Background: The need to focus more on children's abilities to change requires new assessment technologies in education. Process-oriented assessment can be useful in this regard. Dynamic testing has the potential to provide in-depth information about children's learning processes and cognitive abilities. Aim: This study implemented a process-oriented dynamic testing procedure to obtain information regarding children's changes in series-completion skills in a computerised test setting. We studied whether children who received a graduated prompts training would show more progression in series-completion than children who received no training, and whether trained children would use more advanced explanations of their solutions than their untrained peers. Sample: Participants were 164 second-grade children with a mean age of 7;11 years. Children were split into an unguided practice or a dynamic testing condition. Methods: The study employed a pre-test-training-post-test design. Half of the children were trained in series-completion, and the other half did not receive any feedback on their problem solving. Using item response theory analysis, we inspected the progression paths of the children in the two conditions. Results and conclusions: Children who received training showed more progression in their series-completion skills than the children who received no training. In addition, the trained children explained their solutions in a more advanced manner, when compared with the non-trained control group. This information is valuable for educational practice as it provides a better understanding of how learning occurs and which factors contribute to cognitive changes.