Examines 250 sixth-grade students' understanding of arithmetic average by assessing their understanding of the computational algorithm. Results indicate that the majority of the students knew the "add-them-all-up-and-divide" averaging algorithm, but only half of the students were able to correctly apply the algorithm to solve a…

Discusses information retrieval and the use of binary trees as a fast access method for search strategies such as hashing. Proposes new methods based on compact binary trees that provide faster access and more compact storage, explains the theoretical basis, and confirms the validity of the methods through empirical observations. (LRW)

Presents a heuristic, attribute-based, noise-tolerant data mining program, HCV (Version 2.0) based on the newly-developed extension matrix approach. Outlines some techniques implemented in the HCV program for noise handling and discretization of continuous domains; an empirical comparison shows that rules generated by HCV are more compact than the…

Analyzes a didactical sequence for the teaching of addition and subtraction procedures and algorithms. Uses didactical procedures by children in problem solving activities in order to gain a better understanding of the interaction between numbers, numeration, and operations knowledge which are involved in the construction of addition and…

Sixteen middle school students ranked the lengths of various paths in problem-solving interviews. Every student invoked at least one of four intuitions that originated from their everyday experiences: compression, detour, complexity, and straightness. Students continued to use their inadequate intuitions in the posttest before applying learned…

Compares methods of subtraction used by children and teachers. Suggests ways to encourage children to invent their own subtraction algorithms. (CCM)

Although the average, or arithmetic mean, has a rich conceptual meaning, it is often defined simply as the outcome of a procedure. The purpose of this study was to compare the nature and extent of the procedural and conceptual understandings developed by two groups of students who received different forms of instruction, one based on the…

Monte Carlo studies investigated effects of within-group covariance structure on subgroup recovery by several widely used hierarchical clustering methods. In Study 1, subgroup size, within-group correlation, within-group variance, and distance between subgroup centroids were manipulated. All clustering methods were strongly affected by…

This paper describes an attempt to combine the advantages of both example-based translation and stochastic translation methods in an attempt to develop a method for inferring symbolic transfer functions from a bilingual corpus. By formalizing the translation process and applying standard optimization techniques, a system can be developed that will…

It has been shown previously that many students solve chemistry problems using only algorithmic strategies and do not understand the chemical concepts on which the problems are based. It is plausible to suggest that if the information is presented in differing formats the cognitive demand of a problem changes. The main objective of this study…

Conventional methods of multivariate normal analysis do not apply when the variables of interest are not observed directly, but must be inferred from fallible or incomplete data. For example, responses to mental test items may depend upon latent aptitude variables, which modeled in turn as functions of demographic effects in the population. A…

A subtraction algorithm for numbers having several digits is described. The algorithm requires that, for digits in the same place, the smaller is always subtracted from the larger. (SD)

A new subtraction algorithm is described and illustrated. Research by the author has shown the method to be easier for low achievers, as well as useful as enrichment for average students. (SD)