In this article, I present a study in which 12 pairs of 8th-grade students solved problems about a physical device with algebra. The device, called a winch, instantiates motions that can be modeled by pairs of simultaneous linear functions. The following question motivated the study: How can students generate algebraic models without direct…

During the last few decades, the author and his colleagues have developed an instructional framework for infusing thinking into content instruction in every subject and at every grade level. In thinking-based learning, teachers explicitly teach students thinking strategies and important habits of mind and then give students opportunities to apply…

Effective teaching should focus on representational change, which is fundamental to learning and education, rather than conceptual change, which involves transformation of theories in science rather than the gradual building of knowledge that occurs in students. This article addresses the question about how to develop more efficient strategies for…

Strategic communication scholars agree that planning is critical to human action. An investigation tested plan modification aspects of cognitive planning theory. Two experiments tested whether success and failure of a plan served as predictors of plan modification and whether individuals can accurately predict whether and how they will modify a…

This paper describes the characteristics of graphic techniques, such as networks, pattern notes, semantic maps, and graphic organizers, that can be used to acquire knowledge of relationships between concepts in a content area. The implications for research and instructional design are considered, and nine types of these techniques are described…

In this study a distinction is made between routine, semiroutine, and nonroutine problems based on the problem solver's knowledge. Routine problems are solved by applying a known procedure, semiroutine problems require planning that uses functional knowledge, and nonroutine problems require generation of new functional knowledge. Nonroutine…

Reports research designed to explore the possibility that conceptually different forms of common-fraction understanding can be identified. Such forms may be associated with differences in fraction problem solving-performance. Contains 50 references. (DDR)

Analyzes environmental knowledge of high school students using a national probability sample. Results indicate that students can recognize basic facts regarding environmental issues but are unable to apply this knowledge to comprehend consequences or solutions related to the problems. Contains 20 references. (DDR)

This paper examines the category-theoretic formulation of cognitive development introduced by Piaget in the late 1960's and elaborated during the 1970's. The new theory is interpreted as the focal point of Piaget's investigations into topics such as function, correspondences, and commutability. Hypotheses arising from Piaget's new model were…

Chemists have bemoaned for years their students' inability to solve problems in introductory chemistry courses. However, at least part of this inability must be attributed to the fact that chemists have historically tried to teach their students to solve problems by doing nothing more than working examples. In recent years, chemists have begun to…

Examines the interrelationships among cognitive and social rigidity, intelligence and personal adjustment in old age, and evaluates a six-week training program teaching social problem-solving skills to the elderly. The hypothesis that cognitive rigidity is independent of social rigidity was not fully supported, and the findings suggest that social…

Recent research suggests that knowledge is stored in the learner's head as a network of concepts or constructs. Children's mathematical problem-solving strategies become increasingly abstract as they are able to engage in more abstract thinking. An experimental study using an alternative Cognitively Guided Instruction approach is described.…

Three experiments investigated the ability of 79 college students to solve similar algebra word problems. Data indicate that students are able to perceive and use similarities in such problems at the level of a conceptual structure. A training session to explain relevant structural principles was effective in improving performance. (SLD)

Explores the development of understanding of the concept of average with students from grades 3 to 9 through interviews. Observed six levels of response based on an hierarchical model of cognitive functioning. Documents usage of ideas associated with the three standard measures of central tendency and representation as strategies for problem…

Reports on (n=11) student attempts at 3 combinatorial questions focusing mainly on 3 aspects of strategy: (1) listing; (2) subdivision into cases; and (3) use or misuse of 4 standard formulas. (MKR)