The results of an investigation of the development of children's knowledge of addition and subtraction concepts before they start school are detailed. The purpose of the study was to test the predictions of the three-stage model about the distinctions between the last two stages. Twenty-four children participated in the investigation. None of…

The twenty-second in a series, this report describes research in information organization and retrieval conducted by the Department of Computer Science at Cornell University. The report covers work carried out during the period summer 1972 through summer 1974 and is divided into four parts: indexing theory, automatic content analysis, feedback…

Presents thinking-aloud protocols from secondary pupils solving arithmetic story and geometrical problems and analyzes their protocols by using interpretation models founded on a general problem-solving model. A word problem solving simulation is also used to further explicate processes pupils use to solve mathematical tasks. (Author/MBR)

Evaluates and compares two recently proposed automatic methods for relevance feedback of Boolean queries (Dillon method, which uses probabilistic approach as basis, and disjunctive normal form method). Conclusions are drawn concerning the use of effective feedback methods in a Boolean query environment. Nineteen references are included. (EJS)

Structural learning theory and the Rasch model measured learning gain, retention, and transfer in 1,037 students, grades 7-10. Students learned nine functional relationships with either spontaneous or synthetic algorithms. The Rasch model gave the better description of the data. The hypothesis that the synthetic method was superior was refuted.…

In the past, algorithm animation has yielded mixed results as a teaching tool in computer science. This article presents a study in which undergraduates at George Washington University (DC) viewed algorithm animations and then programmed the same algorithms. Results suggest that combing the two is an effective way to use animation and to produce…

Discussed is the effectiveness of using analogies in chemistry instruction. Students' mathematics anxiety, spatial visualization skill, and proportional reasoning ability were found to be important aptitudes for determining chemistry achievement. The relationship between analogs and algorithms is described. (KR)

Among 1,453 male and 1,133 female academically talented 7- to 11-year-old students, boys performed better overall than girls on mathematical reasoning. Gender differences appeared as early as second grade, varying according to mathematics subskills. Male performance was better on tasks requiring application of algebraic rules and understanding of…

Effects of previous training and experience in peer tutoring on student interactions were studied for 16 elementary school classes. Student dyads with experience and training in peer tutoring provided more interactional explanations and incorporated sounder instructional principles. In both situations, student explanations tended to be algorithmic…

Reform efforts in mathematics aim to increase conceptual understanding, an aim that can be supported through concept maps. This study compared the conceptual knowledge of function held by college students in reform and traditional calculus sections at a large state university. Fourteen students from reform sections and 14 from traditional sections…

The reliability of four branching algorithms commonly used in computer adaptive testing (CAT) was examined. These algorithms were: (1) maximum likelihood (MLE); (2) Bayesian; (3) modal Bayesian; and (4) crossover. Sixty-eight undergraduate college students were randomly assigned to one of the four conditions using the HyperCard-based CAT program,…

The problem of determining optimal test lengths with fixed total testing time has proved to be a difficult one for criterion-referenced test developers. An algorithm is needed which can be used by test developers to allocate available testing time to maximize the validity of their total criterion-referenced tests or testing programs. To be…

The central objective of this study was to determine the effects of formal training in the use and types of questions and in the nature and use of algorithms on middle school students' achievement in economic geography. Subjects were 190 eighth grade students in a large metropolitan school district. Three experimental groups received either: (1)…

This issue contains abstracts and critical comments for 11 articles. Three articles focus on problem solving; the remainder concern understanding of the equals sign, mathematical structure, mathematical abilities, the role of language in tasks involving sets, sex differences in mathematical errors, subtraction, algorithms as schemes, and…

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:…