Ways of thinking associated with mathematics teachers’ problem posing in the context of division of fractions
 Boris Koichu,
 Guershon Harel,
 Alfred Manaster
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Twentyfour mathematics teachers were asked to think aloud when posing a word problem whose solution could be found by computing 4/5 divided by 2/3. The data consisted of verbal protocols along with the written notes made by the subjects. The qualitative analysis of the data was focused on identifying the structures of the problems produced and the associated ways of thinking involved in constructing the problems. The results suggest that success in doing the interview task was associated with perception the given fractions as operands for the division operation and, at the same time, the divisor 2/3 as an operator acting over 4/5. The lack of success was associated with perception of division of fractions as division of divisions of whole numbers and using the result of division of fractions as the only reference point. The study sheds new light on the teachers’ difficulties with conceptualization of fractions.
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 Title
 Ways of thinking associated with mathematics teachers’ problem posing in the context of division of fractions
 Journal

Instructional Science
Volume 41, Issue 4 , pp 681698
 Cover Date
 20130701
 DOI
 10.1007/s1125101292541
 Print ISSN
 00204277
 Online ISSN
 15731952
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Mathematics teachers
 Problem posing
 Division of fractions
 Ways of thinking
 Protocol analysis
 Intuitive models of division
 Authors

 Boris Koichu ^{(1)}
 Guershon Harel ^{(2)}
 Alfred Manaster ^{(2)}
 Author Affiliations

 1. Department of Education in Technology and Science, Technion – Israel Institute of Technology, 32000, Haifa, Israel
 2. Department of Mathematics, University of California, San Diego, La Jolla, CA, 920930112, USA