It is shown that the bisector of a segment of a geodesic and the bisector of an angle in hyperbolic geometry can be expressed in terms of points which are equidistant from the end points of the segment, and points that are equidistant from the rays of the angle, respectively. An important tool in the approach is that the shortest distance between…

In this paper it is argued that the characterization of mathematical justifications as inductive or deductive is incomplete. Promoting in classrooms the development of and discourse about a third type of reasoning, transformational reasoning, which considers the results of operations on a set of objects, may contribute to mathematics learning in…

Similarity of parabolas and other conic sections is discussed. The theorem "Any two parabolas are similar" is deduced. (SD)

This study examined the links students are able to make between formal expressions and situations to which they might refer. Students' understanding of a basic set of transformational rules in elementary algebra sign changes in addition and subtraction expressions with parentheses was assessed, exploring: (1) informal intuitive understanding of…

Outlined is a model for transformation of one factor matrix to congruence with a second or target matrix in which the correlations among the transformed factors are constrained to certain pre-specified values. Procedures are developed for implementing the model, and are illustrated with example factor solutions. (Author/RC)

CLASSIFICATION OF DOCUMENTS INVOLVES THREE DISTINCT PROCESSES-- (1) DEFINING A STRUCTURE OF CATEGORIES, (2) DETERMINING A BASIS FOR A CLASSIFICATION DECISION, AND (3) CLASSIFYING DOCUMENTS INTO CATEGORIES. OF THE THREE COMPUTER TECHNIQUES ARE DISCUSSED FOR THE LAST TWO. A WORD SELECTION MEASURE IS USED TO DELETE THOSE TERMS IN THE DOCUMENT THAT…

Comparison of two eleventh-grade mathematics programs was made by evaluations of student and teacher attitudes and of student achievement on specific content as well as performance on the ETS Algebra II exam. An experimental program based on Zalman Usiskin's textbook, "Intermediate Algebra," was matched with programs based on traditional texts.…

The teacher's guide for the eleventh unit in this SMSG series covers the chapter on rigid motions and vectors and the chapter on computers and programs. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed, behavioral…

This monograph is concerned with the uses to which an individualized student information system could be put for obtaining valuable insights into the progress of a variety of students through the educational system. In chapter 1, the concepts and terminology required for an understanding of transition matrixes are introduced, and a mathematical…

Populations of factorially simple and complex data were generated with first the oblique and orthogonal factor models, and then solutions based on special cases of the general orthomax criterion were compared on the basis of these characteristics. The results are discussed and implications noted. (DEP)

A sequential but non-axiomatic high school geometry course which includes Euclidean, transformation, and analytic geometry and vectors and matrices, and emphasizes the invariance property of transformations, is outlined. Sample problems, solutions, and comments are included. (MN)

An asymptotic theory is developed for a new time series model introduced in TM 502 289. An algorithm for computing estimates of the parameters of this time series model is given, and it is shown that these estimators are asymptotically efficient in that they have the same asymptotic distribution as the maximum likelihood estimators. (Author/RC)

This game offers an opportunity for students in grades 4-6 to sharpen their spatial skills and enrich their geometric experience. It presents such concepts as reflection, translation, and rotation (flip, slide, turn). Templates for the game are included. (MNS)

Meredith's method of extracting a factorially invariant solution is adapted to longitudinal settings. An explorational estimation procedure is presented which attempts to identify the longitudinal factor components of an across occasion variance-covariance matrix. Data from 166 subjects on the Wechsler Adult Intelligence Scale is used to…

Examines the cause of confusion arising from ambiguity of units and semantics in length, area, and volume concept formation. Introduces the mimik, a standard area of one thousand square millimeters, and advocates its use as an interim symbol system. (JM)