Humanoid robots, with a focus on personalised social behaviours, are increasingly being deployed in educational settings to support learning. However, crafting pedagogical HRI designs and robot interventions that have a real, positive impact on participants' learning, as well as effectively measuring such impact, is still an open challenge. As a first effort in tackling the issue, in this paper we propose a novel robot-mediated, collaborative problem solving activity for school-children, called JUSThink, aiming at improving their computational thinking skills. JUSThink will serve as a baseline and reference for investigating how the robot's behaviour can influence the engagement of the children with the activity, as well as their collaboration and mutual understanding while working on it. To this end, this first iteration aims at investigating (i) participants' engagement with the activity (Intrinsic Motivation Inventory-IMI), their mutual understanding (IMI-like) and perception of the robot (Godspeed Questionnaire); (ii) participants' performance during the activity, using several performance and learning metrics. We carried out an extensive user-study in two international schools in Switzerland, in which around 100 children participated in pairs in one-hour long interactions with the activity. Surprisingly, we observe that while a teams' performance significantly affects how team members evaluate their competence, mutual understanding and task engagement, it does not affect their perception of the robot and its helpfulness, a fact which highlights the need for baseline studies and multi-dimensional evaluation metrics when assessing the impact of robots in educational activities.