Shows by means of a mathematical example how algorithmic thinking and mathematical thinking complement each other. An algorithmic approach can lead to questions that deepen the understanding of mathematics material. (DDR)

Discusses problem-solving strategies and the successful strategy used to solve stoichiometric problems in general college chemistry courses. Reports that rereading problems, recalling a related concept, and reasoning deductively/inductively are the most heavily used strategies among 13 categories. (YP)

Hypothesized that arithmetic calculating procedures and types of problems that necessitate more subproblems will lead to longer solution times. Data from 36 third grade students who mentally computed problems with sums greater than 20 and less than 100, confirmed both hypotheses. (RH)

Investigates the relationship between student talk in cooperative learning groups and the learning of complex cognitive tasks. Studies 2 classrooms of 51 students in which a social studies unit designed to assess the development of problem-solving skills in a cooperative learning environment was administered. Reports a strong correlation between…

A long-term instructional experiment involving 45 third graders learning LOGO demonstrated that LOGO fulfills some of its early promise when used in carefully crafted educational contexts. There was little evidence of boosting general problem-solving skills as a result of learning programing, but learning geometry appeared enhanced. (SLD)

This study examined the verbalizations of 90 middle school students as they thought aloud while solving mathematical word problems. Results indicated that students with learning disabilities (LD) and average achievers were less strategic in approaching mathematical problem solving than gifted students, and LD students approached problem solving in…

Three fundamentally different uses are described for classroom cases: (1) as instructional tools to help novice teachers connect theory and practice and develop problem-solving skills; (2) as raw data for research on teacher cognition; and (3) as catalysts to promote change in teachers' beliefs and practices. (SLD)

Argues that the formal properties of language reflect the underlying mental processes that individuals deploy in problem-solving situations. This analysis of the linguistic features of "private writing" reveals that writers utilize their linguistic systems to organize and direct strategic mental processes. (69 references) (CK)

Pragmatic and semantic problem solving are examined as processes that enhance acquisition of mathematical knowledge. It is suggested that development of mathematical cognition involves restructuring and that math teachers can help restructure children's knowledge systems by providing them with situations in which semantic and pragmatic problem…

Outdoor leaders with sound judgment can gather many specific experiences, induce them into a collection of general concepts, store these as memory maps in the mind, later recall the general concepts as needed, and deduce a specific prediction from them. Proposes that evaluative reflection after a judgment is made is the component missing from most…

High school students (n=295) were administered variants of the student-professor problem to ascertain whether errors could be traced to implicit versus explicit relationships between the variables. Concludes that implicit variable relationship problems were harder than explicit variable relationship problems. A follow-up study to explore why is…

Reacts to Ohlsson, Ernst, and Rees' paper by initially discussing the costs of methodology that utilizes artificial intelligence (AI) to model cognitive processes. Raises three concerns with the paper: insufficient clarification of the meaning of conceptual versus procedural understanding of base-10 subtraction; realism of the learning model; and…

Presents two cognitive models that illustrate the commonalities between reading for meaning and solving mathematical problems with meaning. Discusses the importance of number sense in the prior knowledge component of the solving with meaning model and the implications of the models in teaching mathematics. (MDH)

Although scaffolds (forms of support to help students bridge the gap between their current abilities and intended goals) can be applied to teaching all skills, they are almost indispensable for teaching higher-level cognitive strategies. Especially helpful scaffolds for clarifying thoughts, summarizing, and solving mathematical problems are…

Asserts that metacognition is one of the most important developments in the contemporary study of learning. Proposes a theoretical analysis of a number of interrelated issues with regard to their importance for metacognition. Focuses on strategy selection in light of the impasse-based theories of problem solving. (CFR)