Intensive quantities: Towards their recognition at primary school level
Abstract:Background. Differences have been identified between extensive quantities (e.g.distance, volume, price) and intensive quantities (e.g.speed, density, value for money). However, while extensive quantities play a focal role in formal education, intensive quantities are overlooked. The implications, and therefore advisability, of this neglect require exploration. Aims. Three studies are reported, whose aim was to examine reasoning with intensive quantities in children who can be assumed not to have received formal teaching. Samples. The participants were primary school children aged 69 years (Study 1, N = 105), 79 years (Study 2, N = 115), and 712 years (Study 3, N = 963). Method. Children attempted to solve intensive quantity problems, which were presented orally supported by coloured illustrations. Data were collected during oneto-one interviews (Study 1) or via written responses after whole-class presentation (Studies 2 and 3). Results. Enduring difficulties with intensive quantities were detected. For instance, even the oldest children could not reliably determine which toy car goes faster, one that covers three pieces of track in 10 s or one that covers seven pieces in 10 s. They also had problems ascertaining the fraction of blue paint in a mixture that comprises two cans of blue paint and two cans of white paint, despite familiarity with simple fractions in extensive contexts. Conclusions. Intensive quantities should be accorded a more prominent role in the curriculum than is currently the case.
Publication date: March 1, 2010
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