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…

Described is how using LOGO tools for manipulating embodiments of geometric objects helps students construct more abstract and coherent concepts. Discussions are included on developing verbal definitions versus constructing concepts, tasks for integrating turns and angles, group discussions, and maze tasks. (KR)

Discusses a variation on tiling that offers opportunities for the construction of the fundamental mathematical concept of constructing abstract units called "unitizing." Tiling integrates geometric and numerical settings to develop spatial sense and present mathematics as constructing patterns. (MDH)

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…

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)

Presents five examples of how technology can be integrated into Family Math nights. Activities involve graphing, managing money, developing mental mathematics skills, developing deductive and spatial reasoning, and using tangrams to explore patterns and spatial relationships. Includes a list of software publishers. (MDH)