There is a growing interest in the mathematics education community in the notion of abstraction and its significance in the learning of mathematics. "Reducing abstraction" is a theoretical framework that examines learners' behavior in terms of coping with abstraction level. It refers to situations in which learners are unable to manipulate…

Literature on relational reasoning mainly focuses on the performance question. It is typically argued that problem difficulty relies on the number of ''mental models'' compatible with the problem. However, no study has ever investigated the wording of conclusions that participants formulate. In the present work, we analyze the relational terms…

When worthwhile mathematical tasks are used in classrooms, they should also become a crucial element of assessment. For teachers, using these tasks in classrooms requires a different way to analyze student thinking than the traditional assessment model. Looking carefully at students' written work on worthwhile mathematical tasks and listening…

This research study deals with the modes of representation that ninth-graders choose in order to communicate their problem solving paths and justifications, and the relation between these modes of representations and achievement level. The findings are based on analysis of 350 answers to problems that demanded communication of reasoning,…

This paper explores one student's attempt to apprehend an abstract mathematical structure (similar to Z[99]). We discuss Karmiloff-Smith's theory of representational redescription as a model for the development of structural understanding and contrast this with existing process-object theories. We use two cycles in Molly's movement from an action…

Too much classroom work is teacher-initiated, labor-intensive, abstraction-rich, and experience-lean. In contrast, science centers offer students a learner-initiated, discovery-rich opportunity to explore stimulating experiences, especially when second trips are made. Optimal learning occurs with a dynamic blending of abstract and experiential…

Modified dilemmas from the Kohlberg Moral Judgment Instrument were administered to 15 hearing-impaired students, aged 12-15. Analyses indicated that subjects reasoned at Stages 1-2, whereas Kohlberg's norms indicate that hearing peers reason at Stages 2-4. A positive correlation was found between subjects' average scores for moral reasoning and…

Creative projects, whether in the arts, literature, or social aspects of education, demand a mixture of the "subconscious" (imaginative) and "intellectual" (rational), not the rejection of one in favor of the other. Rationality and imagination are complementary in speculative research. An advocacy approach may be appropriate in certain cases. (20…

One of the most basic theoretical areas in the study of visual communication and visual literacy is the nature of representation. Some of the important research in this area is reviewed in this paper, and a model of representation is developed that satisfies many of the philosophical concerns. The paper begins with a discussion on the relationship…

We examine eight cases of argumentation in relation to a proportional reasoning task--the "Paint" task--in which the "constant sum" strategy was a significant factor. Our analysis of argument follows Toulmin's (1958) approach and in the discourse we trace factors which seem to facilitate changes in argument. We find that the arguments of "constant…

The focus of this essay on the psychological and pedagogical issues of the college introductory logic course includes a look at the roots of the informal logic movement, an analysis of logic and language, a statement of the need for evaluation of the informal logic course, and some suggested alternatives. (JN)

The teacher's role is not one of a supplier of values. Rather it is that of facilitator and clarifier of the valuing process. Philosophical reasoning, disclosure of differences, and moral significance of those differences can be used to further understanding of a moral dilemma. (JN)

The world is in a constant state of flux and as a consequence, definitions and perceptions of the word "intellectual" are subject to change. This paper undertakes a succinct historical review regarding this notion by considering two paradigms, which are called here the "Lake Paradigm" and the "Well Paradigm". It is argued that these two paradigms…

This paper is concerned with the importance of argumentation in the classroom, especially in relation to the social sciences. Issues of argument and argument evaluation are considered. The paper analyzes the nature of such reasoning and indicates its importance in subject matter learning. Three situations are described in the paper in which…

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…