Researchers and designers have incorporated social media affordances into learning technologies to engage young people and support personally relevant learning, but youth may reject these attempts because they do not meet user expectations. Through in-depth case studies, we explore the sociotechnical ecosystems of six teens (ages 15-18) working at a science center that had recently introduced a digital badge system to track and recognize their learning. By analyzing interviews, observations, ecological momentary assessments, and system data, we examined tensions in how badges as connected learning technologies operate in teens' sociotechnical ecosystems. We found that, due to issues of unwanted context collapse and incongruent identity representations, youth only used certain affordances of the system and did so sporadically. Additionally, we noted that some features seemed to prioritize values of adult stakeholders over youth. Using badges as a lens, we reveal critical tensions and offer design recommendations for networked learning technologies.