This concluding commentary takes the perspective of research on practicing scientists and engineers to consider what open areas and future directions on relational thinking and learning should be considered beyond the impressive research presented in the special issue. Areas for more work include (a) a need to examine educational applications of…

Discusses the level of knowledge, understanding, and ability relative to mathematics for the college graduate in the 21st century. Focuses on mathematical literacy and abstraction such as the definition of abstraction, difficulties in addressing abstraction, and one approach to helping students learn to address abstraction. (Contains 12…

Educators generally assume that questioning promotes learning and that higher level questions do so better than lower level questions. But there are a number of problems with these assumptions. First, the classification of questions as higher level or lower level is ambiguous. The distinction is confused by such issues as non-controversial…

Examines ways in which the varying degrees of distance that occur in drama may help children to engage in more abstract levels of thought and language. (HTH)

This article argues that advanced mathematical thinking, usually conceived as thinking in advanced mathematics, might profitably be viewed as advanced thinking in mathematics (advanced mathematical-thinking). Hence, advanced mathematical-thinking can properly be viewed as potentially starting in elementary school. The definition of mathematical…

This paper analyzes how philosophy enters into inquiry in teacher education, in writings by both philosophers and nonphilosophers. Examples illustrate philosophical activities (such as conceptual and logical analysis, positing and explaining distinctions, evoking shared ideas and values), as well as showing that philosophy plays an important part…

Despite the current emphasis on thinking skills and the resulting concentration on lists and taxonomies that do not succeed beyond research contexts, all reflective people know that critical thought relies not on applying mental steps but on simply trying to figure out what might be right or wrong. This depends on one basic cognitive act,…

Discusses students' inability to make the connection between manipulative materials and pencil-and-paper calculations in mathematics instruction. Outlines the development of mathematical ideas through the concrete, representational, and abstract phases of instruction. An annotated bibliography listing teacher resources for representational-level…

This paper discusses ways to use worked examples in teaching mathematics. It is argued that neither investigative teaching such as discovery learning nor lecturing and starting from the abstract are helpful as they are based on emotive associations with general labels rather than precise details of pedagogic strategies. (KHR)

Creativity can be distinguished from intelligence, but there is no consensus on how the recognized stages of the creative act can be taught. The steps to rational thinking can and should be intentionally taught and rationality may prepare a base for unexpected creative insights. (DB)

Examines the differences between concrete and abstract concepts and their implications for instructional design and teaching. How specific concepts are stored in and retrieved from memory is described, analogies are discussed as an instructional tool in abstract concept learning, and a possible instructional strategy for teaching abstract concepts…

Conventional instruction in critical thinking may ignore the creative and intuitive functions of rationality, thereby encouraging a mechanically rote approach to textual analysis, problem solving, and problem construction. Such an overemphasis upon logical "calculus of justification" functions has epistemological weaknesses and pedagogical…

Considers Richard Ohmann's argument that composition texts which instruct students to emphasize concrete details over abstract concepts encourage conformity with the dominant order. Suggests that Ohmann failed to consider the effects of teachers' and students' viewpoints. Cites methods that encourage students to use detail as a device of broader…

Argues that phonemic awareness in young readers may be knowledge that is constructed in the unique situation of trying to match speech to an alphabetic orthography. Stages of learning about print, teaching children about written language, and the roles of alphabet recognition and perceptual-motor skills in learning to read are discussed.…

The field of education has largely ignored the concept of the dialectic, except in the Socratic teaching method, and even there bipolar meaning or reasoning has not been recognized. Mainstream educational psychology bases its assumptions about human reasoning and learning on current demonstrative concepts of information processing and levels of…