In order to better understand how to design hands-on child-computer interaction, we explore how different styles of interaction facilitate children's thinking while they use their hands to manipulate objects. We present an exploratory study of children solving a spatial puzzle task. We investigate how the affordances of physical, graphical and tangible interfaces may facilitate the development of thinking skills including mental visualisation, problem space exploration and collaboration. We utilise the theory of complementary actions taken from embodied cognition to develop a video coding methodology that allows us to classify behavioural activity and make inferences about thinking skills development. Our findings indicated that the combination of direct hands-on input style with audio-visual feedback facilitated by the tangible user interface enabled a dynamic task completion strategy, which supports the development of mental skills with a slight time cost. The mouse and graphical user interface supported a trial and error approach, which may limit skills development. The physical cardboard puzzle enabled effective task completion but provided less support for social interaction and problem space exploration. We conclude with design recommendations.