ERIC Number: ED294713
Record Type: RIE
Publication Date: 1987-Sep
Reference Count: N/A
A Concrete-to-Abstract Software Ramp: Environments for Learning Multiplication, Division and Intensive Quantity. Technical Report 87-8.
Kaput, James J.; Pattison-Gordon, Laurie
This document is intended to describe several software learning environments in an order that parallels a reasonable sequence of use by students. It also describes a planned an designed, but not yet implemented, extension of these environments from the discrete to the continuous case. Each of the implemented environments was developed in continuous collaboration with teachers and their students from grades three to eight. An important characteristic of these environments is their systematic linking of concrete representations, beginning with iconic representations, to more abstract representations. The report is designed to serve two functions: (1) as an overview to learning the conceptual field of multiplicative structures; and (2) as a guide to software environments. The remainder of the report is organized according to the design of the software environments. This includes descriptions of the icon-based calculation environments, the environment that introduces the numerical and graphic representations, the algebraic representations that extend these environments, the sampling environments, and finally the transitions to the continuous environment. (TW)
Publication Type: Reports - Descriptive; Reports - Research
Education Level: N/A
Audience: Teachers; Researchers; Practitioners
Sponsor: Office of Educational Research and Improvement (ED), Washington, DC.
Authoring Institution: Educational Technology Center, Cambridge, MA.
Note: Some drawings and charts may not reproduce well.