Reports results obtained when 24 14-year-old students were presented with algebra tasks by a computer-based modeling system and, four months later, comparable paper and pencil tests together with detailed interviews. Comparison of the results revealed profound misunderstandings of algebraic notation and identified classes of strategies used by…

Ideas on the long-term effects of using microcomputers in mathematics are presented. The changing perception of mathematics, the role of algorithms, the use of short computer programs, the effects on mathematical understanding, implications for teaching methods, logistic problems, examinations and assessment, and planning for the future are…

Presents methodological considerations in developing an automatic cheap algorithm for computerized path diagraming, gives some plotted results, and describes a program which produces the plots from an input matrix of path coefficients on a standard line printer. The program accommodates unidirectional and reciprocal causation and represents…

In conventional practice, most educators and educational researchers score cognitive tests using a dichotomous right-wrong scoring system. Although simple and straightforward, this method does not take into consideration other factors, such as partial knowledge or guessing tendencies and abilities. This paper discusses alternative scoring models:…

This paper proposes a new Information-Time index as the basis for item selection in computerized classification testing (CCT) and investigates how this new item selection algorithm can help improve test efficiency for item pools with mixed item types. It also investigates how practical constraints such as item exposure rate control, test…

A method of nonmetric multidimensional scaling is described which minimizes pairwise departures from monotonicity. (Author)

Revised and expanded version of a paper read to the Fifteenth Annual Conference on Linguistics, New York City, March 14, 1970. (VM)

Flexibility in the application of instructional methods is the best approach to a teaching situation. Insofar as possible, a combination of traditional learning methods with heuristic (problem solving) and programed ones should be used. (CK)

An approach to how to expand explorations of determinants is detailed that allows evaluation of the fourth order. The method is built from a close examination of the product terms found in the expansions of second- and third-order determinants. Students are provided with an experience in basic mathematical investigation. (MP)

When problems defy solution, mathematicians can settle for "almost." This branch of mathematics (called computational complexity) encompasses both the number of parts involved in a problem and the intricacy of their interrelatedness. Current research in this area is discussed, considering various computer applications involved. (JN)

Variations on a card trick are noted, with a formula for generalizing them. Another trick which can be proved with algebraic principles is then presented. (MNS)