Addresses the principles and problems associated with the use of significant figures. Explains uncertainty, the meaning of significant figures, the Simple Rule, the Three Rule, and the 1-5 Rule. Also provides examples of the Rules. (ML)

Describes three studies in which students (N=515; N=60; N=135) were asked to indicate appropriate operations and numbers used in solving open mathematical sentences. Analysis of data and interviews suggest two error patterns: "finding a solution" and "inverse operation." Indicates that "finding a solution" strategy…

The derivation of a method to drive the general term of a sequence is presented. The difference sequences and binomial coefficents are used in the derivation. An application of this method is made to solve Polya's problems concerned with dividing space in regions by a given number of planes. (JP)

Presents three methods invented by fourth graders for obtaining the arithmetic mean. This presentation is in support of the idea that encouraging children to invent their own mathematical processes is a good way for them to clarify the idea of representativeness and consequently the teacher can facilitate the students' construction of higher…

Describes an instructional sequence that promotes student understanding of a coordinate system while simultaneously facilitating understanding of linear relationships. (Author/NB)

Investigates the extent to which visual considerations in calculus can be taught and be a natural part of college students' mathematical thinking. Recommends that the legitimacy of the visual approach in proofs and problem solving should be emphasized and that the visual interpretations of algebraic notions should be taught. (YP)

Derives the current in the wire joining two points when n points are joined two by two by wires of equal resistance, and two of them are connected to the electrodes of a battery of electromotive force E and resistance R. (YP)

Investigates the problem of finding the expected number of questions necessary to identify 1 out of a set of 30 attribute blocks. Solutions include the use of a tree diagram or a computer simulation. Generalizes the problem for increased numbers of attributes. (MDH)

Interviewed six first-year college students in an introductory physics course about their beliefs about physics. Characterized the students' beliefs about the structure of physics knowledge as isolated facts or a coherent system; content of physics knowledge as formulas or underlying concepts; and process of learning physics as receiving…

Uses the context of rock climbing to discuss the science concept of friction. Presents the mathematics equations that describe the concept. Examines the physics of different rock climbing situations encountered and equipment used. A series of related problems with answers is provided. (MDH)

This article presents two classroom episodes in which students were exposed to the value of asking questions and to the different roles played by proof in mathematics. The conversation in the two episodes is outlined in the article. The setting was a classroom of fifteen good high-school students, who were studying calculus. These episodes…

Interesting problems sometimes have surprising sources. In this paper we take an innocent looking problem from a calculus book and rediscover the radical axis of classical geometry. For intersecting circles the radical axis is the line through the two points of intersection. For nonintersecting, nonconcentric circles, the radical axis still…

A point "E" inside a triangle "ABC" can be coordinatized by the areas of the triangles "EBC," "ECA," and "EAB." These are called the barycentric coordinates of "E." It can also be coordinatized using the six segments into which the cevians through "E" divide the sides of "ABC," or the six angles into which the cevians through "E" divide the angles…

In the seventh century, around 650 A.D., the Indian mathematician Brahmagupta came up with a remarkable formula expressing the area E of a cyclic quadrilateral in terms of the lengths a, b, c, d of its sides. In his formula E = [square root](s-a)(s-b)(s-c)(s-d), s stands for the semiperimeter 1/2(a+b+c+d). The fact that Brahmagupta's formula is…