To broaden and develop reasoning powers in students the teacher should encourage observation, critical questioning of hypotheses, evaluation of conclusions and how they are reached, and propose new avenues of approach to problems. (JD)

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…

Compares two approaches to the teaching of mathematics, rote versus reasoning. Discusses the way to teach mathematics as reasoning in elementary classroom as stated in the NCTM Standards. (YP)

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…

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)

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…

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…

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…

Data on some aspects of the deductive logical competence of nongraduate teachers in the English-speaking Caribbean, primarily Jamaica, are reported in this document. The teachers sampled were those who sat for entrance examinations for the University of the West Indies (Mona) Faculty of Education Bachelor of Education and Certificate of Education…

An experiment was designed to test the hypothesis that abstract materials increase accuracy in solving categorical syllogisms. In an attempt to encourage subjects to reason their way through the problems rather than to make judgments about the truth or desirability of the proffered conclusions, the premises were composed of familiar words in…

This research addresses the actual goals and intentions from which students plan and organize their work in a course of study. Representations can either facilitate or hinder learning and problem solutions. Several salient aspects of adult students' representational systems and how they influenced university study were examined in two studies. The…

Fluid intelligence (Gf) is a general relation-perceiving capacity determined by each person's cortical, neurological connection count development. Its processes are involved in reasoning, concept formation and problem-solving, where acculturation has little effect. Crystallized intelligence (Gc) manifests knowledge and general comprehension,…

Piaget has hypothesized that concrete and formal operations can be described by specific logical models. The present study focused on assessing various aspects of four concrete operational groupings and two variations of two formal operational characteristics. Six hundred twenty-two 9-14 year old students participating in the Human Sciences…

A study was conducted to test the hypothesis that Ss from disadvantaged homes have poorly developed "abstract" thinking skills and that their thought can be characterized as more "concrete" or relational. Four forms of a problem-solving inventory were developed which differed in mode of presentation. The original form consisted of real-life…

This paper describes two experiments in which children in grades 1, 3, and 5 were given three kinds of spatial perspective-taking problems to solve as quickly as they could: (1) C problems, solvable only by computation (that is, noting which features of a particular object array were closest to another observer in order to estimate how the array…