Understanding Algebra Equation Solving Strategies.

Abstract

A task analysis of linear algebraic equation solving is presented. The problem space is shown to have an elegant mathematical form. Several strategies for searching the problem space are delineated, and their properties discussed. The forward search strategy, which appears to be the one most commonly taught in high-school textbooks, tends to generate non-optimal solution paths. An operator-subgoaling search strategy tends to generate shorter paths. Bundy and Welham's waterfall loop strategy is shown to be a variant of operator-subgoaling that is more amenable for use by humans. This task analysis suggests that the waterfall loop strategy may be better for teaching a high-school students than the forward search strategy.

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Document Details

Document Type
Technical Report
Publication Date
Jul 06, 1987
Accession Number
ADA186644

Entities

People

  • Kurt VanLehn
  • William Ball

Organizations

  • Carnegie Mellon University

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algebra
  • Artificial Intelligence
  • Computer Science
  • Department Of Veterans Affairs
  • Education
  • Equations
  • Geometry
  • Linear Algebraic Equations
  • Plane Geometry
  • Plastic Explosives
  • Psychology
  • Schools
  • Students
  • Task Performance And Analysis
  • Three Dimensional
  • Two Dimensional

Readers

  • Operations Research
  • STEM Education

Technology Areas

  • Space
  • Space - Spacecraft Maneuvers