Search

This paper proposed the question "How do we teach logical thinking and sophisticated mathematics to unsophisticated college students?" One answer among many is through the writing of computer programs. The writing of computer algorithms is mathematical problem solving and logic in disguise and it may attract students who would otherwise stop taking mathematics courses after their required sequence is finished. In college classrooms in the United States, there is often an over-involvement with the calculation aspect of mathematics, especially in today's technical environment. The emphasis should fall on the teachers' developing of logic in students. Just like mathematical algorithms, computer algorithms however simple, employ logical steps which will result in the desired conclusion. Mathematics teachers should take advantage of the inumerable opportunities, even in a beginner's computer programming course, to play with algorithms that may aid students in the development of logical ways to approach mathematical problems. (MA)

An item-selection algorithm to neutralize the differential effects of time limits on scores on computerized adaptive tests is proposed. The method is based on a statistical model for the response-time distributions of the examinees on items in the pool that is updated each time a new item has been administered. Predictions from the model are used as constraints in a 0-1 linear programming (LP) model for constrained adaptive testing that maximizes the accuracy of the ability estimator. The method is demonstrated empirically using an item pool from the Armed Services Vocational Aptitude Battery and the responses of 38,357 examinees. The empirical example suggests that the algorithm is able to reduce the speededness of the test for the examinees who otherwise would have suffered from the time limit. Also, the algorithm did not seem to introduce any differential effects on the statistical properties of the theta estimator. (Contains 9 figures and 14 references.) (SLD)

The uses of programable calculators in the mathematics classroom are presented. A discussion of the "microelectronics revolution" that has brought programable calculators into our society is also included. Pointed out is that the logical or mental processes used to program the programable calculator are identical to those used to program any computer. A list and description of thirteen mathematical- and computer-related concepts that students can learn by working with programable calculators is presented. The report concludes with four additional uses of these electronic devices by teachers and pupils in the classroom. (MP)

This study investigated the relationship between the level of conservation of displaced volume and the degree to which sixth graders learn the volume algorithm of a cuboid, i.e., volume = length x width x height (v = l x w x h). The problem is a consequence of an apparent discrepancy between the present school programs and the theory of Piaget concerning the time to introduce the volume algorithm. Data showed that sixth graders could apply the algorithm to computation and comprehension questions regardless of their volume conservation level. There was also an improvement of students' conservation levels regardless of their volume achievement scores or their treatments. (Author/MK)

The critical role of computers in scientific advancement is described in this panel report. With the growing range and complexity of problems that must be solved and with demands of new generations of computers and computer architecture, the importance of computational mathematics is increasing. Multidisciplinary teams are needed; these are found in most advanced and industrial laboratories, but rarely in universities. The existing educational opportunities are not producing the required personnel to meet substantial shortages. Therefore, the panel strongly recommends increased federal support for: (1) research in computational mathematics, methods, algorithms, and software for scientific computing; (2) the development of interdisciplinary research teams; (3) the establishment and continued operation of a suitable research infrastructure for the teams; (4) graduate and post-doctoral students directly involved in the research of some interdisciplinary team; and (5) young researchers and cross-disciplinary visitors. In the second section, research opportunities in a number of mathematical areas are described. New modes of research are discussed next, followed by comments on educational needs and a final section on funding considerations. Appendices contain a list of related reports, information on laboratory facilities for scientific computing, and letters and position papers. (MNS)

Using a system based on standard augmented transition network (ATN) parsing approach, this report describes a technique for the rapid development of natural language parsing, called High-Level Grammar Specification Language (HGSL). The first part of the report describes the syntax and semantics of HGSL and the network implementation of each of its constructs, while the second section discusses the algorithms used in the HGSL compiler and the ATN interpreter. The third section presents a large grammar for technical prose that was developed with the system and which allows parsing of technical training materials in the draft stage of writing as part of a computer-based comprehensible writing aid. The report concludes with a review of some of the results on the coverage of the grammar. The grammar for technical training materials is appended. (FL)

The illustrative method of teaching employed in most undergraduate accounting courses is becoming increasingly burdensome to professors and students due to the rapid proliferation of accounting and auditing professional standards and the increased complexity of the tax law. This teaching method may be near the breaking point in upper division courses in the accounting curriculum. Not only does this condition prevent professors and students from reaching teaching or learning goals, it also prevents many capable students from considering accounting as their major or minor curriculum choice. A shift in teaching approach away from examples and toward explicit algorithms would enable the current quantity of material to be maintained with less burden placed on all participants. The algorithmic teaching approach is readily adaptable to accounting courses, particularly when the latter have been broken into specific learning modules. Microcomputers may be used to simplify the teaching and learning process by allowing students to explore complex accounting and taxation algorithms even before the components of the algorithms are fully understood. Discovery learning techniques, in which students derive their own algorithms, are also facilitated by microcomputers. Some examples of an algorithm-based learning module approach in an undergraduate taxation course are provided as well as a list of 14 references. (Author/MES)

Considers traditional ways in which attempts have been made to help students become fluent in mathematics and offers a model for ways in which fluency can be achieved with a more economic use of students' time and effort than through traditional models of exercises based on repetition. (MKR)

Shows how to characterize language learning in a finite parameter space, such as in the "principles-and-parameters" approach, as a Markov structure. Explains how sample complexity varies with input distributions and learning regimes. Finds that a simple random-step algorithm always converges to the right target language and works faster than a single-step, local parameter-setting method. (BC)

Describes an algorithm that can be used for the construction of an oral presentation. The article suggests how nonnative English-speaking students can be taught to make their presentations more cohesive and to evaluate their cohesiveness with the help of video recordings. (21 references) (Author/CK)

Describes an algorithm for developing a domain knowledge base used in a Japanese language intelligent tutoring system. The domain knowledge represents a model of the expertise required of a student for proficiency in reading "katakana," a Japanese orthography. The algorithm described can generate a knowledge base of Japanese phonological transformation rules automatically. (20 references) (Author/CK)

Describes a new data compression technique that utilizes the common morphological structure of languages. Topics include classification of languages and their morphological structure; structured text compression; the algorithm and an example using Turkish; theoretical implications; and implementation. (LRW)

Discussion of the failure of individual keywords to identify conceptual content of documents in retrieval systems highlights Metric Similarity Modeling, a method for creating vector space representation of documents based on modeling target interdocument similarity values. Semantic relatedness, latent semantic indexing, an indexing and retrieval algorithm, and validating experiments are discussed. (Author/LRW)

Presents results of a project with second and third graders to establish concepts of equality that led to the realization that teachers often help students too much and may push them algorithmically beyond their ability without the development of proper referents. (Author/MKR)

Limitations in children's understanding of the symbols of arithmetic may inhibit choice of appropriate solution procedures. The teacher's role involves negotiation of new meanings for words and symbols to match extensions to solution procedures. (MKR)

Discusses the feasibility of building intelligent rule- or weight-based algorithms into general-purpose software for interactive thesaurus navigation. Previous research is surveyed; practical investigations in thesaurus navigation and query enhancement are described; and implications for automatic or intelligent thesaurus navigation are considered. (16 references) (LRW)

Discusses the problem of enhancing the speed of Huffman decoding of compressed data. Topics addressed include the Huffman decoding tree; multibit decoding; binary string mapping problems; and algorithms for solving mapping problems. (22 references) (LRW)

Describes fast, dynamic update algorithms for document retrieval systems. B-trees are discussed; the M-B-T file directory structure is explained; insertions and deletions in inverted files are described; and performance evaluation is discussed. An appendix provides the formal definition of an M-B-T directory. (Contains 18 references.) (LRW)

The federal Escrowed Encryption Standard (EES) has been opposed by civil liberties advocates and the computer industry. The author argues that the standard does not threaten privacy as long as its use remains voluntary, alternative forms of encryption are allowed, and the power of government to intercept transmission is kept in check. (20 references) (KRN)

Discussion of information retrieval focuses on an Interaction Information Retrieval model in which documents are interconnected; queries and documents are treated in the same way; and retrieval is the result of the interconnection between query and documents. A theoretical mathematical formulation of this type of retrieval is given. (Contains 31 references.) (LRW)

Attempts to describe a notion parallel to number sense, called symbol sense, incorporating the following components: making friends with symbols, reading through symbols, engineering symbolic expressions, equivalent expressions for non-equivalent meanings, choice of symbols, flexible manipulation skills, symbols in retrospect, and symbols in context. (24 references) (MKR)

Discusses end-user searching in Boolean information retrieval systems considers the role of search intermediaries and proposes a model of user preferences that incorporates a user's profile. Highlights include document representation; information queries; document output ranking; calculating user profiles; and selecting documents for a local database using the user's profile. (Contains 28 references.) (LRW)

Discussion of how to teach programming skills to novice programmers focuses on the use of a program animator that uses a copies model of recursion to teach the recursive function. Various mental models are reviewed; testing the recursion animator is described; and possibilities for further research are suggested. (12 references) (LRW)

Presents an interpolation methodology that duplicates and improves the results of mathematical functional relationships useful for designing business enterprise simulations and argues that interpolation is effective over the entire range of production and sales activity. (six references) (EA)

Describes the logical construction of several Russian hypertext systems, and discusses the navigational algorithms used, nodes selected, and coherence demanded. Several illustrative graphs are included, and an overview of the development of linking structures producing logical-semantic models is given. (20 references) (EA)

Provides the transcript of an interview with Dr. Lev Landa that addressed issues related to his algorithmico-heuristic theories of learning and instruction, called Landamatics. Highlights include teaching thinking versus knowledge; algorithms; instructional design; improving training and performance in industry, business, and government; artificial intelligence; knowledge acquisition; and time factors. (LRW)

Discusses effective communication with interactive video and suggests possible barriers. Topics addressed include identifying the user; the need for standards; algorithms; the rapid development of hardware; navigation in interactive media; and interactivity with the user. (LRW)

Discusses the development of successful pricing algorithms for cooperative library automation projects. Highlights include desirable characteristics of pricing measures, including simplicity and the ability to allow for system growth; problems with transaction-based systems; and a review of the pricing strategies of seven library consortia. (Contains two references.) (LRW)

Discusses the use of a historical profile for illustrating the significance of the mathematical components of scientific laws. Addresses the need for the purposive use of scientific laws rather than the blind substitutionary procedures characteristic of most problem solvers. Claims the approach has the potential for increasing female participation in the physical sciences. (Author/MDH)

Discusses the role connectionism plays in the development of cognitive theories and in the explanation of linguistic phenomena inherent in second language acquisition (SLA). Presents a critical look at some existing connectionist models of language functions with a focus on the need for a general cognitive model of SLA that integrates research in several fields. (58 references) (Author/CK)

Explains the Intelligent Maintenance Training System that allows a nonprogramming subject matter expert to produce an interactive graphical model of a complex device for computer simulation. Previous simulation-based training systems are reviewed; simulation algorithms are described; and the student interface is discussed. (Contains 24 references.) (LRW)

Discusses the functions of using visuals in communicating and comprehending information. (AEA)

Describes system design proposed by the Spelling Error Detection Correction Project (SPEEDCOP) at Chemical Abstracts Service. Highlights include principles of detection/correction system; spelling error detection (the dictionary, suffix normalization, bypassing specialized word classes, document-level frequency threshold); spelling error correction; reusing decisions; dictionary construction and maintenance; and typical application. (Fifteen references.) (EJS)

Offers characterization of sign-transmission which is more general than conventional signal-transmission theory. Concepts and terminology, formal description of individual communications process, reconciliation with classical signal-detection theory, applications of sign-detection formalism to information retrieval on MEDLINE database, and a prototype psychological experiment in area of cognitive perception are highlighted. (Twenty-nine references) (EJS)

Three different methods of teaching fraction computation were compared using community college student scores on measures of fraction computation, fraction understanding, and attitude towards mathematics. One method used conventional algorithms; the second, a control for the effect of using a calculator, used conventional algorithms and calculators; the third used calculator-based algorithms. Differences between methods on the three dependent variables were not statistically different. Pretest to posttest differences were significant for all groups with fraction computation scores making the largest contribution to the increase in scores. (Author/MK)

Success in using a computer in education as a problem-solving tool requires a change in the way of thinking or of approaching a problem. An algorithm, i.e., a finite step-by-step solution to a problem, can be designed around the data processing concepts of input, processing, and output to provide a basis for classifying problems. If educators concentrate on the how to, rather than on the correctness of the results, computers in the classroom can speed up the testing of specific algorithms. Developing an adequate, workable algorithm requires the critical steps of precisely defining the problem; careful attention to clarity, detail, and sequence; and a knowledge of the problem in order to explain the phases and smaller steps needed to solve the problem. The concepts of pseudocode and flowcharting standardize, solidify, and simplify the entire process. The ability to classify problems into one of three general categories (narratives, computational/verbal, and inputs/outputs) provides researchers with the framework upon which to build new and refine existing algorithms. Suggestions for the problem definition phase and an outline for this presentation are included. (DJR)

An information retrieval system which aspires to retrieval of relevant documents should have second stage which will order topical set to provide maximum informativeness to requestor. A two-stage system concerned only with topicality can be iterated to generate a high recall set and discard imprecise documents without user input. (EJS)