{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T20:34:08Z","timestamp":1773952448909,"version":"3.50.1"},"reference-count":30,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2010,2,11]],"date-time":"2010-02-11T00:00:00Z","timestamp":1265846400000},"content-version":"vor","delay-in-days":11639,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Cognitive Science"],"published-print":{"date-parts":[[1978,4]]},"abstract":"<jats:p>A new diagnostic modeling system for automatically synthesizing a deep\u2010structure model of a student's misconceptions or bugs in his basic mathematical skills provides a mechanism for explaining <jats:italic>why<\/jats:italic> a student is making a mistake as opposed to simply identifying the mistake. This report is divided into four sections: The first provides examples of the problems that must be handled by a diagnostic model. It then introduces <jats:italic>procedural networks<\/jats:italic> as a general framework for representing the knowledge underlying a skill. The challenge in designing this representation is to find one that facilitates the discovery of misconceptions or bugs existing in a particular student's encoding of this knowledge. The second section discusses some of the pedagogical issues that have emerged from the use of diagnostic models within an instructional system. This discussion is framed in the context of a computer\u2010based tutoring\/gaming system developed to teach students and student teachers how to diagnose bugs strategically as well as how to provide a better understanding of the underlying structure of arithmetic skills. The third section describes our uses of an executable network as a tool for <jats:italic>automatically<\/jats:italic> diagnosing student behavior, for automatically generating \u201cdiagnostic\u201d tests, and for judging the diagnostic quality of a given exam. Included in this section is a discussion of the success of this system in diagnosing 1300 school students from a data base of 20.000 test items. The last section discusses future research directions.<\/jats:p>","DOI":"10.1207\/s15516709cog0202_4","type":"journal-article","created":{"date-parts":[[2005,10,20]],"date-time":"2005-10-20T19:27:43Z","timestamp":1129836463000},"page":"155-192","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":645,"title":["Diagnostic Models for Procedural Bugs in Basic Mathematical Skills*"],"prefix":"10.1111","volume":"2","author":[{"given":"John Seely","family":"Brown","sequence":"first","affiliation":[]},{"given":"Richard R.","family":"Burton","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2010,2,11]]},"reference":[{"key":"e_1_2_1_2_1","volume-title":"A rationale and description of the BASIC instructional program","author":"Barr A.","year":"1974"},{"key":"e_1_2_1_3_1","volume-title":"Structural models of a student's knowledge and inferential processes","author":"Brown J. 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