Diagnostic Models for Procedural Bugs in Basic Mathematical Skills

Anew diagnostic modelingsystem ftor automatically synthesizing a deep structure model of a studentlemiscondeOtious orbugs in his basic mathematic 44skills provides a mechanism for explaining why a'Student is making a mistake as opposed to sii P ratifying the mistake. .This report consists of three sections: Th irst prov des examples of the problems that must be handled by a diagno: is model. then introduces procedural networks as a general framework f r represe g ibe'knoWledge underlying a skill. the challenge in designi this re esentation is to find one that facilitates the discovery : of misconcep ion o bugs existing in a particular student? encoding of this knowledg e nd se tion discusses some of the pedagogical issues '.that have emer ed from the use o diagnostic models within an instrucitional, system. This iscussion is framed in the context of a computer-based tutoring/gami g system developed ti teach students and student teachers how to diagnose b gs strategicall as ell as how to provide a better understanding of the underl ing structure or rithmetic skills. The 4 third section describes our, uses of anl.executable netw rk as a tool for automatically diagnosing Stnd,eint ehavior, for automatically gen Alii.ng " gnostic" tests, and fdrAudking the .!diagnostic quality of a given exa Incl ed in this section is-a discussion ilow. of the success of this system in di osing 1300 school studentslrom a data base of 20,000 test items.