The past thirty years have shown a rise in models of language acquisition in which the state of the learner is characterized as a probability distribution over a set of non-stochastic grammars. In recent years, increasingly powerful models have been constructed as earlier models have failed to generalize well to increasingly complex and realistic…

The rapid development of education informatization has accumulated a large amount of data for learning analytics, and adopting educational data mining to find new patterns of data, develop new algorithms and models, and apply known predictive models to the teaching system to improve learning is the challenge and vision of the education field in…

The purpose of this study was to find out what difficulties Nicaraguan children encounter in doing addition and subtraction exercises. The results were used in the design of radio lessons in mathematics for elementary school. The performance on addition exercises is analyzed with a view toward identifying the distinct skills that are required by…

The article identifies five incorrect beliefs about mathematics often held by students who have difficulty with mathematics. They include: the relative size of numbers is more important than the relationships between quantities; computation problems must be solved by using a step-by-step algorithm; mathematics problems have only one correct…

Difficulty levels of 168 randomly generated multiplication problems were obtained by testing 238 fifth-graders. Variables concerning the number of operations, digits carried, and magnitude of the digits were defined, and a least-squares procedure was used to construct structural models accounting for 60-70 per cent of observed problem difficulty…

Significant differences were found favoring skill-deficient second-graders (N=10) provided with repeated preteaching trials on a selected component skill of a subtraction algorithm before they worked the entire algorithm over students (N=10) who, from the beginning of training, received systematic instruction on working the entire algorithm.…

The theory of unary and binary operations are discussed and illustrated with examples from school mathematics. Presentations of selected inverse operations are made and attention is drawn to certain "typical" problems that occur during instruction and learning of these concepts. (MP)

How teachers can diagnose difficulties with computation is discussed, with emphasis on how to develop diagnostic tests. How to use such tests to plan remediation is considered in terms of several types of errors. (MN)

The National Council of Teachers of Mathematics (NCTM) 1978 Yearbook contains fourteen articles covering a broad spectrum of computational topics. The first article considers the role of computational skills in the world of today and tomorrow. Several articles focus attention on how to help children master the basic facts. Algorithms for…

Students recognized as less successful individuals in mathematics are tested for their understanding of fractions. The data reveals that most were only able to apply remembered rules to problems without actually knowing if the rule worked for the given situation. (MP)

Children's difficulties remembering correct algorithms for operations with fractions are traced to difficulties in the instructional sequence. Many teachers "teach mistakes" by failing to provide sufficient referents for their pupils. (MP)

The ideas and techniques involved in learning about fractions were investigated with students in grades 1-12, in the first 3 years of colleges, in community college mathematics courses, and in graduate school. Also included were some high school mathematics teachers, some mathematicians, and some retired persons. Part I provides the rationale and…

This report describes the algorithm and materials developed at the Research Institute of Logopedics and Phoniatrics (University of Tokyo) for use in testing the abilities of Japanese students in the pronunciation and hearing of English monosyllabic words. The report begins with a description of the method employed for selecting the words to be…

Common mathematical errors of pupils as identified by the Concepts in Secondary Mathematics and Science Project are identified and traced to the use of methods invented by students rather than formally taught methods. (MP)

A computer program named BUGGY is described. The program is designed to duplicate "traditional" student mathematical mistakes; pupils are to identify the nature of the errors the computer makes. (MP)