Knowledge Spaces, 1st Edition

  • Published By:
  • ISBN-10: 3642353290
  • ISBN-13: 9783642353291
  • DDC: 507.1
  • Grade Level Range: College Freshman - College Senior
  • 354 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

  • Price:  Sign in for price



The book describes up-to-date applications and relevant theoretical results. These applications come from various places, but the most important one, numerically speaking, is the internet based educational system ALEKS. The ALEKS system is bilingual English-Spanish and covers all of mathematics, from third grade to the end of high school, and chemistry. It is also widely used in higher education because US students are often poorly prepared when they reach the university level. The chapter by Taagepera and Arasasingham deals with the application of knowledge spaces, independent of ALEKS, to the teaching of college chemistry. The four chapters by Albert and his collaborators strive to give cognitive interpretations to the combinatoric structures obtained and used by the ALEKS system. The contribution by Eppstein is technical and develops means of searching the knowledge structure efficiently.

Table of Contents

Front Cover.
Half Title Page.
Title Page.
Copyright Page.
1: Learning in a Knowledge Space.
2: Overview.
3: Assessing Mathematical Knowledge in a Learning Space.
4: ALEKS-based Placement at the University of Illinois.
5: The Impact of a Mathematical Intelligent Tutoring System on Students' Performance on Standardized High-Stake Tests.
6: A Potential Technological Solution for Reducing the Achievement Gap Between White And Black Students.
7: A Commercial Implementation of Knowledge Space Theory In College General Chemistry.
8: Using Knowledge Space Theory to Assess Student Understanding of Chemistry.
9: Recent Theoretical Progress.
10: Learning Spaces: A Mathematical Compendium.
11: Recent Developments in Performance-based Knowledge Space Theory.
12: Heuristics for Generating and Validating Surmise Relations across, between and within Sets/Tests.
13: Skills, Competencies and Knowledge Structures.
14: Recent Developments in Competence-based Knowledge Space Theory.
15: Learning Sequences: An Efficient Data Structure for Learning Spaces.
16: Projection, Decomposition, and Adaption of Learning Spaces.