Developing shared understanding is essential to productive collaboration where a product is jointly constructed. This is especially true when the different collaborators' contributions need to build coherently on one another, as, for example, when making a story together. This study investigated whether encouraging children to engage in discussion through a Guided Reciprocal Peer Questioning (GRPQ) script whilst drawing together leads to better collaborative storytelling. Thirty-six 6-7 year old children used a computer-drawing application called KidPad to tell collaborative stories supported by interactive drawings, and were trained in the GRPQ script. Using a within-subjects design, it was shown that the GRPQ script promoted engagement in interactive discussion and led to the production of richer and more coherent collaborative stories. Furthermore, this benefit was often maintained once the explicit support was withdrawn. These findings suggest that the GRPQ script is an effective way to improve children's collaborative storytelling and one that children can internalise and apply themselves.