The Jeong (2020) study found that greater use of backward and depth-first processing was associated with higher scores on students' argument maps and that analysis of only the first five nodes students placed in their maps predicted map scores. This study utilized the jMAP tool and algorithms developed in the Jeong (2020) study to determine if the…

This paper explores the correlation between mental calculation performance and the frequency of using written algorithms in mental calculation tasks. Mental calculation is a mathematical tool used in everyday life situations during and after our formal education. After presenting an overview of the professional literature on this topic, the paper…

Transactive discussion during collaborative learning is crucial for building on each other's reasoning and developing problem solving strategies. In a tabletop collaborative learning activity, student actions on the interface can drive their thinking and be used to ground discussions, thus affecting their problem-solving performance and learning.…

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…

Presents model of algorithm design (activity in software development) based on analysis of protocols of two subjects designing three convex hull algorithms. Automation methods, methods for studying algorithm design, role of discovery in problem solving, and comparison of different designs of case study according to model are highlighted.…

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…

This paper describes an investigation of problem sequencing as part of a symposium presenting theoretical concerns and research findings regarding several diverse types of strategies for designing and presenting instructional materials. The first step involved analyzing a set of problems, to determine the knowledge (rules) required for solving the…

The research reported in this paper was designed to analyze the incidence of use of higher-order rules by students solving geometric construction problems. A carefully selected set of construction problems was subjected to rigorous a priori analysis by mathematics educators to determine what basic and second-order rules might be used by able high…

The topic of teaching troubleshooting is examined as an example of the teaching of cognitive strategies for technical problem solving. The traditional behavioral approach to teaching troubleshooting has essentially been algorithmic. Recent cognitive research suggests an approach founded first on task analysis and characterized by: (1) analysis of…

One difficulty that mathematically naive subjects encounter in solving arithmetic word problems involves the limitation on short term memory (STM) capacity. It is hypothesized that naive subjects, not having access to formal problem solving strategies, may find visualization useful in reducing strain on STM. Two experiments are reported. The…

Forty-eight first and second graders were taught an algorithm for solving concept-attainment problems. Using a 2 x 2 factorial design, a comparison was made of the effects of (a) reverse versus forward sequencing of instruction and (b) elicited verbalization of the algorithm versus nonverbal practice. Reverse groups outperformed forward groups on…

Arguments for and against the use of computers in mathematics classes have centered on whether students benefit from or are merely hindered by practicing computational skills. This paper claims that the true essence of mathematics lies not in computation, basically a mechanical operation, but in problem-solving. Since no amount of computational…

The purpose of this study was to ascertain whether children in grade 3 who differ in cognitive processing capacity add and subtract differently. The researchers drew upon information from three sources: individual results from a battery of 14 tests, an objective-referenced achievement test measuring a variety of arithmetic skills related to…

The concept of an algorithm derives from the physical sciences, but it has often been misunderstood and misapplied in the social sciences and in education. The theoretical and practical significance of algorithms stems from their applicability to problems of learning, instruction, and instructional design, and they may potentially provide the…

This study investigated students' conceptual and procedural understanding of calculus within the context of an engineering mechanics course. Four traditional calculus students were compared with three students from one of the calculus reform projects, Calculus & Mathematica. Task-based interviews were conducted with each participant throughout…