Consolidation of Mathematical Abstractions in a Situation Based Functions Curriculum. Draft

Research output: Book/ReportReport

Abstract

This exploratory study had two goals: (1) to identify signs of abstraction and consolidation of abstractions of functional concepts in students in a situation-based curriculum; and (2) to use theoretical arguments as well as experimental evidence in order to shape notions of abstraction and consolidation of abstractions. The methodology was consciously circular because the primary goal of the work was to clarify the notion of consolidation. An instrument was designed to make observations on abstraction and consolidation. Data were used to reshape ideas about the theoretical notion of consolidation and to conclude how consolidation would manifest itself in students' actions. Finally, data were analyzed again to find these "signs of consolidation." An interview was administered to students from classes using CompuMath, a curriculum which involves interactive computer software. Students were asked to use a functions software program with which they were familiar to draw the graph of a quadratic function. The theme of the interview was development of a number of animal populations in a park. Consolidation did occur for some students in the CompuMath curriculum. Furthermore, consolidation of abstract knowledge did not usually occur suddenly; consolidation processes may proceed on a continuum. Appendices include the interview administered and student transcripts. (PVD)
Original languageEnglish
Number of pages61
StatePublished - 1997

Keywords

  • Israel
  • ERIC, Resources in Education (RIE)
  • Curriculum Design
  • Educational Resources
  • Computer Software
  • Mathematical Concepts
  • Foreign Countries
  • Learning Processes
  • Computer Assisted Instruction
  • Instructional Materials
  • Mathematics Curriculum
  • Functions (Mathematics)
  • Secondary Education
  • Abstract Reasoning
  • Concept Formation

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