{"pk":33097,"title":"A Cognitive Analysis of the Task Demands of Early Algebra","subtitle":null,"abstract":"Mathematical problems presenting themselves in the \nworkplace and in academia are often solved by informal \nstrategies in addition to or instead of the normative formal \nstrategies typically taught in school. By itself this observation \ndoes little to tell us whether, when and how much these \ntechniques should be taught. To ground arguments about the \nappropriate role of altemative problem-solving techniques in \neducation, we need to first understand the demands of the \ntasks they address. Our focus here is on algebra and pre?algebra, or, more specifically, on the set of problems that \nresist solution by more elementary arithmetic methods. \nW e present a task analysis of this set of problems that is based \non the identification of mathematical and situational problem \ndifficulty factors. These factors provide a framework for \ncomparing the candidate representations and strategies to \nmeet the demands of more complex problems. W e summarize \nthe altemative techniques that have been observed in effective \nproblem solving and discuss their relative strengths and \nweaknesses. The task analysis along with this comparative \nanalysis provides a basis for hypothesizing developmental \nsequences and for informing instmctional design.","language":"eng","license":{"name":"","short_name":"","text":null,"url":""},"keywords":[],"section":"17","is_remote":true,"remote_url":"https://escholarship.org/uc/item/01p931z9","frozenauthors":[{"first_name":"Hermina","middle_name":"J. M .","last_name":"Tabachneck","name_suffix":"","institution":"Carnegie Mellon University","department":""},{"first_name":"Kenneth","middle_name":"R.","last_name":"Koedinger","name_suffix":"","institution":"Carnegie Mellon University","department":""},{"first_name":"Mitchell","middle_name":"J.","last_name":"Nathan","name_suffix":"","institution":"Vanderbilt University","department":""}],"date_submitted":null,"date_accepted":null,"date_published":"1995-01-01T18:00:00Z","render_galley":null,"galleys":[{"label":"PDF","type":"pdf","path":"https://journalpub.escholarship.org/cognitivesciencesociety/article/33097/galley/24158/download/"}]}