For technology (like serious games) that aims to deliver interactive learning, it is important to address relevant mental experiences such as reflective thinking during problem solving. To facilitate research in this direction, we present the weDraw-1 Movement Dataset of body movement sensor data and reflective thinking labels for 26 children solving mathematical problems in unconstrained settings where the body (full or parts) was required to explore these problems. Further, we provide qualitative analysis of behaviours that observers used in identifying reflective thinking moments in these sessions. The body movement cues from our compilation informed features that lead to average F1 score of 0.73 for binary classification of problem-solving episodes by reflective thinking based on Long Short-Term Memory neural networks. We further obtained 0.79 average F1 score for end-to-end classification, i.e. based on raw sensor data. Finally, the algorithms resulted in 0.64 average F1 score for subsegments of these episodes as short as 4 seconds. Overall, our results show the possibility of detecting reflective thinking moments from body movement behaviours of a child exploring mathematical concepts bodily, such as within serious game play.