Compares two approaches to the teaching of mathematics, rote versus reasoning. Discusses the way to teach mathematics as reasoning in elementary classroom as stated in the NCTM Standards. (YP)

Defines the mathematical concept of proportionality. Uses graphs of linear relationships to explore and make generalizations about the characteristics of proportional situations to help students critically evaluate problems involving proportions. (MDH)

Discusses prerequisites that help students develop multiple strategies for solving problems as recommended in the National Council of Teachers of Mathematics'"Curriculum and Evaluation Standards." Presents two examples of activities involving addition, subtraction, and permutations that promote multiple strategies. Suggests ways to…

Preservice elementary teachers worked cooperatively to explore the relationship between the measure of the central angle and the number of sides of regular polygons using the reflection of a line in a hinged mirror. The experience involved conjecture and experimentation, communication, and building connections between science, geometry, and…

Provides a rationale and overview of the content of the working draft of the Curriculum and Evaluation Standards for School Mathematics, developed by the National Council of Teachers of Matematics. (PK)

Presents a discussion illustrating student reasoning while using LOGO to draw tilted squares and rectangles. Suggests that teachers recognize that many students use visual imagery to reason and discuss visual reasoning with students. Gives examples of tasks to promote discussion. (MDH)