Generative Aspects of Mathematical Thinking:  Formulating   Conjectures and Posing Problems
{'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}
This research project will carefully examine and develop a cognitive            description and analysis of certain generative aspects of mathematical          thinking - posing problems and formulating conjectures in the form of           problems to be solved - as these processes are used by persons at               varying levels of mathematical experience and maturity, ranging from            sixth-grade students to secondary school mathematics teachers.  Careful         attention will be paid to individual differences among and within the           various subject populations and also to the effects on the frequency            and/or effectiveness of use of the processes of support mechanisms, such        as the use of computer software support or paired problem solving.  The         understanding of these processes obtained from observational studies            during the first two years will be operationalized in the third year of         the project in an instructional study in which a set of instructional           activities, based on the descriptive analysis and devised to promote the        development of these generative processes, is used with middle school           students.  The proposed research is directed at important extensions of         extant scientific findings related to mathematical thinking and problem         solving.  Moreover, the work proposed here is related to current efforts        to reform precollege mathematics instruction to make it more                    intellectually stimulating for students by increasing the amount of             instructional time given over the student conjecturing and                      investigation.  Thus, the results of the proposed research program              should be significant not only for the contribution they can make to the        growing scientific knowledge base concerning mathematical cognition and         problem solving but also for their practical relevance for precollege           mathematics education.
{'FirstName': 'Edward', 'LastName': 'Silver', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Edward Silver', 'EmailAddress': 'easilver@umich.edu', 'NSF_ID': '000125269', 'StartDate': '11/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Pittsburgh', 'CityName': 'PITTSBURGH', 'ZipCode': '152600001', 'PhoneNumber': '4126247400', 'StreetAddress': '4200 FIFTH AVENUE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Pennsylvania', 'StateCode': 'PA', 'CONGRESSDISTRICT': '18', 'CONGRESS_DISTRICT_ORG': 'PA18', 'ORG_UEI_NUM': 'MKAGLD59JRL1', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF PITTSBURGH - OF THE COMMONWEALTH SYSTEM OF HIGHER EDUCATION', 'ORG_PRNT_UEI_NUM': None}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '7258', 'Text': 'RESEARCH IN TEACHING & LEARNIN'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8850580.xml'}