Research on the psychological processes involved in early school arithmetic has now accumulated sufficiently to make it possible to construct a coherent account of the changing nature of the child's understanding of number during the early school years. This monograph presents an account of how number concepts are extended and elaborated as a…

An interview of 64 students in eight 3rd- and 4th-grade classrooms and an assessment of their teachers' control orientation were conducted for the purpose of testing the hypothesis that students of autonomy-granting teachers are better means-ends thinkers than those of controlling teachers. Dimensions of students' classroom socialization of…

Rationales for the college learning center to provide consulting services are considered, along with the literature on learning centers as consultants to the university community. Attention is directed to an actual consultation intervention, in which the learning center at the University of Utah worked with the coordinator and teaching assistant…

The main purposes of the seminar were to examine the present status of school mathematics problem solving; to explore classroom practice and what is known about research; to compare the situations appearing in textbook word problems; and to make plans for cross-cultural research in both countries. A paper from each country was presented during the…

This paper illustrates a model of the layperson's reasoning patterns under conditions of uncertainty, the "outcome approach," which was developed from analysis of videotaped problem-solving interviews with 16 undergraduate students. According to the outcome approach, the goal in questions of uncertainty is to predict the outcome of an…

This paper describes NEOMYCIN, a computer program that models one physician's diagnostic reasoning within a limited area of medicine. NEOMYCIN's knowledge base and reasoning procedure constitute a model of how human knowledge is organized and how it is used in diagnosis. The hypothesis is tested that such a procedure can be used to simulate both…

The first three units in this set of mathematical applications cover applications of calculus to economics. Under the title, The Distribution of Resources, are the following: 60-The Lorenz Curve; 61-The Equal Share Coefficient; and 62-The GINI Index. Each of these units contains a set of exercises, a model exam, and answers to both the exercises…

One module is presented in units 203, 204, and 205, as a guide for students, and presents a general strategy for solving integrals effectively. With this material is a solutions manual to exercises. This document set also includes a unit featuring applications of calculus to geography: 206-Mercator's World Map and the Calculus. Unit 207-Management…

Three of the modules deal with applications of calculus to other mathematics. These are: 240-Pi is Irrational; 241-The Wallis Approximation of Pi; and 242-Buffon's Needle Experiment. The first of these units focuses on a proof of the irrational nature of pi, and provides exercises and answers. The second module of this group reviews the history of…

The concept of multiplication is described and illustrated using several different representational systems. A conceptual approach to teaching mathematics is compared with the procedural approach commonly found in the school curriculum. Four different methods of representing the multiplication process with numbers larger than ten are presented:…

The faculty of Denison University have been making heuristic use of gaming and simulation for several years. In the fall of 1974, the college was awarded nearly $300,000 from the Lilly Endowment to continue and expand that heuristic use. Three years later, forms of simulation are being used by fifty per cent of the Denison faculty, and the college…

The Poisson probability distribution is seen to provide a mathematical model from which useful information can be obtained in practical applications. The distribution and some situations to which it applies are studied, and ways to find answers to practical questions are noted. The unit includes exercises and a model exam, and provides answers to…

It is suggested that a reader's idea structure will affect processing of incoming information. Two aspects of the idea structure are further developed--the truth value aspect and the analytic level aspect. The idea structure can be characterized by ideas consisting of propositions which are considered to be more or less true or false (beliefs), or…

School psychology is a very complex field further complicated by current socio-political contexts which mandate the development of a psychology of school psychology, requiring two things as first steps. The first step is a model which outlines the conceptual map of the area, gives direction to investigations in the area, and checks on the…

Hierarchically organized knowledge about actions has been postulated to explain planning in problem solving. Perdix, a simulation of problem solving in geometry with schematic planning knowledge, is described. Perdix' planning knowledge enables it to augment the problem space it is given by constructing auxiliary lines. The planning system also…