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DTSTAMP:20130521T171656Z
DTSTART:20120709T113000Z
DTEND:20120709T133000Z
STATUS:CONFIRMED
TRANSP:OPAQUE
LOCATION:School of Education, Room ED101
SUMMARY:Research Seminar: Dr. Caroline Long, University of Pretoria
DESCRIPTION:Mathematical, cognitive and didactic elements of the multiplic
 ative conceptual field investigated within a Rasch assessment and measurem
 ent framework Presentation available:  http://www.dur.ac.uk/resources
 /education/research/Durhamseminar9thJulyforprintingpurposes.pptx  Thi
 s presentation will draw upon the theory of conceptual fields (Vergnaud, 1
 983, 1988, 2009), which has radical implications for the current school ma
 thematics curriculum. Two aspects, that of clustering curriculum topics in
 to conceptual fields, and that of identifying the mathematical structures 
 that are implicit in arithmetic and early mathematics, which become explic
 it and generalisable in higher mathematics, are worthy of consideration wh
 en elaborating the existing curriculum.   The presentation describes 
 an investigation of the teaching and learning of the critical elements tha
 t constitute the multiplicative conceptual field. In particular the recogn
 ition of concepts-in-action and theorems-in-action provides the links from
  learners current understanding to the required mathematical understanding
  of formal concepts and theorems.   In addition to the discussion of 
 the theoretical component, an empirical study will be described which invo
 lved the construction of a test instrument, administration to 330 learners
  at Grades 7, 8 and 9, and an analysis conducted within the Rasch assessme
 nt and measurement framework. The investigation of items, and of the const
 ruct which the items operationalize, provides insight into the latent trai
 t of interest. The identification of bands of learners together with items
  whose difficulty in relation to the learners is exposed provides insight 
 for the design of lessons appropriate for optimal learning in a zone of pr
 oximal development. This research study provides the foundation for furthe
 r development in particular the design of lesson sequences informed by thi
 s study
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