In "Making Sense of Math," Cathy L. Seeley, former president of the National Council of Teachers of Mathematics, shares her insight into how to turn your students into flexible mathematical thinkers and problem solvers. This practical volume concentrates on the following areas: (1) Making sense of math by fostering habits of mind that…

Problem solving skills and abilities are critical in life and more specifically in the engineering field. Unfortunately, significant numbers of South African students who are accessing higher education lack problem solving skills and this results in poor academic performance jeopardizing their progress especially from first to second year. On the…

Explaining emergent structure remains a challenge for all areas of cognitive science, and problem solving is no exception. The modern study of insight has drawn attention to the issue of emergent cognitive structure in problem solving research. We propose that the explanation of insight is beyond the scope of conventional approaches to cognitive…

Psychology has largely ignored the distinction between constructs and events and what comprises a scientific construct, yet this distinction is basic to some of the major divisions of thought within the discipline. Several kinds of constructs are identified and compared with events, and improper use of constructs is noted of which the mind…

Seeking more effective mathematics instruction, this author decided to incorporate Cognitively Guided Instruction (CGI) into first-grade classroom lessons. Students in CGI mathematics classrooms are prompted to use their prior knowledge to solve new problems, establish cognitive structures to which new learning can be connected, and be driven by…

In this article, the author outlines a variety of ways of defining, making explicit, and supporting effective team-based projects through the basic tenets of Lean Six Sigma and the use of Web-based technologies. A combination of Lean Six Sigma and a handful of project management technologies not only help in fostering the communication central to…

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…

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…

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…

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.…

Explores the relevance of hierarchies to information processing. Suggests that participants in all conditions create hierarchical representations as they work, and those in nonlinear conditions use this structure to guide their exploration of the material. An important function of hierarchies may be to define relationships between concepts.…

Constructivist theory argues that students construct knowledge for themselves and that each knows the world in a different way. The problem for education is how students can construct an "objectified" knowledge. Outlines an integrative framework for the description of information and problem-solving procedures and a problem-solving…

Presents a revised working definition of schema, lists four types of knowledge that individuals have (i.e., identification, elaboration, planning, and execution), and outlines issues in schema theory. The usefulness of schema in problem solving and information problem solving is discussed, and implications for teachers of information literacy are…

This project addressed the question: What knowledge and processes enable individuals to construct and modify representations of novel, nonroutine problems? The theoretical goal was to extend the information-processing theory of problem solving to include processes that have been characterized as restructuring of problems and productive thinking by…

Information-processing students solving problems in the 1960s and 1970s accepted the tradition of early experimental psychology in concentrating primarily on the study of "knowledge-lean" tasks in which competence can usually be acquired over short periods of learning and experience. In recent years, experts have examined knowledge-rich…