(2009) 'The array representation and primary children's understanding and reasoning in multiplication.', Educational studies in mathematics., 70 (3). pp. 217-241.Further information on publisher's website:http://dx.doi.org/10.1007/s10649-008-9145-1Publisher's copyright statement:The original publication is available at www.springerlink.com Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract 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.

. (2010) 'Pre-service primary teachers' conceptions of creativity in mathematics.', Educational studies in mathematics., 73 (2). pp. 143-157. Further information on publisher's website:http://dx.doi.org/10.1007/s10649-009-9207-z Publisher's copyright statement:The nal publication is available at www.springerlink.com Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract Teachers in the UK and elsewhere are now expected to foster creativity in young children (NACCCE, 1999;Ofsted, 2003;DfES, 2003;DfES/DCMS, 2006).Creativity, however, is more often associated with the arts than with mathematics.The aim of the study was to explore and document pre-service i primary teachers" conceptions of creativity in mathematics teaching in the UK. A questionnaire probed their conceptions early in their course and these were supplemented with data from semi-structured interviews. Analysis of the responses indicated that pre-service teachers" conceptions were narrow, predominantly associated with the use of resources and technology and bound up with the idea of "teaching creatively" rather than "teaching for creativity". Conceptions became less narrow as pre-service teachers were preparing to enter schools as newly qualified but they still had difficulty in identifying ways of encouraging and assessing creativity in the classroom. This difficulty suggests that conceptions of creativity need to be addressed and developed directly during pre-service education if teachers are to meet the expectations of government as set out in the above documents.

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.

No abstract

Children of 10-11 years of age were interviewed while undertaking a range of mathematic problems, most of which embedded mathematical operations in textually represented realistic settings. One problem, concerning a lift moving people in the morning rush, comprised a division-with-remainder problem in which children are required, conventionally, to introduce a particular realistic consideration in order to produce the 'correct' answer. Another problem was an extended version of this, requiring children to comment on four competing answers produced by other children. Analysis of responses to the first of these two problems demonstrated that it was working class children who were especially likely to fail to produce the conventionally required answer. Having shown this, the paper concentrates on portraying the ways in which 'failing' working class children interpret and respond to the two problems. Our purpose here is to contribute to understanding the difficulties working class children appear to have in negotiating the demands of contextualized problems.