A generalization of the golden ratio is made, called the silver ratio. Some examples where the golden ratio appears are provided so that the silver ratio appears. (MNS)

Third graders decided to collect 10,000 objects, first determining how many each child would bring. Grouping and other activities were involved, and each child wrote about the experience. (MNS)

Three experiments explored the developmental relationship between counting and number conservation in children from three to six years old. Results indicated that there was a close relationship between the two; that only the oldest children gave evidence of conserving; and that, in general, there is evidence of protracted development in young…

Questionnaires were completed by 100 parents of kindergarten-age children whom the parents thought to be mathematically precocious. Five factors were found to characterize responses: (1) general intellectual factor; (2) short- and long-term memory; (3) rote memory; (4) spatial reasoning; and (5) specific relational knowledge. Parents were able to…

Presents strategies teachers have developed to provide an authentic use of mathematics that enhances children's autonomy in managing classroom activities, including recording and using data on attendance and choices for interest centers and using mathematics to distribute snack food and utensils. (MKR)

Investigation of the presence and effect of intuitive obstacles to the concept of irrational number in (n=30) ninth-grade, (n=32) tenth-grade, and (n=29) college students found that only some students manifest genuine intuitive biases. Most students were unable to classify numbers as rational, irrational, and/or real. (Author/MKR)

Discusses the problem-solving attempts of second-grade students while solving a rate problem. (MKR)

Discusses research findings that relate to teaching fractions for conceptual understanding. Gives teacher/student dialogues that illustrate the thought processes of students as they form part-whole and improper fraction concepts. (MDH)

Suggests structured investigations as a method of teaching mathematics to preservice elementary school teacher. Presents an example problem that asks students to determine the maximum number of regions that can be created by connecting any two points around the circumference of a circle. (MDH)

Presents three investigations that extend the problem of counting the number of squares on a grid in two dimensions to an analogous problem of counting the number of cubes in a three-dimensional cubic array. (MDH)

A constant time delay procedure was used to teach four adolescents with moderate mental retardation to select lower priced grocery items using an adaptive number line. Students reached criterion, maintained the skill up to 14 weeks after training, and generalized the skill from the classroom to a community grocery store. (Author/DB)

Using the notion of the difference between a number and its cube as a starting point, this article presents a wide range of mathematical activities at varying levels of sophistication utilizing numerical, intuitive, and graphical approaches. (JJK)

Introduces the idea of using computer microworlds--interactive software for exploration of specific concepts--for mathematics education, the theme of this issue's articles. Discusses their development and the advantages of their use. Suggests that they can be successfully used for interactive teaching or for interpreting mathematics textbooks,…

After a brief historical account of Leonardo Pisano Fibonacci, some basic results concerning the Fibonacci numbers are developed and proved, and entertaining examples are described. Connections are made between the Fibonacci numbers and the Golden Ratio, biological nature, and other combinatorics examples. (MDH)

Based on a two-tiered epistemological model (preliminary physical concepts and emerging mathematical concepts), studied the construction of number among 91 kindergarten students in France, Canada, and the United States. Subjects' cognitive numerical structures were surprisingly similar despite differences in language and culture. (SV)