students' number sense and provide the teacher the opportunity to make informal student assessment and diagnosis. Provides specific dialogue of the activity being used in a third grade class. (MDH)

Offers seven criteria for developing mathematical thinking, plus suggestions for teaching and assessing students' progress that are compatible with each learning criterion. Provides evaluation sheets that help the teacher assess and grade students on the criteria. (10 references) (MDH)

Presents suggestions for using math performance assessments in elementary classrooms to help students develop mathematical thinking skills. The article lists National Council of Teachers of Mathematics evaluation standards for mathematics assessment and describes a number of problem-solving activities for students. (SM)

Presents three teaching ideas: (1) a scoring rubric to assess students' ability to communicate attempts at solving homework problems; (2) a three-part measurement activity using trigonometry, maps, and compasses to locate hidden treasure; and (3) a demonstration of the effects of numerical coefficients on graphs of quadratic functions. (MDH)

The essentials of Piaget's theory and its application to teaching at the college level are described as part of the Learning and Evaluation Service workshop, Teaching Students to Reason, offered at Michigan State University. Objectives are to enable the teacher to: (1) diagnose and classify reasoning patterns of students; (2) evaluate current…