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Well-Graded Knowledge Structures

In: Learning Spaces

Author

Listed:
  • Jean-Claude Falmagne

    (University of California, Irvine, Department of Cognitive Sciences, Institute of Mathematical Behavioral Sciences)

  • Jean-Paul Doignon

    (Université Libre de Bruxelles, Département de Mathématique)

Abstract

Wellgradedness was introduced in Definition 2.2.2 as a powerful property implied by the two axioms [L1] and [L2] defining learning spaces (cf. Section 2.2). As stated in Theorem 2.2.4, any well-graded knowledge space is in fact a learning space and conversely. In this chapter, we focus on the wellgradedness property per se. We define some new concepts, derive important consequences, and describe a variety of applications to topics quite different from education. The results of this chapter will have applications elsewhere in this book. For example, they will provide the combinatoric skeleton for the learning theories developed in Chapters 9 and 12 and for some of the assessment procedures described in Chapters 13 and 14. To avoid minor technicalities, we restrict consideration to discriminative structures.

Suggested Citation

  • Jean-Claude Falmagne & Jean-Paul Doignon, 2011. "Well-Graded Knowledge Structures," Springer Books, in: Learning Spaces, chapter 4, pages 61-79, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-01039-2_4
    DOI: 10.1007/978-3-642-01039-2_4
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