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)

Asserts that whether students engage in creative and critical thinking depends on how teachers structure the learning situation. Contends that using "academic controversy" among students provides a basis for deliberate discourse and creative problem solving. Presents a five-step instructional model to guide students. (CFR)

This paper describes student performance and beliefs regarding fractions resulting from a five-phase approach toward developing mathematical intuition via physical materials. Interviews with students using this approach and with students using a conventional textbook approach indicated significant differences in problem-solving abilities and…

Counterintuitive moments in the classroom challenge common sense and practice and can be used to help mathematics students appreciate the need to explore, reflect, and reason. Proposed are four examples involving geometry, systems of equations, and matrices as counterintuitive instances. (MDH)

Kindergarten students' (n=7) thought processes were investigated during a problem-solving task to gain insight into students' problem-solving strategies and to guide students toward a closer awareness of their own mathematical thinking. Outlines some of the processes and problems of implementing a constructivist approach by an experienced teacher.…

Examined the quality of responses of six classes of grade six students to four questions requiring multiple and generalized solutions posed under varying conditions. Results indicated that this type of question can be useful in classrooms because students can respond at a variety of levels. (13 references) (MDH)

Thirty-one students (ages 8-14) with learning disabilities or behavior disorders solved arithmetic word problems while a narrative protocol was developed. Eight types of cognitive processing difficulties were identified (such as lack of self-correction and inclusion of extraneous information), and the utility of protocol analysis as an assessment…

Argues that the dichotomy between domain-specific and general theories of cognitive development addressed in the "Merrill-Palmer Quarterly" special issue is unproductive. Suggests that polarities of generality and specificity exist in creative tension as seen through developmental processes. (Author/BB)

Thirteen 8- to 10-year-old students participated in a Lego-LOGO learning environment, coupling Lego building-block activities with Logo computer programming, to evaluate whether this learning environment was conducive to metacognitive awareness and cooperation. Results suggested positive cognitive and affective outcomes, especially for the younger…