Barmby, P. and Harries, T. and Higgins, S. and Suggate, J. (2009) 'The array representation and primary children's understanding and reasoning in multiplication.', Educational studies in mathematics., 70 (3). pp. 217-241.
We examine whether the array representation can support children’s understanding and reasoning in multiplication. To begin, we define what we mean by understanding and reasoning. We adopt a ‘representational-reasoning’ model of understanding, where understanding is seen as connections being made between mental representations of concepts, with reasoning linking together the different parts of the understanding. We examine in detail the implications of this model, drawing upon the wider literature on assessing understanding, multiple representations, self explanations and key developmental understandings. Having also established theoretically why the array representation might support children’s understanding and reasoning, we describe the results of a study which looked at children using the array for multiplication calculations. Children worked in pairs on laptop computers, using Flash Macromedia programs with the array representation to carry out multiplication calculations. In using this approach, we were able to record all the actions carried out by children on the computer, using a recording program called Camtasia. The analysis of the obtained audiovisual data identified ways in which the array representation helped children, and also problems that children had with using the array. Based on these results, implications for using the array in the classroom are considered.
|Keywords:||Array, Multiplication, Representations, Reasoning, Understanding.|
|Full text:||(AM) Accepted Manuscript|
Download PDF (498Kb)
|Publisher Web site:||http://dx.doi.org/10.1007/s10649-008-9145-1|
|Publisher statement:||The original publication is available at www.springerlink.com|
|Record Created:||27 Mar 2009|
|Last Modified:||03 Nov 2011 12:14|
|Social bookmarking:||Export: EndNote, Zotero | BibTex|
|Look up in GoogleScholar | Find in a UK Library|