{"pk":25824,"title":"Transitivity is Not Obvious: Probing Prerequisites for Learning","subtitle":null,"abstract":"Empirical results from a fraction addition task reveal a\nsurprising gap in prior knowledge: difficulty applying the\ntransitive property of equality in a symbolic context. 13 out of\nthe 182 4th and 5th graders (7%) correctly applied the\ntransitive property of equality to identify the sum of two\nfractions in a step-by-step worked example. This difficulty\nwas robust to brief instruction on transitivity (after which\nperformance rose to 11%). Students’ demonstrated difficulty\nwith transitivity is surprising, especially because common\ninstructional techniques, such as worked examples, assume\nthat the learner understands this concept and where it applies.","language":"eng","license":{"name":"","short_name":"","text":null,"url":""},"keywords":[{"word":"conceptual understanding; fraction addition;\nmathematical equality"}],"section":"Papers","is_remote":true,"remote_url":"https://escholarship.org/uc/item/5vm450cr","frozenauthors":[{"first_name":"Eliane","middle_name":"Stampfer","last_name":"Wiese","name_suffix":"","institution":"Carnegie Mellon University","department":""},{"first_name":"Rony","middle_name":"","last_name":"Patel","name_suffix":"","institution":"Carnegie Mellon University","department":""},{"first_name":"Jennifer","middle_name":"K","last_name":"Olsen","name_suffix":"","institution":"Carnegie Mellon University","department":""},{"first_name":"Kenneth","middle_name":"R","last_name":"Koedinger","name_suffix":"","institution":"Carnegie Mellon University","department":""}],"date_submitted":null,"date_accepted":null,"date_published":"2015-01-01T18:00:00Z","render_galley":null,"galleys":[{"label":"PDF","type":"pdf","path":"https://journalpub.escholarship.org/cognitivesciencesociety/article/25824/galley/15448/download/"}]}