Justifications-on-demand as a device to promote shifts of attention associated with relational thinking in elementary arithmetic
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Taylor and Francis
Forms of attentionNumber sentencesRelational thinking
Molina, M. y Mason, J. Justifications-on-demand as a device to promote shifts of attention associated with relational thinking in elementary arithmetic. Canadian Journal of Science, Mathematics and Technology Education, 9(4): 224-242 (2009). [http://hdl.handle.net/10481/23912]
SponsorshipThis study was funded by a Spanish national project of Research, Development and Innovation, identified by the code SEJ2006-09056, financed by the Spanish Ministry of Sciences and Technology and FEDER funds.
Student responses to arithmetical questions that can be solved by using arithmetical structure can serve to reveal the extent and nature of relational, as opposed to computational thinking. Here, student responses to probes which require them to justify-on-demand are analysed using a conceptual framework which highlights distinctions between different forms of attention. We analyse a number of actions observed in students in terms of forms of attention and shifts between them: in the short-term (in the moment), medium-term (over several tasks), and long-term (over a year). The main factors conditioning students´ attention and its movement are identified and some didactical consequences are proposed.