Cognitive Foundations for a Multiplicative Structures       Curriculum
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{'SignBlockName': 'Raymond J. Hannapel', 'PO_EMAI': None, 'PO_PHON': None}
The multiplicative structures curriculum in the middle grades, covering         multiplication, division, rates, ratios, and proportional reasoning, is         widely seen as the locus of serious curricular difficulty and                   underachievement.  These investigators will conduct an intensive set of         year-long teaching experiments involving 8 classes, 5 experimentals and         3 controls,intended to build a robust database and a theoretical                foundation for a new, more effective multiplicative structures                  curriculum for the mid-upper elementary grades.  Four experimental 6th          grade classes and 1 below average ability level 8th grade class whose           students have repeatedly failed to learn the topics will be taught using        specially designed software and materials.  Controls will be taught             using conventional text materials.  Whole-class written measures of             conceptual change accumulated through the year will be overlaid with a          year-long clinical study of a representative subsample of both                  experimentals and controls in each class.  This research will utilize an        elaborated sequence of software environments comprising a                       "concrete-to-abstract software ramp" developed at ETC.  Lower levels of         this ramp feature concretely enactive multiplication, division and              ratios in object-based calculation environments, whereas upper levels           include dynamically varying algebraically represented proportions linked        to tables of data and coordinate graphs.  Throughout, the software              employs actively linked multiple representations of mathematical                concepts and procedures, exploiting the representational power newly            available in school affordable computers.  The study will also compare 3        mid ability level classes taught by the same teacher, one of which uses         it in the teacher-centered, one-computer mode only, and a third acts as         control.  The intent is to determine if and how the representational            power of these types of learning environments can be used effectively in        computer-scarce contexts apart from its interactive power, which                requires computer-dense, hence more expensive, lab contexts.  The               Education Technology Center at Harvard and Weston Middle School are             sharing the costs of conducting this project.
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{'Name': 'Harvard University', 'CityName': 'CAMBRIDGE', 'ZipCode': '021385366', 'PhoneNumber': '6174955501', 'StreetAddress': '1033 MASSACHUSETTS AVE STE 3', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Massachusetts', 'StateCode': 'MA', 'CONGRESSDISTRICT': '05', 'CONGRESS_DISTRICT_ORG': 'MA05', 'ORG_UEI_NUM': 'LN53LCFJFL45', 'ORG_LGL_BUS_NAME': 'PRESIDENT AND FELLOWS OF HARVARD COLLEGE', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '7258', 'Text': 'RESEARCH IN TEACHING & LEARNIN'}
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