{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T16:10:30Z","timestamp":1779120630391,"version":"3.51.4"},"reference-count":32,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2010,2,11]],"date-time":"2010-02-11T00:00:00Z","timestamp":1265846400000},"content-version":"vor","delay-in-days":7165,"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":[[1990,7]]},"abstract":"<jats:p>We report an empirical study of elementary algebra errors, conducted in three separate schools. The errors are diagnosed using mal\u2010rules, as proposed by Sleeman (1984, 1,985). Our analysis uncovers the following properties of algebra mal\u2010rules: The frequency of mal\u2010rules is severely skewed, there are many infrequent mal\u2010rules and few frequent ones; mal\u2010rules are very unstable, students typically use mal\u2010rules very irregularly; different mal\u2010rules have explanatory power in different schools (many of our most powerful mal\u2010rules are previously unreported); mal\u2010rule diagnosis Is more successful with more skilled students; students' confidence ratings do not partition the total set of mal\u2010rules, every mal\u2010rule we find is associated with high confidence ratings by at least one student. The Implications of our data for cognitive theories of error generation are discussed. Contrary to commonplace assumptions, we argue that It is impossible to make a clear distinction between slips and mistakes; most errors depend on properties of the knowledge base and the cognitive architecture. Errors In a procedural skill cannot be assumed to be purely syntactic In orgin.<\/jats:p>","DOI":"10.1207\/s15516709cog1403_4","type":"journal-article","created":{"date-parts":[[2005,7,18]],"date-time":"2005-07-18T01:54:29Z","timestamp":1121651669000},"page":"445-481","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":48,"title":["Algebra Mal\u2010Rules and Cognitive Accounts of Error"],"prefix":"10.1111","volume":"14","author":[{"given":"Stephen J.","family":"Payne","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Helen R.","family":"Squibb","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2010,2,11]]},"reference":[{"key":"e_1_2_1_2_1","volume-title":"The architecture of cognition","author":"Anderson J.R.","year":"1983"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1207\/s15327051hci0102_2"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0140525X00026121"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1207\/s15516709cog0202_4"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1207\/s15516709cog0404_3"},{"key":"e_1_2_1_7_1","volume-title":"The psychology of human\u2010computer interaction","author":"Card S.K.","year":"1983"},{"key":"e_1_2_1_8_1","volume-title":"People and computers: Designing for usability","author":"Gilmore D.J.","year":"1986"},{"key":"e_1_2_1_9_1","volume-title":"Investigations of a cognitive skill","author":"Greeno J.G.","year":"1985"},{"key":"e_1_2_1_10_1","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/3729.001.0001","volume-title":"Induction: Processes of Inference Learning, and Discovery","author":"Holland J.H.","year":"1986"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00116249"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(87)90050-6"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1207\/s15516709cog0902_2"},{"key":"e_1_2_1_14_1","volume-title":"Complex information processing: The impact of Herbert A. 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