The development of abstract mathematical thinking is an essential part of mathematics and the geometry is regarded as a suitable domain to serve this purpose. As different technologies such as computers and graphing calculators are widely being used, curriculum developers on geometry should take these technologies into consideration. Several…

Although mathematics deals with generalizations relating abstract ideas, very little attention has been given in the mathematics education literature to the role of abstraction and generalization in the development of mathematical knowledge. In this paper, the meanings of "abstraction" and "generalization" are first explored by…

This article offers specific strategies to diagnose and remediate difficulties students may have in learning multiplication facts. Analyzes strategies students use to go from a known fact to an unknown fact. The point is made that, for many students, the order of interpretation of a number fact may affect accuracy. (DB)

Panoramic scanning is the capacity to perceive, interpret, and appreciate complex problems from a big-picture vantage point. Barriers to panoramic scanning (sensory bombardment, superficial polarized thought, and tunnel vision) and facilitators (broad interests and knowledge, pattern finding, and connection-making skills) are identified. Educators…

Examined children's ability to settle causal relations and their capacity to make conclusions based on certain experiences and representations. Found that preschool children have a solid explanatory basis for their everyday life, within which facts are not generally accepted but are interpreted through a certain "logic," and the motives…

A study involving 31 adults with Down syndrome investigated their ability to reason. Results found they did not differ from typically developing children, matched on expressive and verbal ability, in transitivity and non-verbal analogical thinking; however, they did differ in categorical reasoning, classical verbal analogies, and short-term…

Quantitative literacy for students with deafness is addressed, noting work by the National Council of Teachers of Mathematics to establish curriculum standards for grades K-12. The standards stress problem solving, communication, reasoning, making mathematical connections, and the need for educators of the deaf to pursue mathematics literacy with…

Offers a theoretical account of moral rationality within a rational constructivist paradigm examining the nature and relationship of rationality and reasoning. Suggests progressive changes through developmental levels of moral rationality. Proposes a developmental moral epistemology that accommodates moral pluralism to a greater degree than does…

Suggests that constructivist rationality may be more pervasive across cultures than Moshman commits to. Proposes that rationality is not always adequate, and there is a need for essentially moral labor, such as differentiating moral from nonmoral or analyzing differing moral constructs and their potential coexistence, coordination, and structural…

Examines U.S. and Chinese 6th grade students' mathematical thinking and reasoning involved in solving six process-constrained and six process-open problems. Concludes that the Chinese sample had a significantly higher mean score than the U.S. sample on the process-constrained tasks, but the sample of U.S. students had a significantly higher mean…

Words are only one way of symbolizing ideas. Numbers, pictures, graphs, maps, diagrams, photographs, and other means are also used to convey information. Researchers refer to notational systems such as graphs, diagrams, and maps as "inscriptions." Inscriptions are tools that help people to perceive and to talk about spatial worlds. Spatial…

Babies are active participants in their learning and need to explore a variety of objects. Nurturing relationships support these explorations. Objects are more clearly remembered and understood. Thus, one activity this article suggests doing with a 12-month-old to encourage abstract thinking, is talking about how squeezing the bottle of ketchup…

Norenzayan, Smith, Jun Kim, and Nisbett (2002) investigated cultural differences in the use of intuitive versus formal reasoning in 4 experiments. Our comment concerns the 4th experiment where Norenzayan et al. reported that, although there were no cultural differences in accuracy on abstract logical arguments, Koreans made more errors than U.S.…

The core of apparel design education is the studio experience. This article discusses an Integrated Apparel Design Curriculum model built on a foundation of creative and technical experimentation and learning which contributes to developing abstract thinking skills. Various learning styles are supported as students work through the design process…

Most schools are unwilling to consider decreasing computer use at school because they fear that without screen time, students will not be prepared for the demands of a high-tech 21st century. Monke argues that having young children spend a significant amount of time on computers in school is harmful, particularly when children spend so much…