Types of errors made by children in addition and subtraction are presented and discussed. Suggestions are given for testing, diagnosing, and prescribing for instruction. (MNS)

Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…

A detailed comparison of four computer programs for analyzing hierarchical linear models is presented. The programs are: VARCL; HLM; ML2; and GENMOD. All are compiled, stand-alone, and specialized. All use maximum likelihood (ML) estimation for decomposition of the variance into different parts; and in all cases, computing the ML estimates…

Directed primarily toward the person familiar with computer technology rather than the traditional art educator, this master's thesis addresses new approaches to color theory and its impact on electronic art media. Technical considerations related to color coming from electronic sources, i.e., radiant light, and differences between radiant and…

The effectiveness of Stout's procedure for assessing latent trait unidimensionality was studied. Strong empirical evidence of the utility of the statistical test in a variety of settings is provided. The procedure was modified to correct for increased bias, and a new algorithm to determine the size of assessment sub-tests was used. The following…

Computer-adaptive testing (CAT) allows improved security, greater scoring accuracy, shorter testing periods, quicker availability of results, and reduced guessing and other undesirable test behavior. Simple approaches can be applied by the classroom teacher, or other content specialist, who possesses simple computer equipment and elementary…

The application of the "back-propagation" learning algorithm to the task of determining the right set of features corresponding to the words in an input sentence is described. Features that are specific to particular nouns and verbs, that indicate whether a nominal constituent is singular or plural, definite or indefinite, and that…

Nine methods for automated test construction are described. All are based on the concepts of information from item response theory. Two general kinds of methods for the construction of parallel tests are presented: (1) sequential test design; and (2) simultaneous test design. Sequential design implies that the tests are constructed one after the…

To demonstrate to computer programmers that the programming language Ada provides superior facilities for use in artificial intelligence applications, the three papers included in this report investigate the capabilities that exist within Ada for "pattern-directed" programming. The first paper (Larry H. Reeker, Tulane University) is…

Item response curves for a set of binary responses are studied from a Bayesian viewpoint of estimating the item parameters. For the two-parameter logistic model with normally distributed ability, restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the EM algorithm. The procedure is illustrated by data…

The materials in this teacher's guide are designed for about 18 weeks of study by secondary school students. For maximum benefit, the student needs contact with a computer, primarily for verifying and trouble-shooting the algorithms which he or she has constructed. The course is usually taught for grade 11 or 12 students. The commentary contains…

With the advent of computers and electronic calculators, the role of logarithms in the curriculum is changing. An intuitive approach to logarithms, stressing the notion of isomorphism, is discussed. (SD)

The calculator is used to explore the distributive property of a unary operator over a binary operator. This is an extension of an earlier paper. The emphasis is on student discovery of the property for various combinations of the operators. Instructional material contained in the report include a reference sheet of questions for potential…

The use of statistical methods in the design and analysis of discrete algorithms is explored. The introductory chapter contains a literature survey and background material on probability theory. In Chapter 2, probabilistic approximation algorithms are discussed with the goal of exposing and correcting some oversights in previous work. Chapter 3…