Skills in reasoning, e.g. argumentation, decision making and negotiations, are partly cognitive skills, partly social skills. The cognitive components of reasoning skills involve analysis and evaluations of grounds underlying a conclusion, standpoint or decision. Cognitive components of reasoning skills are partly based on general, normative models. Such models can be incorporated into software packages for argumentation and decision support. The social components of reasoning skills are embedded in social contexts. The social skills differ between various professions, e.g. between lawyers, scientists and businessmen. Components of such skills vary between genders and cultures. Such skills involve capacities for enacting roles in different social settings. Role-play with feedback from coaches is a fruitful way of teaching social skill components. Ideally, education of reason would aim at integrating cognitive and social skills. However, this is easier said than done. While cognitive components of good reasoning are general and rather well known, the components of social skills are not. My paper conceptualises strategies for cultivating cognitive and social skills in an integrated manner. Pros and cons of various strategies are explored. The paper is based on a theoretical analysis and extrapolation of findings from the Athena project of teaching reasoning via software support (www.athenasoft.org).