The developmental psychology of mathematical thinking and the clinical interview method can make major contributions to education by transforming the process of formative assessment--the attempt to use information concerning student performance, knowledge, learning potential, and motivation to inform instruction. The clinical interview is a…

The premise underlying this article is that identifying and using the "five practices model" can make discussions of cognitively challenging tasks more manageable for teachers. By giving teachers a roadmap that they can follow before and during whole-class discussions, these practices have the potential for helping teachers more effectively…

The critical component of mathematics, the individual mathematician in particular, and the centrality of human thought, were discussed. (Author/RK)

The author has been reading Barry Mazur's "Imagining numbers," one of a number of recent general books about mathematics. This one, typically, is said in the preface to be for "people who have no training in mathematics." It does, perhaps untypically, invoke algebraic symbolism and solve quadratic and cubic equations. More…

This textbook presents definitions and remarks, axioms, properties of polygons, ratios and proportions, planes and their angles, measurement of areas and proportions of figures, solids, and mensuration of surfaces, solids, and round bodies.

The principal objects of the investigation reported were, first, to study qualitative probability relations on Boolean algebras, and secondly, to describe applications in the theories of probability logic, information, automata, and probabilistic measurement. The main contribution of this work is stated in 10 definitions and 20 theorems. The basic…

The major results of this dissertation are theorems to the effect that certain classes of relational structures are not axiomatizable by universal sentences. Some of the particular classes considered are theories of measurement in the sense of the Scott-Suppes definition while others are theories of measurement according to a natural…

The multivariate analog of Hays omega-squared for estimating the strength of the relationship in the multivariate analysis of variance has been proposed in this paper. The multivariate omega-squared is obtained through the use of Wilks' lambda test criterion. Application of multivariate omega-squared to a numerical example has been provided so as…

Description of management games continues a previous article's discussion of how mathematical modeling and microeconomic concepts can be used by players. Highlights include an initial condition simulating a profit-maximizing monopoly; simulating the transition from monopoly to oligopoly; and how mathematical properties of the model affect final…

The stabilities of standardized (ß) and structure (rs) coefficients in canonical (CA) and discriminant analyses (DA) were studied. Four different situations were studied--two pertaining to CA and two to DA. The situations were meant to represent "somewhat typical" and yet varying research conditions that often would not be thought to be…

Number maps afford a clear and graphic means by which students can more readily grasp the concept of change in mathematics and social science. (Author)