{"pk":31771,"title":"Assessing Conceptual Understanding of Arithmmetic Stucture and Language","subtitle":null,"abstract":"We contend that the primary role of an\nillustration or physical manipulable for\nteaching mathematics is to help the learner\nunderstand the language of the mathematics\nby providing the learner with a referential\nsenr«ntics. Having taught this to subjects, w e\naddress the question of how to assess their\nunderstanding. Problem-solving performance,\nw e show, is insufficient by itself. A n\nassessment of students' m e m o r y for the\noriginal problem statement, and their ability to\nuse cues within the referential semantics is\ndemonstrated as a potential method.\nFourth graders (n=24) solved word algebra\nproblem after (a) training with a designed\nreferential semantics from a computer tutor\ncalled the Planner, (b) training with symbolic\nmanipulatives, or (c) receiving no training\n(control). Although pretest-posttest gains\nwere only moderately better for the Planner\ngroup than the symbol group, the former\nshowed reliably better ability to reconstruct the\nproblem statements after a 5-day delay. A\nparticular advantage for recall of algebraic\nrelations (as compared to assignments) was\nevident. Mental representation of relations has\nbeen singled out as a major obstacle to\nsuccessful word problem solving. The support\nthat a well-designed referential semantics\nplays in the formation and retrieval of\nappropriate mental structures for problem\nsolving are discussed, as are methods for\nassessing problem comprehension and\nconceptual change.","language":"eng","license":{"name":"","short_name":"","text":null,"url":""},"keywords":[],"section":"Submitted Presentations","is_remote":true,"remote_url":"https://escholarship.org/uc/item/6q09331v","frozenauthors":[{"first_name":"Baruch","middle_name":"","last_name":"Schwarz","name_suffix":"","institution":"Hebrew University","department":""},{"first_name":"Mitchell","middle_name":"J.","last_name":"Nathan","name_suffix":"","institution":"University of Pittsburgh","department":""}],"date_submitted":null,"date_accepted":null,"date_published":"1993-01-01T18:00:00Z","render_galley":null,"galleys":[{"label":"PDF","type":"pdf","path":"https://journalpub.escholarship.org/cognitivesciencesociety/article/31771/galley/22839/download/"}]}