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…

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…

Data from the 1977-78 mathematics assessment of the National Assessment of Educational Progress (NAEP) on the use of calculators are discussed. (MP) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).

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…

Sixteen Brazilian third graders aged 8-13 were given problems involving multidigit computation. School-taught algorithms were likely to be used in school-taught problems, with little carry-over to real problem situations, but resulted in more incorrect answers. (MNS)

A study to investigate one of the mechanisms teachers may use to convince themselves incorrectly that students have learned science concepts requiring formal operational ability is presented. The investigation indicates instructors may actually teach and test for memorization of algorithms rather than understanding. (MP)

Explains that Year 5 students in ten British schools took a mathematics division test twice in the school year. The test involved context and bare problems to identify changes in approach as the standard algorithm was introduced. Reports that 52 percent of students gained a higher score on the second test. (CMK)

This experiment was conducted to determine the efficiency of three forms of an algorithm of known effectiveness and the effects of its availability following initial instruction. The dependent variable was time to solve computational problems requiring rule application. The algorithm was presented in three forms: prose, flowchart, and gradual…

Presented is a model of problem solving that incorporates elements of hypothetico-deductive reasoning in the Piagetian sense, and heuristic-algorithmic processing in the information-processing sense. It assumes that people invoke both formal reasoning strategies and learned algorithms whenever they solve problems. The proposed model integrates the…

The purpose of this investigation was to identify and describe the differences in the methods used by experts (university chemistry professors) and nonscience major introductory chemistry students, enrolled in a course at the university level, to solve paired algorithmic and conceptual problems. Of the 180 students involved, the problem-solving…

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…

This discussion of information structures in written texts describes how linguistic analysis of short published reports leads to the presentation of an algorithm that depicts the problem-solving process in terms of a series of evaluative questions. (Author/CHC)

A review is presented of the role of algorithms in learning and instruction. The paper first describes an algorithm as a procedure guaranteed to produce a correct result and lists its features as: 1) having a reasonably finite number of unambiguously defined operations; 2) having zero or more inputs from a specified domain; 3) having outputs with…

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…

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…