Despite their prevalence in early years’ education, there seems to be a lack of agreement over how or indeed whether physical objects support children's learning. Understanding the role of physically manipulating representations has gained impetus with the increasing potential to integrate digital technology into physical objects: tangible technology. This thesis aimed to evaluate the potential for tangible technologies to support numerical development by examining young children’s (4-8 years) use of physical objects in a numerical task. This task required them to find all the different ways in which a number (e.g., 7) can be decomposed (e.g., into 2 & 5). Seven carefully designed studies compared children’s numerical strategies using physical objects (cubes) with other materials (paper/virtual representations) or no materials. The studies showed that physical objects not only helped children identify solutions through simple physical actions, but fostered strategies that related solutions such as swapping groups of cubes or moving just one cube to get a new solution. This led to predictions about how a computer might influence strategies by constraining children’s actions to moving just one object at a time using the mouse. These predictions were confirmed, and a further study showed how using materials that changed colour according to the number grouped could support strategies by drawing children’s attention to numerical changes. The research showed that, to help children identify ways to break down a number efficiently, it was more effective to constrain their actions using a graphical, rather than tangible, interface. However, when multiple (physical) objects could be manipulated, children were able to constrain their own actions and used a wider range of strategies. Although moving multiple objects can be facilitated through interfaces such as tabletop computers, this research indicated certain cognitive benefits of physically manipulating representations for children’s numerical development that may inform tangible designs.