In the field of human cognition, language plays a special role that is connected directly to thinking and mental development (e.g., Vygotsky, "1938"). Thanks to "verbal thought", language allows humans to go beyond the limits of immediately perceived information, to form concepts and solve complex problems (Luria, "1975"). So, it appears language…

This paper proposes a semantic analysis in which meanings of word problems are structures that include class and order relations, and suggests a hypothesis of developmental levels that can account for children's performance of these problems at various ages. The different kinds of problems vary in the complexity of semantic structures and the…

College students were given two paper-and-pencil conditional reasoning tests, one week apart, in varying order. The three problems on each test were presented either verbally or with line drawings as concrete referents. Performance was significantly poorer on the problems with drawings. (MNS)

The thought processes of 507 elementary, secondary, and university students engaged in problem-solving situations are examined in this study. Results indicated that pupils who got correct answers often showed incorrect reasoning justifications. No significant sex differences were indicated. (MP)

Experiments by Russian educators on teaching algebra in elementary grades are summarized by the author. The algebra taught consisted of generalized solutions to concrete problems that are usually presented with fixed numerical values. (JP)

Research conducted in several countries has shown consistent patterns of performance on "change,""combine," and "compare" word problems involving addition and subtraction. These findings are interpreted within a theoretical framework which emphasizes development of levels of word problem-solving ability related to…

This study considers two problems related to cognitive development: "Is development hierarchical?" and "If so, what are the mechanisms involved in the process of development?" Analysis of the results of an experiment lead to differentiation of stages of development, and problem-solving strategies at each level are discussed.…

Discussed is the type of evidence children find to be convincing using either empirical or deductive methods to justify propositions which they consider to be true. Included are the problem, research design, and the conclusion. (KR)

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…

Reported are the effects of a conceptually oriented unit on decimal fractions. The relationships between short-term changes in solving processes and the stability of these processes over time, performance of students, and entry achievement level and the long-term effects of conceptually based instruction are discussed. (KR)

Investigated is whether children would spontaneously model problems with superfluous information and whether their modeling would facilitate problem solving. Included are the addition/subtraction story problems used in this study, introduction, method, results, discussion, and conclusions. (KR)

Interviews with 72 mixed ability students, aged 7 to 12, about arithmetic problem-solving strategies, indicated that the preference between procedural and deductive strategies becomes a divergent reality across ability levels. Among the conclusions is that more able children tend to be doing a qualitatively different sort of mathematics than their…

Described is a year-long study of the way a group of six 12-year-old children went about solving a special class of geometric problems using a computer and a limited set of LOGO programing tools. Examines solution strategies deciding whether those strategies led to insights about mathematical relations. (Author/MVL)