Journal article

Drawing on a theoretical model to study students' understandings of fractions

Charalambous C, Pitta-Pantazi D ...see all

Educational Studies in Mathematics, vol. 64, issue 3 (2007) pp. 293-316

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Abstract

Learning contributes to the development of mutual mimicry in group mates. The aim of our study was to investigate whether dogs would initiate walking a detour if they were repeatedly exposed to the detouring behaviour of their owner. Eight dog owners were asked to modify their usual way of approaching their home at the end of their daily walks, namely, to make a short detour before the entrance. Owners performed the detour at least 180 times, over a period of 3-6 months. During the first 30 detours (trials 1-30) all dogs followed the owner on the new route. Between trials 151 and 180, four dogs started to walk the detour before the owner displayed any intention to walk in that direction in 50-93% of the cases. Further observations that were carried out on one dog showed that the initialisation of the detours manifested sooner if a second familiar person started to walk the detours. Interestingly, the dog persisted in initialising detours long after the owners stopped detouring. We describe the observed phenomenon in the framework of social anticipation that manifests when an animal learns the proper sequence of an act performed by another animal, so that it can (1) predict the action in this sequence, and (2) as a result start either a similar or a complementary action as a response. These observations suggest that the dogs' social anticipation ability contributes to behavioural synchronisation and cooperative processes between dog and owner.

Author-supplied keywords

  • Equivalence
  • Fraction operations
  • Fraction subconstructs
  • Measure
  • Operator
  • Part-whole
  • Problem-solving
  • Quotient
  • Ratio
  • Structural equation modeling

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Authors

  • Charalambos Y. Charalambous

  • Demetra Pitta-Pantazi

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