These modules view aspects of computer use in the problem-solving process, and introduce techniques and ideas that are applicable to other modes of problem solving. The first unit looks at algorithms, flowchart language, and problem-solving steps that apply this knowledge. The second unit describes ways in which computer iteration may be used…

A study of 130 undergraduate students enrolled in a course on auiovisual techniques sought to determine whether heuristic or algorithmic computer-based problem solving training would be differentially effective for students varying in cognitive complexity as measured by the Educational Set Scale (ESS). The interaction was investigated between one…

About 25 children in each of grades 3, 5, 7, 9, and 11 were tested in their ability to solve linear syllogisms, such as: John is taller than Mary. Mary is taller than Pete. Who is tallest--John, Mary, or Pete? Response latencies and error rates decreased across grade levels and sessions. Component latencies also generally decreased with increasing…

Summarizes a simple design algorithm which identifies nested loops of equations which must be solved by trial-and-error methods. The algorithm is designed to minimize such loops, provides guidance to the selection of variables, and delineates the order in which systems of equations are to be solved. Examples are included. (TW)

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)

Presents the text of a message sent to Susan Gerofsky by Robert Thomas after reading her article on a linguistic and narrative view of word problems in mathematics education. Gerofsky's response is also included. (DDR)

Investigates high school students' understanding of the physical relationship of chromosomes and genes as expressed in their conceptual models and in their ability to manipulate the models to explain solutions to dihybrid cross problems. Describes three typical models and three students' reasoning processes. Discusses four implications. (YP)

This paper presents a theoretical framework for investigating the role of algorithms in mathematical thinking using a combined ontological-psychological outlook. The intent is to demonstrate that the processes of learning and of problem solving incorporate an elaborate interplay between operational and structural conceptualizations of the same…

A study on the impact of misconceptions on preservice elementary teachers' processes in solving problems involving multiplication and division of decimals is described. Included are the purpose of the study, a description of the subjects, instruments, and interviews, the findings, and discussion. (KR)

Online information retrieval is pervasive and its development in libraries is accelerating. Within the near future, most college and research libraries will provide direct access to their patrons to vast information resources via CD-ROMs, locally mounted databases, and gateways. The computer terminal and the "frame" of information it…

This paper presents an examination of the construction of logic in multidigit subtraction. Interviews were conducted with 90 grade 2 and grade 3 students to determine whether they understood the logic of borrowing and whether the construction of the logic was related to procedural expertise or corresponding conceptual knowledge. Of 34 students…

Applied mathematics is seen often to involve the solution of single equations or systems of equations. A particular technique for solving equations in the context of functions on the real line is examined. This technique includes an iterative process, which is viewed as an algorithm that can be implemented readily on inexpensive and widely…

This module is designed to apply mathematical models to nuclear deterrent problems, and to aid users in developing enlightened skepticism about the use of linear models in stability analyses and long-term predictions. An attempt is made at avoiding overwhelming complexities through concentration on land-based missile forces. It is noted that after…

This material contains two units which view applications of computer science. The first of these examines Horner's scheme; and is designed to instruct the user on how to apply both this scheme and related algorithms. The second unit aims for student understanding of standard bisection, secant, and Newton methods of root finding and appreciation of…