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…

Studied high school and university students' use of mental representations in reasoning, and the developmental progression of their reasoning with concrete and abstract content. Reasoning was more difficult with abstract content. Abstract problems followed by concrete ones led to reduced concrete problem performance for high schoolers but not for…

The study examined methods of mathematical problem solving with 34 gifted and 34 average Dutch 10 year olds. Typical questioning protocols are diagrammed and results tabulated. Preliminary findings suggest the potential value of explicit teaching of advanced mathematical problem-solving skills to pupils of average ability. (DB)

Shows that the construction of mental representations that capture a situation based on the comprehension of a diagram are mediated by the possession of appropriate background knowledge. Indicates that background knowledge deficiencies may make it difficult for beginning students of a domain to construct suitable mental representations from…

Three third graders with a history of low achievement in math were first given verbal (abstract) instruction in solving word problems. Students were then introduced to manipulatives instruction using Cuisenaire rods to set up word problems. Students exhibited immediate and sustained improvement on subsequent probes administered without…

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…

This article presents research on students' understanding of basic concepts in Graph Theory. Students' understanding is analyzed through the lens of the theoretical framework of reducing abstraction (Hazzan, 1999). As it turns out, in spite of the relative simplicity of the concepts that are introduced in the introductory part of a traditional…

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…

Most children who are congenitally deafblind are severely delayed in their communication development and many will not achieve symbolic understanding and expression. This article discusses developmental markers cited in the research literature as predictive of or facilitative of the development of symbolism. These markers include the growth toward…

In education research, a polar distinction is frequently made to describe and produce different kinds of research: "quantitative" versus "qualitative." In this article, the authors argue against that polarization and the associated polarization of the "subjective" and the "objective," and they question the attribution of generalizability to only…

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…