Carol Murphy

HOW DO CHILDREN COME TO USE A TAUGHT MENTAL CALCULATION STRATEGY

This study provides an in-depth analysis of childrens use of a taught mental calculation strategy. Three children (aged eight to nine years) who demonstrated contrasting spontaneous calculation approaches, were interviewed following the direct instruction of a calculation strategy. Their responses are explored in relation to constructivist and participation perspectives of learning. In response to a unified view of these theories, hypotheses are generated that ask fundamental questions related to the did actics of mental calculation strategies.

Comparing the use of the empty number line in England and the Netherlands

Efforts to meet the needs of childrens learning in arithmetic has led to an increased emphasis on the teaching of mental calculation strategies in England. This has included the adoption of didactical tools such as the empty number line (ENL) that was developed as part of the realistic mathematics 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.

How Might Apps Reshape the Mathematical Learning Experience

This chapter reports on how the use of mathematics apps has the potential to reshape the learning experience , a particular aspect of learning with apps that emerged from a research project examining the ways mobile technologies are used in primary-school mathematics. The chapter will consider a number of key themes related to student learning that have emerged through the research. When using some of the apps in the study, students used different digital tools within the app to solve word problems, while the affordances, including multi-representation, dynamic and haptic, made the learning experience different from when using pencil-and-paper technology. Other themes that were identified included: collaboration, socio-material assemblages, and personalisation. All of these appeared influential in the development of mathematical thinking. While the affordances of the mobile technologies are important, the teacher’s pedagogical approach and the dialogue that the apps evoked were central in the learning.

Reshaping the learning experience through apps: Affordances

This paper reports on how the affordances of the app Math Shake reshaped the learning experience—an aspect of a research project examining the ways mobile technologies are used in primary-school mathematics. Students used different digital tools within the app to solve word problems, while the affordances, including simultaneous linking, focussed constraint, creative variation, dynamic and haptic, made the learning experience different from when using pencil-and-paper technology. However, while the affordances of the mobile technologies are important, the teacher’s pedagogical approach was also influential in the learning.