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ERIC Number: ED279536
Record Type: Non-Journal
Publication Date: 1986
Reference Count: N/A
Sense and Reference in the Design of Interactive Illustrations for Rational Numbers.
It is a common tactic in the teaching of arithmetic to provide the learner with pictures and embodiments of various kinds. However, the pedagogy of illustrations is not well understood. Analysis of the concept of meaning in relation to arithmetic shows that full understanding of arithmetic implies intellectual possession of a number of different intellectual constructions, among them a teleological, an analytical, and a referential semantics for arithmetic. It is argued that the primary purpose of illustrations for elementary arithmetic is to clarify the semantics of the language of arithmetic. An informal analytic semantics for rational number concepts is presented, revealing a rather complex system of concepts. Construction of a referential semantics for the concept of ratio leads to the conjecture that illustrations for rational numbers are necessarily incomplete in the sense that they can, in principle, only illustrate some aspects of rational numbers but not others. The results of these analyses are summarized in a prescriptive theory of illustration design. (Author)
Descriptors: Arithmetic, Computer Graphics, Educational Research, Educational Theories, Elementary Education, Elementary School Mathematics, Illustrations, Language Role, Manipulative Materials, Mathematical Vocabulary, Mathematics Instruction, Rational Numbers, Ratios (Mathematics), Research Tools, Symbols (Mathematics)
Publication Type: Information Analyses; Opinion Papers; Reports - Research
Education Level: N/A
Audience: Researchers; Teachers; Practitioners
Sponsor: National Inst. of Education (ED), Washington, DC.
Authoring Institution: Pittsburgh Univ., PA. Learning Research and Development Center.