Describes a method for determining the distance to the horizon which leads to determining the radius of the Earth. The article answers two interesting science questions: (1) Can you see the state of Kansas from Pike's Peak in Colorado? and (2) Can you see two sunsets in one day on the Keys of Florida? (MVL)

A classroom exercise to help college students of economics conceptualize, create, and learn from graphs is described. The technique is illustrated with an exercise concerning the concept of supply and demand in consumer markets. Classroom time required for the activity is small, and students become adept at manipulating models without anxiety.…

Fifty children, ranging in age from 4 to 10, were individually administered a series of tasks involving different combinations of 2 items selected from a discrete set of items. Analyses of their performances revealed a series of six, increasingly sophisticated, solution strategies ranging from random number selection of items to a systematic…

Presents an activity applicable at the beginning of the year to review necessary algebra concepts that are often misunderstood by students. Presents a true/false worksheet made up of examples illustrating common algebra and trigonometry errors made by students. (MDH)

A number for which the number of digits categorizes the number is called a star number. A set of star numbers having a designated property is called a constellation. Discusses nature and cardinality of constellations made up of star square, star prime, star abundant, and star deficient numbers. Presents five related problems for exploration. (MDH)

In this article, constructivism is examined as an epistemological basis for school science and mathematics instruction. The nature and process of constructing scientific and mathematical knowledge in school settings is also considered. A distinction is made between truth and feasibility, and the implications for science education are discussed.…

Reviews recent research in the area of mathematical understanding and compares and contrasts it with a model formulated for the growth of understanding. Uses the analysis of a transcript from an interview with an eight-year-old boy to illustrate the power of the model to describe and map the growth of his mathematical understanding. (18…

Presented is a concrete, realistic way of representing concepts of coordinate geometry. Students represent the coordinates in a living version of a five-by-five square geoboard. Procedures and examples for using this activity are included. (KR)

Much constructive computer and programable calculator activity can be stimulated by BASIC programs that are only three or four lines in length. This article illustrates several ideas with accompanying BASIC program, particularly related to the learning of algebraic concepts, that can be explored with both elementary and secondary mathematics…

Tips are given on how and when to use videotaped lessons to provide for continued classroom productivity in spite of anticipated, or even unexpected, absence of the mathematics teacher. In an accompanying article, a graphical approach to determine whether a limit exists is explored with numerous examples and illustrations. (JJK)

Discusses the differences between teaching for procedural understanding and teaching for conceptual understanding by asking several penetrating, open-ended questions, directed at teachers, about the type of mathematical understanding students are achieving within several examples of classroom situations. (JJK)

This study examined the construct validity of the KeyMath-Revised by testing the factorial model proposed by the test author. Results failed to confirm the proposed factorial model and suggested that the KeyMath-Revised assesses two domains that are difficult to interpret, rather than the three proposed by the test author. (Author/JDD)

The purpose of this paper is to show, by computer examples, that very different results can be obtained by rearranging selected conditionally convergent series. Computer programs allow the students to select the real number to which they wish the rearrangement to converge. Two computer programs are appended. (KR)

Described are the variations found between the western and African versions of the same logic puzzle. It is demonstrated that mathematical ideas are of concern in traditional non-Western cultures as well as in the West. (KR)

Explored are the distributions of residual components in two model systems. A system of components with exponentially distributed lifetimes and the two-dimensional "leaf model" in which objects fall on a plane with positions independent and normally distributed are discussed. Included are the definition, application, computations, and theorem. (KR)