British Educational Research Journal Vol. 37, No. 1, February 2011, pp. 147–161 ISSN 0141-1926 (print)/ISSN 1469-3518 (online)/11/010147-15 © 2011 British Educational Research Association DOI: 10.1080/01411920903447423 Comparing the use of the empty number line in England and the Netherlands Carol Murphy * School of Education and Lifelong Learning, University of Exeter, Exeter, UK Taylor and Francis CBER_A_445103.sgm 10.1080/01411920903447423 British Education Research Journal 0141-1926 (print)/1469-3518 (online) Original Article 2009 British Educational Research Association> 00 0000002009 Mrs CarolMurphy C.M.Murphy@exeter.ac.uk Efforts to meet the needs of children’s learning in arithmetic has led to an increased emphasis on the teaching of mental calculation strategies in England. This has included the adoption of didacti- cal tools such as the empty number line (ENL) that was developed as part of the realistic mathe- matics movement in the Netherlands. It has been claimed that the English use of the ENL differs from that of the Dutch. In this study curriculum guidance materials are examined to investigate these differences. Two examples of teaching sequences are provided to illustrate them further. It is proposed that the different uses stem from different pedagogical principles. The implications of the English use are discussed in relation to the presentation of mental calculation strategies in an algorithmic way. Introduction The use of mental calculation strategies has long been recognised in England as an active way to support children’s understanding in arithmetic (Plunkett, 1979). Plunkett proposed that the use of mental calculation strategies required the active selection of the user. He saw that mental calculation strategies were often constructed as the user worked through the calculation. This is contrasted with the passive learning associated with the use of standard algorithms, which require the user to follow prescribed rules with limited decisions (Freudenthal, 1983). Anghileri et al. (2002) have claimed that the standard algorithms, such as those for division, do not build on children’s intuitive understanding of the operation. The authors found evidence that the early teaching of these algorithms led to ‘mechanistic’ uses that inhibited thinking about the numbers and the processes. So, in an aim for children to learn to use standard algorithms in a less mechanistic way, it would seem *School of Education and Lifelong Learning, Graduate School of Education, University of Exeter, St Luke’s Campus, Heavitree Road, Exeter, EX1 2LU, UK. Email: c.m.murphy@exeter.ac.uk