Activities in this article are a practical response to the philosophical debate about the use of technology in mathematics classes. Shows how technology can help students understand the sophisticated mathematics embedded in r, the correlation coefficient. Includes reproducible student worksheets. (MKR)

Shows how to model Newton's method for approximating roots on a spreadsheet. (MKR)

To understand an individual student's learning in the complexity of the mathematics classroom, it is necessary to examine the events before, during, and after learning. To illustrate, the process by which two children each construct new mathematical meanings is examined from these perspectives. (Author/MKR)

Describes the use of a graphic organizer--webs--to help students learn to connect concepts in mathematics. (MKR)

Discusses past research involving Piagetian conservation concepts in Native American students; the relation of language to mathematics education; holism in mathematics learning; mathematics and culture; the Outdoor World Science and Mathematics Project, which developed learning modules involving Native Americans; and mentorship in an atmosphere of…

Discusses the probability of seeing a tire explode or disintegrate while traveling down the highway. Suggests that a person observing 10 hours a day would see a failure on the average of once every 300 years. (MVL)

Investigated the acquisition and maturation of the infinity concept in mathematics of students ages 13-15. Found the infinity concept is learned by students only when provided with appropriate guidance. (Author/MKR)

Compared children's performance on initial-unknown and final-unknown problems involving the addition or subtraction of a single item. Found that although 4-year olds responded in a directionally appropriate way to the final-unknown problems but not to the corresponding initial-unknown ones, 5-year olds were able to respond appropriately to both.…

Included are the description, operating characteristics, uses, and future plans for the Topological Panorama Camera, which is an experimental, robotic photographic device capable of producing visual renderings of the mathematical characteristics of an equation in terms of position changes of an object or in terms of the shape of the space…

Discussed is the difficulty that students encounter when attempting to distinguish between independent and dependent variables, not only in the mathematics classroom, but also when devising and labeling graphs resulting from chemistry or physics experiments. (JJK)

Why children under 10 years do not use their mathematics knowledge to build a shortcut strategy to solve inversion problems was studied with 88 elementary school students in Munich (Germany). Most could use the shortcut but did so only when it did not compete with a more familiar strategy. (SLD)

Provided are examples from many domains of mathematics that illustrate the Fubini Principle in its discrete version: the value of a summation over a rectangular array is independent of the order of summation. Included are: counting using partitions as in proof by pictures, combinatorial arguments, indirect counting as in the inclusion-exclusion…

The discrete mathematics topics of trees and computational complexity are implemented in a simple reliability program which illustrates the process advantages of the PASCAL programing language. The discussion focuses on the impact that reliability research can provide in assessment of the risks found in complex technological ventures. (Author/JJK)

Discusses, through quotes about mathematical understanding from mathematicians, the experience of understanding, a nonobjectivist theory of meaning, the origins of mathematical objects, and reification as the birth of metaphor.(Contains 35 references.) (MKR)

Describes classroom activities that integrate math concepts with environmental science, demography, and language arts. The lesson helps students understand the competition between natural resources and the law of supply and demand. (HTH)