This report summarizes findings on strategies chosen by students (n=38) when solving algebra problems related to various functions with the freedom to use a TI-83 graphing calculator, influences on student problem-solving strategy choices, student ability to approach algebra problems with use of multiple representations, and student beliefs on how…

The Golden Section, also known as the "Golden Mean" and the "Divine Proportion," is a ratio found in art and nature that has mathematical properties. This book explores these geometric and algebraic properties in a variety of activities. Construction problems, designs using the pentagon and pentagram, and opportunities to work…

Marginal cost is the cost of producing an additional unit. In higher education, one marginal cost would be cost of educating an additional student. Formula-based budget determination for public higher education is usually based on average cost per student. This study estimates marginal cost and compares it with average cost. There are several…

A review of cross-validation shrinkage formulas is presented which focuses on the theoretical and practical problems in the use of various formulas. Practical guidelines for use of both formulas and empirical cross-validation are provided. A comparison of results using these formulas in a range of situations is then presented. The result of these…

Five methods are given for computing the area of a regular octahedron. It is suggested that students first construct an octahedron as this will aid in space visualization. Six further extensions are left for the reader to try. (LS)

In this appendix to the study of subcounty allocation of Title I of the Elementary and Secondary Education Act, state by state profiles of subcounty allocation are provided. The allocation formula and procedures used by each state for fiscal year 1977 are explained. Other data for each state, such as number of school districts and counties which…

The merits of double exponential smoothing are discussed relative to other types of pattern-based enrollment forecasting methods. The difficulties associated with selecting an appropriate weight factor are discussed, and their potential effects on prediction results are illustrated. Two methods for objectively selecting the "best" weight…

This paper presents two extensions of the full-rank multivariate linear model that are particularly useful in multivariate analysis of covariance (MANCOVA) and repeated measurements designs. After a review of the basic full-rank model, an extension is described which allows restrictions of a more general nature. This model is useful in the…

The author argues for a clarification of standard notation rather than the use of flow diagrams to make the meaning of algebraic formulas more obvious to the beginning algebra student. (MN)

Describes an investigation of the use of document components, such as terms, sentences, and whole documents, for indexing and retrieval. A number of probabilistic similarity measures based on document components are studied, as well as a new method of handling probability estimations involving small sample sizes. (24 references) (Author/CLB)

A step-by-step outline is presented for testing the applicability of Lotka's law of scientific productivity. Steps include the computation of the values of the exponent and constant based on Lotka's method and the test for significance of observed frequency distribution against the estimated theoretical distribution derived from Lotka's formula.…

This paper reports on five students' explorations of structural relationships between problem situations that they worked on over several years as participants in a long-term study. In particular, we describe the case of students who recognized isomorphisms between and among two problem situations and who used particular features of the problems…

A procedure for generating the "nth" term of figurate numbers is given. (MNS)

The RKR method for determining accurate potential energy curves is described. Advantages of using the method (compared to Morse procedure) and a TRS-80 computer program which calculates the classical turning points by an RKR method are also described. The computer program is available from the author upon request. (Author/JN)