Diagnosing Knowledge States in Algebra Using the Rule Space Model

Abstract

This paper illustrates the use of rule space as a tool to support cognitive analysis of students' mathematical behavior. The rule space approach is explained and is then used to classify students into one of two methods for solving linear algebraic equations in one unknown and to diagnose their knowledge states in this topic. A 32-item test with open-ended questions was administered to 231 eighth and ninth graders. The following out comes of the rule space model were presented: (a) a classification of examinees into knowledge states resulting from the two solution approaches at the group level along with individual examples; (b) tree- diagrams of the transitional relationships among the states for each strategy. Implications for using the feedback provided by the rule space model in the context of instruction and assessment are discussed.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1992
Accession Number
ADA257757

Entities

People

  • Anthony E. Kelly
  • Kikumi K. Tatsuoka
  • Menucha Birenbaum

Organizations

  • Educational Testing Service

Tags

Communities of Interest

  • Air Platforms
  • Human Systems
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algebra
  • Algorithms
  • Arithmetic
  • Classification
  • Cognitive Science
  • Computer Programs
  • Education
  • Equations
  • Heuristic Methods
  • Instructions
  • Instructors
  • Linear Algebra
  • Linear Algebraic Equations
  • Mathematics
  • Probability
  • Schools
  • Students

Fields of Study

  • Education

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Instructional Design and Training Evaluation.
  • Psychometric Testing or Psychological Assessment.

Technology Areas

  • Space