Cognitive Effects of Multiple Representations of Mathe-     matical Concepts:  An Exploratory Study
{'Code': '11090000', 'Directorate': {'Abbreviation': 'EDU', 'LongName': 'Directorate for STEM Education'}, 'Division': {'Abbreviation': 'DRL', 'LongName': 'Division Of Research On Learning'}}
{'SignBlockName': 'Raymond J. Hannapel', 'PO_EMAI': None, 'PO_PHON': None}
Mathematics learning consists of more than simply memorizing                    rules and procedures.  Unfortunately, much of the mathematics                   currently being learned is of this type.  A concensus is                        emerging, however, that a necessary condition for students to                   understand important mathematical concepts is that they posess                  multiple representational systems for those concepts and be able                to translate smoothly and efficiently among them.                                                                                                               This project will study how we can teach effectively for                        students' development of multiple representational systems and                  how such instruction affects their development of concepts and                  skills. Two computer programs will be designed for this project;                one for decimal numeration and one for algebra.  Both programs                  will present simultaneous, "linked" representational systems.                   Students will solve problems by acting directly upon one                        representational system  with their actions being automatically                 reflected in the other.  Operations on decimals numbers will be                 studied for five weeks with a class of seventh graders.  Concepts               of expression, identity, linear equation, and solving linear                    equations will be studied with pre-algebra eighth graders over a                school year.                                                                                                                                                    The basic research methodology will be that of the constructivist               teaching experiment. Through carefully planned individual and                   small group interview protocols, a model (models) of student                    knowledge will be constructed which describes the relationship                  beween the representations taught. Curriculum materials to                      facilitate mathematical understanding will also be developed.                                                                                                   The proposed research is challenging and should lead to                         significant advances in mathematics and science education.  The                 Principal Investigator is highly regarded in the mathematics                    education community and this is reflected in this well conceived                research project.
{'FirstName': 'Patrick', 'LastName': 'Thompson', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Patrick Thompson', 'EmailAddress': 'pat.thompson@asu.edu', 'NSF_ID': '000668092', 'StartDate': '08/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Board of Trustees of Illinois State University', 'CityName': 'NORMAL', 'ZipCode': '617901100', 'PhoneNumber': '3094382528', 'StreetAddress': 'CAMPUS BOX 1100', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Illinois', 'StateCode': 'IL', 'CONGRESSDISTRICT': '17', 'CONGRESS_DISTRICT_ORG': 'IL17', 'ORG_UEI_NUM': 'V6WTL4T5FFJ3', 'ORG_LGL_BUS_NAME': 'BOARD OF TRUSTEES OF ILLINOIS STATE UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '7258', 'Text': 'RESEARCH IN TEACHING & LEARNIN'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8751381.xml'}